In developing complex engineering systems, model-based design approaches often face critical challenges due to pervasive uncertainties and high computational expense. These challenges could be alleviated to a significant extent though informed modeling decisions, such as model substitution, parameter estimation, localized re-sampling, or grid refine- ment. Informed modeling decisions therefore necessitate (currently lacking) design frame- works that effectively integrate design automation and human decision-making. In this paper, we seek to address this necessity in the context of designing wind farm layouts, by taking an information flow perspective of this typical model-based design process. Specif- ically, we develop a visual representation of the uncertainties inherited and generated by models and the inter-model sensitivities. This framework is called the Visually-Informed Decision-Making Platform (VIDMAP) for wind farm design. The eFAST method is used for sensitivity analysis, in order to determine both the first-order and the total-order in- dices. The uncertainties in the independent inputs are quantified based on their observed variance. The uncertainties generated by the upstream models are quantified through a Monte Carlo simulation followed by probabilistic modeling of (i) the error in the output of the models (if high-fidelity estimates are available), or (ii) the deviation in the outputs estimated by different alternatives/versions of the model. The GUI in VIDMAP is cre- ated using value-proportional colors for each model block and inter-model connector, to respectively represent the uncertainty in the model output and the impact (downstream) of the information being relayed by the connector. Wind farm layout optimization (WFLO) serves as an excellent platform to develop and explore VIDMAP, where WFLO is generally performed using low fidelity models, as high-fidelity models (e.g. LES) tend to be compu- tationally prohibitive in this context. The final VIDMAP obtained sheds new light into the sensitivity of wind farm energy estimation on the different models and their associated uncertainties.
One of the primary drawbacks plaguing wider acceptance of surrogate models is their low fidelity in general. This issue can be in a large part attributed to the lack of automated model selection techniques, particularly ones that do not make limiting assumptions regarding the choice of model types and kernel types. A novel model selection technique was recently developed to perform optimal model search concurrently at three levels: (i) optimal model type (e.g., RBF), (ii) optimal kernel type (e.g., multiquadric), and (iii) optimal values of hyper-parameters (e.g., shape parameter) that are conventionally kept constant. The error measures to be minimized in this optimal model selection process are determined by the Predictive Estimation of Model Fidelity (PEMF) method, which has been shown to be significantly more accurate than typical cross-validation-based error metrics. In this paper, we make the following important advancements to the PEMF-based model selection framework, now called the Concurrent Surrogate Model Selection or COS- MOS framework: (i) The optimization formulation is modified through binary coding to allow surrogates with differing num- bers of candidate kernels and kernels with differing numbers of hyper-parameters (which was previously not allowed). (ii) A robustness criterion, based on the variance of errors, is added to the existing criteria for model selection. (iii) A larger candidate pool of 16 surrogate-kernel combinations is considered for selection − possibly making COSMOS one of the most comprehensive surrogate model selection framework (in theory and implementation) currently available. The effectiveness of the COSMOS framework is demonstrated by successfully applying it to four benchmark problems (with 2-30 variables) and an airfoil design problem. The optimal model selection results illustrate how diverse models provide important tradeoffs for different problems.
Wind farm layout optimization (WFLO) is the process of optimizing the location of turbines in a wind farm site, with the possible objective of maximizing the energy production or minimizing the average cost of energy. Conventional WFLO methods not only limit themselves to prescribing the site boundaries, they are also generally applicable to designing only small-to-medium scale wind farms (<100 turbines). Large-scale wind farms entail greater wake-induced turbine interactions, thereby increasing the computa- tional complexity and expense by orders of magnitude. In this paper, we further advance the Unrestricted WFLO framework by designing the layout of large-scale wind farms with 500 turbines (where energy pro- duction is maximized). First, the high-dimensional layout optimization problem (involving 2N variables for a N turbine wind farm) is reduced to a 6-variable problem through a novel mapping strategy, which allows for both global siting (overall land configuration) and local exploration (turbine micrositing). Sec- ondly, a surrogate model is used to substitute the expensive analytical WF energy production model; the high computational expense of the latter is attributed to the factorial increase in the number of calls to the wake model for evaluating every candidate wind farm layout that involves a large number of turbines. The powerful Concurrent Surrogate Model Selection (COSMOS) framework is applied to identify the best surrogate model to represent the wind farm energy production as a function of the reduced variable vector. To accomplish a reliable optimum solution, the surrogate-based optimization (SBO) is performed by implementing the Adaptive Model Refinement (AMR) technique within Particle Swarm Optimization (PSO). In AMR, both local exploitation and global exploration aspects are considered within a single optimization run of PSO, unlike other SBO methods that often either require multiple (potentially mis- leading) optimizations or are model-dependent. By using the AMR approach in conjunction with PSO and COSMOS, the computational cost of designing very large wind farms is reduced by a remarkable factor of 26, while preserving the reliability of this WFLO within 0.05% of the WFLO performed using the original energy production model.
Approximation models (or surrogate models) provide an efficient substitute to expen- sive physical simulations and an efficient solution to the lack of physical models of system behavior. However, it is challenging to quantify the accuracy and reliability of such ap- proximation models in a region of interest or the overall domain without additional system evaluations. Standard error measures, such as the mean squared error, the cross-validation error, and the Akaikes information criterion, provide limited (often inadequate) informa- tion regarding the accuracy of the final surrogate. This paper introduces a novel and model independent concept to quantify the level of errors in the function value estimated by the final surrogate in any given region of the design domain. This method is called the Re- gional Error Estimation of Surrogate (REES). Assuming the full set of available sample points to be fixed, intermediate surrogates are iteratively constructed over a sample set comprising all samples outside the region of interest and heuristic subsets of samples inside the region of interest (i.e., intermediate training points). The intermediate surrogate is tested over the remaining sample points inside the region of interest (i.e., intermediate test points). The fraction of sample points inside region of interest, which are used as interme- diate training points, is fixed at each iteration, with the total number of iterations being pre-specified. The estimated median and maximum relative errors within the region of in- terest for the heuristic subsets at each iteration are used to fit a distribution of the median and maximum error, respectively. The estimated statistical mode of the median and the maximum error, and the absolute maximum error are then represented as functions of the density of intermediate training points, using regression models. The regression models are then used to predict the expected median and maximum regional errors when all the sample points are used as training points. Standard test functions and a wind farm power generation problem are used to illustrate the effectiveness and the utility of such a regional error quantification method.
The analysis of complex system behavior often demands expensive experiments or computational simulations. Surrogates modeling techniques are often used to provide a tractable and inexpensive approximation of such complex system behavior. Owing to the lack of knowledge regarding the suitability of particular surrogate modeling techniques, model selection approach can be helpful to choose the best surrogate technique. Popular model selection approaches include: (i) split sample, (ii) cross-validation, (iii) bootstrapping, and (iv) Akaike's information criterion (AIC) (Queipo et al. 2005; Bozdogan et al. 2000). However, the effectiveness of these model selection methods is limited by the lack of accurate measures of local and global errors in surrogates.
This paper develops a novel and model-independent concept to quantify the local/global reliability of surrogates, to assist in model selection (in surrogate applications). This method is called the Generalized-Regional Error Estimation of Surrogate (G-REES). In this method, intermediate surrogates are iteratively constructed over heuristic subsets of the available sample points (i.e., intermediate training points), and tested over the remaining available sample points (i.e., intermediate test points). The fraction of sample points used as intermediate training points is fixed at each iteration, with the total number of iterations being pre-specified. The estimated median and maximum relative errors for the heuristic subsets at each iteration are used to fit a distribution of the median and maximum error, respectively. The statistical mode of the median and the maximum error distributions are then determined. These mode values are then represented as functions of the density of training points (at the corresponding iteration). Regression methods, called Variation of Error with Sample Density (VESD), are used for this purpose. The VESD models are then used to predict the expected median and maximum errors, when all the sample points are used as training points.
The effectiveness of the proposed model selection criterion is explored to find the best surrogate between candidates including: (i) Kriging, (ii) Radial Basis Functions (RBF), (iii) Extended Radial Basis Functions (ERBF), and (iv) Quadratic Response Surface (QRS), for standard test functions and a wind farm capacity factor function. The results will be compared with the relative accuracy of the surrogates evaluated on additional test points, and also with the prediction sum of square (PRESS) error given by leave-one-out cross-validation.
The application of G-REES to a standard test problem with two design variables (Branin-hoo function) show that the proposed method predicts the median and the maximum value of the global error with a higher level of confidence compared to PRESS. It also shows that model selection based on G-REES method is significantly more reliable than that currently performed using error measures such as PRESS. The
In spite of the recent developments in surrogate modeling techniques, the low fidelity of these models often limits their use in practical engineering design optimization. When surrogate models are used to represent the behavior of a complex system, it is challenging to simultaneously obtain high accuracy over the entire design space. When such surrogates are used for optimization, it becomes challenging to find the optimum/optima with certainty. Sequential sampling methods offer a powerful solution to this challenge by providing the surrogate with reasonable accuracy where and when needed. When surrogate-based design optimization (SBDO) is performed using sequential sampling, the typical SBDO process is repeated multiple times, where each time the surrogate is improved by addition of new sample points. This paper presents a new adaptive approach to add infill points during SBDO, called Adaptive Sequential Sampling (ASS). In this approach, both local exploitation and global exploration aspects are considered for updating the surrogate during optimization, where multiple iterations of the SBDO process is performed to increase the quality of the optimal solution. This approach adaptively improves the accuracy of the surrogate in the region of the current global optimum as well as in the regions of higher relative errors. Based on the initial sample points and the fitted surrogate, the ASS method adds infill points at each iteration in the locations of: (i) the current optimum found based on the
fitted surrogate; and (ii) the points generated using cross-over between sample points that
have relatively higher cross-validation errors. The Nelder and Mead Simplex method is adopted as the optimization algorithm. The effectiveness of the proposed method is illustrated using a series of standard numerical test problems.
This paper proposes a novel model management technique to be applied in population- based heuristic optimization. This technique adaptively selects different computational models (both physics-based and statistical models) to be used during optimization, with the overall goal to end with high fidelity solutions in a reasonable time period. For example, in optimizing an aircraft wing to obtain maximum lift-to-drag ratio, one can use low-fidelity models such as given by the vortex lattice method, or a high-fidelity finite volume model (that solves the full Navier-Stokes equations), or a surrogate model that substitutes the high-fidelity model.The information from models with different levels of fidelity is inte- grated into the heuristic optimization process using a novel model-switching metric. In this context, models could be surrogate models, low-fidelity physics-based analytical mod- els, and medium-to-high fidelity computational models (based on grid density). The model switching technique replaces the current model with the next higher fidelity model, when a stochastic switching criterion is met at a given iteration during the optimization process. The switching criteria is based on whether the uncertainty associated with the current model output dominates the latest improvement of the fitness function. In the case of the physics-based models, the uncertainty in their output is quantified through an inverse assessment process by comparing with high-fidelity model responses or experimental data (if available). To determine the fidelity of surrogate models, the Predictive Estimation of Model Fidelity (PEMF) method is applied. The effectiveness of the proposed method is demonstrated by applying it to airfoil optimization with the objective to maximize the lift to drag ratio of the wing under different flow regimes. It was found that the tuned low fidelity model dominates the optimization process in terms of computational time and function calls.
The performance of a wind farm is affected by several key factors that can be classified into two cate- gories: the natural factors and the design factors. Hence, the planning of a wind farm requires a clear quantitative understanding of how the balance between the concerned objectives (e.g., socia-economic, engineering, and environmental objectives) is affected by these key factors. This understanding is lacking in the state of the art in wind farm design. The wind farm capacity factor is one of the primary perfor- mance criteria of a wind energy project. For a given land (or sea area) and wind resource, the maximum capacity factor of a particular number of wind turbines can be reached by optimally adjusting the layout of turbines. However, this layout adjustment is constrained owing to the limited land resource. This paper proposes a Bi-level Multi-objective Wind Farm Optimization (BMWFO) framework for planning effective wind energy projects. Two important performance objectives considered in this paper are: (i) wind farm Capacity Factor (CF) and (ii) Land Area per MW Installed (LAMI). Turbine locations, land area, and nameplate capacity are treated as design variables in this work. In the proposed framework, the Capacity Factor - Land Area per MW Installed (CF - LAMI) trade-off is parametrically represented as a function of the nameplate capacity. Such a helpful parameterization of trade-offs is unique in the wind energy literature. The farm output is computed using the wind farm power generation model adopted from the Unrestricted Wind Farm Layout Optimization (UWFLO) framework. The Smallest Bounding Rectangle (SBR) enclosing all turbines is used to calculate the actual land area occupied by the farm site. The wind farm layout optimization is performed in the lower level using the Mixed-Discrete Particle Swarm Optimization (MDPSO), while the CF - LAMI trade-off is parameterized in the upper level. In this work, the CF - LAMI trade-off is successfully quantified by nameplate capacity in the 20 MW to 100 MW range. The Pareto curves obtained from the proposed framework provide important in- sights into the trade-offs between the two performance objectives, which can significantly streamline the decision-making process in wind farm development.
Owing to the multitude of surrogate modeling techniques, developed in the recent years and the diverse characteristics offered by them, automated adaptive model selection ap- proaches could be helpful in selecting the most suitable surrogate for a given problem. Surrogate selection could be performed at three different levels: (i) model type selection, (ii) basis (or kernel) function selection, and (iii) hyper-parameter selection where hyper- parameters are those kernel parameters that are generally given by the users. Unlike the majority of existing model selection techniques, this paper explores the development of a method that performs selection coherently at all the three levels. In this context, the REES method is used to provide measures of the median and maximum errors of a candi- date surrogate model. Two approaches are used for the 3-level selection; (i) A Cascaded approach performs each level in a nested loop in the order going from model-kernel-hyper- parameters; (ii) A more advanced One-Step approach solves a MINLP to simultaneously optimize the model, kernel, and hyper-parameters. In both approaches, multiobjective optimization is performed to yield the best trade-offs between the estimated median and maximum errors. Candidate surrogates that are considered include (i) Kriging, (ii) Radial Basis Function (RBF), and (iii) Support Vector Regression (SVR), and multiple candidate kernels are allowed within these surrogate models. The 3-level REES-based model selec- tion is compared with model selection based on error estimated on a large set of additional test points, for validation purposes. Numerical experiments on a 2-variable, 6-variable, and 18-variable test problems, and wind farm power generation problem, show that the proposed approach provides unique flexibility in model selection and is also reasonably ac- curate when compared with selection based on errors estimated on additional test points.
One of the primary drawbacks plaguing wider acceptance of surrogate models is their low fidelity in general. This issue can be in a large part attributed to the lack of automated model selection techniques, particularly ones that do not make limiting assumptions regarding the choice of model types and kernel types. A novel model selection technique was recently developed to perform optimal model search concurrently at three levels: (i) optimal model type (e.g., RBF), (ii) optimal kernel type (e.g., multiquadric), and (iii) optimal values of hyper-parameters (e.g., shape parameter) that are conventionally kept constant. The error measures to be minimized in this optimal model selection process are determined by the Predictive Estimation of Model Fidelity (PEMF) method, which has been shown to be significantly more accurate than typical cross-validation-based error metrics. In this paper, we make the following important advancements to the PEMF-based model selection framework, now called the Concurrent Surrogate Model Selection or COS- MOS framework: (i) The optimization formulation is modified through binary coding to allow surrogates with differing num- bers of candidate kernels and kernels with differing numbers of hyper-parameters (which was previously not allowed). (ii) A robustness criterion, based on the variance of errors, is added to the existing criteria for model selection. (iii) A larger candidate pool of 16 surrogate-kernel combinations is considered for selection − possibly making COSMOS one of the most comprehensive surrogate model selection framework (in theory and implementation) currently available. The effectiveness of the COSMOS framework is demonstrated by successfully applying it to four benchmark problems (with 2-30 variables) and an airfoil design problem. The optimal model selection results illustrate how diverse models provide important tradeoffs for different problems.
Wind farm layout optimization (WFLO) is the process of optimizing the location of turbines in a wind farm site, with the possible objective of maximizing the energy production or minimizing the average cost of energy. Conventional WFLO methods not only limit themselves to prescribing the site boundaries, they are also generally applicable to designing only small-to-medium scale wind farms (<100 turbines). Large-scale wind farms entail greater wake-induced turbine interactions, thereby increasing the computa- tional complexity and expense by orders of magnitude. In this paper, we further advance the Unrestricted WFLO framework by designing the layout of large-scale wind farms with 500 turbines (where energy pro- duction is maximized). First, the high-dimensional layout optimization problem (involving 2N variables for a N turbine wind farm) is reduced to a 6-variable problem through a novel mapping strategy, which allows for both global siting (overall land configuration) and local exploration (turbine micrositing). Sec- ondly, a surrogate model is used to substitute the expensive analytical WF energy production model; the high computational expense of the latter is attributed to the factorial increase in the number of calls to the wake model for evaluating every candidate wind farm layout that involves a large number of turbines. The powerful Concurrent Surrogate Model Selection (COSMOS) framework is applied to identify the best surrogate model to represent the wind farm energy production as a function of the reduced variable vector. To accomplish a reliable optimum solution, the surrogate-based optimization (SBO) is performed by implementing the Adaptive Model Refinement (AMR) technique within Particle Swarm Optimization (PSO). In AMR, both local exploitation and global exploration aspects are considered within a single optimization run of PSO, unlike other SBO methods that often either require multiple (potentially mis- leading) optimizations or are model-dependent. By using the AMR approach in conjunction with PSO and COSMOS, the computational cost of designing very large wind farms is reduced by a remarkable factor of 26, while preserving the reliability of this WFLO within 0.05% of the WFLO performed using the original energy production model.
Approximation models (or surrogate models) provide an efficient substitute to expen- sive physical simulations and an efficient solution to the lack of physical models of system behavior. However, it is challenging to quantify the accuracy and reliability of such ap- proximation models in a region of interest or the overall domain without additional system evaluations. Standard error measures, such as the mean squared error, the cross-validation error, and the Akaikes information criterion, provide limited (often inadequate) informa- tion regarding the accuracy of the final surrogate. This paper introduces a novel and model independent concept to quantify the level of errors in the function value estimated by the final surrogate in any given region of the design domain. This method is called the Re- gional Error Estimation of Surrogate (REES). Assuming the full set of available sample points to be fixed, intermediate surrogates are iteratively constructed over a sample set comprising all samples outside the region of interest and heuristic subsets of samples inside the region of interest (i.e., intermediate training points). The intermediate surrogate is tested over the remaining sample points inside the region of interest (i.e., intermediate test points). The fraction of sample points inside region of interest, which are used as interme- diate training points, is fixed at each iteration, with the total number of iterations being pre-specified. The estimated median and maximum relative errors within the region of in- terest for the heuristic subsets at each iteration are used to fit a distribution of the median and maximum error, respectively. The estimated statistical mode of the median and the maximum error, and the absolute maximum error are then represented as functions of the density of intermediate training points, using regression models. The regression models are then used to predict the expected median and maximum regional errors when all the sample points are used as training points. Standard test functions and a wind farm power generation problem are used to illustrate the effectiveness and the utility of such a regional error quantification method.
The analysis of complex system behavior often demands expensive experiments or computational simulations. Surrogates modeling techniques are often used to provide a tractable and inexpensive approximation of such complex system behavior. Owing to the lack of knowledge regarding the suitability of particular surrogate modeling techniques, model selection approach can be helpful to choose the best surrogate technique. Popular model selection approaches include: (i) split sample, (ii) cross-validation, (iii) bootstrapping, and (iv) Akaike's information criterion (AIC) (Queipo et al. 2005; Bozdogan et al. 2000). However, the effectiveness of these model selection methods is limited by the lack of accurate measures of local and global errors in surrogates.
This paper develops a novel and model-independent concept to quantify the local/global reliability of surrogates, to assist in model selection (in surrogate applications). This method is called the Generalized-Regional Error Estimation of Surrogate (G-REES). In this method, intermediate surrogates are iteratively constructed over heuristic subsets of the available sample points (i.e., intermediate training points), and tested over the remaining available sample points (i.e., intermediate test points). The fraction of sample points used as intermediate training points is fixed at each iteration, with the total number of iterations being pre-specified. The estimated median and maximum relative errors for the heuristic subsets at each iteration are used to fit a distribution of the median and maximum error, respectively. The statistical mode of the median and the maximum error distributions are then determined. These mode values are then represented as functions of the density of training points (at the corresponding iteration). Regression methods, called Variation of Error with Sample Density (VESD), are used for this purpose. The VESD models are then used to predict the expected median and maximum errors, when all the sample points are used as training points.
The effectiveness of the proposed model selection criterion is explored to find the best surrogate between candidates including: (i) Kriging, (ii) Radial Basis Functions (RBF), (iii) Extended Radial Basis Functions (ERBF), and (iv) Quadratic Response Surface (QRS), for standard test functions and a wind farm capacity factor function. The results will be compared with the relative accuracy of the surrogates evaluated on additional test points, and also with the prediction sum of square (PRESS) error given by leave-one-out cross-validation.
The application of G-REES to a standard test problem with two design variables (Branin-hoo function) show that the proposed method predicts the median and the maximum value of the global error with a higher level of confidence compared to PRESS. It also shows that model selection based on G-REES method is significantly more reliable than that currently performed using error measures such as PRESS. The
In spite of the recent developments in surrogate modeling techniques, the low fidelity of these models often limits their use in practical engineering design optimization. When surrogate models are used to represent the behavior of a complex system, it is challenging to simultaneously obtain high accuracy over the entire design space. When such surrogates are used for optimization, it becomes challenging to find the optimum/optima with certainty. Sequential sampling methods offer a powerful solution to this challenge by providing the surrogate with reasonable accuracy where and when needed. When surrogate-based design optimization (SBDO) is performed using sequential sampling, the typical SBDO process is repeated multiple times, where each time the surrogate is improved by addition of new sample points. This paper presents a new adaptive approach to add infill points during SBDO, called Adaptive Sequential Sampling (ASS). In this approach, both local exploitation and global exploration aspects are considered for updating the surrogate during optimization, where multiple iterations of the SBDO process is performed to increase the quality of the optimal solution. This approach adaptively improves the accuracy of the surrogate in the region of the current global optimum as well as in the regions of higher relative errors. Based on the initial sample points and the fitted surrogate, the ASS method adds infill points at each iteration in the locations of: (i) the current optimum found based on the
fitted surrogate; and (ii) the points generated using cross-over between sample points that
have relatively higher cross-validation errors. The Nelder and Mead Simplex method is adopted as the optimization algorithm. The effectiveness of the proposed method is illustrated using a series of standard numerical test problems.
This paper proposes a novel model management technique to be applied in population- based heuristic optimization. This technique adaptively selects different computational models (both physics-based and statistical models) to be used during optimization, with the overall goal to end with high fidelity solutions in a reasonable time period. For example, in optimizing an aircraft wing to obtain maximum lift-to-drag ratio, one can use low-fidelity models such as given by the vortex lattice method, or a high-fidelity finite volume model (that solves the full Navier-Stokes equations), or a surrogate model that substitutes the high-fidelity model.The information from models with different levels of fidelity is inte- grated into the heuristic optimization process using a novel model-switching metric. In this context, models could be surrogate models, low-fidelity physics-based analytical mod- els, and medium-to-high fidelity computational models (based on grid density). The model switching technique replaces the current model with the next higher fidelity model, when a stochastic switching criterion is met at a given iteration during the optimization process. The switching criteria is based on whether the uncertainty associated with the current model output dominates the latest improvement of the fitness function. In the case of the physics-based models, the uncertainty in their output is quantified through an inverse assessment process by comparing with high-fidelity model responses or experimental data (if available). To determine the fidelity of surrogate models, the Predictive Estimation of Model Fidelity (PEMF) method is applied. The effectiveness of the proposed method is demonstrated by applying it to airfoil optimization with the objective to maximize the lift to drag ratio of the wing under different flow regimes. It was found that the tuned low fidelity model dominates the optimization process in terms of computational time and function calls.
The performance of a wind farm is affected by several key factors that can be classified into two cate- gories: the natural factors and the design factors. Hence, the planning of a wind farm requires a clear quantitative understanding of how the balance between the concerned objectives (e.g., socia-economic, engineering, and environmental objectives) is affected by these key factors. This understanding is lacking in the state of the art in wind farm design. The wind farm capacity factor is one of the primary perfor- mance criteria of a wind energy project. For a given land (or sea area) and wind resource, the maximum capacity factor of a particular number of wind turbines can be reached by optimally adjusting the layout of turbines. However, this layout adjustment is constrained owing to the limited land resource. This paper proposes a Bi-level Multi-objective Wind Farm Optimization (BMWFO) framework for planning effective wind energy projects. Two important performance objectives considered in this paper are: (i) wind farm Capacity Factor (CF) and (ii) Land Area per MW Installed (LAMI). Turbine locations, land area, and nameplate capacity are treated as design variables in this work. In the proposed framework, the Capacity Factor - Land Area per MW Installed (CF - LAMI) trade-off is parametrically represented as a function of the nameplate capacity. Such a helpful parameterization of trade-offs is unique in the wind energy literature. The farm output is computed using the wind farm power generation model adopted from the Unrestricted Wind Farm Layout Optimization (UWFLO) framework. The Smallest Bounding Rectangle (SBR) enclosing all turbines is used to calculate the actual land area occupied by the farm site. The wind farm layout optimization is performed in the lower level using the Mixed-Discrete Particle Swarm Optimization (MDPSO), while the CF - LAMI trade-off is parameterized in the upper level. In this work, the CF - LAMI trade-off is successfully quantified by nameplate capacity in the 20 MW to 100 MW range. The Pareto curves obtained from the proposed framework provide important in- sights into the trade-offs between the two performance objectives, which can significantly streamline the decision-making process in wind farm development.
Owing to the multitude of surrogate modeling techniques, developed in the recent years and the diverse characteristics offered by them, automated adaptive model selection ap- proaches could be helpful in selecting the most suitable surrogate for a given problem. Surrogate selection could be performed at three different levels: (i) model type selection, (ii) basis (or kernel) function selection, and (iii) hyper-parameter selection where hyper- parameters are those kernel parameters that are generally given by the users. Unlike the majority of existing model selection techniques, this paper explores the development of a method that performs selection coherently at all the three levels. In this context, the REES method is used to provide measures of the median and maximum errors of a candi- date surrogate model. Two approaches are used for the 3-level selection; (i) A Cascaded approach performs each level in a nested loop in the order going from model-kernel-hyper- parameters; (ii) A more advanced One-Step approach solves a MINLP to simultaneously optimize the model, kernel, and hyper-parameters. In both approaches, multiobjective optimization is performed to yield the best trade-offs between the estimated median and maximum errors. Candidate surrogates that are considered include (i) Kriging, (ii) Radial Basis Function (RBF), and (iii) Support Vector Regression (SVR), and multiple candidate kernels are allowed within these surrogate models. The 3-level REES-based model selec- tion is compared with model selection based on error estimated on a large set of additional test points, for validation purposes. Numerical experiments on a 2-variable, 6-variable, and 18-variable test problems, and wind farm power generation problem, show that the proposed approach provides unique flexibility in model selection and is also reasonably ac- curate when compared with selection based on errors estimated on additional test points.
The performance expectations for commercial wind turbines, from a variety of geograph- ical regions with differing wind regimes, present significant techno-commercial challenges to manufacturers. The determination of which commercial turbine types perform the best under differing wind regimes can provide unique insights into the complex demands of a concerned target market. In this paper, a comprehensive methodology is developed to explore the suitability of commercially available wind turbines (when operating as a group/array) to the various wind regimes occurring over a large target market. The three major steps of this methodology include: (i) characterizing the geographical variation of wind regimes in the target market, (ii) determining the best performing turbines (in terms of minimum COE accomplished) for different wind regimes, and (iii) developing a metric to investigate the performance-based expected market suitability of currently available tur- bine feature combinations. The best performing turbines for different wind regimes are determined using the Unrestricted Wind Farm Layout Optimization (UWFLO) method. Expectedly, the larger sized and higher rated-power turbines provide better performance at lower average wind speeds. However, for wind resources higher than class-4, the perfor- mances of lower-rated power turbines are fairly competitive, which could make them better choices for sites with complex terrain or remote location. In addition, turbines with direct drive are observed to perform significantly better than turbines with more conventional gear-based drive-train. The market considered in this paper is mainland USA, for which wind map information is obtained from NREL. Interestingly, it is found that overall higher rated-power turbines with relatively lower tower heights are most favored in the onshore US market.
Surrogate-based design is an effective approach for modeling computationally expensive system behavior. In such application, it is often challenging to characterize the expected accuracy of the surrogate. In addition to global and local error measures, regional error measures can be used to understand and interpret the surrogate accuracy in the regions of interest. This paper develops the Regional Error Estimation of Surrogate (REES) method to quantify the level of the error in any given subspace (or region) of the entire domain, when all the available training points have been invested to build the surrogate. In this approach, the accuracy of the surrogate in each subspace is estimated by modeling the variations of the mean and the maximum error in that subspace with increasing number of training points (in an iterative process). A regression model is used for this purpose. At each iteration, the intermediate surrogate is constructed using a subset of the entire training data, and tested over the remaining points. The evaluated errors at the intermediate test points at each iteration are used for training the regression model that represents the error variation with sample points. The effectiveness of the proposed method is illustrated using standard test problems. To this end, the predicted regional errors of the surrogate constructed using all the training points are compared with the regional errors estimated over a large set of test points.
Wind resources vary significantly in strength from one location to another over a wide geographical region. The major turbine manufacturers offer a family/series of wind tur- bines to suit the market needs of different wind regimes. The current state of the art in wind farm design however does not provide quantitative guidelines regarding what turbine feature combinations are suitable for different wind regimes, when turbines are operating as a group in an optimized layout. This paper provides a unique exploration of the best tradeoffs between the cost and the capacity factor of wind farms (of specified nameplate capacity), provided by the currently available turbines for different wind classes. To this end, the best performing turbines for different wind resource strengths are identified by minimizing the cost of energy through wind farm layout optimization. Exploration of the “cost - capacity factor” tradeoffs are then performed for the wind resource strengths cor- responding to the wind classes defined in the 7-class system. The best tradeoff turbines are determined by searching for the non-dominated set of turbines out of the pool of best performing turbines of different rated powers. The medium priced turbines are observed to provide the most attractive tradeoffs − 15% more capacity factor than the cheapest tradeoff turbines and only 5% less capacity factor than the most expensive tradeoff turbines. It was found that although the “cost - capacity factor” tradeoff curve expectedly shifted towards higher capacity factors with increasing wind class, the trend of the tradeoff curve remained practically similar. Further analysis showed that the “rated power - rotor diameter” com- bination and the “rotor diameter/hub height” ratios are very important considerations in the current selection and further evolution of turbine designs. We found that larger rotor diameters are not preferred for mid-range turbines with rated powers between 1.5 - 2.5 MW, and “rotor diameter/hub height” ratios greater than 1.1 are not preferred by any of the wind classes.
A parsimonious SVM model selection criterion for classification of real-world ...o_almasi
This paper proposes and optimizes a two-term cost function consisting of a sparseness term and a generalized v-fold cross-validation term by a new adaptive particle swarm optimization (APSO). APSO updates its parameters adaptively based on a dynamic feedback from the success rate of the each particle’s personal best. Since the proposed cost function is based on the choosing fewer numbers of support vectors, the complexity of SVM models decreased while the accuracy remains in an acceptable range. Therefore, the testing time decreases and makes SVM more applicable for practical applications in real data sets. A comparative study on data sets of UCI database is performed between the proposed cost function and conventional cost function to demonstrate the effectiveness of the proposed cost function.
This paper proposes a novel model management technique to be applied in population- based heuristic optimization. This technique adaptively selects different computational models (both physics-based and statistical models) to be used during optimization, with the overall goal to end with high fidelity solutions in a reasonable time period. For example, in optimizing an aircraft wing to obtain maximum lift-to-drag ratio, one can use low-fidelity models such as given by the vortex lattice method, or a high-fidelity finite volume model (that solves the full Navier-Stokes equations), or a surrogate model that substitutes the high-fidelity model.The information from models with different levels of fidelity is inte- grated into the heuristic optimization process using a novel model-switching metric. In this context, models could be surrogate models, low-fidelity physics-based analytical mod- els, and medium-to-high fidelity computational models (based on grid density). The model switching technique replaces the current model with the next higher fidelity model, when a stochastic switching criterion is met at a given iteration during the optimization process. The switching criteria is based on whether the uncertainty associated with the current model output dominates the latest improvement of the fitness function. In the case of the physics-based models, the uncertainty in their output is quantified through an inverse assessment process by comparing with high-fidelity model responses or experimental data (if available). To determine the fidelity of surrogate models, the Predictive Estimation of Model Fidelity (PEMF) method is applied. The effectiveness of the proposed method is demonstrated by applying it to airfoil optimization with the objective to maximize the lift to drag ratio of the wing under different flow regimes. It was found that the tuned low fidelity model dominates the optimization process in terms of computational time and function calls.
This paper advances the Domain Segmentation based on Uncertainty in the Surrogate (DSUS) framework which is a novel approach to characterize the uncertainty in surrogates. The leave-one-out cross-validation technique is adopted in the DSUS framework to measure local errors of a surrogate. A method is proposed in this paper to evaluate the performance of the leave-out-out cross-validation errors as local error measures. This method evaluates local errors by comparing: (i) the leave-one-out cross-validation error with (ii) the actual local error estimated within a local hypercube for each training point. The comparison results show that the leave-one-out cross-validation strategy can capture the local errors of a surrogate. The DSUS framework is then applied to key aspects of wind resource as- sessment and wind farm cost modeling. The uncertainties in the wind farm cost and the wind power potential are successfully characterized, which provides designers/users more confidence when using these models
Comparison of Emergency Medical Services Delivery Performance using Maximal C...IJECEIAES
Ambulance location is one of the critical factors that determine the efficiency of emergency medical services delivery. Maximal Covering Location Problem is one of the widely used ambulance location models. However, its coverage function is considered unrealistic because of its ability to abruptly change from fully covered to uncovered. On the contrary, Gradual Cover Location Problem coverage is considered more realistic compared to Maximal Cover Location Problem because the coverage decreases over distance. This paper examines the delivery of Emergency Medical Services under the models of Maximal Covering Location Problem and Gradual Cover Location Problem. The results show that the latter model is superior, especially when the Maximal Covering Location Problem has been deemed fully covered.
A REVIEW ON OPTIMIZATION OF LEAST SQUARES SUPPORT VECTOR MACHINE FOR TIME SER...ijaia
Support Vector Machine has appeared as an active study in machine learning community and extensively
used in various fields including in prediction, pattern recognition and many more. However, the Least
Squares Support Vector Machine which is a variant of Support Vector Machine offers better solution
strategy. In order to utilize the LSSVM capability in data mining task such as prediction, there is a need to
optimize its hyper parameters. This paper presents a review on techniques used to optimize the parameters
based on two main classes; Evolutionary Computation and Cross Validation.
Owing to the multitude of surrogate modeling techniques, developed in the recent years and the diverse characteristics offered by them, automated adaptive model selection ap- proaches could be helpful in selecting the most suitable surrogate for a given problem. Surrogate selection could be performed at three different levels: (i) model type selection, (ii) basis (or kernel) function selection, and (iii) hyper-parameter selection where hyper- parameters are those kernel parameters that are generally given by the users. Unlike the majority of existing model selection techniques, this paper explores the development of a method that performs selection coherently at all the three levels. In this context, the REES method is used to provide measures of the median and maximum errors of a candi- date surrogate model. Two approaches are used for the 3-level selection; (i) A Cascaded approach performs each level in a nested loop in the order going from model-kernel-hyper- parameters; (ii) A more advanced One-Step approach solves a MINLP to simultaneously optimize the model, kernel, and hyper-parameters. In both approaches, multiobjective optimization is performed to yield the best trade-offs between the estimated median and maximum errors. Candidate surrogates that are considered include (i) Kriging, (ii) Radial Basis Function (RBF), and (iii) Support Vector Regression (SVR), and multiple candidate kernels are allowed within these surrogate models. The 3-level REES-based model selec- tion is compared with model selection based on error estimated on a large set of additional test points, for validation purposes. Numerical experiments on a 2-variable, 6-variable, and 18-variable test problems, and wind farm power generation problem, show that the proposed approach provides unique flexibility in model selection and is also reasonably ac- curate when compared with selection based on errors estimated on additional test points.
Performance improvement of a Rainfall Prediction Model using Particle Swarm O...ijceronline
The performances of the statistical methods of time series forecast can be improved by precise selection of their parameters. Various techniques are being applied to improve the modeling accuracy of these models. Particle swarm optimization is one such technique which can be conveniently used to determine the model parameters accurately. This robust optimization technique has already been applied to improve the performance of artificial neural networks for time series prediction. This study uses particle swarm optimization technique to determine the parameters of an exponential autoregressive model for time series prediction. The model is applied for annual rainfall prediction and it shows a fairly good performance in comparison to the statistical ARIMA model
PREDICTION OF REPAIR & MAINTENANCE COSTS OF DIESEL ENGINEijmech
Diesel engine is widely use for different applications, the failure frequency of diesel engine is more increase to increase the age & use of engine in order to take decision to replacement of engine on the basis of Repair & Maintenance cost (R&M) & predication of future Repair & Maintenance costs of diesel engine used in Borewell compressor. Present case study discusses prediction of accumulated R&M costs (Y) of Diesel engine against usage in hours (X). Recorded data from the company service station is used to determine regression models for predicting total R&M costs based on total usage hours. The statistical results of the study indicates that in order to predict total R&M costs is more useful for replacement
decisions than annual charge.
A Response Surface Based Wind Farm Cost (RS-WFC) model, is developed to evaluate the economics of wind farms. The RS-WFC model is developed using Extended Radial Basis Functions (E-RBF) for onshore wind farms in the U.S.. This model is then used to explore the in uence of di erent design and economic parameters, including number of turbines, rotor diameter and labor cost, on the cost of a wind farm. The RS-WFC model is composed of three parts that estimate (i) the installation cost, (ii) the annual Operation and Maintenance (O&M) cost, and (iii) the total annual cost of a wind farm. The accuracy of the cost model is favorably established through comparison with pertinent commercial data. Moreover, the RS-WFC model is integrated with an analytical power generation model of a wind farm. A recently developed Unrestricted Wind Farm Layout Optimization (UWFLO) model is used to determine the power generated by a farm. The ratio of the total annual cost and the energy generated by the wind farm in one year (commonly known as the Cost of Energy, COE) is minimized in this paper. The results show that the COE could decreasesigni cantlythroughlayoutoptimization,toobtainmillionsofannualcostsavings.
Comparative Study on the Performance of A Coherency-based Simple Dynamic Equi...IJAPEJOURNAL
Earlier, a simple dynamic equivalent for a power system external area containing a group of coherent generators was proposed in the literature. This equivalent is based on a new concept of decomposition of generators and a two-level generator aggregation. With the knowledge of only the passive network model of the external area and the total inertia constant of all the generators in this area, the parameters of this equivalent are determinable from a set of measurement data taken solely at a set of boundary buses which separates this area from the rest of the system. The proposed equivalent, therefore, does not require any measurement data at the external area generators. This is an important feature of this equivalent. In this paper, the results of a comparative study on the performance of this dynamic equivalent aggregation with the new inertial aggregation in terms of accuracy are presented. The three test systems that were considered in this comparative investigation are the New England 39-bus 10-generator system, the IEEE 162-bus 17-generator system and the IEEE 145-bus 50-generator system.
A major challenge in hydrological modelling is to identification of optimal
parameter set of different data, catchment characteristics and objectives. Although, the
identification of optimal parameter set is difficult because of conceptual hydrological
models contain more number of parameters and accuracy also depends upon all the
relevant number of parameters influencing in a model. This identification process
cannot estimate directly and therefore it measured based on calibrating the model
which minimizing an objective function. Here, the objective function can depend upon
the sensitivity of model parameters and calibration of model. In this paper, we proposed
the Emulator Based Optimization (EBO) for reducing number of runs and improving
conceptual model efficiency. Where, emulator models are used to represent the
response surface of the simulation models and it can play a valuable role for
optimization. In this study evaluates EBO for calibrating of SWAT hydrological model
with following steps like input design, simulation model, emulator modelling,
convergence criteria and validation. The results show that EBO calibrates the model
with high accuracy and it captured the observed model with consuming less time. This
study helps for decision making, planning and designing of water resources.
The performance of a wind farm is affected by several key factors that can be classified into two cate- gories: the natural factors and the design factors. Hence, the planning of a wind farm requires a clear quantitative understanding of how the balance between the concerned objectives (e.g., socia-economic, engineering, and environmental objectives) is affected by these key factors. This understanding is lacking in the state of the art in wind farm design. The wind farm capacity factor is one of the primary perfor- mance criteria of a wind energy project. For a given land (or sea area) and wind resource, the maximum capacity factor of a particular number of wind turbines can be reached by optimally adjusting the layout of turbines. However, this layout adjustment is constrained owing to the limited land resource. This paper proposes a Bi-level Multi-objective Wind Farm Optimization (BMWFO) framework for planning effective wind energy projects. Two important performance objectives considered in this paper are: (i) wind farm Capacity Factor (CF) and (ii) Land Area per MW Installed (LAMI). Turbine locations, land area, and nameplate capacity are treated as design variables in this work. In the proposed framework, the Capacity Factor - Land Area per MW Installed (CF - LAMI) trade-off is parametrically represented as a function of the nameplate capacity. Such a helpful parameterization of trade-offs is unique in the wind energy literature. The farm output is computed using the wind farm power generation model adopted from the Unrestricted Wind Farm Layout Optimization (UWFLO) framework. The Smallest Bounding Rectangle (SBR) enclosing all turbines is used to calculate the actual land area occupied by the farm site. The wind farm layout optimization is performed in the lower level using the Mixed-Discrete Particle Swarm Optimization (MDPSO), while the CF - LAMI trade-off is parameterized in the upper level. In this work, the CF - LAMI trade-off is successfully quantified by nameplate capacity in the 20 MW to 100 MW range. The Pareto curves obtained from the proposed framework provide important in- sights into the trade-offs between the two performance objectives, which can significantly streamline the decision-making process in wind farm development.
Approximation models (or surrogate models) provide an efficient substitute to expen- sive physical simulations and an efficient solution to the lack of physical models of system behavior. However, it is challenging to quantify the accuracy and reliability of such ap- proximation models in a region of interest or the overall domain without additional system evaluations. Standard error measures, such as the mean squared error, the cross-validation error, and the Akaikes information criterion, provide limited (often inadequate) informa- tion regarding the accuracy of the final surrogate. This paper introduces a novel and model independent concept to quantify the level of errors in the function value estimated by the final surrogate in any given region of the design domain. This method is called the Re- gional Error Estimation of Surrogate (REES). Assuming the full set of available sample points to be fixed, intermediate surrogates are iteratively constructed over a sample set comprising all samples outside the region of interest and heuristic subsets of samples inside the region of interest (i.e., intermediate training points). The intermediate surrogate is tested over the remaining sample points inside the region of interest (i.e., intermediate test points). The fraction of sample points inside region of interest, which are used as interme- diate training points, is fixed at each iteration, with the total number of iterations being pre-specified. The estimated median and maximum relative errors within the region of in- terest for the heuristic subsets at each iteration are used to fit a distribution of the median and maximum error, respectively. The estimated statistical mode of the median and the maximum error, and the absolute maximum error are then represented as functions of the density of intermediate training points, using regression models. The regression models are then used to predict the expected median and maximum regional errors when all the sample points are used as training points. Standard test functions and a wind farm power generation problem are used to illustrate the effectiveness and the utility of such a regional error quantification method.
The performance expectations for commercial wind turbines, from a variety of geograph- ical regions with differing wind regimes, present significant techno-commercial challenges to manufacturers. The determination of which commercial turbine types perform the best under differing wind regimes can provide unique insights into the complex demands of a concerned target market. In this paper, a comprehensive methodology is developed to explore the suitability of commercially available wind turbines (when operating as a group/array) to the various wind regimes occurring over a large target market. The three major steps of this methodology include: (i) characterizing the geographical variation of wind regimes in the target market, (ii) determining the best performing turbines (in terms of minimum COE accomplished) for different wind regimes, and (iii) developing a metric to investigate the performance-based expected market suitability of currently available tur- bine feature combinations. The best performing turbines for different wind regimes are determined using the Unrestricted Wind Farm Layout Optimization (UWFLO) method. Expectedly, the larger sized and higher rated-power turbines provide better performance at lower average wind speeds. However, for wind resources higher than class-4, the perfor- mances of lower-rated power turbines are fairly competitive, which could make them better choices for sites with complex terrain or remote location. In addition, turbines with direct drive are observed to perform significantly better than turbines with more conventional gear-based drive-train. The market considered in this paper is mainland USA, for which wind map information is obtained from NREL. Interestingly, it is found that overall higher rated-power turbines with relatively lower tower heights are most favored in the onshore US market.
The performance expectations for commercial wind turbines, from a variety of geograph- ical regions with differing wind regimes, present significant techno-commercial challenges to manufacturers. The determination of which commercial turbine types perform the best under differing wind regimes can provide unique insights into the complex demands of a concerned target market. In this paper, a comprehensive methodology is developed to explore the suitability of commercially available wind turbines (when operating as a group/array) to the various wind regimes occurring over a large target market. The three major steps of this methodology include: (i) characterizing the geographical variation of wind regimes in the target market, (ii) determining the best performing turbines (in terms of minimum COE accomplished) for different wind regimes, and (iii) developing a metric to investigate the performance-based expected market suitability of currently available tur- bine feature combinations. The best performing turbines for different wind regimes are determined using the Unrestricted Wind Farm Layout Optimization (UWFLO) method. Expectedly, the larger sized and higher rated-power turbines provide better performance at lower average wind speeds. However, for wind resources higher than class-4, the perfor- mances of lower-rated power turbines are fairly competitive, which could make them better choices for sites with complex terrain or remote location. In addition, turbines with direct drive are observed to perform significantly better than turbines with more conventional gear-based drive-train. The market considered in this paper is mainland USA, for which wind map information is obtained from NREL. Interestingly, it is found that overall higher rated-power turbines with relatively lower tower heights are most favored in the onshore US market.
Surrogate-based design is an effective approach for modeling computationally expensive system behavior. In such application, it is often challenging to characterize the expected accuracy of the surrogate. In addition to global and local error measures, regional error measures can be used to understand and interpret the surrogate accuracy in the regions of interest. This paper develops the Regional Error Estimation of Surrogate (REES) method to quantify the level of the error in any given subspace (or region) of the entire domain, when all the available training points have been invested to build the surrogate. In this approach, the accuracy of the surrogate in each subspace is estimated by modeling the variations of the mean and the maximum error in that subspace with increasing number of training points (in an iterative process). A regression model is used for this purpose. At each iteration, the intermediate surrogate is constructed using a subset of the entire training data, and tested over the remaining points. The evaluated errors at the intermediate test points at each iteration are used for training the regression model that represents the error variation with sample points. The effectiveness of the proposed method is illustrated using standard test problems. To this end, the predicted regional errors of the surrogate constructed using all the training points are compared with the regional errors estimated over a large set of test points.
Wind resources vary significantly in strength from one location to another over a wide geographical region. The major turbine manufacturers offer a family/series of wind tur- bines to suit the market needs of different wind regimes. The current state of the art in wind farm design however does not provide quantitative guidelines regarding what turbine feature combinations are suitable for different wind regimes, when turbines are operating as a group in an optimized layout. This paper provides a unique exploration of the best tradeoffs between the cost and the capacity factor of wind farms (of specified nameplate capacity), provided by the currently available turbines for different wind classes. To this end, the best performing turbines for different wind resource strengths are identified by minimizing the cost of energy through wind farm layout optimization. Exploration of the “cost - capacity factor” tradeoffs are then performed for the wind resource strengths cor- responding to the wind classes defined in the 7-class system. The best tradeoff turbines are determined by searching for the non-dominated set of turbines out of the pool of best performing turbines of different rated powers. The medium priced turbines are observed to provide the most attractive tradeoffs − 15% more capacity factor than the cheapest tradeoff turbines and only 5% less capacity factor than the most expensive tradeoff turbines. It was found that although the “cost - capacity factor” tradeoff curve expectedly shifted towards higher capacity factors with increasing wind class, the trend of the tradeoff curve remained practically similar. Further analysis showed that the “rated power - rotor diameter” com- bination and the “rotor diameter/hub height” ratios are very important considerations in the current selection and further evolution of turbine designs. We found that larger rotor diameters are not preferred for mid-range turbines with rated powers between 1.5 - 2.5 MW, and “rotor diameter/hub height” ratios greater than 1.1 are not preferred by any of the wind classes.
A parsimonious SVM model selection criterion for classification of real-world ...o_almasi
This paper proposes and optimizes a two-term cost function consisting of a sparseness term and a generalized v-fold cross-validation term by a new adaptive particle swarm optimization (APSO). APSO updates its parameters adaptively based on a dynamic feedback from the success rate of the each particle’s personal best. Since the proposed cost function is based on the choosing fewer numbers of support vectors, the complexity of SVM models decreased while the accuracy remains in an acceptable range. Therefore, the testing time decreases and makes SVM more applicable for practical applications in real data sets. A comparative study on data sets of UCI database is performed between the proposed cost function and conventional cost function to demonstrate the effectiveness of the proposed cost function.
This paper proposes a novel model management technique to be applied in population- based heuristic optimization. This technique adaptively selects different computational models (both physics-based and statistical models) to be used during optimization, with the overall goal to end with high fidelity solutions in a reasonable time period. For example, in optimizing an aircraft wing to obtain maximum lift-to-drag ratio, one can use low-fidelity models such as given by the vortex lattice method, or a high-fidelity finite volume model (that solves the full Navier-Stokes equations), or a surrogate model that substitutes the high-fidelity model.The information from models with different levels of fidelity is inte- grated into the heuristic optimization process using a novel model-switching metric. In this context, models could be surrogate models, low-fidelity physics-based analytical mod- els, and medium-to-high fidelity computational models (based on grid density). The model switching technique replaces the current model with the next higher fidelity model, when a stochastic switching criterion is met at a given iteration during the optimization process. The switching criteria is based on whether the uncertainty associated with the current model output dominates the latest improvement of the fitness function. In the case of the physics-based models, the uncertainty in their output is quantified through an inverse assessment process by comparing with high-fidelity model responses or experimental data (if available). To determine the fidelity of surrogate models, the Predictive Estimation of Model Fidelity (PEMF) method is applied. The effectiveness of the proposed method is demonstrated by applying it to airfoil optimization with the objective to maximize the lift to drag ratio of the wing under different flow regimes. It was found that the tuned low fidelity model dominates the optimization process in terms of computational time and function calls.
This paper advances the Domain Segmentation based on Uncertainty in the Surrogate (DSUS) framework which is a novel approach to characterize the uncertainty in surrogates. The leave-one-out cross-validation technique is adopted in the DSUS framework to measure local errors of a surrogate. A method is proposed in this paper to evaluate the performance of the leave-out-out cross-validation errors as local error measures. This method evaluates local errors by comparing: (i) the leave-one-out cross-validation error with (ii) the actual local error estimated within a local hypercube for each training point. The comparison results show that the leave-one-out cross-validation strategy can capture the local errors of a surrogate. The DSUS framework is then applied to key aspects of wind resource as- sessment and wind farm cost modeling. The uncertainties in the wind farm cost and the wind power potential are successfully characterized, which provides designers/users more confidence when using these models
Comparison of Emergency Medical Services Delivery Performance using Maximal C...IJECEIAES
Ambulance location is one of the critical factors that determine the efficiency of emergency medical services delivery. Maximal Covering Location Problem is one of the widely used ambulance location models. However, its coverage function is considered unrealistic because of its ability to abruptly change from fully covered to uncovered. On the contrary, Gradual Cover Location Problem coverage is considered more realistic compared to Maximal Cover Location Problem because the coverage decreases over distance. This paper examines the delivery of Emergency Medical Services under the models of Maximal Covering Location Problem and Gradual Cover Location Problem. The results show that the latter model is superior, especially when the Maximal Covering Location Problem has been deemed fully covered.
A REVIEW ON OPTIMIZATION OF LEAST SQUARES SUPPORT VECTOR MACHINE FOR TIME SER...ijaia
Support Vector Machine has appeared as an active study in machine learning community and extensively
used in various fields including in prediction, pattern recognition and many more. However, the Least
Squares Support Vector Machine which is a variant of Support Vector Machine offers better solution
strategy. In order to utilize the LSSVM capability in data mining task such as prediction, there is a need to
optimize its hyper parameters. This paper presents a review on techniques used to optimize the parameters
based on two main classes; Evolutionary Computation and Cross Validation.
Owing to the multitude of surrogate modeling techniques, developed in the recent years and the diverse characteristics offered by them, automated adaptive model selection ap- proaches could be helpful in selecting the most suitable surrogate for a given problem. Surrogate selection could be performed at three different levels: (i) model type selection, (ii) basis (or kernel) function selection, and (iii) hyper-parameter selection where hyper- parameters are those kernel parameters that are generally given by the users. Unlike the majority of existing model selection techniques, this paper explores the development of a method that performs selection coherently at all the three levels. In this context, the REES method is used to provide measures of the median and maximum errors of a candi- date surrogate model. Two approaches are used for the 3-level selection; (i) A Cascaded approach performs each level in a nested loop in the order going from model-kernel-hyper- parameters; (ii) A more advanced One-Step approach solves a MINLP to simultaneously optimize the model, kernel, and hyper-parameters. In both approaches, multiobjective optimization is performed to yield the best trade-offs between the estimated median and maximum errors. Candidate surrogates that are considered include (i) Kriging, (ii) Radial Basis Function (RBF), and (iii) Support Vector Regression (SVR), and multiple candidate kernels are allowed within these surrogate models. The 3-level REES-based model selec- tion is compared with model selection based on error estimated on a large set of additional test points, for validation purposes. Numerical experiments on a 2-variable, 6-variable, and 18-variable test problems, and wind farm power generation problem, show that the proposed approach provides unique flexibility in model selection and is also reasonably ac- curate when compared with selection based on errors estimated on additional test points.
Performance improvement of a Rainfall Prediction Model using Particle Swarm O...ijceronline
The performances of the statistical methods of time series forecast can be improved by precise selection of their parameters. Various techniques are being applied to improve the modeling accuracy of these models. Particle swarm optimization is one such technique which can be conveniently used to determine the model parameters accurately. This robust optimization technique has already been applied to improve the performance of artificial neural networks for time series prediction. This study uses particle swarm optimization technique to determine the parameters of an exponential autoregressive model for time series prediction. The model is applied for annual rainfall prediction and it shows a fairly good performance in comparison to the statistical ARIMA model
PREDICTION OF REPAIR & MAINTENANCE COSTS OF DIESEL ENGINEijmech
Diesel engine is widely use for different applications, the failure frequency of diesel engine is more increase to increase the age & use of engine in order to take decision to replacement of engine on the basis of Repair & Maintenance cost (R&M) & predication of future Repair & Maintenance costs of diesel engine used in Borewell compressor. Present case study discusses prediction of accumulated R&M costs (Y) of Diesel engine against usage in hours (X). Recorded data from the company service station is used to determine regression models for predicting total R&M costs based on total usage hours. The statistical results of the study indicates that in order to predict total R&M costs is more useful for replacement
decisions than annual charge.
A Response Surface Based Wind Farm Cost (RS-WFC) model, is developed to evaluate the economics of wind farms. The RS-WFC model is developed using Extended Radial Basis Functions (E-RBF) for onshore wind farms in the U.S.. This model is then used to explore the in uence of di erent design and economic parameters, including number of turbines, rotor diameter and labor cost, on the cost of a wind farm. The RS-WFC model is composed of three parts that estimate (i) the installation cost, (ii) the annual Operation and Maintenance (O&M) cost, and (iii) the total annual cost of a wind farm. The accuracy of the cost model is favorably established through comparison with pertinent commercial data. Moreover, the RS-WFC model is integrated with an analytical power generation model of a wind farm. A recently developed Unrestricted Wind Farm Layout Optimization (UWFLO) model is used to determine the power generated by a farm. The ratio of the total annual cost and the energy generated by the wind farm in one year (commonly known as the Cost of Energy, COE) is minimized in this paper. The results show that the COE could decreasesigni cantlythroughlayoutoptimization,toobtainmillionsofannualcostsavings.
Comparative Study on the Performance of A Coherency-based Simple Dynamic Equi...IJAPEJOURNAL
Earlier, a simple dynamic equivalent for a power system external area containing a group of coherent generators was proposed in the literature. This equivalent is based on a new concept of decomposition of generators and a two-level generator aggregation. With the knowledge of only the passive network model of the external area and the total inertia constant of all the generators in this area, the parameters of this equivalent are determinable from a set of measurement data taken solely at a set of boundary buses which separates this area from the rest of the system. The proposed equivalent, therefore, does not require any measurement data at the external area generators. This is an important feature of this equivalent. In this paper, the results of a comparative study on the performance of this dynamic equivalent aggregation with the new inertial aggregation in terms of accuracy are presented. The three test systems that were considered in this comparative investigation are the New England 39-bus 10-generator system, the IEEE 162-bus 17-generator system and the IEEE 145-bus 50-generator system.
A major challenge in hydrological modelling is to identification of optimal
parameter set of different data, catchment characteristics and objectives. Although, the
identification of optimal parameter set is difficult because of conceptual hydrological
models contain more number of parameters and accuracy also depends upon all the
relevant number of parameters influencing in a model. This identification process
cannot estimate directly and therefore it measured based on calibrating the model
which minimizing an objective function. Here, the objective function can depend upon
the sensitivity of model parameters and calibration of model. In this paper, we proposed
the Emulator Based Optimization (EBO) for reducing number of runs and improving
conceptual model efficiency. Where, emulator models are used to represent the
response surface of the simulation models and it can play a valuable role for
optimization. In this study evaluates EBO for calibrating of SWAT hydrological model
with following steps like input design, simulation model, emulator modelling,
convergence criteria and validation. The results show that EBO calibrates the model
with high accuracy and it captured the observed model with consuming less time. This
study helps for decision making, planning and designing of water resources.
The performance of a wind farm is affected by several key factors that can be classified into two cate- gories: the natural factors and the design factors. Hence, the planning of a wind farm requires a clear quantitative understanding of how the balance between the concerned objectives (e.g., socia-economic, engineering, and environmental objectives) is affected by these key factors. This understanding is lacking in the state of the art in wind farm design. The wind farm capacity factor is one of the primary perfor- mance criteria of a wind energy project. For a given land (or sea area) and wind resource, the maximum capacity factor of a particular number of wind turbines can be reached by optimally adjusting the layout of turbines. However, this layout adjustment is constrained owing to the limited land resource. This paper proposes a Bi-level Multi-objective Wind Farm Optimization (BMWFO) framework for planning effective wind energy projects. Two important performance objectives considered in this paper are: (i) wind farm Capacity Factor (CF) and (ii) Land Area per MW Installed (LAMI). Turbine locations, land area, and nameplate capacity are treated as design variables in this work. In the proposed framework, the Capacity Factor - Land Area per MW Installed (CF - LAMI) trade-off is parametrically represented as a function of the nameplate capacity. Such a helpful parameterization of trade-offs is unique in the wind energy literature. The farm output is computed using the wind farm power generation model adopted from the Unrestricted Wind Farm Layout Optimization (UWFLO) framework. The Smallest Bounding Rectangle (SBR) enclosing all turbines is used to calculate the actual land area occupied by the farm site. The wind farm layout optimization is performed in the lower level using the Mixed-Discrete Particle Swarm Optimization (MDPSO), while the CF - LAMI trade-off is parameterized in the upper level. In this work, the CF - LAMI trade-off is successfully quantified by nameplate capacity in the 20 MW to 100 MW range. The Pareto curves obtained from the proposed framework provide important in- sights into the trade-offs between the two performance objectives, which can significantly streamline the decision-making process in wind farm development.
Approximation models (or surrogate models) provide an efficient substitute to expen- sive physical simulations and an efficient solution to the lack of physical models of system behavior. However, it is challenging to quantify the accuracy and reliability of such ap- proximation models in a region of interest or the overall domain without additional system evaluations. Standard error measures, such as the mean squared error, the cross-validation error, and the Akaikes information criterion, provide limited (often inadequate) informa- tion regarding the accuracy of the final surrogate. This paper introduces a novel and model independent concept to quantify the level of errors in the function value estimated by the final surrogate in any given region of the design domain. This method is called the Re- gional Error Estimation of Surrogate (REES). Assuming the full set of available sample points to be fixed, intermediate surrogates are iteratively constructed over a sample set comprising all samples outside the region of interest and heuristic subsets of samples inside the region of interest (i.e., intermediate training points). The intermediate surrogate is tested over the remaining sample points inside the region of interest (i.e., intermediate test points). The fraction of sample points inside region of interest, which are used as interme- diate training points, is fixed at each iteration, with the total number of iterations being pre-specified. The estimated median and maximum relative errors within the region of in- terest for the heuristic subsets at each iteration are used to fit a distribution of the median and maximum error, respectively. The estimated statistical mode of the median and the maximum error, and the absolute maximum error are then represented as functions of the density of intermediate training points, using regression models. The regression models are then used to predict the expected median and maximum regional errors when all the sample points are used as training points. Standard test functions and a wind farm power generation problem are used to illustrate the effectiveness and the utility of such a regional error quantification method.
The performance expectations for commercial wind turbines, from a variety of geograph- ical regions with differing wind regimes, present significant techno-commercial challenges to manufacturers. The determination of which commercial turbine types perform the best under differing wind regimes can provide unique insights into the complex demands of a concerned target market. In this paper, a comprehensive methodology is developed to explore the suitability of commercially available wind turbines (when operating as a group/array) to the various wind regimes occurring over a large target market. The three major steps of this methodology include: (i) characterizing the geographical variation of wind regimes in the target market, (ii) determining the best performing turbines (in terms of minimum COE accomplished) for different wind regimes, and (iii) developing a metric to investigate the performance-based expected market suitability of currently available tur- bine feature combinations. The best performing turbines for different wind regimes are determined using the Unrestricted Wind Farm Layout Optimization (UWFLO) method. Expectedly, the larger sized and higher rated-power turbines provide better performance at lower average wind speeds. However, for wind resources higher than class-4, the perfor- mances of lower-rated power turbines are fairly competitive, which could make them better choices for sites with complex terrain or remote location. In addition, turbines with direct drive are observed to perform significantly better than turbines with more conventional gear-based drive-train. The market considered in this paper is mainland USA, for which wind map information is obtained from NREL. Interestingly, it is found that overall higher rated-power turbines with relatively lower tower heights are most favored in the onshore US market.
The analysis of complex system behavior often demands expensive experiments or computational simula- tions. Surrogate modeling techniques are often used to provide a tractable and inexpensive approximation of such complex system behavior. Owing to the lack of any general guidelines regarding the suitability of different surrogate models for different applications, model selection approach can be helpful to choose the best surrogate technique. This paper investigates the effectiveness of a recently developed method for surrogate error quantification called, Regional Error Estimation of Surrogate (REES), to select the best surrogate model based on the level of accuracy. The REES method is developed based on the concept that the accuracy of the approximation methods is related to the amount of available resources. In the REES method, intermediate surrogates are iteratively constructed over heuristic subsets of the available sample points (i.e., intermediate training points) and tested over the remaining available sample points (i.e., intermediate test points). The statistical mode of the median and the maximum error distributions are selected to represent the overall and maximum error at each iteration. The estimated modes of the median and maximum error distributions are then represented as functions of the number of interme- diate training points using a regression model. The regression models are used to predict the overall and minimum accuracy of the final surrogate. These two error measures are then applied to select the best surrogate. The proposed model selection technique is applied to select the best surrogate among (i) Kriging, (ii) Radial Basis Functions (RBF), (iii) Extended Radial basis Functions (E-RBF), and (iv) Quadratic Response Surface (QRS), for standard test functions and a wind farm power generation func- tion. The REES-based model selection is compared with (i) model-selection based on cross-validation errors and (ii) model-selection based on error estimated on a large set of additional test points; the lat- ter is assumed to provide the correct model selection. The REES-based model selection is found to be significantly more accurate than that based on cross-validation errors.
This paper proposes a novel model management technique to be applied in population- based heuristic optimization. This technique adaptively selects different computational models (both physics-based and statistical models) to be used during optimization, with the overall goal to end with high fidelity solutions in a reasonable time period. For example, in optimizing an aircraft wing to obtain maximum lift-to-drag ratio, one can use low-fidelity models such as given by the vortex lattice method, or a high-fidelity finite volume model (that solves the full Navier-Stokes equations), or a surrogate model that substitutes the high-fidelity model.The information from models with different levels of fidelity is inte- grated into the heuristic optimization process using a novel model-switching metric. In this context, models could be surrogate models, low-fidelity physics-based analytical mod- els, and medium-to-high fidelity computational models (based on grid density). The model switching technique replaces the current model with the next higher fidelity model, when a stochastic switching criterion is met at a given iteration during the optimization process. The switching criteria is based on whether the uncertainty associated with the current model output dominates the latest improvement of the fitness function. In the case of the physics-based models, the uncertainty in their output is quantified through an inverse assessment process by comparing with high-fidelity model responses or experimental data (if available). To determine the fidelity of surrogate models, the Predictive Estimation of Model Fidelity (PEMF) method is applied. The effectiveness of the proposed method is demonstrated by applying it to airfoil optimization with the objective to maximize the lift to drag ratio of the wing under different flow regimes. It was found that the tuned low fidelity model dominates the optimization process in terms of computational time and function calls.
This paper advances the Domain Segmentation based on Uncertainty in the Surrogate (DSUS) framework which is a novel approach to characterize the uncertainty in surrogates. The leave-one-out cross-validation technique is adopted in the DSUS framework to measure local errors of a surrogate. A method is proposed in this paper to evaluate the performance of the leave-out-out cross-validation errors as local error measures. This method evaluates local errors by comparing: (i) the leave-one-out cross-validation error with (ii) the actual local error estimated within a local hypercube for each training point. The comparison results show that the leave-one-out cross-validation strategy can capture the local errors of a surrogate. The DSUS framework is then applied to key aspects of wind resource as- sessment and wind farm cost modeling. The uncertainties in the wind farm cost and the wind power potential are successfully characterized, which provides designers/users more confidence when using these models.
Surrogate-based design is an effective approach for modeling computationally expensive system behavior. In such application, it is often challenging to characterize the expected accuracy of the surrogate. In addition to global and local error measures, regional error measures can be used to understand and interpret the surrogate accuracy in the regions of interest. This paper develops the Regional Error Estimation of Surrogate (REES) method to quantify the level of the error in any given subspace (or region) of the entire domain, when all the available training points have been invested to build the surrogate. In this approach, the accuracy of the surrogate in each subspace is estimated by modeling the variations of the mean and the maximum error in that subspace with increasing number of training points (in an iterative process). A regression model is used for this purpose. At each iteration, the intermediate surrogate is constructed using a subset of the entire train- ing data, and tested over the remaining points. The evaluated errors at the intermediate test points at each iteration are used for training the regression model that represents the error variation with sample points. The effectiveness of the proposed method is illustrated using standard test problems. To this end, the predicted regional errors of the surrogate constructed using all the training points are compared with the regional errors estimated over a large set of test points.
Wind resources vary significantly in strength from one location to another over a wide geographical region. The major turbine manufacturers offer a family/series of wind tur- bines to suit the market needs of different wind regimes. The current state of the art in wind farm design however does not provide quantitative guidelines regarding what turbine feature combinations are suitable for different wind regimes, when turbines are operating as a group in an optimized layout. This paper provides a unique exploration of the best tradeoffs between the cost and the capacity factor of wind farms (of specified nameplate capacity), provided by the currently available turbines for different wind classes. To this end, the best performing turbines for different wind resource strengths are identified by minimizing the cost of energy through wind farm layout optimization. Exploration of the “cost - capacity factor” tradeoffs are then performed for the wind resource strengths cor- responding to the wind classes defined in the 7-class system. The best tradeoff turbines are determined by searching for the non-dominated set of turbines out of the pool of best performing turbines of different rated powers. The medium priced turbines are observed to provide the most attractive tradeoffs − 15% more capacity factor than the cheapest tradeoff turbines and only 5% less capacity factor than the most expensive tradeoff turbines. It was found that although the “cost - capacity factor” tradeoff curve expectedly shifted towards higher capacity factors with increasing wind class, the trend of the tradeoff curve remained practically similar. Further analysis showed that the “rated power - rotor diameter” com- bination and the “rotor diameter/hub height” ratios are very important considerations in the current selection and further evolution of turbine designs. We found that larger rotor diameters are not preferred for mid-range turbines with rated powers between 1.5 - 2.5 MW, and “rotor diameter/hub height” ratios greater than 1.1 are not preferred by any of the wind classes.
Wind Farm Layout Optimization (WFLO) is a typical model-based complex system design process, where the popular use of low-medium fidelity models is one of the primary sources of uncertainties propagating into the esti- mated optimum cost of energy (COE). Therefore, the (currently lacking) understanding of the degree of uncertainty inherited and introduced by different models is absolutely critical (i) for making informed modeling decisions, and (ii) for being cognizant of the reliability of the obtained results. A framework called the Visually-Informed Decision-Making Platform (VIDMAP) was recently introduced to quantify and visualize the inter-model sensi- tivities and the model inherited/induced uncertainties in WFLO. Originally, VIDMAP quantified the uncertainties and sensitivities upstream of the energy production model. This paper advances VIDMAP to provide quantifica- tion/visualization of the uncertainties propagating through the entire optimization process, where optimization is performed to determine the micro-siting of 100 turbines with a minimum COE objective. Specifically, we deter- mine (i) the sensitivity of the minimum COE to the top-level system model (energy production model), (ii) the uncertainty introduced by the heuristic optimization algorithm (PSO), and (iii) the net uncertainty in the minimum COE estimate. In VIDMAP, the eFAST method is used for sensitivity analysis, and the model uncertainties are quantified through a combination of Monte Carlo simulation and probabilistic modeling. Based on the estimated sensitivity and uncertainty measures, a color-coded model-block flowchart is then created using the MATLAB GUI.
In spite of the recent developments in surrogate modeling techniques, the low fidelity of these models often limits their use in practical engineering design optimization. When surrogate models are used to represent the behavior of a complex system, it is challenging to simultaneously obtain high accuracy over the entire design space. When such surrogates are used for optimization, it becomes challening to find the optimum/optima with certainty. Sequential sampling methods offer a powerful solution to this challenge by providing the surrogate with reasonable accuracy where and when needed. When surrogate-based design optimization (SBDO) is performed using sequential sampling, the typical SBDO process is repeated multiple times, where each time the surrogate is improved by addition of new sam- ple points. This paper presents a new adaptive approach to add infill points during SBDO, called Adaptive Sequential Sampling (ASS). In this approach, both local exploitation and global exploration aspects are considered for updating the surrogate during optimization, where multiple iterations of the SBDO process is performed to increase the quality of the optimal solution. This approach adaptively improves the accuracy of the surrogate in the region of the current global optimum as well as in the regions of higher relative errors. Based on the initial sample points and the fitted surrogate, the ASS method adds infill points at each iteration in the locations of: (i) the current optimum found based on the fitted surrogate; and (ii) the points generated using cross-over between sample points that have relatively higher cross-validation errors. The Nelder and Mead Simplex method is adopted as the optimization algorithm. The effectiveness of the proposed method is illus- trated using a series of standard numerical test problems.
In developing complex engineering systems, model-based design approaches often face critical challenges due to pervasive uncertainties and high computational expense. These challenges could be alleviated to a significant extent though informed modeling decisions, such as model substitution, parameter estimation, localized re-sampling, or grid refine- ment. Informed modeling decisions therefore necessitate (currently lacking) design frame- works that effectively integrate design automation and human decision-making. In this paper, we seek to address this necessity in the context of designing wind farm layouts, by taking an information flow perspective of this typical model-based design process. Specif- ically, we develop a visual representation of the uncertainties inherited and generated by models and the inter-model sensitivities. This framework is called the Visually-Informed Decision-Making Platform (VIDMAP) for wind farm design. The eFAST method is used for sensitivity analysis, in order to determine both the first-order and the total-order in- dices. The uncertainties in the independent inputs are quantified based on their observed variance. The uncertainties generated by the upstream models are quantified through a Monte Carlo simulation followed by probabilistic modeling of (i) the error in the output of the models (if high-fidelity estimates are available), or (ii) the deviation in the outputs estimated by different alternatives/versions of the model. The GUI in VIDMAP is cre- ated using value-proportional colors for each model block and inter-model connector, to respectively represent the uncertainty in the model output and the impact (downstream) of the information being relayed by the connector. Wind farm layout optimization (WFLO) serves as an excellent platform to develop and explore VIDMAP, where WFLO is generally performed using low fidelity models, as high-fidelity models (e.g. LES) tend to be compu- tationally prohibitive in this context. The final VIDMAP obtained sheds new light into the sensitivity of wind farm energy estimation on the different models and their associated uncertainties.
The planning of a wind farm, which minimizes the project costs and maximizes the power generation capacity, presents significant challenges to today’s wind energy industry. An optimal wind farm planning strategy that accounts for the key factors (that can be designed) influencing the net power generation offers a powerful solution to these daunting challenges. This paper explores the influences of (i) the number of turbines, (ii) the farm size, and (iii) the use of a combination of turbines with differing rotor diameters, on the optimal power generated by a wind farm. We use a recently developed method of arranging turbines in a wind farm (the Unrestricted Wind Farm Layout Optimization (UWFLO)) to maximize the farm efficiency. Response surface based cost models are used to estimate the cost of the wind farm as a function of the the turbine rotor diameters and number of tur- bines. Optimization is performed using a Particle Swarm Optimization (PSO) algorithm. A robust mixed-discrete version of the PSO algorithm is implemented to appropriately account for the discrete choice of feasible rotor diameters. The use of an optimal combi- nation of turbines with differing rotor diameters was observed to significantly improve the net power generation. Exploration of the influences of (i) the number of turbines, and (ii) the farm size, on the cost per KW of power produced, provided interesting observations.
This paper presents a new method (the Unrestricted Wind Farm Layout Optimization (UWFLO)) of arranging turbines in a wind farm to achieve maximum farm efficiency. The powers generated by individual turbines in a wind farm are dependent on each other, due to velocity deficits created by the wake effect. A standard analytical wake model has been used to account for the mutual influences of the turbines in a wind farm. A variable induction factor, dependent on the approaching wind velocity, estimates the velocity deficit across each turbine. Optimization is performed using a constrained Particle Swarm Optimization (PSO) algorithm. The model is validated against experimental data from a wind tunnel experiment on a scaled down wind farm. Reasonable agreement between the model and experimental results is obtained. A preliminary wind farm cost analysis is also performed to explore the effect of using turbines with different rotor diameters on the total power generation. The use of differing rotor diameters is observed to play an important role in improving the overall efficiency of a wind farm.
Impact of Different Wake Models on the Estimation of Wind Farm Power GenerationWeiyang Tong
For citations, please refer to the journal version of this paper,
by Tong et al., "Sensitivity of Wind Farm Output to Wind Conditions, Land Configuration, and Installed Capacity, Under Different Wake Models", J. Mech. Des. 137(6), 061403 (Jun 01, 2015) (11 pages), Paper No: MD-14-1339; doi: 10.1115/1.4029892
available at:
http://mechanicaldesign.asmedigitalcollection.asme.org/article.aspx?articleid=2173776
Sensitivity of Array-like and Optimized Wind Farm Output to Key Factors and C...Weiyang Tong
For citations, please refer to the journal version of this paper,
by Tong et al., "Sensitivity of Wind Farm Output to Wind Conditions, Land Configuration, and Installed Capacity, Under Different Wake Models", J. Mech. Des. 137(6), 061403 (Jun 01, 2015) (11 pages), Paper No: MD-14-1339; doi: 10.1115/1.4029892
available at:
http://mechanicaldesign.asmedigitalcollection.asme.org/article.aspx?articleid=2173776
The creation of wakes, with unique turbulence charac- teristics, downstream of turbines significantly increases the complexity of the boundary layer flow within a wind farm. In conventional wind farm design, analytical wake models are generally used to compute the wake-induced power losses, with different wake models yielding significantly different estimates. In this context, the wake behavior, and subsequently the farm power generation, can be expressed as functions of a series of key factors. A quantitative understanding of the relative impact of each of these factors is paramount to the development of more reliable power generation models; such an understanding is however missing in the current state of the art in wind farm design. In this paper, we quantitatively explore how the farm power generation, estimated using four different analytical wake models, is influenced by the following key factors: (i) incoming wind speed, (ii) land configuration, and (iii) ambient turbulence. The sensitivity of the maximum farm output potential to the input factors, when using different wake models, is also analyzed. The extended Fourier Amplitude Sensitivity Test (eFAST) method is used to perform the sensitivity analysis. The power generation model and the optimization strategy is adopted from the Unrestricted Wind Farm Layout Optimization (UWFLO) framework. In the case of an array-like turbine arrangement, both the first-order and the total-order sensitivity analysis indices of the power output with respect to the incoming wind speed were found to reach a value of 99%, irrespective of the choice of wake models. However, in the case of maximum power output, significant variation (around 30%) in the indices was observed across different wake models, especially when the incoming wind speed is close to the rated speed of the turbines.
In this paper, we develop a flexible design platform to ac- count for the influences of key factors in optimal planning of commercial scale wind farms. The Unrestricted Wind Farm Lay- out Optimization (UWFLO) methodology, which avoids limit- ing assumptions regarding the farm layout and the selection of turbines, is used to develop this design platform. This paper presents critical advancements to the UWFLO methodology to allow the synergistic consideration of (i) the farm layout, (ii) the types of commercial turbines to be installed, and (iii) the ex- pected annual distribution of wind conditions at a particular site. We use a recently developed Kernel Density Estimation (KDE) based method to characterize the multivariate distribution of wind speed and wind direction. Optimization is performed using an advanced mixed discrete Particle Swarm Optimization algo- rithm. We also implement a high fidelity wind farm cost model that is developed using a Radial Basis Function (RBF) based response surface. The new optimal farm planning platform is applied to design a 25-turbine wind farm at a North Dakota site. We found that the optimal layout is significantly sensitive to the annual variation in wind conditions. Allowing the turbine-types to be selected during optimization was observed to improve the annual energy production by 49% compared to layout optimiza- tion alone.
The development of utility-scale wind farms that can produce energy at a cost comparable to that of conventional energy resources presents significant challenges to today’s wind energy industry. The consideration of the combined impact of key design and environmental factors on the performance of a wind farm is a crucial part of the solution to this challenge. The state of the art in optimal wind project planning includes wind farm layout design and more recently turbine selection. The scope of farm layout optimization and the predicted wind project performance however depends on several other critical site-scale factors, which are often not explicitly accounted for in the wind farm planning literature. These factors include: (i) the land area per MW installed (LAMI), and (ii) the nameplate capacity (in MW) of the farm. In this paper, we develop a framework to quantify and analyze the roles of these crucial design factors in optimal wind farm planning. A set of sample values of LAMI and installed farm capacities is first defined. For each sample farm definition, simultaneous optimization of the farm layout and turbine selection is performed to maximize the farm capacity factor (CF). To this end, we apply the recently de- veloped Unrestricted Wind Farm Layout Optimization (UWFLO) method. The CF of the optimized farm is then represented as a function of the nameplate capacity and the LAMI, using response surface methodologies. The variation of the optimized CF with these site-scale factors is investigated for a representative wind site in North Dakota. It was found that, a desirable CF value corresponds to a cutoff “LAMI vs nameplate capacity” curve – the identification of this cutoff curve is critical to the development of an economically viable wind energy project.
The power generation of a wind farm is significantly less than the summation of the power generated by each turbine when operating as a standalone entity. This power reduction can be attributed to the energy loss due to the wake effects − the resulting velocity deficit in the wind downstream of a turbine. In the case of wind farm design, the wake losses are generally quantified using wake models. The effectiveness of wind farm design (seeking to maximize the farm output) therefore depends on the accuracy and the reliability of the wake models. This paper compares the impact of the following four analytical wake
models on the wind farm power generation: (i) the Jensen model, (ii) the Larsen model, (iii) the Frandsen model, and (iv) the Ishihara model. The sensitivity of this impact to the Land Area per Turbine (LAT) and the incoming wind speed is also investigated. The wind farm power generation model used in this paper is adopted from the Unrestricted Wind Farm Layout Optimization (UWFLO) methodology. Single wake case studies show that the velocity deficit and the wake diameter estimated by the different analytical wake models can be significantly different. A maximum difference of 70% was also observed for the wind farm capacity factor values estimated using different wake models.
The development of large scale wind farms that can produce energy at a cost comparable to that of other conventional energy resources presents significant challenges to today’s wind energy industry. The consideration of the key design and environmental factors that influence the performance of a wind farm is a crucial part of the solution to this challenge. In this paper, we develop a methodology to account for the configuration of the farm land (length-to-breadth ratio and North-South-East-West orientation) within the scope of wind farm optimization. This approach appropriately captures the correlation between the (i) land configuration, (ii) the farm layout, and (iii) the selection of turbines-types. Simultaneous optimization of the farm layout and turbine selection is performed to minimize the Cost of Energy (COE), for a set of sample land configurations. The optimized COE and farm efficiency are then represented as functions of the land aspect ratio and the land orientation. To this end, we apply a recently developed response surface method known as the Reliability-Based Hybrid Functions. The overall wind farm design methodology is applied to design a 25MW farm in North Dakota. This case study provides helpful insights into the influence of the land configuration on the optimum farm performance that can be obtained for a particular site.
Wind farm development is an extremely complex process, most often driven by three im- portant performance criteria: (i) annual energy production, (ii) lifetime costs, and (iii) net impact on surroundings. Generally, planning a commercial scale wind farm takes several years. Undesirable concept-to-installation delays are primarily attributed to the lack of an upfront understanding of how different factors collectively affect the overall performance of a wind farm. More specifically, it is necessary to understand the balance between the socio-economic, engineering, and environmental objectives at an early stage in the design process. This paper proposes a Wind Farm Tradeoff Visualization (WiFToV) framework that aims to develop first-of-its-kind generalized guidelines for the conceptual design of wind farms, especially at early stages of wind farm development. Two major performance objectives are considered in this work: (i) cost of energy (COE) and (ii) land area per MW installed (LAMI). The COE is estimated using the Wind Turbine Design Cost and Scaling Model (WTDCS) and the Annual Energy Production (AEP) model incorporated by the Unrestricted Wind Farm Layout Optimization (UWFLO) framework. The LAMI is esti- mated using an optimal-layout based land usage model, which is treated as a post-process of the wind farm layout optimization. A Multi-Objective Mixed-Discrete Particle Swarm Optimization (MO-MDPSO) algorithm is used to perform the bi-objective optimization, which simultaneously optimizes the location and types of turbines. Together with a novel Pareto translation technique, the proposed WiFToV framework allows the exploration of the trade-off between COE and LAMI, and their variations with respect to multiple values of nameplate capacity.
The planning of a wind farm, which minimizes the lifecycle project costs and maximizes the reliability of the expected power generation, presents significant challenges to today’s wind energy industry. An optimal wind farm planning strategy that simultaneously (i) accounts for the key engineering design factors, and (ii) addresses the major sources of un- certainty in a wind farm, can offer a powerful solution to these daunting challenges. In this paper, we develop a new methodology to characterize the long term uncertainties, partic- ularly those introduced by the ill-predictability of the annual variation in wind conditions (wind speed and direction, and air density). The annual variation in wind conditions is rep- resented using a non-parametric wind distribution model. The uncertainty in the predicted annual wind distribution is then characterized using a set of lognormal distributions. The uncertainties in the estimated (i) farm power generation and (ii) Cost of energy (COE) are represented as functions of the variances of these lognormal distributions. Subsequently, we minimize the uncertainty in the COE through wind farm optimization. To this end, we apply the Unrestricted Wind Farm Layout Optimization (UWFLO) framework, which provides a comprehensive platform for wind farm design. This methodology for robust wind farm optimization is applied to design a 25MW wind farm in N. Dakota. We found that layout optimization is appreciably sensitive to the uncertainties in wind conditions.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)
AIAA-Aviation-Vidmap-2014
1. A Visually-Informed Decision-Making Platform for
Model-based Design of Wind Farms
Souma Chowdhury#, Ali Mehmani*, Weiyang Tong*, and Achille Messac#
* Syracuse University, Department of Mechanical and Aerospace Engineering
# Mississippi State University, Bagley College of Engineering
Research supported by the NSF Award: CMMI 1437746
The AIAAAviation and Aeronautics Forum and Exposition
June 16 – 20, 2014 Atlanta, Georgia
2. Wind Farm Design
2
Natural resource
System
Environmental
System
Power Generation
System
Power
Transmission
System
Addressing inter & intra-system interactions
• Farm Power Generation
• Annual Energy Production
• Capacity Factor
• Cost of Energy
Wind Farm Design
Conditions Design Variables
• Farm Layout
• Type(s) of Turbines
Objectives/Output
Other Design Factors
• Nameplate Capacity
• Land Area per MW inst.
• Distribution of Wind
Speed and Direction
• Atmospheric Turbulence
• Wind Shear
• Topography
Wake Effects
A Complex System
3. Model-based Wind Farm Design: Challenges
Owing to the complexity of the system, and the multitude of factors,
model-based systems design is the de facto standard in wind farm design.
Uncertainties are inherent in various forms in this MBSD process, e.g.:
Resource uncertainties: The wind resource is naturally uncertain, and the lack of a clear
understanding/knowledge of the ABL leads to further uncertainties.
Model inadequacies: High-fidelity analysis of wind farm flow is extremely expensive
(30 CPU-hr/simulation), leading to the use of lower-fidelity models in the design process.
Unrealistic assumptions: The impact of various natural and design factors is highly
coupled and their interactions are often not duly accounted for.
Existing wind farm layout optimization (WFLO) methods* generally only
consider certain aspects of resource variations.
3
*Mosetti et al., Grady et al., Sisbot et al., OWFLO, Wan et al.; Gonzalez et al., 2010; Chowdhury et al. 2012
4. 4
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Ambient
turbulence
Land area/MW
installed
Land aspect ratio
Jensen model
first-order index total-order index
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Ambient
turbulence
Land area/MW
installed
Land aspect ratio
Larsen model
first-order index total-order index
Models w/o turbulence
Models with turbulence
Sensitivity Analysis of Array-like Farm Output
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Ambient
turbulence
Land area/MW
installed
Land aspect ratio
Jensen model
first-order index total-order index
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Ambient
turbulence
Land area/MW
installed
Land aspect ratio
Larsen model
first-order index total-order index
Fixed incoming wind speed at 7 m/s Fixed incoming wind speed at 11 m/s
Weiyang et al.
IDETC 2013
5. Sensitivity Analysis of Optimized Farm Output
(Region II: incoming wind speed 10.35m/s – 12.65 m/s)
5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Incoming wind
speed
Ambient
turbulence
Land area/MW
installed
Land aspect
ratio
Nameplate
capacity
Ishihara model
first-order index total-order index
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Incoming wind
speed
Ambient
turbulence
Land area/MW
installed
Land aspect
ratio
Nameplate
capacity
Larsen model
first-order index total-order index
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Incoming wind
speed
Ambient
turbulence
Land area/MW
installed
Land aspect
ratio
Nameplate
capacity
Frandsen model
first-order index total-order index
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Incoming wind
speed
Ambient
turbulence
Land area/MW
installed
Land aspect
ratio
Nameplate
capacity
Jensen model
first-order index total-order index
Weiyang et al.
IDETC 2013
6. Visually-Informed Decision-Making Platform
(VIDMAP)
Overall Concept
Considering WFLO frameworks to be comprised of a series of interconnected
models, we will take an information flow perspective to WFLO to aid informed
(hence more reliable) decision-making.
Specific Objectives
1. To quantify and illustrate the criticality of information exchanged between
different models (i.e., inter-model sensitivities) in the WFLO process.
2. To quantify the model-induced uncertainties in the WFLO process.
6
7. Presentation Outline
Information Flow Perspective to Model-based Systems Design (MBSD)
Visually Informed Decision-Making Platform (VIDMAP)
Wind Farm Energy Production Modeling
Quantifying Input Variability and Model-induced Uncertainties
Sensitivity Analysis of Energy Production Model
Graphical Illustration of VIDMAP
Concluding Remarks
7
8. 8
A Design Process can be conceived as a flow of information.
Information
Criticality
Information
Expense
Information
Uncertainty
The Information Flow Perspective to MBSD
9. Motivating Approaches from Literature
McManus et al., (2005) construct component behavior model to capture faulty
behavior (for design verification and validation in complex systems design).
Allaire et al., (2012) developed a quantitative metric for measuring system
complexity based on information theory.
Otto et al., (2013) elaborated on what challenges mechanical complex design
faces to reach the level of design automation in the embedded systems domain.
Allaire et al., (2013) developed a multifidelity approach for complex systems
design and analysis to exploit optimally of all available models.
Mehmani at al., (2013, 2014) developed a new approach to quantify the
uncertainty in surrogate models – for effective model selection and multi-fidelity
optimization.
Visualization has been used in the context of multi-attribute/multi-objective
decision-making (Chiu and Bloebaum, 2009-2010), as well as in the context of
value–driven design Bertoni et al. (2013-2014).
9
10. VIDMAP: Structure
10
Uncertainty Quantification
Quantifying the variability of first-level inputs
and the uncertainty introduced by the
upstream models
Sensitivity Analysis
Analyzing the sensitivity of downstream
models to the first-level inputs and the
upstream model outputs
Information Visualization
Visualizing the uncertainty introduced by
constituent models and inter-model
sensitivities in the design process
12. Wind Farm Energy Production
12
Annual Energy Production (AEP) of a farm is given by:
AEP is numerically expressed as:
Capacity Factor:
Probability of
wind condition
Wind farm power
generation
13. Wind Farm Power Generation: Inflow & Shading
13 13
The complex flow in a wind farm is due to turbine-wind interactions.
A multi-step model is developed to estimate the farm power generation.
Rotor averaged velocity derived from the wind shear profile
Wake losses are modeled rank-wise:
Turbine-j is in the wake of Turbine-i, if and only if
Cal et al., 2010
Dedicated data More generic
Considers turbines with differing
rotor-diameters and hub-heights
Turbines ranked in order
of encountering wind
Modeling
turbine-wind-turbine
interactions
14. Wind Farm Power Generation: Wake Losses
14
Effective velocity of wind approaching Turbine-j:*
Accounts for wake merging & partial wake-rotor overlap
The power generated by turbine-j:
Power generated
by wind farm:
Wake model
Incoming
wind speed
Downstream
spacing
Radial
spacing
Induction
factor
Rotor
Diameter
Hub height
Turbulence
intensity
Jensen √ √ √ √
Frandsen √ √ √ √
Larsen √ √ √ √ √ √ √
Ishihara √ √ √ √ √ √
2
2
3
4 1
1
2 4
g b
P
a a
D
k k U
Wake model:
At distance s
downstream
Novel dynamically-updated
turbine-adaptive energy loss
(variable induction factor, a)
GE 2.5MW
1
N
farm j
j
P P
15. VIDMAP: Structure
15
Uncertainty Quantification
Quantifying the variability of first-level inputs
and the uncertainty introduced by the
upstream models
Sensitivity Analysis
Analyzing the sensitivity of downstream
models to the first-level inputs and the
upstream model outputs
Information Visualization
Visualizing the uncertainty introduced by
constituent models and inter-model
sensitivities in the design process
16. First-Level Inputs
The natural or commercial distributions of the first-level
inputs are determined, in order to generate samples for:
Quantifying the uncertainty in the upstream models
Performing the sensitivity analysis
Natural Inputs:
1. Wind Resource – Average Wind Speed (Rayleigh distribution)
Design Inputs:
2. Turbine Array Layout – Land Area/MW installed (7/3 aspect ratio)
3. Turbine Type – Turbine Features (major manufacturers)
16
17. Design Input Variability
Turbine Features: A sample set of 130 turbines from major
manufacturers, ranging from 0.6MW to 3.0MW, was created.
Each turbine is defined in terms of its rotor diameter, hub height, rated power,
cut-in/cut-out/rated speed, and drivetrain type.
LHS is used to prepare the integer-coded sample set of turbine features.
Land Area/MW Installed: The range is motivated by the reported
land footprint of US wind farms 1 (34.5 ± 22.4 ha/MW).
LHS is used to generate the sample set of land area/MW installed.
Assuming a N×N layout of turbines (N=10), with rated power, PR, for each
sample land area/MW of AMW, the turbine spacing is given by:
𝑑 𝑠 =
1
𝑁 − 1
7
3 𝑁𝑃𝑅 𝐴
1/2
; 𝑑𝑙 =
1
𝑁 − 1
3
7 𝑁𝑃𝑅 𝐴
1/2
171 Denholm et al., Technical Report NREL/TP-6A2-45834, NREL, August 2009.
18. Wind Resource Input Variability
The distribution of wind resource is defined in terms of the distribution of
average wind speed (AWS), derived from the US wind map.
A normal distribution of the average wind speed, reported by Chowdhury
et al., (AIAA SDM 2012) is adopted here to generate the AWS samples.
For each sample AWS, we generate a Rayleigh wind speed distribution –
to serve as an input to energy production model.
18
19. Quantifying Model Uncertainty
High-fidelity estimates of the outputs of the upstream (or
constituent) models are not readily available, due to
lack of data (e.g., vertical wind profile, decade-long met-tower data);
Lack of access to data (e.g., proprietary turbine power data); or
lack of understanding of the physical systems involved (e.g., ABL).
Hence, we have employed different approaches to quantify
the model-induced uncertainties, such as:
quantify the variance in the output of low-fidelity model choices; or
Use recorded data from a single site/case to estimate model error.
19
20. Uncertainty in Wind Distribution Model
Model error is given by the difference between the Rayleigh wind
distribution estimated using 1-year data and the scaled histogram of the
actual recorded wind conditions over the subsequent 10 years (a ND site).
20
The output of the wind distribution model,
for given conditions (U i), is the set of wind
speed probabilities:
The errors in the estimated wind speed
probabilities are treated as linearly
dependent random variables.
Distribution of the normalized errors gives
the uncertainty in the wind distribution
model.
21. Uncertainty in Wind Shear Model
Wind shear in ABL scarcely follows the power law or log law, which are
typically used in modeling and design.
Power Law:
𝑈
𝑈 𝑟
=
𝑧
𝑧 𝑟
𝛼
; Log Law:
𝑈
𝑈 𝑟
=
𝑙𝑛 𝑧 𝑧0
𝑙𝑛 𝑧 𝑟 𝑧0
Dedicated wind shear data is often lacking in practical wind energy
projects. LIDAR and SODAR are likely solutions (not yet widely used).
Uncertainty is quantified in terms of the distribution of the deviations
between different implementations of the two models, which rely on local
surface roughness assumptions (e.g., smooth ground – foot high grass).
Output of wind shear model (hub-height wind speed):
The deviation is estimated as:
21
22. Uncertainty in Turbine Power Response Model
The power response of turbines often deviate from that given by the
manufacturer-reported power curves (e.g., due to atm. stability issues).
Since access to actual turbine power response data is limited, we use
reported data from literature1 to quantify the deviations, and define
uncertainty as the distribution of these deviations.
Output of turbine power response model:
22
1Wharton and Lundquist, Environmental
Research Letters, January 2012
23. Uncertainty in Wake Model
Generally, analytical wake models are used in wind farm layout design.
Access to actual field data is limited, and high-fidelity wake models are
too expensive (e.g., 30 CPU-hrs) to conduct Monte Carlo simulations.
Hence, we quantify the uncertainty in the wake model as the deviations in
the estimates made by the four popular analytical wake models.
Two model outputs (wake speed and wake width):
23
Wake speed Wake width
Tong et al.,
ASME IDETC 2013
24. Uncertainty in the Wake Model
The deviations in the wake model outputs are given by
Frandsen model is used as the scaling reference.
A 10% ambient turbulence intensity is assumed.
24
Wake speed Wake width
25. VIDMAP: Structure
25
Uncertainty Quantification
Quantifying the variability of first-level inputs
and the uncertainty introduced by the
upstream models
Sensitivity Analysis
Analyzing the sensitivity of downstream
models to the first-level inputs and the
upstream model outputs
Information Visualization
Visualizing the uncertainty introduced by
constituent models and inter-model
sensitivities in the design process
26. Sensitivity Analysis of Energy Production
Sensitivity analysis is performed to quantify the sensitivity of the
energy production model for a 100-turbine wind farm with respect to:
1. the independent first-level inputs; and
2. the deviations/errors in the upstream models.
To perform sensitivity analysis, the sample set was prepared from:
26
Independent first-level inputs
Normalized errors/deviations in upstream models
27. Sensitivity Analysis Method
We use the Extended Fourier Amplitude of Sensitivity Test (eFAST),
which is a variance-based global sensitivity analysis method
Based on Fourier analysis, the first-order index is defined as the ratio of the
conditional variance due to each input parameter to the variance of the model
output
𝑆𝑖 =
𝜎 𝑌 𝑋𝑖
2
𝜎 𝑌
2
The total-order index estimates the sum of all effects involving the associated
input parameter
𝑆 𝑇 𝑖
= 1 −
𝜎 𝑌 𝑋≠𝑖
2
𝜎 𝑌
2
We employ the eFAST implementation through the statistical tool, R,
using a sample set of 20,000 data points.
27
28. VIDMAP: Structure
28
Uncertainty Quantification
Quantifying the variability of first-level inputs
and the uncertainty introduced by the
upstream models
Sensitivity Analysis
Analyzing the sensitivity of downstream
models to the first-level inputs and the
upstream model outputs
Information Visualization
Visualizing the uncertainty introduced by
constituent models and inter-model
sensitivities in the design process
29. VIDMAP: Illustration
29
Connectors are colored based on 1st order sensitivity indices.
Total order indices are dominant, indicating highly coupled impact.
Model blocks are colored based on the variance of the model error or
model deviation.
30. VIDMAP: Important Observations
30
Among the independent inputs, turbine features have the strongest impact.
The turbine power response model and the wake width estimation model are
observed to have the strongest impact among model.
These two models are also associated with the highest degrees of uncertainty.
31. Concluding Remarks
We developed a visualization framework (VIDMAP) for informed
model-based design of wind farms.
Specifically, we quantified and presented a MBSD visualization for:
1. Inter-model sensitivities and model-input sensitivities;
2. Model-induced uncertainties.
The VIDMAP obtained is found to be uniquely helpful in pointing out:
Which models/inputs in the WFLO process have stronger impact on the
energy production estimates – turbine features, turbine power response
model, and wake model.
Which models have higher degrees of uncertainty - turbine power response
model, and wake width estimation model.
31
32. Future Directions
Develop and implement a more standardized quantification of model
uncertainty, e.g., in comparison to measured data.
Develop informed decision-making rules/strategies that directly utilize
VIDMAP – towards faster and more reliable wind farm design.
32
34. 34/85
Major Challenges: Wind Farm Modeling
*Mosetti et al., Grady et al., Sisbot et al., OWFLO, Wan et
al.
Model Based Systems
Design
Integrative Modeling and
Design of Wind Farms
Energy-Sustainable Smart
Buildings
Reconfigurable Unmanned
Aerial Vehicles (UAV)
The state of the art (2009) in modeling wind farm energy
production (for design purposes) does not capture the coupled
impact of the key natural/design factors at affordable
computational costs*:
1. Turbines with differing features (size/power characteristics) are not considered;
2. Variability of induction factor or energy loss fraction/turbine is not considered;
3. Coupled variation of wind speed, wind direction, and turbulence intensity not captured
4. High-fidelity wake models are computational prohibitive: current LES models [NREL SOFWA, 2012]
would need 600 million CPU-hours for optimizing a 25-turbine farm
5. Current WF energy output models do not account for spatial variations of the boundary layer over the
site (e.g., due to vegetation cover or topographic variations)
Different turbine
sizes available
CT and energy
loss varies
IPCC, 2011; Chowdhury et al., 2013; ETH LEC,
Prior
Research
ABL over topography
35. 35/85
Major Challenges: Wind Farm Design
*Mosetti et al., Grady et al., Sisbot et al., OWFLO, Wan et al.; Gonzalez et al., 2010
Model Based Systems
Design
Integrative Modeling and
Design of Wind Farms
Energy-Sustainable Smart
Buildings
Reconfigurable Unmanned
Aerial Vehicles (UAV)
The state of art in wind farm layout design makes
limiting assumptions*:
1. Selection and siting of turbines are not simultaneously optimized.
2. The flexibility of installing non-identical turbines on a site is generally lacking.
3. The extent of the site to be used (land area and shape) and the total nameplate capacity
are prescribed prior to farm layout design (not quantitatively decided) .
4. Existing methods do not allow exploration of the important trade-offs among the
engineering, socio-economic, & environmental objectives of wind farm development.
5. Existing methods generally pursue decision-making at a single scale of wind power
generation technology (e.g., blade-scale or turbine-scale or farm-scale) – propagation
of performance uncertainties and the impact of design-decisions across scales remain
unexplored. Prior Research