AIAA-SciTech-ModelSelection-2014-Mehmani
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This document presents a new 3-level approach to simultaneously select the best surrogate model type, kernel function, and hyper-parameters for approximation models. The approach uses Regional Error Estimation of Surrogates (REES) to evaluate error and select models. It compares a cascaded technique that performs sequential optimization versus a one-step technique. Numerical examples on benchmark problems show the one-step technique reduces maximum and median errors by at least 60% with lower computational cost compared to the cascaded approach. Future work involves applying the one-step method to more complex problems and developing an online platform for collaborative surrogate model selection.
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This document presents an adaptive model switching technique for variable fidelity optimization using population-based algorithms. The technique aims to provide reliable high-fidelity optimum designs with reasonable computational expense by leveraging multiple models of varying fidelity. It switches models by comparing the error distribution of the current model to the distribution of recent fitness function improvements over the population. The method was tested on airfoil and cantilever beam design problems, showing substantially better balance of optimum quality and efficiency than purely low- or high-fidelity optimizations.
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International Journal of Engineering Research and Applications (IJERA) is a team of researchers not publication services or private publications running the journals for monetary benefits, we are association of scientists and academia who focus only on supporting authors who want to publish their work. The articles published in our journal can be accessed online, all the articles will be archived for real time access.
Our journal system primarily aims to bring out the research talent and the works done by sciaentists, academia, engineers, practitioners, scholars, post graduate students of engineering and science. This journal aims to cover the scientific research in a broader sense and not publishing a niche area of research facilitating researchers from various verticals to publish their papers. It is also aimed to provide a platform for the researchers to publish in a shorter of time, enabling them to continue further All articles published are freely available to scientific researchers in the Government agencies,educators and the general public. We are taking serious efforts to promote our journal across the globe in various ways, we are sure that our journal will act as a scientific platform for all researchers to publish their works online.
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AIAA-SDM-SequentialSampling-2012
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.
AIAA-Aviation-VariableFidelity-2014-Mehmani
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.
AIAA-Aviation-Vidmap-2014
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.
ASME-IDETC-Sensitivity-2013
This document presents the results of a sensitivity analysis of key factors that influence the power output of array-like and optimized wind farms. The analysis investigated how sensitive farm output is to factors such as incoming wind speed, ambient turbulence, land area per MW installed, land aspect ratio, and nameplate capacity. It found that for array-like farms, incoming wind speed has the dominant impact on power generation across different wake models. For optimized farms, incoming wind speed remains the dominant factor at lower wind speeds, but design factors like land area and aspect ratio influence output more when wind speeds are near rated levels. Overall, natural factors like wind speed have a greater contribution to farm output than design factors.
AIAA-SDM-PEMF-2013
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.
AIAA-MAO-WFLO-2012
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.
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AIAA-SDM-SequentialSampling-2012
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.
AIAA-Aviation-VariableFidelity-2014-Mehmani
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.
AIAA-Aviation-Vidmap-2014
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.
ASME-IDETC-Sensitivity-2013
This document presents the results of a sensitivity analysis of key factors that influence the power output of array-like and optimized wind farms. The analysis investigated how sensitive farm output is to factors such as incoming wind speed, ambient turbulence, land area per MW installed, land aspect ratio, and nameplate capacity. It found that for array-like farms, incoming wind speed has the dominant impact on power generation across different wake models. For optimized farms, incoming wind speed remains the dominant factor at lower wind speeds, but design factors like land area and aspect ratio influence output more when wind speeds are near rated levels. Overall, natural factors like wind speed have a greater contribution to farm output than design factors.
AIAA-SDM-PEMF-2013
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.
AIAA-MAO-WFLO-2012
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.
AIAA-MAO-DSUS-2012
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.
WCSMO-Wind-2013-Tong
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.
WCSMO-ModelSelection-2013
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.
AIAA-MAO-RegionalError-2012
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.
AIAA-SDM-WFLO-2012
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.
WCSMO-Vidmap-2015
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.
Research Paper Expectations
The document outlines the requirements and deadlines for a research paper assignment. Students must develop 3 potential topics with 3 research questions each, and collect at least 7 sources including an internet source, hardcover source, and interview. A rough draft is due October 19th, and the final paper with works cited and research materials is due October 25th in a manila envelope. Peer editing will take place in class on October 19th.
Differences Cluster Sampling and Adaptive Cluster Sampling
The document compares and contrasts cluster sampling and adaptive cluster sampling. Both methods involve dividing a population into clusters and randomly selecting some clusters for sampling. However, adaptive cluster sampling allows for additional sampling units to be added to selected clusters, while cluster sampling samples fixed units within selected clusters. Adaptive cluster sampling provides more precise estimates but is more expensive than standard cluster sampling.
A Template for Research Presentation (Google Presentation Format)
Edit this Google Presentation for delivering your research. This simple how-to template helps you organize your talk for academic contexts that require you to deliver findings. Ideal for conferences or even graduate seminars.
Presentation Of Research Work
This document provides tips for making an effective presentation of research work in 3 sentences or less:
The document outlines best practices for creating clear and readable presentation slides, including using point form, limiting text per slide, using large and contrasting fonts, simple backgrounds, and properly formatted graphs and tables. Common mistakes to avoid are discussed, such as small fonts, excessive use of colors and animation, and distracting backgrounds. The presentation should be proofread for spelling and grammar errors, and conclude with a summary of key points and an invitation for questions.
Research Presentation Format
This research presentation compares two camera options and makes a recommendation. It outlines the purpose and methodology of the study, including the data sources and a decision matrix. The results are presented by showing the strengths and weaknesses of each camera option, and a comparison matrix informs the final recommendation of which camera is best and why.
Research project ppt
The document summarizes a study that surveyed 130 newly admitted undergraduate teacher education students about their views on parent involvement in education. The survey aimed to understand students' memories of their own families' school involvement and how they conceptualize the roles of parents and teachers. It found that students viewed parent knowledge as long-term and individual while teacher knowledge was seen as professional and unbiased. Students anticipated doing more school-based parent involvement like conferences rather than community activities. The authors advocate giving greater attention to families in teacher education programs.
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Differences Cluster Sampling and Adaptive Cluster Sampling
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Machine Learning and AI: Core Methods and Applications
This session was presented at the CFA Institute on May 6th 2020
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COSMOS_IDETC_2014_Souma
One of the primary drawbacks plaguing wider acceptance of surrogate models is their low fidelity (in general), which can be in a large part attributed to the lack of quantitative guidelines regarding the suitability of different models for diverse classes of problems. In this context, model selection techniques are immensely helpful in ensuring the selection and use of an optimal model for a particular design problem. A novel model selection technique was recently developed to perform optimal model search 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 maximum and the median error measures to be minimized in this optimal model selection process are given by the REES error metrics, which have been shown to be significantly more accurate than typical cross-validation-based error metrics. Motivated by the promising results given by REES-based model selection, in this paper we develop a framework called Collaborative Surrogate Model Selection (COSMOS). The primary goal of COSMOS is to allow the selection and usage of globally competitive surrogate models. More specifically, this framework will offer an open online platform where users from within and beyond the Engineering Design (and MDO) community can submit training data to identify best surrogates for their problem, as well as contribute new and advanced surrogate models to the pool of models in this framework. This first-of-its-kind global platform will facilitate sharing of ideas in the area of surrogate modeling, benchmarking of existing surrogates, validation of new surrogates, and identification of the right surrogate for the right problem. In developing this framework, this paper makes three important fundamental advancements to the original REES-based model selection - (i) The optimization approach is modified through binary coding to allow surrogates with differing numbers of candidate kernels and kernels with differ- ing numbers of hyper-parameters. (ii) A robustness criterion, based on the variance of errors, is added to the existing criteria for model selection. (iii) Users are allowed to perform model selection for a specified region of the input space and not only for the entire input domain, subject to empirical constraints that are related to the relative sample strength of the region. The effectiveness of the COSMOS framework is demonstrated using a comprehensive pool of five major surrogate model-types (with up to five constitutive kernel types), which are tested on two standard test problems and an airfoil design problem.
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- 1. A Novel Approach to Simultaneous Selection of Surrogate Models, Constitutive Kernels, and Hyper-parameter Values Ali Mehmani*, Souma Chowdhury#, and Achille Messac# * Syracuse University, Department of Mechanical and Aerospace Engineering # Mississippi State University, Bagley College of Engineering 10th Multi-Disciplinary Design Optimization Conference AIAA Science and Technology Forum and Exposition January 13 – 17, 2014 National Harbor, Maryland
- 2. Surrogate model • Surrogate models are commonly used for providing a tractable and inexpensive approximation of the actual system behavior in many routine engineering analysis and design activities: 2
- 3. Surrogate model • Surrogate models are commonly used for providing a tractable and inexpensive approximation of the actual system behavior in many routine engineering analysis and design activities: 3 Kriging . . .Model Type RBF SVR Kernel / basis function Linear Exponential Gaussian Cubic Multiquadric . . . Hyper-parameter Correlation parameter Shape parameter . . . 𝒇 𝒙 = 𝒊=𝟏 𝒏 𝒘𝒊 𝝍( 𝒙 − 𝒙𝒊 ) 𝝍 𝒓 = (𝒓 𝟐 + 𝒄 𝟐 ) 𝟏/𝟐 𝒓= 𝒙 − 𝒙𝒊 𝒄𝒍𝒐𝒘𝒆𝒓 < 𝒄 < 𝒄 𝒖𝒑𝒑𝒆𝒓
- 4. Research Objective Develop a new model selection approach, which simultaneously select the best model type, kernel function, and hyper-parameter. 4 Types of model Types of basis/kernel Hyper-parameter(s) • RBF, • Kriging, • E-RBF, • SVR, • QRS, • … • Linear • Gaussian • Multiquadric • Inverse multiquadric • Kriging • … • Shape parameter in RBF, • Smoothness and width parameters in Kriging, • Kernel parameter in SVM, • …
- 5. Presentation Outline 5 • Surrogate model selection • REES-based Model Selection • 3-Level model selection • Regional Error Estimation of Surrogate (REES) • Numerical Examples • Concluding Remarks
- 6. Surrogate model selection 6 • Dimension and nature of sample points, • Level of a noise, • Application domain, • … Suitable Surrogate Error measures are used to select the best surrogate Experienced-based model selection Automated model selection • RMSE, • Cross-validation, • REES, • … Hyper-parameter selection (Kriging-Guassian) using cross validation and maximum likelihood estimation (Martin and Simpson) Model type and basis function selection using cross validation (Viana and Haftka) Model type selection using leave-one-out cross validation (Drik Gorisson et al.)
- 7. 3-Level model selection 7 In 3-level model selection, the selection criteria could depend on the user preference. Standard surrogate-based analysis Structural optimization applications lower median error lower maximum error
- 8. 3-Level model selection 8 Median error Maximum error Two model selection criteria evaluated using advanced surrogate error estimation method presented in REES Depending on the problem and the available data set, the median and maximum errors might be mutually conflicting mutually promoting Pareto models A single optimum model
- 9. 3-Level model selection 9 To implement a 3-level model selection, two approaches are proposed: (i) Cascaded technique, and (ii) One-Step technique.
- 10. 3-Level model selection 10 Cascaded technique For each candidate kernel function, hyper-parameter optimization is performed to minimize the median and maximum error. Post hyper-parameter optimizations, Pareto filter is used to reach the final Pareto models. Hyper-parameter optimization is the process of quantitative search to find optimum hyper-parameter value(s).
- 11. 3-Level model selection 11 Cascaded technique Solutions of the hyper-parameter optimization in the cascaded technique for multiquadric basis function of RBF surrogate for Baranin-hoo function
- 12. 3-Level model selection 12 One-Step technique To escape the potentially high computational cost of the cascaded technique Subjected to The three-level model selection could also be performed by solving a single uniquely formulated mixed integer nonlinear programming (MINLP) problem. model type basis function hyper-parameter(s)
- 13. Regional Error Estimation of Surrogate (REES) 13 The REES method is derived from the hypothesis that the accuracy of approximation models is related to the amount of data resources leveraged to train the model. • Mehmani, A., Chowdhury, S., Zhang, Jie, and Messac, A., “Quantifying Regional Error in Surrogates by Modeling its Relationship with Sample Density,” 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Paper No. AIAA 2013-1751, Boston, Massachusetts, April 8-11, 2013. • Mehmani, et. al., “Model Selection based on Generalized-Regional Error Estimation for Surrogate,” 10th World Congress on Structural and Multidisciplinary Optimization, Paper No. 5447, Orlando, Florida, May 19-24, 2013. • Mehmani, et. al.., “Regional Error Estimation of Surrogates (REES),” 14th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Paper No. AIAA 2012-5707, Indianapolis, Indiana, September 17-19, 2012.
- 15. Test Point Training Point 1st Iter. 2nd Iter. 3rd Iter. 4th Iter. Error Surrogate ε1 ε2 ε3 ε4 ? 8 16 12 12 16 8 20 4 24 0 1st 2nd 3rd 4th REES
- 16. Test Point Training Point 1st MedianofRAEs 1st ε = 𝒎𝒆𝒅 | 𝒇𝒊 − 𝒇𝒊 𝒇𝒊 | , 𝐢 = 𝟏, … , 𝟏𝟔 Actual modelIntermediate surrogate model ... REES 16
- 17. 17 MedianofRAEs Momed Number of Training Points t1 t2 t3 t4 It. 1 REES
- 18. 18 MedianofRAEs Number of Training Points t1 t2 t3 t4 Momed It. 2It. 1 REES
- 19. 19 MedianofRAEs Number of Training Points t1 t2 t3 t4 Momed It. 3It. 2It. 1 REES
- 20. 20 It. 3It. 1 MedianofRAEs Number of Training Points t1 t2 t3 t4 It. 2 Momed It. 4 ModelofMedian REES
- 21. 21 It. 3It. 1 MedianofRAEs Number of Training Points t1 t2 t3 t4 It. 2 Momed It. 4 ModelofMedian Predicted Median Error REES
- 22. 22 It. 3It. 1 MedianofRAEs Number of Training Points t1 t2 t3 t4 It. 2 Momed It. 4 ModelofMedian Momax Mode of maximum error distribution at each iteration Predicted Median Error Predicted Maximum Error REES
- 23. 23 The effectiveness of the new 3-level model selection method is investigated by considering the following three candidate surrogates: The methods are implemented on three benchmark problems and an engineering design problem are tested. Gaussian basis function Multiquadric basis function Gaussian correlation function Exponential correlation function Radial basis kernel function Sigmoid kernel function SVR RBF Kriging Model type Kernel function Hyper-parameter Numerical Examples
- 24. 24 Numerical Setting The numerical settings for the implementation of REES-based model selection for the benchmark problems The numerical settings for the hyper-parameter optimization Numerical Examples 24
- 25. 25 Hyper-parameter optimization of Cascaded technique in different surrogate type and Kernel functions for Branin-Hoo function with 2 design variables Numerical Examples
- 26. 26 Numerical Setting The numerical settings for One-Step technique Integer design variables Numerical Examples
- 27. 27 Results; Branin-hoo 2 design variables Computational cost One-Step Technique Cascaded technique RBF-Multiquadric
- 28. 28 Cascaded technique Actual error RBF-Multiquadric One-Step Technique Results; Branin-hoo 2 design variables RBF-Multiquadric
- 29. 29 Computational cost One-Step Technique Cascaded technique Results; Hartmann function with 6 design variables SVR-Radial basis
- 30. 30 Cascaded technique Results; Hartmann function with 6 design variables One-Step Technique SVR-Radial basis Actual error SVR-Radial basis
- 31. 31 Computational cost Cascaded technique Results; Dixon & Price function with 18 design variables One-Step Technique RBF-Multiquadric
- 32. 32 Cascaded technique One-Step Technique RBF-Multiquadric Actual error RBF-Multiquadric Results; Dixon & Price function with 18 design variables
- 33. 33 Numerical Examples Initial Value Final Solution Emax EmaxEmax Emed Emed Emed RBF-Multiquadric (C=0.9)
- 34. 34 Concluding Remarks A new 3-level model selection approach is developed to select the best surrogate among available surrogate candidates based on the level of accuracy. This approach is based on the model independent error measure given by the Regional Error Estimation of Surrogates (REES) method. The preliminary results on problems indicate at least 60% reduction in maximum and median error values. (i) model type selection, (ii) kernel function selection, and (iii) hyper-parameter selection.
- 35. 35 Future Work Implementation of One-Step technique with larger pool of surrogates with different number of kernels higher dimensional and more computationally intensive problems Develop an open online platform called Collaborative Surrogate Model Selection (COSMOS) to allow users to submit - training data for identifying an ideal model from existing pool of surrogate models, and - their own new surrogate into the pool of surrogate candidates. If interested in COSMOS please contact me at amehmani@syr.edu
- 36. Acknowledgement I would like to acknowledge my research adviser Prof. Achille Messac, and my co-adviser Dr. Souma Chowdhury for their immense help and support in this research. I would also like to thank my friend and colleague Weiyang Tong for his valuable contributions to this paper. Support from the NSF Awards is also acknowledged. 36
- 38. Quantifying the mode of median and maximum errors 38
- 39. 39 A chi-square (χ2) goodness-of-fit criterion is used to select the type of distribution from a list of candidates such as lognormal, Gamma, Weibull, logistic, log logistic, inverse Gaussian, and generalized extreme value distribution.