The document discusses methods for integrating imprecise or biased secondary data from multiple sources into mineral resource estimates. It examines techniques including cokriging (CK), multicollocated cokriging (MCCK), and ordinary kriging with variance of measurement error (OKVME). Where abundant imprecise but unbiased secondary data are available, the document recommends using OKVME, as it improves estimation precision over using the primary data alone or pooling the data and using ordinary kriging. For abundant imprecise and biased secondary data, CK is recommended as it provides an unbiased estimate and some improvement in precision relative to using only the primary data. The document evaluates these techniques using a case study iron
This document summarizes and compares methods for evaluating the performance of ground motion prediction equations (GMPEs) using observed ground motion databases. It evaluates several CENA GMPEs using the NGA-East database through residual analysis and other statistical tests to check for bias and normality. It then ranks the GMPEs using the log-likelihood and Euclidean distance-based methods to determine the most appropriate models for the target region.
A robust data treatment approach for fuel cells system analysisISA Interchange
The document describes a robust approach for analyzing data from fuel cell stack testing. It addresses challenges in handling large amounts of data from multiple devices. The approach includes:
1) Developing an interface in Excel to automate data handling and analysis across Excel and MATLAB for improved efficiency.
2) Using dynamic time warping to synchronize data sequences and align them based on time for better comparison.
3) Applying data reconciliation to optimally adjust measurements so they obey physical constraints like conservation of voltage sums, improving accuracy of analysis.
This document summarizes a study that integrated seismic velocity and electrical resistivity data to probabilistically evaluate rock quality designation (RQD) between boreholes. The study used indicator kriging to create an initial RQD distribution from borehole observations. It then improved this distribution by incorporating the geophysical data using a permanence ratio, which calculates the probability of an event based on multiple information sources. The final probabilistic RQD distribution allowed for a more quantitative rock quality assessment and informed decision making for tunnel design and safety.
Arbitrary Lagrange Eulerian Approach for Bird-Strike Analysis Using LS-DYNAdrboon
In this third and last sequence paper we focus on developing a model to simulate bird-strike events using Lagrange and Arbitrary Lagrange Eulerian (ALE) in LS-DYNA. We developed a standard work for the two-and three-dimensional models for bird-strike events. We modeled the bird as a cylinder fluid and the fan blade as a plate. The case study was that of frontal impact of soft-bodies on rigid plates based on the Lagrangian Bird Model. Results show very good agreement with available test data and within 7% error when compared with the Lagrange and SPH methods. The developed ALE approach is suitable for bird-strike events in tapered plates.
A Land Data Assimilation System Utilizing Low Frequency Passive Microwave Rem...drboon
To address the gap in bridging global and smaller modelling scales, downscaling approaches have been reported as an appropriate solution. Downscaling on its own is not wholly adequate in the quest to produce local phenomena, and in this paper we use a physical downscaling method combined with data assimilation strategies, to obtain physically consistent land surface condition prediction. Using data assimilation strategies, it has been demonstrated that by minimizing a cost function, a solution utilizing imperfect models and observation data including observation errors is feasible. We demonstrate that by assimilating lower frequency passive microwave brightness temperature data using a validated theoretical radiative transfer model, we can obtain very good predictions that agree well with observed conditions.
Smooth Particle Hydrodynamics for Bird-Strike Analysis Using LS-DYNAdrboon
In this second of a three-paper sequence, we developed a standard work using the Smoothed Particle Hydrodynamic (SPH) approach in LS-DYNA and compared the results against those the Lagrangian model and available experimental results. First, the SPH model was validated against a one-dimensional beam centered impact’s analytical solution and the results are within 3% error. Bird-strike events were divided into three separate problems: frontal impact on rigid flat plate, 0 and 30 deg impact on deformable tapered plate. The bird model was modeled as a cylindrical fluid. We successfully identified the most influencing parameters when using SPH in LS-DYNA. The case for 0 deg tapered plate impact shows little bird-plate interaction because the bird is sliced in two parts and the results are within 5% difference from the test data available in the literature, which is an improvement over the Lagrangian model. Conclusion: The developed SPH approach is suitable for bird-strike events within 10% error.
Comparison of statistical methods commonly used in predictive modelingSalford Systems
This document compares four statistical methods commonly used in predictive modelling: Logistic Multiple Regression (LMR), Principal Component Regression (PCR), Classification and Regression Tree analysis (CART), and Multivariate Adaptive Regression Splines (MARS). It applies these methods to two ecological data sets to test their accuracy, reliability, ease of use, and implementation in a geographic information system (GIS). The results show that independent data is needed to validate models, and that MARS and CART achieved the best prediction success, although CART models became too complex for cartographic purposes with a large number of data points.
Small medium sized nuclear coal and gas power plant a probabilistic analysis ...d4vid3k0
This document presents a probabilistic analysis comparing the financial performance and levelized unit electricity costs (LUEC) of small-medium sized (335 MWe) nuclear, coal, and gas power plants. It aims to investigate the effect of carbon tax costs on the economics of these plants. The analysis uses a Monte Carlo simulation with input data and distributions based on literature rather than expert judgments. It finds that without a carbon tax, a coal plant has the lowest LUEC and highest net present value (NPV), but introducing a carbon tax changes the rankings depending on the tax amount. A higher carbon tax increases investment risk for coal plants relative to nuclear. The uncertainty in carbon tax costs is a key factor in the economic comparison of these
This document summarizes and compares methods for evaluating the performance of ground motion prediction equations (GMPEs) using observed ground motion databases. It evaluates several CENA GMPEs using the NGA-East database through residual analysis and other statistical tests to check for bias and normality. It then ranks the GMPEs using the log-likelihood and Euclidean distance-based methods to determine the most appropriate models for the target region.
A robust data treatment approach for fuel cells system analysisISA Interchange
The document describes a robust approach for analyzing data from fuel cell stack testing. It addresses challenges in handling large amounts of data from multiple devices. The approach includes:
1) Developing an interface in Excel to automate data handling and analysis across Excel and MATLAB for improved efficiency.
2) Using dynamic time warping to synchronize data sequences and align them based on time for better comparison.
3) Applying data reconciliation to optimally adjust measurements so they obey physical constraints like conservation of voltage sums, improving accuracy of analysis.
This document summarizes a study that integrated seismic velocity and electrical resistivity data to probabilistically evaluate rock quality designation (RQD) between boreholes. The study used indicator kriging to create an initial RQD distribution from borehole observations. It then improved this distribution by incorporating the geophysical data using a permanence ratio, which calculates the probability of an event based on multiple information sources. The final probabilistic RQD distribution allowed for a more quantitative rock quality assessment and informed decision making for tunnel design and safety.
Arbitrary Lagrange Eulerian Approach for Bird-Strike Analysis Using LS-DYNAdrboon
In this third and last sequence paper we focus on developing a model to simulate bird-strike events using Lagrange and Arbitrary Lagrange Eulerian (ALE) in LS-DYNA. We developed a standard work for the two-and three-dimensional models for bird-strike events. We modeled the bird as a cylinder fluid and the fan blade as a plate. The case study was that of frontal impact of soft-bodies on rigid plates based on the Lagrangian Bird Model. Results show very good agreement with available test data and within 7% error when compared with the Lagrange and SPH methods. The developed ALE approach is suitable for bird-strike events in tapered plates.
A Land Data Assimilation System Utilizing Low Frequency Passive Microwave Rem...drboon
To address the gap in bridging global and smaller modelling scales, downscaling approaches have been reported as an appropriate solution. Downscaling on its own is not wholly adequate in the quest to produce local phenomena, and in this paper we use a physical downscaling method combined with data assimilation strategies, to obtain physically consistent land surface condition prediction. Using data assimilation strategies, it has been demonstrated that by minimizing a cost function, a solution utilizing imperfect models and observation data including observation errors is feasible. We demonstrate that by assimilating lower frequency passive microwave brightness temperature data using a validated theoretical radiative transfer model, we can obtain very good predictions that agree well with observed conditions.
Smooth Particle Hydrodynamics for Bird-Strike Analysis Using LS-DYNAdrboon
In this second of a three-paper sequence, we developed a standard work using the Smoothed Particle Hydrodynamic (SPH) approach in LS-DYNA and compared the results against those the Lagrangian model and available experimental results. First, the SPH model was validated against a one-dimensional beam centered impact’s analytical solution and the results are within 3% error. Bird-strike events were divided into three separate problems: frontal impact on rigid flat plate, 0 and 30 deg impact on deformable tapered plate. The bird model was modeled as a cylindrical fluid. We successfully identified the most influencing parameters when using SPH in LS-DYNA. The case for 0 deg tapered plate impact shows little bird-plate interaction because the bird is sliced in two parts and the results are within 5% difference from the test data available in the literature, which is an improvement over the Lagrangian model. Conclusion: The developed SPH approach is suitable for bird-strike events within 10% error.
Comparison of statistical methods commonly used in predictive modelingSalford Systems
This document compares four statistical methods commonly used in predictive modelling: Logistic Multiple Regression (LMR), Principal Component Regression (PCR), Classification and Regression Tree analysis (CART), and Multivariate Adaptive Regression Splines (MARS). It applies these methods to two ecological data sets to test their accuracy, reliability, ease of use, and implementation in a geographic information system (GIS). The results show that independent data is needed to validate models, and that MARS and CART achieved the best prediction success, although CART models became too complex for cartographic purposes with a large number of data points.
Small medium sized nuclear coal and gas power plant a probabilistic analysis ...d4vid3k0
This document presents a probabilistic analysis comparing the financial performance and levelized unit electricity costs (LUEC) of small-medium sized (335 MWe) nuclear, coal, and gas power plants. It aims to investigate the effect of carbon tax costs on the economics of these plants. The analysis uses a Monte Carlo simulation with input data and distributions based on literature rather than expert judgments. It finds that without a carbon tax, a coal plant has the lowest LUEC and highest net present value (NPV), but introducing a carbon tax changes the rankings depending on the tax amount. A higher carbon tax increases investment risk for coal plants relative to nuclear. The uncertainty in carbon tax costs is a key factor in the economic comparison of these
IMPROVED NEURAL NETWORK PREDICTION PERFORMANCES OF ELECTRICITY DEMAND: MODIFY...csandit
Accurate prediction of electricity demand can bring extensive benefits to any country as the
forecast values help the relevant authorities to take decisions regarding electricity generation,
transmission and distribution much appropriately. The literature reveals that, when compared
to conventional time series techniques, the improved artificial intelligent approaches provide
better prediction accuracies. However, the accuracy of predictions using intelligent approaches
like neural networks are strongly influenced by the correct selection of inputs and the number of
neuro-forecasters used for prediction. This research shows how a cluster analysis performed to
group similar day types, could contribute towards selecting a better set of neuro-forecasters in
neural networks. Daily total electricity demands for five years were considered for the analysis
and each date was assigned to one of the thirteen day-types, in a Sri Lankan context. As a
stochastic trend could be seen over the years, prior to performing the k-means clustering, the
trend was removed by taking the first difference of the series. Three different clusters were
found using Silhouette plots, and thus three neuro-forecasters were used for predictions. This
paper illustrates the proposed modified neural network procedure using electricity demand
data.
Bird-Strike Modeling Based on the Lagrangian Formulation Using LSDYNAdrboon
This document summarizes research on modeling bird-strike events using LS-DYNA's Lagrangian formulation. Key points:
- Bird-strikes pose safety risks and costs to the aviation industry, motivating efforts to model and predict damage through simulation.
- The bird is modeled as a fluid, and the Lagrangian method tracks material deformation. Initial validation involved a beam impact problem, with results within 2.5% of analytical solutions.
- Bird-strike events were divided into impacts on rigid and deformable plates at different angles, modeled after existing literature. Peak pressures and forces from simulations were within 10% of test data.
- The developed Lagrangian approach is suitable for modeling bird-strikes to predict
This document summarizes a research paper that develops a modified grain contact theory to better model the pressure-dependent elastic properties of uncemented sediments. The Hertz-Mindlin theory typically overpredicts shear modulus values compared to laboratory measurements and does not capture the observed increasing ratio of bulk to shear modulus with decreasing effective pressure. The authors introduce two new pressure-dependent calibration parameters to account for grain relaxation effects and porosity changes not included in existing theories. Their modified model provides an improved fit to laboratory data and can predict elastic properties over a wider range of effective pressures.
APPLICATION OF COMPUTER FOR ANALYZING WORLD CO2 EMISSIONIJCSEA Journal
Global climate change due to CO2 emissions is an issue of international concern that primarily attributed
to fossil fuels. In this study, Genetic Algorithm (GA) is used for analyzing world CO2 emission based on the
global energy consumption. Linear and non-linear forms of equations were developed to forecast CO2
emission using Genetic Algorithm (GA) based on the global oil, natural gas, coal, and primary energy
consumption figures. The related data between 1980 and 2010 were used, partly for installing the models
(finding candidates of best weighting factors for each model (1980-2003)) and partly for testing the models
(2004–2010). Global CO2 emission is forecasted up to year 2030.
The document presents a study that compares five methods for estimating missing values in building sensor data: linear regression, weighted k-nearest neighbors, support vector machines, mean imputation, and replacing missing values with zero. The methods were evaluated using data from sensors in an office building in Japan, with the amount of missing data varied from 5% to 20%. Feature selection and inclusion of lagged variables as predictors were also examined to determine their effect on the methods' performance.
Performance based Comparison of Wind and Solar Distributed Generators using E...Editor IJLRES
Distributed Generation (DG) technologies have become more and more important in power systems. The objective of the paper is to optimize the distributed energy resource type and size based on uncertainties in the distribution network. The three things are considered in stand point of uncertainties are listed as, (i) Future load growth, (ii) Variation in the solar radiation, (iii) Wind output variation. The challenge in Optimal DG Placement (ODGP) needs to be solved with optimization problem with many objectives and constraints. The ODGP is going to be done here, by using Non-dominated Sorting Genetic Algorithm II (NSGA II). NSGA II is one among the available multi objective optimization algorithms with reduced computational complexity (O=MN2). Because of this prominent feature of NSGA II, it is widely applicable in all the multi objective optimization problems irrespective of disciplines. Hence it is selected to be employed here in order to obtain the reduced cost associated with the DG units. The proposed NSGA II is going to be applied on the IEEE 33-bus and the different performance characteristics were compared for both wind and solar type DG units.
The study evaluated 4 anti-fatigue mats (Mats A-D) and a no-mat control for their effects on worker height loss and flexibility changes over an 8-hour workday. Eighteen subjects were recruited from two industrial sites and used each mat/control for 5 days. Height and flexibility measurements were taken before and after each workday. Statistical analysis found that only Mat A (Let's Gel) produced significantly less height loss and greater flexibility increases compared to the no-mat control. The other mats were not significantly different than the control for either measurement. Mat A appears to be the most effective mat at reducing spinal compression and maintaining flexibility over an 8-hour workday.
Austin Statistics is an open access, peer reviewed, scholarly journal dedicated to publish articles in all areas of statistics.
The aim of the journal is to provide a forum for scientists, academicians and researchers to find most recent advances in the field statistics.
Austin Statistics accepts original research articles, review articles, case reports and rapid communication on all the aspects of statistics.
Cost Aware Expansion Planning with Renewable DGs using Particle Swarm Optimiz...IJERA Editor
This Paper is an attempt to develop the expansion-planning algorithm using meta heuristics algorithms. Expansion Planning is always needed as the power demand is increasing every now and then. Thus for a better expansion planning the meta heuristic methods are needed. The cost efficient Expansion planning is desired in the proposed work. Recently distributed generation is widely researched to implement in future energy needs as it is pollution free and capability of installing it in rural places. In this paper, optimal distributed generation expansion planning with Particle Swarm Optimization (PSO) and Cuckoo Search Algorithm (CSA) for identifying the location, size and type of distributed generator for future demand is predicted with lowest cost as the constraints. Here the objective function is to minimize the total cost including installation and operating cost of the renewable DGs. MATLAB based `simulation using M-file program is used for the implementation and Indian distribution system is used for testing the results.
This document introduces MSATSI, a MATLAB package for stress inversion that combines the Solid Earth methodology with a simplified user interface and visualization tools. MSATSI implements the SATSI stress inversion algorithm within MATLAB. It handles input/output data consistently for inversions of varying dimensions from 0D to 3D. MSATSI automates calculation of an optimal damping parameter, inverts for stress orientations, and assesses uncertainties through bootstrap resampling. Results can be visualized through various stereographic and map plots to aid analysis of stress field distributions. The package aims to make formal stress inversion more accessible and its results more interpretable.
This document discusses several methods for estimating the fatigue life of Type 304LN stainless steel under strain-controlled cyclic loading, including the four-point correlation method, modified four-point correlation method, universal slopes method, modified universal slopes method, uniform material law, hardness method, median's method, and methods proposed by Mitchell and Basan. The results of estimating fatigue life using these methods are compared to experimental strain-controlled fatigue test results on Type 304LN stainless steel at various strain amplitudes. Most methods overestimate fatigue life except the median's method, which provides a reasonably accurate estimation of fatigue life, especially at higher strain amplitudes. Basan's method, modified universal slopes method, and uniform material law also predict fatigue life with reasonable accuracy
GIS-3D Analysis of Susceptibility Landslide Disaster in Upstream Area of Jene...AM Publications
The assessment of landslide hazard and risk has become a topic of major interest for both geoscientists and engineering professionals as well as for local communities and administrations in many parts of the world. Recently, Geographic Information Systems (GIS), with their excellent spatial data processing capacity, have attracted great attention in natural disaster assessment. In this paper, an assessment of landslide hazard at Upper Area of Jeneberang Watershed has been studied using GIS technology. By simulating the potential landslide according the minimum safety factor value using GIS, it can be expected that great contribution as a basic decision making for many prevention works before future landslide occurs at upstream area of Jeneberang River Watershead, South Sulawesi, Indonesia
Numerical modeling of uneven thermoplastic polymers behaviour using experimen...Marcos Bianchi (Msc_Mba)
This document discusses numerical modeling of the behavior of uneven thermoplastic polymers using experimental stress-strain data and pressure dependent yield criteria to improve design practices. It presents the following:
1) Four polymers (PA-66, PA-6, PP, HDPE) were tested under tension and compression to determine their unevenness levels. PA-6 and PP showed significant unevenness, with compressive yield strengths 25-70% higher than tensile strengths.
2) Pressure dependent yield criteria that account for unevenness, such as conical and parabolic modified von Mises models, were reviewed. These criteria incorporate the effect of hydrostatic pressure on yield strength.
3) Experimental stress-strain data was
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.
This document discusses the concept of equifinality in complex environmental systems modeling. Equifinality refers to the idea that there are many different model structures and parameter sets that can produce similar and acceptable results when modeling system behavior. The generalized likelihood uncertainty estimation (GLUE) methodology is described as a way to account for equifinality by using ensembles of behavioral models weighted by their likelihood to estimate prediction uncertainties. An example application to rainfall-runoff modeling is used to illustrate the GLUE methodology.
Cornah and vann 2012 non-mg multivariate cs - paperAlastair Cornah
This document proposes a new Direct Sequential Cosimulation algorithm to generate multivariate simulations that can reproduce inter-variable correlations without relying on multi-Gaussian assumptions. The algorithm draws pairwise simulated point values directly from the discrete multivariate conditional distribution using local kriging weights, ensuring inter-variable correlations are embedded in each realization without being constrained by maximum entropy properties of multi-Gaussian tools. This addresses issues with existing multi-Gaussian approaches that can generate mineralogically impossible pairings when data violates multi-Gaussian assumptions.
This document describes a methodology called Generalized Likelihood Uncertainty Estimation (GLUE) for calibrating and estimating uncertainty in distributed hydrological models. GLUE recognizes that multiple parameter sets may be equally likely to simulate a catchment's behavior. It calibrates by running the model with many random parameter sets and assigning each a likelihood based on how well it matches observations. Parameter sets with likelihoods above zero are retained. The methodology is demonstrated on a storm event in the Gwy catchment using the Institute of Hydrology Distributed Model.
Classification accuracy analyses using Shannon’s EntropyIJERA Editor
There are many methods for determining the Classification Accuracy. In this paper significance of Entropy of
training signatures in Classification has been shown. Entropy of training signatures of the raw digital image
represents the heterogeneity of the brightness values of the pixels in different bands. This implies that an image
comprising a homogeneous lu/lc category will be associated with nearly the same reflectance values that would
result in the occurrence of a very low entropy value. On the other hand an image characterized by the
occurrence of diverse lu/lc categories will consist of largely differing reflectance values due to which the
entropy of such image would be relatively high. This concept leads to analyses of classification accuracy.
Although Entropy has been used many times in RS and GIS but its use in determination of classification
accuracy is new approach.
Relevance Vector Machines for Earthquake Response Spectra drboon
This study uses Relevance Vector Machine (RVM) regression to develop a probabilistic model for the average horizontal component of 5%-damped earthquake response spectra. Unlike conventional models, the proposed approach does not require a functional form, and constructs the model based on a set predictive variables and a set of representative ground motion records. The RVM uses Bayesian inference to determine the confidence intervals, instead of estimating them from the mean squared errors on the training set. An example application using three predictive variables (magnitude, distance and fault mechanism) is presented for sites with shear wave velocities ranging from 450 m/s to 900 m/s. The predictions from the proposed model are compared to an existing parametric model. The results demonstrate the validity of the proposed model, and suggest that it can be used as an alternative to the conventional ground motion models. Future studies will investigate the effect of additional predictive variables on the predictive performance of the model.
Relevance Vector Machines for Earthquake Response Spectra drboon
This study uses Relevance Vector Machine (RVM) regression to develop a probabilistic model for the average horizontal component of 5%-damped earthquake response spectra. Unlike conventional models, the proposed approach does not require a functional form, and constructs the model based on a set predictive variables and a set of representative ground motion records. The RVM uses Bayesian inference to determine the confidence intervals, instead of estimating them from the mean squared errors on the training set. An example application using three predictive variables (magnitude, distance and fault mechanism) is presented for sites with shear wave velocities ranging from 450 m/s to 900 m/s. The predictions from the proposed model are compared to an existing parametric model. The results demonstrate the validity of the proposed model, and suggest that it can be used as an alternative to the conventional ground motion models. Future studies will investigate the effect of additional predictive variables on the predictive performance of the model.
This document discusses applying a novel approach using multi-criterion decision analysis (MCDA) with the generalized likelihood uncertainty estimation (GLUE) method to quantify uncertainty in hydrological modeling. Specifically, it examines uncertainty in the SLURP hydrological model. Rather than considering overall Nash-Sutcliffe efficiency, the approach considers NSE values for different flow magnitudes simultaneously. The TOPSIS MCDA method is used to compute predictive intervals by considering NSE values for different flow periods simultaneously. The Kootenay Catchment case study is used to demonstrate the MCDA-GLUE approach.
IMPROVED NEURAL NETWORK PREDICTION PERFORMANCES OF ELECTRICITY DEMAND: MODIFY...csandit
Accurate prediction of electricity demand can bring extensive benefits to any country as the
forecast values help the relevant authorities to take decisions regarding electricity generation,
transmission and distribution much appropriately. The literature reveals that, when compared
to conventional time series techniques, the improved artificial intelligent approaches provide
better prediction accuracies. However, the accuracy of predictions using intelligent approaches
like neural networks are strongly influenced by the correct selection of inputs and the number of
neuro-forecasters used for prediction. This research shows how a cluster analysis performed to
group similar day types, could contribute towards selecting a better set of neuro-forecasters in
neural networks. Daily total electricity demands for five years were considered for the analysis
and each date was assigned to one of the thirteen day-types, in a Sri Lankan context. As a
stochastic trend could be seen over the years, prior to performing the k-means clustering, the
trend was removed by taking the first difference of the series. Three different clusters were
found using Silhouette plots, and thus three neuro-forecasters were used for predictions. This
paper illustrates the proposed modified neural network procedure using electricity demand
data.
Bird-Strike Modeling Based on the Lagrangian Formulation Using LSDYNAdrboon
This document summarizes research on modeling bird-strike events using LS-DYNA's Lagrangian formulation. Key points:
- Bird-strikes pose safety risks and costs to the aviation industry, motivating efforts to model and predict damage through simulation.
- The bird is modeled as a fluid, and the Lagrangian method tracks material deformation. Initial validation involved a beam impact problem, with results within 2.5% of analytical solutions.
- Bird-strike events were divided into impacts on rigid and deformable plates at different angles, modeled after existing literature. Peak pressures and forces from simulations were within 10% of test data.
- The developed Lagrangian approach is suitable for modeling bird-strikes to predict
This document summarizes a research paper that develops a modified grain contact theory to better model the pressure-dependent elastic properties of uncemented sediments. The Hertz-Mindlin theory typically overpredicts shear modulus values compared to laboratory measurements and does not capture the observed increasing ratio of bulk to shear modulus with decreasing effective pressure. The authors introduce two new pressure-dependent calibration parameters to account for grain relaxation effects and porosity changes not included in existing theories. Their modified model provides an improved fit to laboratory data and can predict elastic properties over a wider range of effective pressures.
APPLICATION OF COMPUTER FOR ANALYZING WORLD CO2 EMISSIONIJCSEA Journal
Global climate change due to CO2 emissions is an issue of international concern that primarily attributed
to fossil fuels. In this study, Genetic Algorithm (GA) is used for analyzing world CO2 emission based on the
global energy consumption. Linear and non-linear forms of equations were developed to forecast CO2
emission using Genetic Algorithm (GA) based on the global oil, natural gas, coal, and primary energy
consumption figures. The related data between 1980 and 2010 were used, partly for installing the models
(finding candidates of best weighting factors for each model (1980-2003)) and partly for testing the models
(2004–2010). Global CO2 emission is forecasted up to year 2030.
The document presents a study that compares five methods for estimating missing values in building sensor data: linear regression, weighted k-nearest neighbors, support vector machines, mean imputation, and replacing missing values with zero. The methods were evaluated using data from sensors in an office building in Japan, with the amount of missing data varied from 5% to 20%. Feature selection and inclusion of lagged variables as predictors were also examined to determine their effect on the methods' performance.
Performance based Comparison of Wind and Solar Distributed Generators using E...Editor IJLRES
Distributed Generation (DG) technologies have become more and more important in power systems. The objective of the paper is to optimize the distributed energy resource type and size based on uncertainties in the distribution network. The three things are considered in stand point of uncertainties are listed as, (i) Future load growth, (ii) Variation in the solar radiation, (iii) Wind output variation. The challenge in Optimal DG Placement (ODGP) needs to be solved with optimization problem with many objectives and constraints. The ODGP is going to be done here, by using Non-dominated Sorting Genetic Algorithm II (NSGA II). NSGA II is one among the available multi objective optimization algorithms with reduced computational complexity (O=MN2). Because of this prominent feature of NSGA II, it is widely applicable in all the multi objective optimization problems irrespective of disciplines. Hence it is selected to be employed here in order to obtain the reduced cost associated with the DG units. The proposed NSGA II is going to be applied on the IEEE 33-bus and the different performance characteristics were compared for both wind and solar type DG units.
The study evaluated 4 anti-fatigue mats (Mats A-D) and a no-mat control for their effects on worker height loss and flexibility changes over an 8-hour workday. Eighteen subjects were recruited from two industrial sites and used each mat/control for 5 days. Height and flexibility measurements were taken before and after each workday. Statistical analysis found that only Mat A (Let's Gel) produced significantly less height loss and greater flexibility increases compared to the no-mat control. The other mats were not significantly different than the control for either measurement. Mat A appears to be the most effective mat at reducing spinal compression and maintaining flexibility over an 8-hour workday.
Austin Statistics is an open access, peer reviewed, scholarly journal dedicated to publish articles in all areas of statistics.
The aim of the journal is to provide a forum for scientists, academicians and researchers to find most recent advances in the field statistics.
Austin Statistics accepts original research articles, review articles, case reports and rapid communication on all the aspects of statistics.
Cost Aware Expansion Planning with Renewable DGs using Particle Swarm Optimiz...IJERA Editor
This Paper is an attempt to develop the expansion-planning algorithm using meta heuristics algorithms. Expansion Planning is always needed as the power demand is increasing every now and then. Thus for a better expansion planning the meta heuristic methods are needed. The cost efficient Expansion planning is desired in the proposed work. Recently distributed generation is widely researched to implement in future energy needs as it is pollution free and capability of installing it in rural places. In this paper, optimal distributed generation expansion planning with Particle Swarm Optimization (PSO) and Cuckoo Search Algorithm (CSA) for identifying the location, size and type of distributed generator for future demand is predicted with lowest cost as the constraints. Here the objective function is to minimize the total cost including installation and operating cost of the renewable DGs. MATLAB based `simulation using M-file program is used for the implementation and Indian distribution system is used for testing the results.
This document introduces MSATSI, a MATLAB package for stress inversion that combines the Solid Earth methodology with a simplified user interface and visualization tools. MSATSI implements the SATSI stress inversion algorithm within MATLAB. It handles input/output data consistently for inversions of varying dimensions from 0D to 3D. MSATSI automates calculation of an optimal damping parameter, inverts for stress orientations, and assesses uncertainties through bootstrap resampling. Results can be visualized through various stereographic and map plots to aid analysis of stress field distributions. The package aims to make formal stress inversion more accessible and its results more interpretable.
This document discusses several methods for estimating the fatigue life of Type 304LN stainless steel under strain-controlled cyclic loading, including the four-point correlation method, modified four-point correlation method, universal slopes method, modified universal slopes method, uniform material law, hardness method, median's method, and methods proposed by Mitchell and Basan. The results of estimating fatigue life using these methods are compared to experimental strain-controlled fatigue test results on Type 304LN stainless steel at various strain amplitudes. Most methods overestimate fatigue life except the median's method, which provides a reasonably accurate estimation of fatigue life, especially at higher strain amplitudes. Basan's method, modified universal slopes method, and uniform material law also predict fatigue life with reasonable accuracy
GIS-3D Analysis of Susceptibility Landslide Disaster in Upstream Area of Jene...AM Publications
The assessment of landslide hazard and risk has become a topic of major interest for both geoscientists and engineering professionals as well as for local communities and administrations in many parts of the world. Recently, Geographic Information Systems (GIS), with their excellent spatial data processing capacity, have attracted great attention in natural disaster assessment. In this paper, an assessment of landslide hazard at Upper Area of Jeneberang Watershed has been studied using GIS technology. By simulating the potential landslide according the minimum safety factor value using GIS, it can be expected that great contribution as a basic decision making for many prevention works before future landslide occurs at upstream area of Jeneberang River Watershead, South Sulawesi, Indonesia
Numerical modeling of uneven thermoplastic polymers behaviour using experimen...Marcos Bianchi (Msc_Mba)
This document discusses numerical modeling of the behavior of uneven thermoplastic polymers using experimental stress-strain data and pressure dependent yield criteria to improve design practices. It presents the following:
1) Four polymers (PA-66, PA-6, PP, HDPE) were tested under tension and compression to determine their unevenness levels. PA-6 and PP showed significant unevenness, with compressive yield strengths 25-70% higher than tensile strengths.
2) Pressure dependent yield criteria that account for unevenness, such as conical and parabolic modified von Mises models, were reviewed. These criteria incorporate the effect of hydrostatic pressure on yield strength.
3) Experimental stress-strain data was
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.
This document discusses the concept of equifinality in complex environmental systems modeling. Equifinality refers to the idea that there are many different model structures and parameter sets that can produce similar and acceptable results when modeling system behavior. The generalized likelihood uncertainty estimation (GLUE) methodology is described as a way to account for equifinality by using ensembles of behavioral models weighted by their likelihood to estimate prediction uncertainties. An example application to rainfall-runoff modeling is used to illustrate the GLUE methodology.
Cornah and vann 2012 non-mg multivariate cs - paperAlastair Cornah
This document proposes a new Direct Sequential Cosimulation algorithm to generate multivariate simulations that can reproduce inter-variable correlations without relying on multi-Gaussian assumptions. The algorithm draws pairwise simulated point values directly from the discrete multivariate conditional distribution using local kriging weights, ensuring inter-variable correlations are embedded in each realization without being constrained by maximum entropy properties of multi-Gaussian tools. This addresses issues with existing multi-Gaussian approaches that can generate mineralogically impossible pairings when data violates multi-Gaussian assumptions.
This document describes a methodology called Generalized Likelihood Uncertainty Estimation (GLUE) for calibrating and estimating uncertainty in distributed hydrological models. GLUE recognizes that multiple parameter sets may be equally likely to simulate a catchment's behavior. It calibrates by running the model with many random parameter sets and assigning each a likelihood based on how well it matches observations. Parameter sets with likelihoods above zero are retained. The methodology is demonstrated on a storm event in the Gwy catchment using the Institute of Hydrology Distributed Model.
Classification accuracy analyses using Shannon’s EntropyIJERA Editor
There are many methods for determining the Classification Accuracy. In this paper significance of Entropy of
training signatures in Classification has been shown. Entropy of training signatures of the raw digital image
represents the heterogeneity of the brightness values of the pixels in different bands. This implies that an image
comprising a homogeneous lu/lc category will be associated with nearly the same reflectance values that would
result in the occurrence of a very low entropy value. On the other hand an image characterized by the
occurrence of diverse lu/lc categories will consist of largely differing reflectance values due to which the
entropy of such image would be relatively high. This concept leads to analyses of classification accuracy.
Although Entropy has been used many times in RS and GIS but its use in determination of classification
accuracy is new approach.
Relevance Vector Machines for Earthquake Response Spectra drboon
This study uses Relevance Vector Machine (RVM) regression to develop a probabilistic model for the average horizontal component of 5%-damped earthquake response spectra. Unlike conventional models, the proposed approach does not require a functional form, and constructs the model based on a set predictive variables and a set of representative ground motion records. The RVM uses Bayesian inference to determine the confidence intervals, instead of estimating them from the mean squared errors on the training set. An example application using three predictive variables (magnitude, distance and fault mechanism) is presented for sites with shear wave velocities ranging from 450 m/s to 900 m/s. The predictions from the proposed model are compared to an existing parametric model. The results demonstrate the validity of the proposed model, and suggest that it can be used as an alternative to the conventional ground motion models. Future studies will investigate the effect of additional predictive variables on the predictive performance of the model.
Relevance Vector Machines for Earthquake Response Spectra drboon
This study uses Relevance Vector Machine (RVM) regression to develop a probabilistic model for the average horizontal component of 5%-damped earthquake response spectra. Unlike conventional models, the proposed approach does not require a functional form, and constructs the model based on a set predictive variables and a set of representative ground motion records. The RVM uses Bayesian inference to determine the confidence intervals, instead of estimating them from the mean squared errors on the training set. An example application using three predictive variables (magnitude, distance and fault mechanism) is presented for sites with shear wave velocities ranging from 450 m/s to 900 m/s. The predictions from the proposed model are compared to an existing parametric model. The results demonstrate the validity of the proposed model, and suggest that it can be used as an alternative to the conventional ground motion models. Future studies will investigate the effect of additional predictive variables on the predictive performance of the model.
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This document summarizes a study that used the Generalized Likelihood Uncertainty Estimation (GLUE) method to analyze parametric uncertainty in hydrological modeling of the Kootenay Watershed in Canada. The study used the SLURP hydrological model and analyzed over 1 million parameter combinations using the GLUE method. The results identified distributions for key model parameters and showed variability in parameter averages and distributions between different land cover types within the watershed. This provided insights into parametric uncertainties and improved understanding of hydrological processes in the study area.
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Clustering heterogeneous categorical data using enhanced mini batch K-means ...IJECEIAES
This document presents a proposed framework called MBKEM (Mini Batch K-means with Entropy Measure) for clustering heterogeneous categorical data. MBKEM uses an entropy distance measure within a mini batch k-means algorithm. The framework is evaluated using secondary data from a public survey. Evaluation metrics show MBKEM outperforms other clustering algorithms with high accuracy, v-measure, adjusted rand index, and Fowlkes-Mallow's index. MBKEM also has faster average cluster generation time than other methods. The proposed framework provides an improved solution for clustering heterogeneous categorical data.
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This study evaluated the performance of bootstrap confidence intervals for estimating slope coefficients in Model II regression with three or more variables. Simulation studies were conducted for different correlation structures between variables, sampling from both normal and lognormal distributions. The results showed that bootstrap intervals provided less than the nominal 95% coverage. Scenarios with strong relationships between variables produced better coverage, while scenarios with weaker relationships and bias produced poorer coverage, even with larger sample sizes. Future work could explore additional scenarios and alternative interval methods to improve accuracy of confidence intervals in Model II regression.
www.elsevier.comlocatecompstrucComputers and Structures .docxjeffevans62972
www.elsevier.com/locate/compstruc
Computers and Structures 85 (2007) 235–243
On the treatment of uncertainties in structural mechanics and analysis q
G.I. Schuëller *
Institute of Engineering Mechanics, Leopold-Franzens University Innsbruck, Technikerstr. 13, 6020 Innsbruck, Austria
Received 9 August 2006; accepted 31 October 2006
Available online 22 December 2006
Abstract
In this paper the need for a rational treatment of uncertainties in structural mechanics and analysis is reasoned. It is shown that the
traditional deterministic conception can be easily extended by applying statistical and probabilistic concepts. The so-called Monte Carlo
simulation procedure is the key for those developments, as it allows the straightforward use of the currently used deterministic analysis
procedures.
A numerical example exemplifies the methodology. It is concluded that uncertainty analysis may ensure robust predictions of vari-
ability, model verification, safety assessment, etc.
� 2006 Elsevier Ltd. All rights reserved.
Keywords: Uncertainty; Monte Carlo simulaton; Finite elements; Response variability; Model verification; Robustness
1. Introduction
Structural mechanics analysis up to this date, generally is
still based on a deterministic conception. Observed varia-
tions in loading conditions, material properties, geometry,
etc. are taken into account by either selecting extremely
high, low or average values, respectively, for representing
the parameters. Hence, this way, uncertainties inherent in
almost every analysis process are considered just intuitively.
Observations and measurements of physical processes,
however, show not only variability, but also random char-
acteristics. Statistical and probabilistic procedures provide
a sound frame work for a rational treatment of analysis
of these uncertainties. Moreover there are various types of
uncertainties to be dealt with. While the uncertainties in
mechanical modeling can be reduced as additional knowl-
edge becomes available, the physical or intrinsic uncertain-
ties, e.g. of environmental loading, can not. Furthermore,
0045-7949/$ - see front matter � 2006 Elsevier Ltd. All rights reserved.
doi:10.1016/j.compstruc.2006.10.009
q Plenary Keynote Lecture presented at the 3rd MIT Conference on
Computational Fluid and Solid Mechanics, Boston, MA, USA, June 14–
17, 2005.
* Tel.: +43 512 507 6841; fax: +43 512 507 2905.
E-mail address: [email protected]
the entire spectrum of uncertainties is also not known. In
reality, neither the true model nor the model parameters
are deterministically known. Assuming that by finite ele-
ment (FE) procedures structures and continua can be repre-
sented reasonably well the question of the effect of the
discretization still remains. It is generally expected, that
an increase in the size of the structural models, in terms of
degrees of freedom, will increase the level of realism of the
model. Comparisons with measurements, however, clearly
show that this expect.
Reliability and Fuzzy Logic Concepts as Applied to Slope Stability Analysis –...IJERA Editor
Considerable uncertainty exist with regard to stability of slopes due to several factors and recognition of these uncertainties has made designees to introduce factor of safety. Several studies, during recent years on analytical methods using soil properties have improved understanding the several uncertainties. The reliability analysis of slopes can be used to represent uncertainty in mathematical models, which can be assumed to follow the characteristic of random uncertainty. The distribution uncertain variable, which is unknown, makes its estimation difficult. Hence, the concepts of fuzzy set theory appear to be quite reliable when limited information is available. This paper attempts to review the slope stability problem and deals with the intricacies of the concept of reliability and fuzzy logic as applied to stability analysis of slope. It has been suggested that the FOSM algorithm provides a general agreement among the different slope stability solutions.
Reliability and Fuzzy Logic Concepts as Applied to Slope Stability Analysis –...IJERA Editor
Considerable uncertainty exist with regard to stability of slopes due to several factors and recognition of these uncertainties has made designees to introduce factor of safety. Several studies, during recent years on analytical methods using soil properties have improved understanding the several uncertainties. The reliability analysis of slopes can be used to represent uncertainty in mathematical models, which can be assumed to follow the characteristic of random uncertainty. The distribution uncertain variable, which is unknown, makes its estimation difficult. Hence, the concepts of fuzzy set theory appear to be quite reliable when limited information is available. This paper attempts to review the slope stability problem and deals with the intricacies of the concept of reliability and fuzzy logic as applied to stability analysis of slope. It has been suggested that the FOSM algorithm provides a general agreement among the different slope stability solutions.
2. Integration of imprecise and biased data into mineral resource estimates
Pickers (2005) compared kriging with external drift (KED)
and collocated cokriging (CCK) against OK for the integration
of two different generations of sample assays, finding that
KED and CCK significantly improved the accuracy of grade
estimation when compared with conventional OK.
This paper firstly re-examines the case where imprecise
but unbiased secondary data are available for incorporation
into the resource estimate; the imprecise and biased case is
then considered. Various techniques are trialled, including
integration through CK, multicollocated cokriging (MCCK),
and OK with variance of measurement error (OKVME).
CK is classically the estimation of one variable based
upon the measured values of that variable and secondary
variable(s). Estimation uses not only the spatial correlation of
the primary variable (modelled by the primary variogram) but
also the inter-variable spatial correlations (modelled by cross-
variograms). By making use of data from a secondary
variable(s) as well as the primary variable, CK aims to reduce
estimation variance associated with the primary variable
(Myers, 1982; Olea, 1999); it also seeks to enforce
relationships between variables as measured within the data.
CK coincides with independent OK if all variables are
sampled at all locations (isotopic sampling) and the variables
of interest are also intrinsically correlated (see Wackernagel,
2003); this is a condition known as autokrigeability (Journel
and Huijbregts, 1978; Matheron, 1979; Wackernagel, 2003).
However, in the isotopic sampling but non-intrinsic case, real
and perceived difficulties are usually deemed to outweigh the
benefit of CK over OK (see Myers, 1991; Künsch et al., 1997;
Goovaerts, 1997). Various authors including Journel and
Huijbregts (1978) and Goovaerts (1997) suggest that CK is
worthwhile only where correlations between attributes are
strong and the variable of interest is under-sampled with
respect to secondary variables (heterotopic sampling) (see
Wackernagel, 2003).
Even in the heterotopic sampling case, secondary data
that are co-located or located near unknown primary data
tend to screen the influence of distant secondary data; the
high degree of data redundancy can produce large negative
weights and instability within CK systems (Xu et al., 1992).
In addition, fitting a positive definite linear model of
coregionalization (LMC) to multiple attributes is often
considered problematic (Journel, 1999), although significant
improvements have been made in automated fitting routines
(for example see Goulard and Voltz, 1992; Künsch et al.,
1997; Pelletier et al., 2004; Oman and Vakulenko-Lagun.,
2009; Emery, 2010). Furthermore, the inference of cross-
variograms is problematic in the displaced heterotopic
sampling case where the sample locations of the secondary
variable do not coincide with the primary variable.
In this paper CK is used to integrate dislocated heterotopic
primary and secondary sample data representing the same
attribute in cases where the latter is imprecise or biased or
both, but spatially correlated to the former.
CCK was proposed by Xu et al. (1992) to avoid the matrix
instability associated with CK discussed above. It is usually
applied in cases where primary data is sparsely distributed
but secondary data is quasi-exhaustively measured (for
example seismic attributes in petroleum applications). Under
a Markov-type screening hypothesis (Xu et al., 1992), the
primary data point screens the influence of any other data
point on the secondary collocated variable. This assumption
allows CK to be simplified to CCK in that only the secondary
data located at the estimation target is retained within the CK
system; the neighbourhood of the auxiliary variable is
reduced to only one point: the estimation location (Xu et al.,
1992; Goovaerts, 1997). Under the Markov model the cross-
covariance is available as a rescaled version of the primary
covariance (Xu et al., 1992).
MCCK makes use of the auxiliary variable at the
estimation location and also at sample locations where the
target variable is available, but not at other locations where
only the auxiliary variable is available (Rivoirard, 2001).
This study investigates the possibility of integrating the
secondary sample data, which represents the same attribute
by MCCK.
Another alternative is to integrate data sources of varying
precision using OKVME (Delhomme, 1976). The method
requires that the precision of each sample incorporated into
the estimation is known. The approach also requires the
assumption that measurement errors represent pure nugget
effect; that is, the measurement errors are non-spatial noise
which is independent of the data values (see Wackernagel,
2003). The specific measurement error variance of each data
point is added to the diagonal terms of the left-hand kriging
matrix. The response is re-appropriation of the kriging
weights in favour of sample locations with low measurement
error variance and against samples with high measurement
error variance. In practice it is unlikely that the precision of
every measurement is known: sampling errors may be
broadly assessed for each campaign based upon quality
control metadata, allowing progressive penalization of
progressively imprecise data. Details of procedures for
measuring and monitoring precision and accuracy in
geochemical data are given by Abzalov (2008, 2009).
Modelling
Experimentation was carried out using a two-dimensional
iron ore data-set that comprises a set of exploration samples
from a single geological unit configured at approximately
75 m × 75 m spacing. These samples were derived from
diamond drill core and for the purpose of this experiment are
assumed to be error-free; herein they are referred to as the
‘primary data’, Z1.
An exhaustive ‘punctual ground truth’ model of Fe grades
within the data-set area was generated at 1 m × 1 m spaced
nodes by conditional simulation (CS) of the primary data
(Journel, 1974; Chilès and Delfiner, 1999). CS allows multiple
images of the deposit to be generated which are realistically
variable but are ‘conditional’ in the sense that they honour
the known but limited drill-hole sampling data from the
deposit. In this case, a single realization of Fe grade (which
adequately represented the statistical moments of the input
data) was selected from a set of 25 that were generated using
the turning bands algorithm (Journel, 1974). This ‘punctual
ground truth’ realization was averaged into 50 m × 50 m
mining blocks as shown in Figure 1 to provide a ‘block
ground truth’ (Z) against which estimations based upon the
primary and secondary data could be compared.
The top left-hand plot in Figure 1 portrays the primary
data locations (shown as solid black discs) and the CS
realization built from this data, the histogram of Fe grades
▲
524 JUNE 2015 VOLUME 115 The Journal of The Southern African Institute of Mining and Metallurgy
3. pertaining to this is shown below; the re-blocked realization
is shown in the top right graphic and the histogram
pertaining to this below. The figure demonstrates the key
features of up-scaling from punctual to block support under
the multigaussian model assumptions that underpin the CS
realization (see Journel and Alabert, 1989): the range and
skewness of the distribution is reduced, but the mean is
preserved.
In order to provide a series of abundant secondary sample
data-sets (Z2), ‘virtual’ samples were extracted from the
punctual ground truth. Multi-generational data sources often
overlap, but are rarely exactly coincident unless they
represent re-assay of older pulps or rejects. The Z2 data
locations were therefore made irregular and dislocated from
Z1 in order to provide a realistic representation of a multi-
generational drilling campaign (the displaced heterotopic
sample arrangement; see Wackernagel, 2003). Regular 25 m
× 25 m locations were adjusted by easting and northing
values drawn from a uniform distribution over [−3,3] to
provide the Z2 extraction locations. This geometry results in
Z2 to Z1 frequency of approximately 10:1.
Six unbiased normal error distributions were applied to
the extracted Z2 samples with absolute error standard
deviation (σα
Z2) ranging between 0.25 and 3 (see Figure 2),
termed unbiased cases hereafter. Because the error distrib-
utions are symmetric and unbounded, imprecision has no
implication with respect to bias. In addition, six positively
biased error distributions centred upon absolute +1% were
applied, and six negatively biased distributions centred upon
absolute -1% were applied, each with the same range in σα
Z2
(termed biased cases hereafter).
An OK block estimate incorporating the primary data only
represents the base case (Z1
OK
) and is compared against the
block ground truth in the scatter plot shown in Figure 3.
In bedded iron ore data-sets, the Fe distribution is
typically negatively skewed (see Figure 1), the data is charac-
teristically heteroscedastic (i.e. subsets of the data show
differences in variability), and the proportional effect usually
exists (local variability is related to the local mean; see
Journel and Huijbregts, 1978). Figure 3 indicates that the
variance of estimation error is least where the local mean is
greatest but increases as the local mean declines. This implies
Integration of imprecise and biased data into mineral resource estimates
525The Journal of The Southern African Institute of Mining and Metallurgy VOLUME 115 JUNE 2015
▲
Figure 1 – Conditional simulation of punctual ground truth (top left) with drill-hole locations shown as discs; punctual ground truth histogram (bottom left);
ground truth up-scaled to 50 m x 50 m blocks (top right); and block ground truth histogram (bottom right)
4. Integration of imprecise and biased data into mineral resource estimates
that the proportional effect exists in this data-set with local
variability, and consequently estimation error, greatest in
lower grade areas and least in high-grade areas. This is
common in iron ore data-sets where the low-grade areas may
pertain to deformed shale bands, discrete clay pods, diabase
sills, or unaltered banded iron formation.
The Pearson correlation coefficient (shown as rho in
Figure 3) measures the linear dependency between Z and
Z1
OK
and thus quantifies the precision of the estimate.
However, following a review of the various precision metrics
used in geochemical data-sets, Stanley and Lawie (2007) and
Abzalov (2008) both recommend using the average
coefficient of variation (CVAVR(%)) as the universal measure
of relative precision error in mining geology applications:
Errors in geochemical determinations can be considered
analogous to estimation errors in this case, and the CVAVR(%)
metric is thus used as the basis for comparison between
estimation precision in this paper. In the base case estimate
shown in Figure 3, CVAVR(Z, Z1
OK
)=0.88.
Analysis of imprecise but unbiased cases
The Z1 and unbiased but increasingly imprecise Z2 data-sets
were integrated into estimation through OK (Z1,2
OK
), CK (Z1,2
CK
),
MCCK (Z1,2
MCCK
), and OKVME (Z1,2
OKVME
). Given the displaced
heterotopic geometry of the data-sets, the Z2 locations
adjacent to Z1 were migrated into collocation to allow cross-
variography in CK cases, and to allow implementation of
MCCK. The resulting loss of accuracy represents a
compromise of these methods in the common displaced
heterotopic sample geometry case and is discussed further
below. The resulting estimates are quantitatively compared
against the base case CVAVR(Z, Z1
OK
) and against each other
in Figure 4.
The figure firstly shows that CVAVR(Z, Z1
OK
) is
independent of σα
Z2; secondly, that pooling the primary and
secondary data and estimating using OK (Z1,2
OK
) results in
CVAVR(Z,Z1,2
OK
)=0.56 where σα
Z2=0. Incorporating secondary
samples with zero measurement error through OK clearly
improves estimation precision and is therefore preferable to
excluding them. However, as σα
Z2 increases, so CVAVR(Z,Z1,2
OK
)
also increases rapidly (indicating that estimation precision
declines). Figure 4 shows that, in this particular case, where
σα
Z2=1.5 there is no benefit to including Z2 samples in the OK
estimate:
σα
Z2=1.5 → CVAVR(Z,Z1,2
OK
) ≈ CVAVR(Z, Z1
OK
).
▲
526 JUNE 2015 VOLUME 115 The Journal of The Southern African Institute of Mining and Metallurgy
Figure 2 – Secondary data locations shown as coloured discs with primary data locations shown as black discs (left); unbiased error distributions which
were applied to the secondary data locations also shown (right)
Figure 3 – Comparison of base case estimation against the ground
truth; rho represents the Pearson correlation coefficient
5. Where measurement errors are large, the OK estimate
using the pooled data-set is less precise than the base case,
which excludes the secondary data. In the discussed case
study:
σα
Z2>1.5 → CVAVR(Z,Z1,2
OK
) > CVAVR(Z, Z1
OK
)
Figure 4 shows that where σα
Z2=0, some improvement in
estimation precision is achieved by incorporating secondary
samples through CK (Z1,2
CK
) compared to Z1
OK
. However, in this
circumstance the improvement in accuracy is not as great as
that gained through Z1,2
OK
:
σα
Z2=0 → CVAVR(Z,Z1,2
CK
) > CVAVR(Z, Z1,2
OK
)
This is due to the vagaries of CK compared to OK, which
were discussed above. However, as σα
Z2 increases, the benefit
of Z1,2
OK
declines relative to Z1,2
CK
. In this case, where σα
Z2≈1.4,
CVAVR(Z, Z1,2
OK
)≈CVAVR(Z,Z1,2
CK
), both of which are more
precise than the base case. Where the precision of the
secondary data is poorer than this, integrating it through CK
is preferable to integrating it through OK. In this case:
σα
Z2>1.4 → CVAVR(Z,Z1,2
CK
) < CVAVR(Z, Z1,2
OK
)
Unlike OK, integrating the secondary data using CK
provides an improvement in estimation precision compared to
the base case in all of the cases tested:
CVAVR(Z,Z1,2
CK
) < CVAVR(Z, Z1
OK
)
As discussed above, MCCK is an approximation of full CK
and some loss of estimation precision is to be expected in this
case by the migration of data locations required by non-
colocation of primary and secondary data-sets. This is
evident within the results shown in Figure 4: MCCK mirrors
fully the CK result, with some loss of estimation precision
where σα
Z2<2. However where σα
Z2>2 the difference between
the two approaches is negligible, suggesting that at higher
σα
Z2 levels the simplifications associated with MCCK represent
a worthwhile trade-off compared to CK. In addition,
integration of secondary data through MCCK is preferable to
the base case in all σα
Z2 cases that were tested:
CVAVR(Z,Z1,2
MCCK
) < CVAVR(Z, Z1
OK
)
Finally, Figure 4 shows the results of integrating
secondary data through OKVME estimation (Z,Z1,2
OKVME
). In all
σα
Z2 cases that were tested, this approach outperformed the
base case:
CVAVR(Z,Z1,2
OKVME
) < CVAVR(Z, Z1
OK
)
The figure confirms that the Z1,2
OKVME
result converges on
Z1,2
OK
where zero error is associated with the secondary
variable:
σα
Z2=0 → CVAVR(Z,Z1,2
OKVME
) = CVAVR(Z, Z1
OK
)
However, as the precision of the secondary data declines,
Z1,2
OKVME
outperforms Z1,2
OK
by an increasing margin; it also
out-performs both Z1,2
CK
and Z1,2
MCCK
. Therefore in all of the σα
Z2
cases that were tested the following relationship holds:
σα
Z2>0 → CVAVR(Z,Z1,2
OKVME
) < CVAVR(Z, Z1,2
CK
)
< CVAVR(Z, Z1,2
MCCK
) < CVAVR(Z, Z1
OK
)
To further elucidate the OKVME technique, the
cumulative kriging weights allocated to each sample during
the OK and OKVME estimations were recorded. The mean
values for each σα
Z2 that was tested are shown in Figure 5.
Integration of imprecise and biased data into mineral resource estimates
The Journal of The Southern African Institute of Mining and Metallurgy VOLUME 115 JUNE 2015 527
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Figure 4 – Average coefficient of variation for each of the estimation approaches, with increasing standard deviation of measurement error associated
with the secondary samples in the unbiased cases
6. Integration of imprecise and biased data into mineral resource estimates
The figure firstly shows that in the Z1,2
OK
case the mean
cumulative OK weight that is applied to the secondary
samples exceeds that applied to the primary samples; this is
because the secondary samples are typically in closer
proximity to block centroids than the primary samples. As the
secondary samples are also more numerous than the primary
samples, they are clearly more influential in the OK
estimation.
The figure confirms that the OK weight is independent of
σα
Z2; this results in the rapidly increasing CVAVR(Z, Z1,2
OK
) with
increasing σα
Z2, as shown in Figure 4. Figure 5 also shows
that where no measurement error is associated with the
secondary samples, the OKVME weights converge on the OK
weights. As σα
Z2 increases the OKVME weights are rebalanced
in favour of the Z1 samples. In this case, where σα
Z2 is 0.5 or
greater the mean cumulative OKVME weight assigned to Z1
samples exceeds that assigned to the Z2 samples.
Given that in the case study Z2 samples are significantly
more numerous than Z1, a small decrease in the mean
cumulative weight applied to the former must be balanced by
a larger increase in the mean cumulative weight applied to
the latter, due to the requirement that the weights sum to
unity.
Analysis of imprecise and biased cases
The imprecise and biased Z2 data-sets were also integrated
into estimation through OK, CK, MCCK, and OKVME. Mean
estimated grades are compared against each other and the
ground truth mean in Figure 6.
The figure firstly shows that the base case Z1
OK
is
unbiased with respect to the ground truth. In the Z1,2
OK
,
estimate weights associated with the pooled Z1 and Z2
samples sum to unity; consequently bias associated with Z2
samples is directly transferred into the estimate in all σα
Z2
cases, as is shown in Figure 6. The Z1,2
OKVME
weights
associated with the pooled Z1 and Z2 samples also sum to
unity. However, because increasing weight is re-appropriated
from Z2 to Z1 samples as σα
Z2 increases, less bias is retained
within the estimate in the higher σα
Z2 cases compared to
Z1,2
OK
; this is also evident in Figure 6.
In the Z1,2
CK
and Z1,2
MCCK
estimations, Z1 sample weights
sum to unity and Z2 samples are zero-sum weighted. Figure
6 confirms that as a consequence the resulting estimations
are unbiased, regardless of the bias associated with Z2, and
regardless of σα
Z2. Consequently, CK or MCCK represent the
only viable options to integrate Z2 data that are imprecise and
biased. The positive and negative bias cases are coincident
for Z1,2
CK
and for Z1,2
MCCK
.
Conclusions
If precise, unbiased, and abundant secondary data are
available, their basic integration through OK of a pooled data-
set is pertinent (see Table I). The estimate is directly
improved compared to the base case (exclusion of the
secondary data) by reduction of the information effect.
However, abundant secondary data that are imprecise or
biased or both are often excluded from resource estimations
by practitioners, typically under an intuitive but untested
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528 JUNE 2015 VOLUME 115 The Journal of The Southern African Institute of Mining and Metallurgy
Figure 5 – Mean cumulative kriging weights in OKVME at increasing standard deviation of measurement error associated with secondary samples
7. assumption that inclusion will result in loss of estimation
precision or that the estimation may be biased, or both.
Experimentation outlined in this paper demonstrates that this
may be true if the secondary data are not handled
appropriately in the estimation; also that such a decision is
generally wasteful.
Where imprecise but unbiased secondary data are
available, it is recommended to integrate them into the
estimation using OKVME (see Table I). This provides an
improvement in estimation precision compared to the base
case and compared to OK of a pooled data-set. CK and MCCK
also provide some improvement in estimation precision
compared to the base case, but do not outperform OK of a
pooled data-set if abundant secondary data are relatively
precise, and never out-performed OKVME in the unbiased
cases that were tested.
If secondary data are associated with bias in addition to
imprecision, CK is recommended as the biased data are zero-
sum weighted (see Table I). CK consequently provides an
unbiased estimate but with some improvement in estimation
precision compared to the base case. MCCK suffers some loss
of estimation precision compared to CK where the secondary
data are relatively precise, but is similar to CK where the
secondary data are less precise.
Acknowledgements
The authors would like to sincerely thank Dr Michael Harley
of Anglo American, Scott Jackson of Anglo American, Dr John
Forkes (independent consultant), and John Vann of Anglo
American; their excellent comments and constructive criticism
of earlier versions of this paper significantly improved its
final content.
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Integration of imprecise and biased data into mineral resource estimates
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