# A dual surrogate driven L-moments based robust design with scarce samples in the presence of extremes

About: This article is published in Structural and Multidisciplinary Optimization.The article was published on 2022-02-08. It has received 2 citations till now. The article focuses on the topics: Surrogate model & Measure (data warehouse).

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IBM

^{1}TL;DR: The authors define L-moments as the expectations of certain linear combinations of order statistics, which can be defined for any random variable whose mean exists and form the basis of a general theory which covers the summarization and description of theoretical probability distributions.

Abstract: L-moments are expectations of certain linear combinations of order statistics. They can be defined for any random variable whose mean exists and form the basis of a general theory which covers the summarization and description of theoretical probability distributions, the summarization and description of observed data samples, estimation of parameters and quantiles of probability distributions, and hypothesis tests for probability distributions. The theory involves such established procedures as the use of order statistics and Gini's mean difference statistic, and gives rise to some promising innovations such as the measures of skewness and kurtosis and new methods of parameter estimation

2,668 citations

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TL;DR: In this paper, the application of the lognormal curve to the frequency distribution of gold values is discussed, and some fundamental concepts in application of statistics to mine valuation on the Witwatersrand are discussed.

Abstract: Certain fundamental concepts in the application of statistics to mine valuation on the Witwatersrand are discussed, and general conclusions are drawn regarding the application of the lognormal curve to the frequency distribution of gold values An indication is given of the reliability of present valuation methods on the Rand It is shown that the existing over- and under-valuation of blocks of ore listed as high-grade and low-grade, respectively, can be explained statistically Suggestions are made for the elimination of such errors and for the improvement of the general standard of mine valuation by the use of statistical theory

2,353 citations

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IBM

^{1}TL;DR: In this paper, the authors present a regional L-moments algorithm for detecting homogeneous regions in a set of homogeneous data points and then select a frequency distribution for each region.

Abstract: Preface 1. Regional frequency analysis 2. L-moments 3. Screening the data 4. Identification of homogeneous regions 5. Choice of a frequency distribution 6. Estimation of the frequency distribution 7. Performance of the regional L-moment algorithm 8. Other topics 9. Examples Appendix References Index of notation.

2,329 citations

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18 Jul 2008

TL;DR: In this article, the authors propose a sampling approach to estimate the distribution of elementary effects and then use this information to construct a kriging model of the data set, which is then used for regression.

Abstract: Preface. About the Authors. Foreword. Prologue. Part I: Fundamentals. 1. Sampling Plans. 1.1 The 'Curse of Dimensionality' and How to Avoid It. 1.2 Physical versus Computational Experiments. 1.3 Designing Preliminary Experiments (Screening). 1.3.1 Estimating the Distribution of Elementary Effects. 1.4 Designing a Sampling Plan. 1.4.1 Stratification. 1.4.2 Latin Squares and Random Latin Hypercubes. 1.4.3 Space-filling Latin Hypercubes. 1.4.4 Space-filling Subsets. 1.5 A Note on Harmonic Responses. 1.6 Some Pointers for Further Reading. References. 2. Constructing a Surrogate. 2.1 The Modelling Process. 2.1.1 Stage One: Preparing the Data and Choosing a Modelling Approach. 2.1.2 Stage Two: Parameter Estimation and Training. 2.1.3 Stage Three: Model Testing. 2.2 Polynomial Models. 2.2.1 Example One: Aerofoil Drag. 2.2.2 Example Two: a Multimodal Testcase. 2.2.3 What About the k -variable Case? 2.3 Radial Basis Function Models. 2.3.1 Fitting Noise-Free Data. 2.3.2 Radial Basis Function Models of Noisy Data. 2.4 Kriging. 2.4.1 Building the Kriging Model. 2.4.2 Kriging Prediction. 2.5 Support Vector Regression. 2.5.1 The Support Vector Predictor. 2.5.2 The Kernel Trick. 2.5.3 Finding the Support Vectors. 2.5.4 Finding . 2.5.5 Choosing C and epsilon. 2.5.6 Computing epsilon : v -SVR 71. 2.6 The Big(ger) Picture. References. 3. Exploring and Exploiting a Surrogate. 3.1 Searching the Surrogate. 3.2 Infill Criteria. 3.2.1 Prediction Based Exploitation. 3.2.2 Error Based Exploration. 3.2.3 Balanced Exploitation and Exploration. 3.2.4 Conditional Likelihood Approaches. 3.2.5 Other Methods. 3.3 Managing a Surrogate Based Optimization Process. 3.3.1 Which Surrogate for What Use? 3.3.2 How Many Sample Plan and Infill Points? 3.3.3 Convergence Criteria. 3.3.4 Search of the Vibration Isolator Geometry Feasibility Using Kriging Goal Seeking. References. Part II: Advanced Concepts. 4. Visualization. 4.1 Matrices of Contour Plots. 4.2 Nested Dimensions. Reference. 5. Constraints. 5.1 Satisfaction of Constraints by Construction. 5.2 Penalty Functions. 5.3 Example Constrained Problem. 5.3.1 Using a Kriging Model of the Constraint Function. 5.3.2 Using a Kriging Model of the Objective Function. 5.4 Expected Improvement Based Approaches. 5.4.1 Expected Improvement With Simple Penalty Function. 5.4.2 Constrained Expected Improvement. 5.5 Missing Data. 5.5.1 Imputing Data for Infeasible Designs. 5.6 Design of a Helical Compression Spring Using Constrained Expected Improvement. 5.7 Summary. References. 6. Infill Criteria With Noisy Data. 6.1 Regressing Kriging. 6.2 Searching the Regression Model. 6.2.1 Re-Interpolation. 6.2.2 Re-Interpolation With Conditional Likelihood Approaches. 6.3 A Note on Matrix Ill-Conditioning. 6.4 Summary. References. 7. Exploiting Gradient Information. 7.1 Obtaining Gradients. 7.1.1 Finite Differencing. 7.1.2 Complex Step Approximation. 7.1.3 Adjoint Methods and Algorithmic Differentiation. 7.2 Gradient-enhanced Modelling. 7.3 Hessian-enhanced Modelling. 7.4 Summary. References. 8. Multi-fidelity Analysis. 8.1 Co-Kriging. 8.2 One-variable Demonstration. 8.3 Choosing X c and X e . 8.4 Summary. References. 9. Multiple Design Objectives. 9.1 Pareto Optimization. 9.2 Multi-objective Expected Improvement. 9.3 Design of the Nowacki Cantilever Beam Using Multi-objective, Constrained Expected Improvement. 9.4 Design of a Helical Compression Spring Using Multi-objective, Constrained Expected Improvement. 9.5 Summary. References. Appendix: Example Problems. A.1 One-Variable Test Function. A.2 Branin Test Function. A.3 Aerofoil Design. A.4 The Nowacki Beam. A.5 Multi-objective, Constrained Optimal Design of a Helical Compression Spring. A.6 Novel Passive Vibration Isolator Feasibility. References. Index.

1,447 citations

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TL;DR: A survey of recent publications in the field of aerospace where interest in MDO has been particularly intense is presented, focused on the interaction of the structures discipline with other disciplines.

Abstract: The increasing complexity of engineering systems has sparked increasing interest in multidisciplinary optimization (MDO). This paper presents a survey of recent publications in the field of aerospace where interest in MDO has been particularly intense. The two main challenges of MDO are computational expense and organizational complexity. Accordingly the survey is focused on various ways different researchers use to deal with these challenges. The survey is organized by a breakdown of MDO into its conceptual components. Accordingly, the survey includes sections on Mathematical Modeling, Design- oriented Analysis, Approximation Concepts, Optimization Procedures, System Sensitivity, and Human Interface. With the authors'' main expertise being in the structures area, the bulk of the references focus on the interaction of the structures discipline with other disciplines. In particular, two sections at the end focus on two such interactions that have recently been pursued with a particular vigor: Simultaneous Optimization of Structures and Aerodynamics, and Simultaneous Optimization of Structures Combined With Active Control.

1,049 citations