Statistics for Spatial Data.

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.

Engineering Design via Surrogate Modelling: A Practical Guide

https://eprints.soton.ac.uk/65935/01/Forr_09.pdf

Recent advances in surrogate-based optimization

Engineering Design via Surrogate Modelling

One of the most exciting tools that have entered the material science toolbox in recent years is machine learning. This collection of statistical methods has already proved to be capable of considerably speeding up both fundamental and applied research. At present, we are witnessing an explosion of works that develop and apply machine learning to solid-state systems. We provide a comprehensive overview and analysis of the most recent research in this topic. As a starting point, we introduce machine learning principles, algorithms, descriptors, and databases in materials science. We continue with the description of different machine learning approaches for the discovery of stable materials and the prediction of their crystal structure. Then we discuss research in numerous quantitative structure–property relationships and various approaches for the replacement of first-principle methods by machine learning. We review how active learning and surrogate-based optimization can be applied to improve the rational design process and related examples of applications. Two major questions are always the interpretability of and the physical understanding gained from machine learning models. We consider therefore the different facets of interpretability and their importance in materials science. Finally, we propose solutions and future research paths for various challenges in computational materials science.

/pdf/recent-advances-and-applications-of-machine-learning-in-55gs85xsws.pdf

Recent advances and applications of machine learning in solid-state materials science

This study assessed the accuracy of marker-based kinematic analysis of the fingers, considering soft tissue artefacts (STA) and marker imaging uncertainty. We collected CT images of the hand from healthy volunteers with fingers in full extension, mid- and full-flexion, including motion capture markers. Bones and markers were segmented and meshed. The bone meshes for each volunteer's scans were aligned using the proximal phalanx to study the proximal interphalangeal joint (PIP), and using the middle phalanx to study the distal interphalangeal joint (DIP). The angle changes between positions were extracted. The HAWK protocol was used to calculate PIP and DIP joint flexion angles in each position based on the marker centroids. Finally the marker locations were 'corrected' relative to the underlying bones, and the flexion angles recalculated. Static and dynamic marker imaging uncertainty was evaluated using a wand. A strong positive correlation was observed between marker- and CT-based joint angle changes with 0.980 and 0.892 regression slopes for PIP and DIP, respectively, and Root Mean Squared Errors below 4°. Notably for the PIP joint, correlation was worsened by STA correction. The 95% imaging uncertainty interval was < ± 1° for joints, and < ± 0.25 mm for segment lengths. In summary, the HAWK marker set's accuracy was characterised for finger joint flexion angle changes in a small group of healthy individuals and static poses, and was found to benefit from skin movements during flexion.

/pdf/quantifying-soft-tissue-artefacts-and-imaging-variability-in-55e1k9jqua.pdf

Quantifying Soft Tissue Artefacts and Imaging Variability in Motion Capture of the Fingers

Two different methods of measuring the passive resistance of swimmers are used to compare system accuracy and repeatability. Method I uses a submerged glide tow, and Method II, a novel, simpler approach, is based on measuring deceleration during a submerged push-off glide. The comparison of each method is made for specific changes in passive resistance. A set of three male and three female swimmers compare the use of drag shorts to make swimmer-specific increases in drag. In a second study, the effect of hair removal is quantified on a single male swimmer (Method I 9.7% reduction and Method II 9.4% reduction). For five repeat tests, a 1.8% difference in resistance can be resolved with 95% and 70% confidence levels for the passive tow and push-off glide experiments, respectively

Repeatable techniques for assessing changes in passive swimming resistance

Exploring and Exploiting a Surrogate

Efficient human force transmission tailored for the individual cyclist

The design of wings with morphing capabilities is known to give aerodynamic benefits. These aero-dynamic benefits come from both the use of hinge-less surfaces and the greater adaptability to flight conditions. This paper describes the structural design of a twisting wing to be used for an unmanned air vehicle (UAV) and presents finite element analysis and experiment results. This is part of a research project carried out at the University of Southampton in which one of the goals is to compare different novel wing designs and technologies to determine which one of them gives the best performance. The twisting capability provides roll control without hinged surfaces hence providing aerodynamic improvement. The wing is manufactured using polystyrene foam and is cut out of block of this material using a hot wire machine. In order to link this foam structure to a main spar, ABS plastic inserts were manufactured using a 3D printer. The mechanisms used to actuate the wing are also made from this material. A full scale UAV wing has been manufactured and tested in order to compare with FEA results.

Alexander I. J. Forrester

Papers

Quantifying Soft Tissue Artefacts and Imaging Variability in Motion Capture of the Fingers

Repeatable techniques for assessing changes in passive swimming resistance

Exploring and Exploiting a Surrogate

Efficient human force transmission tailored for the individual cyclist

Design, analysis and experimental validation of a morphing UAV wing