Mechanical Engineering in Uncertainties From Classical Approaches to Some Recent Developments

6 Chapter 6Figure 6.1. Presentation of the AK family of methods (active learning and Krigin...Figure 6.2. Illustration of Kriging prediction with the function y = x sin(x) wit...Figure 6.3. Illustration of an example of the AK-MCS method with a single random...Figure 6.4. Illustration of the AK-MCS method with an example with two random va...Figure 6.5. Illustration of the AK-IS method with an example using two random va...Figure 6.6. Illustration of the AK-SYS method with a serial system using two com...Figure 6.7. Modified oblate spheroid performance function. Influence of interact...

7 Chapter 7Figure 7.1. Illustration of the uncertainty quantification methodology. For a co...Figure 7.2. Flowchart of the proposed methodology to compute | -indices under a ...Figure 7.3. Reference | -indices estimated for Example #1 under a single-level u...Figure 7.4. Reference | -indices estimated for Example #1 under a bi-level uncer...Figure 7.5. A roof truss Figure 7.6. Reference | -indices estimated for Example #2 under a single-level u...Figure 7.7. Reference | -indices estimated for Example #2 under a bi-level uncer...Figure 7.8. Illustration scheme of a launch vehicle first stage fallout phase in...Figure 7.9. | -indices estimated under single-level uncertainty (CMC of Nsim = 1...Figure 7.10. | -indices estimated under bi-level uncertainty (ARA/CMC of Nsim = ...

8 Chapter 8Figure 8.1. Example: calculation of a subdifferential of a convex function. For ...Figure 8.2. Approximation of the subdifferential of a non-convex function. For a...Figure 8.3. Example of dominance according to Pareto for a two-objective problem...Figure 8.4. Pareto fronts and dispersion due to uncertainties. For a color versi...Figure 8.5. Comparison of performance measures. For a color version of this figu...Figure 8.6. Comparison of performance measures. For a color version of this figu...Figure 8.7. Beam under study under compression Figure 8.8. Pareto front in the objective domain for the reliability problem. Fo...

1 Chapter 3Table 3.1. List of independent random parameters and distributions of the result...Table 3.2. List of independent random parameters and their distributions Table 3.3. Overall sensitivity analysis, as defined by Sobol’ (2001), applied to...

2 Chapter 4Table 4.1. Estimators of the Sobol’ indices calculated by polynomial chaos, the ...Table 4.2. Wing tip twist. Estimators of the Sobol’ indices calculated by polyno...

3 Chapter 5Table 5.1. Application of the standard Metropolis-Hasting sampler, construction ...Table 5.2. Application of the componentwise Metropolis sampler proposed by Au an...Table 5.3. Multilevel CE algorithm for rare-event probability estimation

4 Chapter 7Table 7.1. Overall strategy for the numerical tests of the proposed methodology Table 7.2. Input probabilistic model for Example #1 Table 7.3. Results for Example #1 Table 7.4. Results for Example #1 (★) Table 7.5. Input probabilistic model for Example #2 Table 7.6. Results for Example #2 Table 7.7. Input probabilistic model Table 7.8. Input probabilistic model under bi-level input uncertainty Table 7.9. Results for step #3

5 Chapter 8Table 8.1. Test problems (Huband et al. 2006) Table 8.2. Probabilistic uncertainty modeling

1 Cover

2 Table of Contents

3 Title Page SCIENCES Mechanics , Field Director – Gilles Pijaudier-Cabot Numerical Methods in Mechanics , Subject Head – Sylvain Drapier

4 Copyright First published 2021 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address: ISTE Ltd 27-37 St George’s Road London SW19 4EU UK www.iste.co.uk John Wiley & Sons, Inc. 111 River Street Hoboken, NJ 07030 USA www.wiley.com © ISTE Ltd 2021 The rights of Christian Gogu to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988. Library of Congress Control Number: 2020946721 British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British Library ISBN 978-1-78945-010-1 ERC code: PE1 Mathematics PE1_13 Probability PE1_14 Statistics PE8 Products and Processes Engineering PE8_3 Civil engineering, architecture, maritime/hydraulic engineering, geotechnics, waste treatment PE8_7 Mechanical and manufacturing engineering (shaping, mounting, joining, separation)

5 Foreword

6 Preface

7 Begin Reading

8 List of Authors

9 Index

10 End User License Agreement

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