The modeling of extreme values is important to scientists in such  elds as hydrology, civil engineering, environmental science, oceanography and  nance. Stuart Coles’s book on the modeling of extreme values provides an introductory text on the topic. It is a modeling-oriented text with an emphasis on different types of data and analytical approaches. The book is laid out in nine chapters. Following introductory material and discussion of necessary theoretical background are chapters on approaches to extreme values that focus on the different types of data that might be used in an extreme value analysis. These include models for block maximums, threshold models, models for data from stationary and nonstationary processes, and approaches based on point processes. A chapter covers analysis of multivariate extremes, and the  nal chapter brie y covers such topics as Bayesian inference, Markov chains, and spatial extremes. Although this is not a data-driven text, it does contain numerous examples and analyses. These examples are used to illustrate the methodology; I would have preferred to see more motivation and interpretation of the results of the analyses. Datasets and S-PLUS programs for the analyses in the text are available at a website. These are easy to use for those slightly familiar with S-PLUS. The appendix describes the programs and illustrates how to access data and use the programs. It also gives links to sites that provide other software. The text does not include problem sets; these would have been useful, especially if the text is to be used in coursework. The text by Reiss and Thomas (2001) contains more thoroughly analyzed datasets, although it is twice the length and not as streamlined as the text under review. The book is meant for individuals with moderate statistical background. Those with coursework in maximum likelihood methods should have no dif culty reading and comprehending the text. Overall, this is a good text for someone getting started in extreme value methods.

Statistical Quality Control

Optimization for structural crashworthiness and energy absorption has become an important topic of research attributable to its proven benefits to public safety and social economy. This paper provides a comprehensive review of the important studies on design optimization for structural crashworthiness and energy absorption. First, the design criteria used in crashworthiness and energy absorption are reviewed and the surrogate modeling to evaluate these criteria is discussed. Second, multiobjective optimization, optimization under uncertainties and topology optimization are reviewed from concepts, algorithms to applications in relation to crashworthiness. Third, the crashworthy structures are summarized, from generically novel structural configurations to industrial applications. Finally, some conclusions and recommendations are provided to enable academia and industry to become more aware of the available capabilities and recent developments in design optimization for structural crashworthiness and energy absorption.

On design optimization for structural crashworthiness and its state of the art

Surrogate assisted global optimization is gaining popularity. Similarly, modern advances in computing power increasingly rely on parallelization rather than faster processors. This paper examines some of the methods used to take advantage of parallelization in surrogate based global optimization. A key issue focused on in this review is how different algorithms balance exploration and exploitation. Most of the papers surveyed are adaptive samplers that employ Gaussian Process or Kriging surrogates. These allow sophisticated approaches for balancing exploration and exploitation and even allow to develop algorithms with calculable rate of convergence as function of the number of parallel processors. In addition to optimization based on adaptive sampling, surrogate assisted parallel evolutionary algorithms are also surveyed. Beyond a review of the present state of the art, the paper also argues that methods that provide easy parallelization, like multiple parallel runs, or methods that rely on population of designs for diversity deserve more attention.

/pdf/parallel-surrogate-assisted-global-optimization-with-5bfsamfoyq.pdf

Parallel surrogate-assisted global optimization with expensive functions --- a survey

This paper proposes an efficient Kriging-based subset simulation (KSS) method for hybrid reliability analysis under random and interval variables (HRA-RI) with small failure probability. In this method, Kriging metamodel is employed to replace the true performance function, and it is smartly updated based on the samples in the first and last levels of subset simulation (SS). To achieve the smart update, a new update strategy is developed to search out samples located around the projection outlines on the limit-state surface. Meanwhile, the number of samples in each level of SS is adaptively adjusted according to the coefficients of variation of estimated failure probabilities. Besides, to quantify the Kriging metamodel uncertainty in the estimation of the upper and lower bounds of the small failure probability, two uncertainty functions are defined and the corresponding termination conditions are developed to control Kriging update. The performance of KSS is tested by four examples. Results indicate that KSS is accurate and efficient for HRA-RI with small failure probability.

An efficient Kriging-based subset simulation method for hybrid reliability analysis under random and interval variables with small failure probability

This paper presents a review of the state-of-the-art for digital twins in the application domain of engineering dynamics. The focus on applications in dynamics, is because: (i) they offer some of the most challenging aspects of creating an effective digital twin, and (ii) they are relevant to important industrial applications such as energy generation and transport systems. The history of the digital twin is discussed first, along with a review of the associated literature; the process of synthesising a digital twin is then considered, including definition of the aims and objectives of the digital twin. An example of the asset management phase for a wind turbine is included in order to demonstrate how the synthesis process might be applied in practice. In order to illustrate modelling issues arising in the construction of a digital twin, a detailed case study is presented, based on a physical twin which is a small-scale three-storey structure. This case study shows the progression towards a digital twin highlighting key processes including: system identification, data-augmented modelling and verification and validation. Finally, a discussion of some open research problems and technological challenges is given, including: workflow, joints, uncertainty management and the quantification of trust. In a companion paper, as part of this special issue, a mathematical framework for digital twin applications is developed, and together the authors believe this represents a firm framework for developing digital twin applications in the area of engineering dynamics.

/pdf/digital-twins-state-of-the-art-and-future-directions-for-3b77zvagal.pdf

Digital Twins: State-of-the-Art and Future Directions for Modeling and Simulation in Engineering Dynamics Applications

Robust design is an effective approach to design under uncertainty. Many works exist on mitigating the influence of parametric uncertainty associated with design or noise variables. However, simulation models are often computationally expensive and need to be replaced by metamodels created using limited samples. This introduces the so-called metamodeling uncertainty. Previous metamodel-based robust designs often treat a metamodel as the real model and ignore the influence of metamodeling uncertainty. In this study, we introduce a new uncertainty quantification method to evaluate the compound effect of both parametric uncertainty and metamodeling uncertainty. Then the new uncertainty quantification method is used for robust design. Simplified expressions of the response mean and variance is derived for a Kriging metamodel. Furthermore, the concept of robust design is extended for metamodel-based robust design accounting for both sources of uncertainty. To validate the benefits of our method, two mathematical examples without constraints are first illustrated. Results show that a robust design solution can be misleading without considering the metamodeling uncertainty. The proposed uncertainty quantification method for robust design is shown to be effective in mitigating the effect of metamodeling uncertainty, and the obtained solution is found to be more "robust" compared to the conventional approach. An automotive crashworthiness example, a highly expensive and non-linear problem, is used to illustrate the benefits of considering both sources of uncertainty in robust design with constraints. Results indicate that the proposed method can reduce the risk of constraint violation due to metamodel uncertainty and results in a "safer" robust solution.

Concurrent treatment of parametric uncertainty and metamodeling uncertainty in robust design

Use of support vector regression in structural optimization: Application to vehicle crashworthiness design

Metamodel-based robust design methods are commonly used to mitigate the influence of parametric uncertainty associated in sheet gauges and material properties in crashworthiness-based vehicle lightweight design. Since the crash performances are highly nonlinear and high-dimensional responses, the prediction error of metamodels inevitably introduces the so-called metamodeling uncertainty in robust design that may mislead to a wrong solution. In this article, a new robust design method considering both parametric uncertainty and metamodeling uncertainty is proposed in the autobody lightweight design problem. Six crash responses in side impact and roof crush are defined as the constraint responses. The results demonstrate that the proposed robust design method is superior to the conservative-surrogatebased robust design method. The final confirmed robust solution achieves 14.39% weight reduction. The method provides an efficient way to reduce the risk of constraint violation and avoids an over-conservative design due to metamodel uncertainty in crashworthiness-based lightweight design problems.

https://journals.sagepub.com/doi/pdf/10.1177/0954406212460824

Crashworthiness-based lightweight design problem via new robust design method considering two sources of uncertainties

Metamodelling techniques are widely used to approximate system responses of expensive simulation models. In association with the use of metamodels, objective-oriented sequential sampling methods have been demonstrated to be effective in balancing the need for searching an optimal solution versus reducing the metamodelling uncertainty. However, existing infilling criteria are developed for deterministic problems and restricted to one sampling point in one iteration. To exploit the use of multiple samples and identify the true robust solution in fewer iterations, a multi-point objective-oriented sequential sampling strategy is proposed for constrained robust design problems. In this article, earlier development of objective-oriented sequential sampling strategy for unconstrained robust design is first extended to constrained problems. Next, a double-loop multi-point sequential sampling strategy is developed. The proposed methods are validated using two mathematical examples followed by a highly nonlinear au...

Multi-point objective-oriented sequential sampling strategy for constrained robust design

The invention discloses an approximation model uncertainty state salon car body structure steady design method in the technical field of automobile manufacturing, based on parameter uncertainty of vehicle body design variable, and taking vehicle body performance to respond a Kriging model. The salon car body structure steady design method aims at overcoming the defects that at present, a vehicle steady design method just considers parameter uncertainty to obtain steady solving which easily generates big forecast error, and even generates failure constraints, vehicle body parameter uncertainty can be reduced, and approximation model uncertainty affects vehicle body structural performance. The salon car body structure steady design method improves accuracy of design scheme target performance of a vehicle body structure and effectiveness of restraint performance.

Siliang Zhang

Papers

Concurrent treatment of parametric uncertainty and metamodeling uncertainty in robust design

Use of support vector regression in structural optimization: Application to vehicle crashworthiness design

Crashworthiness-based lightweight design problem via new robust design method considering two sources of uncertainties

Multi-point objective-oriented sequential sampling strategy for constrained robust design

Vehicle body structure steady design method based two uncertain saloon cars