Reliability-based design optimization using SORM and SQP

Strömberg, Niclas

doi:10.1007/s00158-017-1679-3

Cited by 20 publications

(6 citation statements)

References 42 publications

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“…To deal with high curvatures of the limit-state surfaces, one approach has been the introduction of the second-order reliability method (SORM). This was already discussed in Shetty et al (1998), while more recently Strömberg (2017) proposed coupling SORM and sequential quadratic programming (SQP). The MPP-based dimension reduction method (Rahman and Xu, 2004) has also been used to improve the accuracy of failure probability estimates w.r.t.…”

Section: Use Of Advanced Techniques and Simulation In Rbdomentioning

confidence: 97%

Surrogate-assisted reliability-based design optimization: a survey and a unified modular framework

Moustapha

Sudret

2019

Struct Multidisc Optim

140

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Reliability-based design optimization (RBDO) is an active field of research with an ever increasing number of contributions. Numerous methods have been proposed for the solution of RBDO, a complex problem that combines optimization and reliability analysis. Classical approaches are based on approximation methods and have been classified in review papers. In this paper, we first review classical approaches based on approximation methods such as FORM, and also more recent methods that rely upon surrogate modelling and Monte Carlo simulation.We then propose a general framework for the solution of RBDO problems that includes three independent blocks, namely adaptive surrogate modelling, reliability analysis and optimization.These blocks are non-intrusive with respect to each other and can be plugged independently in the framework. After a discussion on numerical considerations that require attention for the framework to yield robust solutions to various types of problems, the latter is applied to three examples (using two analytical functions and a finite element model). Kriging and support vector machines together with their own active learning schemes are considered in the surrogate model block. In terms of reliability analysis, the proposed framework is illustrated using both crude Monte Carlo and subset simulation. Finally, the covariance-matrix adaptation -evolution scheme (CMA-ES), a global search algorithm, or sequential quadratic programming (SQP), a local gradient-based method, are used in the optimization block. The comparison of the results to benchmark studies show the effectiveness and efficiency of the proposed framework. of risk-based or life-cycle cost optimization (Beck and Gomes, 2012;Frangopol and Maute, 2003).Alternative formulations for RBDO have henceforth emerged. One, for instance, consists in maximizing the reliability, or equivalently minimizing the failure probability, under given cost constraints (See for instance Kuschel and Rackwitz (1997); Royset et al. (2001); Taflanidis and Beck (2008)).The approach we consider in this paper, which is also the prevalent in current research, consists in minimizing an initial cost under some probabilistic constraints (Hilton and Feigen, 1960). Let d ∈ R M d be an M d −dimensional vector defining some design parameters of the structure. In the presence of uncertainties, the variability of these parameters can be described by introducing random variables X ∈ X ⊂ R M d ∼ f X|d . These variables are called design parameters with uncertainty, or by slight abuse, random design variables in the sequel. In some cases, design parameters are purely deterministic. To simplify the notation, they are equally considered as X (d) at this stage, where the related random variables would simply have a

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Section: Use Of Advanced Techniques and Simulation In Rbdomentioning

confidence: 97%

Surrogate-assisted reliability-based design optimization: a survey and a unified modular framework

Moustapha

Sudret

2019

Struct Multidisc Optim

140

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“…Recently, a FORM-based SQP approach for RBDO with SORM and MC corrections was proposed in [12]. For non-Gaussian variables, we derive the following FORM-based QPproblem in the standard normal space:…”

Section: Sqp-based Rbdo Approachmentioning

confidence: 99%

“…But, in this work, we do not adapt the approach of affine combinations of metamodels, instead we suggest to use convex combinations of metamodels for robust treatment of the limit state surface. The optimal ensembles of metamodels are then used to set up RBDO problems which we solve by using the FORM-based sequential quadratic programming (SQP) approach presented by Strömberg [12].…”

Section: Introductionmentioning

confidence: 99%

Reliability-Based Design Optimization by Using Ensemble of Metamodels

Strömberg¹

2019

Proceedings of the 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

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The standard approach when establishing optimal ensembles of metamodels (OEM) is to apply affine combinations of metamodels. However, we have found when performing reliability-based design optimization (RBDO) that this choice might sometimes result in poor representation of the limit state surfaces. Therefore, in this work, we suggest to use convex combinations instead of affine combinations in order to get robust RBDO by using OEM. Optimal convex combinations of metamodels are established by minimizing the taxicab, Euclidean or infinity norm of the PRESS vector. The PRESS vector is defined by the leave-one-out crossvalidation errors of a linear combination of ten metamodels, which constitute different settings of quadratic regression, Kriging, radial basis functions, polynomial chaos and support vector regression. Thus, the minimization of the norms are constrained such that the sum of weights of the linear combination equals one and only non-negative weights are allowed. We have found that the latter constraints might be extremely important when the ensembles of metamodels represent the limit surfaces. The most probable point (MPP) of the OEM is established in the physical space where the distance is minimized in the metric of Hasofer-Lind. The solution to the corresponding Karush-Kuhn-Tucker conditions is obtained by using Newton's method with an inexact Jacobian and a line-search of Armijo type. At the MPP, we perform Taylor expansions of the OEM using intermediate variables defined by the iso-probabilistic transformation. In such manner, we derive a quadratic programming (QP) problem which is solved in the standard normal space. This is done for several probability distributions such as e.g. lognormal, Gumbel, gamma and Weibull. The optimal solution to the QP problem is mapped back to the physical space and new Taylor expansions of the OEM are derived and a new QP problem is formulated and solved. This procedure continues in sequence until we obtain convergence of our RBDO problem. The steps presented above constitute our proposed FORM-based sequential QP approach for RBDO by using OEM. The implementation of the approach in an in-house toolbox is very robust and efficient.

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“…However, the proposed solution is applicable for the stationary stochastic process. In addition, Stromberg [10] is also proposed a deterministic solution using second order approach in the reliability-based design optimization for non-Gaussian variables in a sequential quadratic programming. The proposed solution is tested on the benchmark problems and demonstrated very good performance with higher number of stochastic variables and constraints.…”

Section: Introductionmentioning

confidence: 99%

An Enhancement of the NSGA-II Reliability Optimization Using Extended Kalman Filter Based Initialization

Yuce

2021

Advances in Intelligent Systems and Computing

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The real-life design and engineering problems are multi-objective and nonlinear problems that also contain high level uncertainty. Finding the optimal solution for uncertain problems is a huge challenge, because of the uncertainty. These uncertain variables can be satisfied with reliable boundary conditions. In literature, there are several reliability-based optimization methods using moments methods which are mainly approximated approaches using the first-order Taylor expansion in the limit state function. These methods are easy to integrate with the performance measurement (objective) functions to determine reliable and optimal solutions. In this study, a novel reliability-based design optimization approach is proposed using FORM and SORM based reliability methods for a real-life engineering and safety problem (car side impact and deflection problem) and other benchmark functions. The optimization engine is a Kalman filter based enhanced evolutionary optimization algorithm (NSGA-II). Since the basic Kalman filter is suitable to minimize the noise in linear type problems, they are efficient solutions for nonlinear problems. In this study, an extended Kalman filter-based approach is utilized with evolutionary algorithm to obtain a better solution set at the initialization stage. The performances of the proposed algorithms are assessed using hypervolume indicator approach for the basic NSGA-II, FORM and SORM based reliability added NSGA-II, basic NSGA-II with extended Kalman filter (EKF); and FORM and SORM based reliability added NSGA-II with EKF. According to the hypervolume indicator results, EKF filter performed better with reliability-based NSGA-II.

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Reliability-based design optimization using SORM and SQP

Cited by 20 publications

References 42 publications

Surrogate-assisted reliability-based design optimization: a survey and a unified modular framework

Surrogate-assisted reliability-based design optimization: a survey and a unified modular framework

Reliability-Based Design Optimization by Using Ensemble of Metamodels

An Enhancement of the NSGA-II Reliability Optimization Using Extended Kalman Filter Based Initialization

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