A local adaptive sampling method for reliability-based design optimization using Kriging model

Chen, Zhenzhong; Qiu, Haobo; Gao, Liang; Li, Xiaoke; Li, Peigen

doi:10.1007/s00158-013-0988-4

Cited by 113 publications

(41 citation statements)

References 53 publications

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“…A metamodel is applied within RO or RBDO algorithms to reduce the computa-tional demands resulting from computationally complex models of engineering structures. Some of the commonly considered metamodels in structural reliability literature include: polynomial response surfaces (e.g., [8]), Kriging (e.g., [18,10,29]), Artificial Neural Networks (e.g., [41]) and Support Vector Machines (e.g., [3]). The majority of the proposed metamodel-based algorithms consider the RBDO formulation (e.g., [10,29]), while several approaches examine the RO formulation (e.g., [18,41]).…”

Section: Short Literature Reviewmentioning

confidence: 99%

“…Some of the commonly considered metamodels in structural reliability literature include: polynomial response surfaces (e.g., [8]), Kriging (e.g., [18,10,29]), Artificial Neural Networks (e.g., [41]) and Support Vector Machines (e.g., [3]). The majority of the proposed metamodel-based algorithms consider the RBDO formulation (e.g., [10,29]), while several approaches examine the RO formulation (e.g., [18,41]). Similar to the decoupling approaches with approximate reliability methods, the decoupling approaches for RBDO problems with sampling-based reliability methods attempt to approximate the probability of failure throughout the optimization process.…”

Section: Short Literature Reviewmentioning

confidence: 99%

“…8: end for 9:ĥ k ← arg min hRk (h) Estimate the optimal bandwith by minimizing the leave-one-out cross-validation score for the kth failure state. 10:…”

Section: Algorithm 2 Ce-ls For Unconstrained Romentioning

confidence: 99%

“…The CE-LS method is applied to an RBDO problem studied in [10], which features a deterministic objective function with deterministic and reliability constraints. The problem is selected to investigate the performance of the CE-LS algorithm on a classic RBDO problem and the implementation of deterministic and reliability constraints.…”

Section: Nonlinear Rbdo Problemmentioning

confidence: 99%

See 3 more Smart Citations

Coupling the cross-entropy with the line sampling method for risk-based design optimization

Depina

Papaioannou²,

Straub³

et al. 2016

Struct Multidisc Optim

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An algorithm for risk-based optimization (RO) of engineering systems is proposed, which couples the Cross-entropy (CE) optimization method with the Line Sampling (LS) reliability method. The CE-LS algorithm relies on the CE method to optimize the total cost of a system that is composed of the design and operation cost (e.g., production cost) and the expected failure cost (i.e., failure risk). Guided by the random search of the CE method, the algorithm proceeds iteratively to update a set of random search distributions such that the optimal or near-optimal solution is likely to occur. The LS-based failure probability estimates are required to evaluate the failure risk. Throughout the optimization process, the coupling relies on a local weighted average approximation of the probability of failure to reduce the computational demands associated with RO. As the CE-LS algorithm proceeds to locate a region of design parameters with near-optimal solutions, the local weighted average approximation of the probability of failure is refined. The adaptive refinement procedure is repeatedly applied until convergence criteria with respect to both the optimization and the approximation of the failure probability are satisfied. The performance of the proposed optimization heuristic is examined empiri- cally on several RO problems, including the design of a monopile foundation for offshore wind turbines.

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Section: Short Literature Reviewmentioning

confidence: 99%

Section: Short Literature Reviewmentioning

confidence: 99%

“…8: end for 9:ĥ k ← arg min hRk (h) Estimate the optimal bandwith by minimizing the leave-one-out cross-validation score for the kth failure state. 10:…”

Section: Algorithm 2 Ce-ls For Unconstrained Romentioning

confidence: 99%

Section: Nonlinear Rbdo Problemmentioning

confidence: 99%

See 2 more Smart Citations

Coupling the cross-entropy with the line sampling method for risk-based design optimization

Depina

Papaioannou²,

Straub³

et al. 2016

Struct Multidisc Optim

View full text Add to dashboard Cite

show abstract

“…For Kriging, linear weighted combination of the information of nearby points is also needed for predicting unknown points, which can be determined by minimizing the variance of the estimated value error, which means Kriging is also a best linear unbiased estimator problem [8]. Kriging surrogate model is simple and stable compared to other methods and has been widely used in many fields [9][10][11][12]. Some improved Kriging models have 2 Mathematical Problems in Engineering also been studied, such as Gradient-Enhanced Kriging [13], CoKriging [14], and Hierarchical Kriging [15].…”

Section: Introductionmentioning

confidence: 99%

Kernel Parameter Optimization for Kriging Based on Structural Risk Minimization Principle

Gong

2017

Mathematical Problems in Engineering

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An improved kernel parameter optimization method based on Structural Risk Minimization (SRM) principle is proposed to enhance the generalization ability of traditional Kriging surrogate model. This article first analyses the importance of the generalization ability as an assessment criteria of surrogate model from the perspective of statistics and proves the applicability to Kriging. Kernel parameter optimization method is used to improve the fitting precision of Kriging model. With the smoothness measure of the generalization ability and the anisotropy kernel function, the modified Kriging surrogate model and its analysis process are established. Several benchmarks are tested to verify the effectiveness of the modified method under two different sampling states: uniform distribution and nonuniform distribution. The results show that the proposed Kriging has better generalization ability and adaptability, especially for nonuniform distribution sampling.

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A new hybrid reliability‐based design optimization method under random and interval uncertainties

Zhang

Gao

Xiao

2020

Numerical Meth Engineering

Self Cite

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Summary This article proposes a new method for hybrid reliability‐based design optimization under random and interval uncertainties (HRBDO‐RI). In this method, Monte Carlo simulation (MCS) is employed to estimate the upper bound of failure probability, and stochastic sensitivity analysis (SSA) is extended to calculate the sensitivity information of failure probability in HRBDO‐RI. Due to a large number of samples involved in MCS and SSA, Kriging metamodels are constructed to substitute true constraints. To avoid unnecessary computational cost on Kriging metamodel construction, a new screening criterion based on the coefficient of variation of failure probability is developed to judge active constraints in HRBDO‐RI. Then a projection‐outline‐based active learning Kriging is achieved by sequentially select update points around the projection outlines on the limit‐state surfaces of active constraints. Furthermore, the prediction uncertainty of Kriging metamodel is quantified and considered in the termination of Kriging update. Several examples, including a piezoelectric energy harvester design, are presented to test the accuracy and efficiency of the proposed method for HRBDO‐RI.

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A local adaptive sampling method for reliability-based design optimization using Kriging model

Cited by 113 publications

References 53 publications

Coupling the cross-entropy with the line sampling method for risk-based design optimization

Coupling the cross-entropy with the line sampling method for risk-based design optimization

Kernel Parameter Optimization for Kriging Based on Structural Risk Minimization Principle

A new hybrid reliability‐based design optimization method under random and interval uncertainties

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