Fast Convergence Reliability-Based Design Optimization Method Considering Random and Evidence Variables

Cid, Clara; Baldomir, Aitor; Hernández, Santiago

doi:10.2514/1.j060953

Cited by 4 publications

(3 citation statements)

References 23 publications

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“…Although both methods are the most understandable way to address HRBDO problems, the high computational burden limits their application in engineering. Thus, the RIA-based and PMA-based nested optimization methods are often used to obtain the reference solution for solving HRBDO problems [3]- [8].…”

Section: Reliability Regionmentioning

confidence: 99%

“…Epistemic uncertainty comes from some level of ignorance or incomplete information and is typically quantified by interval variables, convex variables, evidence variables, etc. When both aleatory and epistemic uncertainties are considered in the engineering design, it is referred to as hybrid reliability-based design optimization (HRBDO) [3]- [8].…”

Section: Introductionmentioning

confidence: 99%

“…Tian et al [7] proposed an extended SORA method to address HRBDO including random variables with interval distribution parameters and the coexistence of random and interval variables. Cid et al [8] addressed HRBDO involving both random and evidence variables. To address HRBDO, the key issue is to improve efficiency without compromising accuracy.…”

Section: Introductionmentioning

confidence: 99%

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Kriging-Based Performance Measure Function Approximation Method for Hybrid Reliability-Based Design Optimization

et al. 2023

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Hybrid reliability-based design optimization (HRBDO) can provide an effective way to obtain the optimum design in the presence of both random and interval variables. HRBDO is typically described as a nested optimization model. It is computationally expensive when directly solving the HRBDO problem by the nested optimization method. To address this issue, this paper develops an efficient decoupled HRBDO method that aims at performance measure function approximation by the adaptive Kriging model (KPMFA). The proposed KPMFA method includes three main blocks, namely hybrid inverse reliability analysis, performance measure function approximation, and equivalent deterministic optimization. In KPMFA, the adaptation of the adaptive chaos control (ACC) algorithm for inverse reliability analysis that accommodates interval variables is developed. Moreover, an adaptive strategy with two-stage of enrichment for the Kriging model is developed to approximate performance measure functions on the region of interest. Then, the optimization can be proceeded using the Kriging model of performance measure functions. Finally, five illustrative HRBDO problems are investigated to demonstrate the accuracy and efficiency of the proposed KPMFA method.INDEX TERMS Hybrid reliability-based design optimization (HRBDO); random and interval variables; adaptive kriging model; performance measure function approximation

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Section: Reliability Regionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Kriging-Based Performance Measure Function Approximation Method for Hybrid Reliability-Based Design Optimization

et al. 2023

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A neural network copula function approach for solving joint basic probability assignment in structural reliability analysis

Yang,

Sun,

et al. 2024

Quality & Reliability Eng

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Applying evidence theory to structural reliability analysis under epistemic uncertainty, it is necessary to consider the correlation of evidence variables. Among them, solving the joint basic probability assignment (BPA) of the evidence variables is a crucial link. In this study, a solution method of joint BPA based on neural network copula function is proposed. This method is to automatically construct copula function through neural network, which avoids the process of selecting the optimal copula function. Firstly, the neural network copula function is constructed based on the sample set of evidence variables. Then, the expression for solving the joint BPA using the neural network copula function is derived through vectors. Furthermore, the expression is used to map the marginal BPA of evidence variables to joint BPA, thus realizing the solution of joint BPA. Finally, the effectiveness of this method is verified by three examples. The results show that the neural network copula function describes the data distribution better than the optimal copula function selected by the traditional method. In addition, there is actually an error in solving the reliability intervals using the traditional optimal copula function method, whereas the results of this paper's neural network copula function method are more accurate and better for decision making.

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Single-Loop Sampling for Estimating Failure-Probability Upper-Bound Function

Yan,

Lu,

Feng

et al. 2024

AIAA Journal

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Under random-interval mixed uncertainties of structures, failure-probability upper-bound function (FPUBF), which varies with the distribution parameters of random inputs, can not only provide the influence of distribution parameters on the failure-probability upper bound (FPUB), but also contribute to decoupling a reliability-based design optimization model. Although FPUBF can be estimated by repeatedly evaluating FPUBs at different distribution parameter realizations, it suffers from unaffordable computational cost resulting from this double-loop framework. To address this issue, this paper proposes a single-loop sampling strategy (SL) to estimate FPUBF at arbitrary realizations in the interested distribution parameter region. Instead of the huge computational cost of a double-loop framework, the SL estimates the entire FPUBF only by one simulation analysis. Moreover, importance sampling (IS) variance reduction technique is introduced, and a single-loop IS probability density function (PDF), or SL-IS-PDF, is constructed to more efficiently estimate FPUBF by reducing the required size of the candidate sample pool. For approximating the optimal SL-IS-PDF and identifying the states of candidate samples efficiently, the double-loop adaptive Kriging model of performance function is introduced to further reduce the number of performance function evaluations. A numerical example and two composite structure examples are employed to verify the accuracy, efficiency, and feasibility of the proposed methods.

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Fast Convergence Reliability-Based Design Optimization Method Considering Random and Evidence Variables

Cited by 4 publications

References 23 publications

Kriging-Based Performance Measure Function Approximation Method for Hybrid Reliability-Based Design Optimization

Kriging-Based Performance Measure Function Approximation Method for Hybrid Reliability-Based Design Optimization

A neural network copula function approach for solving joint basic probability assignment in structural reliability analysis

Single-Loop Sampling for Estimating Failure-Probability Upper-Bound Function

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