A multi-constraint failure-pursuing sampling method for reliability-based design optimization using adaptive Kriging
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ORIGINAL ARTICLE
A multi-constraint failure-pursuing sampling method for reliabilitybased design optimization using adaptive Kriging Xiaoke Li1 • Xinyu Han1 • Zhenzhong Chen2 • Wuyi Ming1 • Yang Cao1 • Jun Ma1 Received: 19 May 2020 / Accepted: 28 July 2020 Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract Using surrogate models to substitute the computationally expensive limit state functions is a promising way to decrease the cost of implementing reliability-based design optimization (RBDO). To train the models efficiently, the active learning strategies have been intensively studied. However, the existing learning strategies either do not individually build the models according to importance measurement or do not completely relate to the reliability analysis results. Consequently, some points that are useless to refine the limit state functions or far away from the RBDO solutions are generated. This paper proposes a multi-constraint failure-pursuing sampling method to maximize the reward of adding new training points. A simultaneous learning strategy is employed to sequentially update the Kriging models with the points selected in the current approximate safe region. Moreover, the sensitive Kriging model as well as the sensitive sample point are identified based on the failure-pursuing scheme. A new point that is highly potential to improve the accuracy of reliability analysis and optimization can then be generated near the sensitive sample point and used to update the sensitive model. Besides, numerical examples and engineering application are used to validate the performance of the proposed method. Keywords Reliability-based design optimization Adaptive Kriging modeling Failure-pursuing sampling Simultaneous learning
1 Introduction Reliability-based design optimization (RBDO) is an effective tool to consider the various uncertainties in the initial design stage. The optimal solution of RBDO can achieve the balance between the performance and the reliability of a product. The formulation of RBDO is generally defined as [1–4]
& Jun Ma [email protected] 1
2
Henan Key Laboratory of Mechanical Equipment Intelligent Manufacturing, School of Mechanical and Electrical Engineering, Zhengzhou University of Light Industry, Zhengzhou 450002, China College of Mechanical Engineering, Donghua University, Shanghai 201620, China
Find lX Min f ðlX Þ S.t. Probðgc ðXÞ 0Þ Ptf ;c ; c ¼ 1; . . .; Nc lLX lX lU X ð1Þ where lX are the mean values of random design variables X, lLX and lU X are the lower and upper bounds of lX respectively. Due to the uncertainties that exists in X, the failure probability is used to measure the reliability of a certain design. In the probabilistic constraint, it is defined that the failure probability calculated by Prob(Þ should be smaller than the maximum allowable failure probability Ptf ;c . The failure event occurs when the limit state function (i.e. performance function) gc ðXÞ is smaller than or equal to zero.
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