A probability feasible region enhanced important boundary sampling method for reliability-based design optimization
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RESEARCH PAPER
A probability feasible region enhanced important boundary sampling method for reliability-based design optimization Zihao Wu 1 & Zhenzhong Chen 1
&
Ge Chen 1 & Xiaoke Li 2 & Chen Jiang 3 & Xuehui Gan 1 & Liang Gao 3 & Shengze Wang 1
Received: 17 January 2020 / Revised: 22 June 2020 / Accepted: 23 July 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Reliability-based design optimization (RBDO) is powerful for probabilistic constraint problems. Metamodeling is usually used in RBDO to reduce the computational cost. Kriging model-based RBDO is very suitable to solve engineering problems with implicit constraint functions. However, the efficiency and accuracy of the kriging model constrain its use in RBDO. In this research, the importance boundary sampling (IBS) method is enhanced by the probability feasible region (PFR) method to fit kriging model with high accuracy. The proposed probability feasible region enhanced importance boundary sampling (PFREIBS) method selects sample points for inactive constraint functions only in its important region, thus reducing the number of sample points to improve the efficiency of sampling method. In order to verify the efficiency and accuracy of the proposed PFREIBS method, three RBDO problems are used in this paper. The comparison results with other sampling methods show that the proposed PFRE-IBS method is very efficient and accurate. Keywords RBDO . Kriging model . Importance boundary sampling . Probability feasible region
1 Introduction The RBDO methods handle uncertainties which are from industrial design or manufacturing, such as geometric size, material properties, operational uncertainties, environmental uncertainties, and numerical uncertainties. The RBDO problems are difficult to solve because the uncertainties are needed to be
evaluated. After decades of development, a lot of methods for RBDO have been proposed. RBDO usually has two parts: design optimization loop and reliability analysis loop. Based on the relationship between the two loops, these methods can be divided into three categories: double-loop strategy, singleloop strategy, and decoupled strategy. The double-loop strategy is computationally intensive with nested structure.
Highlights 1. In the proposed probability feasible region enhanced important boundary sampling (PFRE-IBS) method, sample points selected for the constraint functions are executed separately. PFRE-IBS method can build metamodel efficiently and accurately. 2. Probabilistic feasible region (PFR) method is used to solve reliabilitybased design optimization (RBDO) problems. PFR method can also classify functions and distinguish whether they are active or inactive. 3. PFRE-IBS method only selects sample points for active constraint functions. Responsible Editor: Byeng D Youn * Zhenzhong Chen [email protected] 1
College of Mechanical Engineering, Donghua University, 2999 Renmin Road North, Songjiang, Shanghai 201620, People’s Republic of China
2
Henan Key Laboratory of Mechanical Equipment In
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