Component and system reliability-based design optimization under multiple simulation models

Abstract

Complex engineering systems have various types of uncertainties due to manufacturing environment conditions, distribution of material properties, and complex connections between systems. To account for the uncertainties, reliability-based design optimization (RBDO) and system reliability-based design optimization (SRBDO) have been studied and are widely applied to numerous mechanical systems. RBDO/SRBDO calculates the failure probability by reliability analysis with a distribution of random variables and optimizes the design variables under some constraints. In the early periods, analytical methods which approximate performance functions to analytic functions were widely researched. However, the estimated failure probability derived from these methods is inaccurate due to reliability estimation error. Thus, sampling-based reliability analysis methods which utilize Monte Carlo simulation (MCS) or importance sampling (IS) have been researched based on the surrogate model. Especially, active learning Kriging methods are widely utilized for updating the surrogate model efficiently and accurately. Some strategies have been proposed to apply the active learning method to RBDO/SRBDO by integrating sampling and optimization skills. However, there has not been a method to resolve general cases when performance functions can be obtained from different simulation models. To resolve this problem, new active learning strategies for RBDO and SRBDO problems under multiple simulation models are proposed. In the proposed RBDO method, a new active learning function is derived by predicting the change in the reliability of active constraints after adding a point to the sample points of performance functions included in each simulation model. For the derivation, a concept of the activity function is proposed to find how the performance function is active. Different from the RBDO method, the proposed SRBDO method derives another active learning function according to the system type. In addition to these active learning functions, a new active learning function which considers the cost of each simulation model is also proposed. With proposed active learning functions, the Kriging model is sequentially updated by adding the optimal sample point to the train points of performance functions included in the critical simulation model, which have the maximum value of the learning function. The accuracy of the Kriging model and RBDO/SRBDO optimum convergence are utilized as the stop criteria. The proposed methods are applied to numerical and real engineering examples, and the validation results show that the proposed method is efficient and accurate in finding the RBDO/SRBDO optimum under multiple simulation models.