Probability, Reliability and Statistical Methods in Engineering Design

LIF: A new Kriging based learning function and its application to structural reliability analysis

Reliability analysis of complex multi-state system with common cause failure based on evidential networks

An essential issue in surrogate model-based reliability analysis is the selection of training points. Approaches such as efficient global reliability analysis (EGRA) and adaptive Kriging Monte Carlo simulation (AK-MCS) methods have been developed to adaptively select training points that are close to the limit state. Both the learning functions and convergence criteria of selecting training points in EGRA and AK-MCS are defined from the perspective of individual responses at Monte Carlo samples. This causes two problems: (1) some extra training points are selected after the reliability estimate already satisfies the accuracy target; and (2) the selected training points may not be the optimal ones for reliability analysis. This paper proposes a Global Sensitivity Analysis enhanced Surrogate (GSAS) modeling method for reliability analysis. Both the convergence criterion and strategy of selecting new training points are defined from the perspective of reliability estimate instead of individual responses of MCS samples. The new training points are identified according to their contribution to the uncertainty in the reliability estimate based on global sensitivity analysis. The selection of new training points stops when the accuracy of the reliability estimate reaches a specific target. Five examples are used to assess the accuracy and efficiency of the proposed method. The results show that the efficiency and accuracy of the proposed method are better than those of EGRA and AK-MCS.

Global sensitivity analysis-enhanced surrogate (GSAS) modeling for reliability analysis

A novel projection outline based active learning method and its combination with Kriging metamodel for hybrid reliability analysis with random and interval variables

Hybrid reliability analysis (HRA) with both random and interval variables is investigated in this paper. Firstly, it is figured out that a surrogate model just rightly predicting the sign of performance function can meet the requirement of HRA in accuracy. According to this idea, a methodology based on active learning Kriging (ALK) model named ALK-HRA is proposed. When constructing the Kriging model, the presented method only finely approximates the performance function in the region of interest: the region where the sign tends to be wrongly predicted. Based on the constructed Kriging model, Monte Carlo Simulation (MCS) is carried out to estimate both the lower and upper bounds of failure probability. ALK-HRA is accurate enough with calling the performance function as few times as possible. Four numerical examples and one engineering application are investigated to demonstrate the performance of the proposed method.

An active learning kriging model for hybrid reliability analysis with both random and interval variables

An efficient reliability method combining adaptive importance sampling and Kriging metamodel

Surrogate models are used to dramatically improve the design efficiency of numerical aerodynamic shape optimization, where high-fidelity, expensive computational fluid dynamics (CFD) is often employed. Traditionally, in adaptation, only one single sample point is chosen to update the surrogate model during each updating cycle, after the initial surrogate model is built. To enable the selection of multiple new samples at each updating cycle, a few parallel infilling strategies have been developed in recent years, in order to reduce the optimization wall clock time. In this article, an alternative parallel infilling strategy for surrogate-based constrained optimization is presented and demonstrated by the aerodynamic shape optimization of transonic wings. Different from existing methods in which multiple sample points are chosen by a single infill criterion, this article uses a combination of multiple infill criteria, with each criterion choosing a different sample point. Constrained drag minimizations of the ONERA-M6 and DLR-F4 wings are exercised to demonstrate the proposed method, including low-dimensional (6 design variables) and higher-dimensional problems (up to 48 design variables). The results show that, for surrogate-based optimization of transonic wings, the proposed method is more effective than the existing parallel infilling strategies, when the number of initial sample points are in the range from Nv to 8Nv (Nv here denotes the number of design variables). Each case is repeated 50 times to eliminate the effect of randomness in our results.

Efficient aerodynamic shape optimization of transonic wings using a parallel infilling strategy and surrogate models

Probability and convex set hybrid reliability analysis based on active learning Kriging model

Hybrid reliability analysis (HRA) with both aleatory and epistemic uncertainties is investigated in this paper. The aleatory uncertainties are described by random variables, and the epistemic uncertainties are described by a probability-box (p-box) model. Although tremendous efforts have been devoted to propagating random or p-box uncertainties, much less attention has been paid to analyzing the hybrid reliability with both of them. For HRA, optimization-based Interval Monte Carlo Simulation (OIMCS) is available to estimate the bounds of failure probability, but it requires enormous computational performance. A new method combining the Kriging model with OIMCS is proposed in this paper. When constructing the Kriging model, we only locally approximate the performance function in the region where the sign is prone to be wrongly predicted. It is based on the idea that a surrogate model only exactly predicting the sign of performance function could satisfy the demand of accuracy for HRA. Then OIMCS can be effectively performed based on the Kriging model. Three numerical examples and an engineering application are investigated to demonstrate the performance of the proposed method.

Yishang Zhang

Papers

An active learning kriging model for hybrid reliability analysis with both random and interval variables

An efficient reliability method combining adaptive importance sampling and Kriging metamodel

Efficient aerodynamic shape optimization of transonic wings using a parallel infilling strategy and surrogate models

Probability and convex set hybrid reliability analysis based on active learning Kriging model

Hybrid reliability analysis with both random and probability-box variables