Evidence-Theory-Based Reliability Analysis Through Kriging Surrogate Model

2021 ◽  
Vol 144 (3) ◽  
Author(s):  
Dequan Zhang ◽  
Yunfei Liang ◽  
Lixiong Cao ◽  
Jie Liu ◽  
Xu Han
Keyword(s):  
Active Learning ◽  
Reliability Analysis ◽  
Surrogate Model ◽  
Evidence Theory ◽  
Kriging Model ◽  
High Approximation ◽  
Analysis Method ◽  
Performance Function ◽  
Intersection Points ◽  
Sample Points

Abstract It is generally understood that intractable computational intensity stemming from repeatedly calling performance function when evaluating the contribution of joint focal elements hinders the application of evidence theory in practical engineering. In order to promote the practicability of evidence theory for the reliability evaluation of engineering structures, an efficient reliability analysis method based on the active learning Kriging model is proposed in this study. To start with, a basic variable is selected according to basic probability assignment (BPA) of evidence variables to divide the evidence space into sub-evidence spaces. Intersection points between the performance function and the sub-evidence spaces are then determined by solving the univariate root-finding problem. Sample points are randomly identified to enhance the accuracy of the subsequently established surrogate model. Initial Kriging model with high approximation accuracy is subsequently established through these intersection points and additional sample points generated by Latin hypercube sampling. An active learning function is employed to sequentially refine the Kriging model with minimal sample points. As a result, belief (Bel) measure and plausibility (Pl) measure are derived efficiently via the surrogate model in the evidence-theory-based reliability analysis. The currently proposed analysis method is exemplified with three numerical examples to demonstrate the efficiency and is applied to reliability analysis of positioning accuracy for an industrial robot.

scholarly journals A High-Dimensional Reliability Analysis Method for Simulation-Based Design Under Uncertainty

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Mohammad Kazem Sadoughi ◽  
Meng Li ◽  
Chao Hu ◽  
Cameron A. MacKenzie ◽  
Soobum Lee ◽  
...  
Keyword(s):  
Reliability Analysis ◽  
Surrogate Model ◽  
Efficient Estimation ◽  
High Dimensional ◽  
Design Under Uncertainty ◽  
Performance Function ◽  
Simulation Based Design ◽  
Simulation Based ◽  
Computationally Expensive ◽  
Sample Points

Reliability analysis involving high-dimensional, computationally expensive, highly nonlinear performance functions is a notoriously challenging problem in simulation-based design under uncertainty. In this paper, we tackle this problem by proposing a new method, high-dimensional reliability analysis (HDRA), in which a surrogate model is built to approximate a performance function that is high dimensional, computationally expensive, implicit, and unknown to the user. HDRA first employs the adaptive univariate dimension reduction (AUDR) method to construct a global surrogate model by adaptively tracking the important dimensions or regions. Then, the sequential exploration–exploitation with dynamic trade-off (SEEDT) method is utilized to locally refine the surrogate model by identifying additional sample points that are close to the critical region (i.e., the limit-state function (LSF)) with high prediction uncertainty. The HDRA method has three advantages: (i) alleviating the curse of dimensionality and adaptively detecting important dimensions; (ii) capturing the interactive effects among variables on the performance function; and (iii) flexibility in choosing the locations of sample points. The performance of the proposed method is tested through three mathematical examples and a real world problem, the results of which suggest that the method can achieve an accurate and computationally efficient estimation of reliability even when the performance function exhibits high dimensionality, high nonlinearity, and strong interactions among variables.

scholarly journals A reliability analysis method for earthquake resistance of large complex building structure

2021 ◽  
Vol 39 (1) ◽  
pp. 55-61
Author(s):  
Yanjie Xiao ◽  
Xun'an Zhang ◽  
Ronggang Xue
Keyword(s):  
Reliability Analysis ◽  
Surrogate Model ◽  
Simulation Analysis ◽  
Seismic Action ◽  
Building Structures ◽  
Analysis Method ◽  
Performance Function ◽  
Seismic Reliability ◽  
Reliability Calculation ◽  
Complex Building

The seismic reliability calculation of complex building structures requires a lot of simulation analysis and therefore the calculation cost is high. Fitting performance function with surrogate model can improve computational efficiency, but how to ensure the calculation accuracy while improving the reliability analysis efficiency of the engineering structure is a problem worthy of study. This paper proposes a Kriging-based reliability analysis method, which establishes the Kriging surrogate model with fewer calculations of the performance function, improves the accuracy of the surrogate model of performance function by infill-sampling, and obtains the approximate failure probability combined with Monte Carlo simulation. Two numerical examples are analyzed; the results show that this method is efficient and accurate. The method is applied to the seismic reliability calculation of mega-sub controlled structural system, in which the randomness of structure and seismic action is considered. The application results show that it is an effective method for reliability analysis of complex building structures.

High-Dimensional Reliability Analysis of Engineered Systems Involving Computationally Expensive Black-Box Simulations

2017 ◽  
Author(s):  
Mohammad Kazem Sadoughi ◽  
Meng Li ◽  
Chao Hu ◽  
Cameron A. Mackenzie
Keyword(s):  
Reliability Analysis ◽  
Surrogate Model ◽  
Limit State ◽  
Efficient Estimation ◽  
High Dimensional ◽  
State Function ◽  
Performance Function ◽  
Highly Nonlinear ◽  
Computationally Expensive ◽  
Sample Points

Reliability analysis involving high-dimensional, computationally expensive, highly nonlinear performance functions is a notoriously challenging problem. In this paper, we tackle this problem by proposing a new method, high-dimensional reliability analysis (HDRA), in which a surrogate model is built to approximate a performance function that is high dimensional, computationally expensive, implicit and unknown to the user. HDRA first employs the adaptive univariate dimension reduction (AUDR) method to build a global surrogate model by adaptively tracking the important dimensions or regions. Then, the sequential exploration-exploitation with dynamic trade-off (SEEDT) method is utilized to locally refine the surrogate model by identifying additional sample points that are close to the critical region (i.e., the limit-state function) with high prediction uncertainty. The HDRA method has three advantages: (i) alleviating the curse of dimensionality and adaptively detecting important dimensions; (ii) capturing the interactive effects among variables on the performance function; and (iii) flexibility in choosing the locations of sample points. The performance of the proposed method is tested through two mathematical examples, the results of which suggest that the method can achieve accurate and computationally efficient estimation of reliability even when the performance function exhibits high dimensionality, high nonlinearity, and strong interactions among variables.

Sign in / Sign up

Export Citation Format

Share Document