Reliability analysis of geotechnical engineering problems based on an RBF metamodeling technique

2014 ◽  
pp. 297-300 ◽  
Author(s):  
Q Wang ◽  
J Lin ◽  
J Ji ◽  
H Fang
Keyword(s):  
Reliability Analysis ◽  
Geotechnical Engineering ◽  
Engineering Problems ◽  
Metamodeling Technique

AN ENGINEERING RELIABILITY ANALYSIS METHOD BASED ON ADAPTIVE METAMODELS

2019 ◽  
Vol 6 (1) ◽  
Author(s):  
Qian Wang ◽  
Erica Jarosch ◽  
Hongbing Fang
Keyword(s):  
Reliability Analysis ◽  
Fe Method ◽  
Performance Function ◽  
Design Point ◽  
Reliability Method ◽  
Engineering Problems ◽  
Practical Engineering ◽  
Metamodeling Technique ◽  
Gradient Based ◽  
Adaptive Metamodeling

In practical engineering problems, numerical analyses using the finite element (FE) method or other methods are generally required to evaluate system responses including stresses and deformations. For problems involving expensive FE analyses, it is not efficient or straightforward to directly apply conventional sampling-based or gradient-based reliability analysis approaches. To reduce computational efforts, it is useful to develop efficient and accurate metamodeling techniques to replace the original FE analyses. In this work, an adaptive metamodeling technique and a First-Order Reliability Method (FORM) were integrated. In each adaptive iteration, a compactly supported radial basis function (RBF) was adopted and a metamodel was created to explicitly express a performance function. An alternate FORM was implemented to calculate reliability index of the current iteration. Based on the design point, additional samples were generated and added to the existing sample points to re-generate the metamodel. The accuracy of the RBF metamodel could be improved in the neighborhood of the design point at each iteration. This procedure continued until the convergence of the reliability analysis results was achieved. A numerical example was studied. The proposed adaptive approach worked well and reliability analysis results were found with a reasonable number of iterations.

ENGINEERING PROBABILISTIC ANALYSIS USING MODEL REDUCTION AND AUGMENTED RADIAL BASIS FUNCTIONS

2020 ◽  
Vol 7 (2) ◽  
Author(s):  
Qian Wang
Keyword(s):  
Model Reduction ◽  
Reliability Analysis ◽  
Radial Basis Functions ◽  
Probabilistic Analysis ◽  
Basis Functions ◽  
Engineering System ◽  
Performance Function ◽  
First Order ◽  
Engineering Problems ◽  
Radial Basis

Probabilistic analysis of practical engineering problems has long been based on traditional sampling-based approaches, such as Monte Carlo Simulations (MCS) and gradient-based first-order and second-order methods. Since the finite element (FE) or other numerical methods are required to evaluate engineering system responses, such as forces or displacements, it is not efficient to directly integrate FE and sampling-based analysis approaches. Over the years, various approximate methods have been developed and applied to the reliability analysis of engineering problems. In this study, an efficient model reduction technique based on high-dimensional model reduction (HDMR) method has been developed using augmented radial basis functions (RBFs). The basic idea is to use augmented RBFs to construct HDMR component functions. The first-order HDMR model only requires sample points along each variable axis. The HDMR model, once created and used to explicitly express a performance function, is further combined with MCS to perform probabilistic calculations. As test problems, a mathematical problem and a 10-bar truss example are studied using the proposed reliability analysis approach. The proposed method works well, and accurate reliability analysis results are found with a small number of original performance function evaluations, i.e., FE simulations.

An Efficient Reliability Analysis Method for Structures With Epistemic Uncertainty Using Evidence Theory

2014 ◽  
Author(s):  
Zhe Zhang ◽  
Chao Jiang ◽  
G. Gary Wang ◽  
Xu Han
Keyword(s):  
Reliability Analysis ◽  
Structural Reliability ◽  
Epistemic Uncertainty ◽  
Limit State ◽  
Computational Cost ◽  
Evidence Theory ◽  
State Function ◽  
Limited Information ◽  
Design Point ◽  
Engineering Problems

Evidence theory has a strong ability to deal with the epistemic uncertainty, based on which the uncertain parameters existing in many complex engineering problems with limited information can be conveniently treated. However, the heavy computational cost caused by its discrete property severely influences the practicability of evidence theory, which has become a main difficulty in structural reliability analysis using evidence theory. This paper aims to develop an efficient method to evaluate the reliability for structures with evidence variables, and hence improves the applicability of evidence theory for engineering problems. A non-probabilistic reliability index approach is introduced to obtain a design point on the limit-state surface. An assistant area is then constructed through the obtained design point, based on which a small number of focal elements can be picked out for extreme analysis instead of using all the elements. The vertex method is used for extreme analysis to obtain the minimum and maximum values of the limit-state function over a focal element. A reliability interval composed of the belief measure and the plausibility measure is finally obtained for the structure. Two numerical examples are investigated to demonstrate the effectiveness of the proposed method.

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