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.

Reliability Analysis of Underground Structures Using Metamodels and FORM

2019 ◽  
Author(s):  
Qian Wang ◽  
Jun Ji
Keyword(s):  
Reliability Analysis ◽  
Alternative Form ◽  
Underground Structures ◽  
Mathematical Functions ◽  
Performance Function ◽  
Reliability Indices ◽  
Nonlinear Responses ◽  
Reliability Method ◽  
Practical Engineering ◽  
Implicit Response

<p>An engineering reliability analysis method of underground structures using metamodels and a first-order reliability method (FORM) was studied. Surrogate models, or metamodels are approximate models that can be constructed to replace implicit response functions that involve finite element analyses. The radial basis functions (RBFs) are suitable for creating metamodels for general linear or nonlinear responses and they are locally and globally adaptive. After a performance function was replaced by an augmented RBF metamodel, an alternative FORM was applied. The method was tested using mathematical functions and applied to a tunnel engineering example. Different numbers of samples were tested and reliability analyses were performed. The failure probabilities and reliability indices were found to have a good accuracy. The proposed method combining RBFs and FORM is useful for practical engineering problems involving expensive response simulations.</p>

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.

scholarly journals Reliability Analysis Based on Artificial Bee Colony (ABC) and Its Application in Geotechnical Engineering

2018 ◽  
Vol 12 (1) ◽  
pp. 96-107 ◽  
Author(s):  
Hongbo Zhao ◽  
Changxing Zhu ◽  
Zhongliang Ru
Keyword(s):  
Reliability Analysis ◽  
Reliability Index ◽  
Artificial Bee Colony ◽  
Geotechnical Engineering ◽  
Engineering System ◽  
Good Tool ◽  
Abc Algorithm ◽  
Design Point ◽  
Bee Colony ◽  
Reliability Method

Introduction:Reliability analysis is a good tool to deal with the uncertainty and has been widely used in the engineering system. The first order reliability method (FORM) is generally used to calculate the reliability index but FORM is time-consuming and requires derivative computing.Methods:Artificial Bee Colony (ABC) algorithm is a very simple, robust and population-based stochastic optimization algorithm. In this study, an ABC-based reliability analysis was proposed to calculate the reliability index of engineering system through combining Artificial Bee Colony (ABC) algorithm with FORM. FORM was adopted to calculate the reliability index and design point. ABC is used to solve the constrained optimization about FORM. The procedure of ABC-based reliability analysis was presented in detail.Results and Conclusion:The proposed method was verified by two classic examples and then applied to geotechnical engineering. The results show that the ABC algorithm can effectively solve the global optimization problem in FORM. Results demonstrate that ABC-based reliability analysis is a good approach to obtain the reliability index and design point with a good accuracy so that it can be applied to analyze the reliability of a complex engineering system.

Sampling-Based Reliability Analysis Using Deep Feedforward Neural Network (DFNN)

2020 ◽  
Author(s):  
Ungki Lee ◽  
Ikjin Lee
Keyword(s):  
Neural Network ◽  
Reliability Analysis ◽  
Surrogate Model ◽  
Small Sample Size ◽  
Small Sample ◽  
Feedforward Neural Network ◽  
Training Data ◽  
Performance Function ◽  
Design Point ◽  
Previous Design

Abstract Reliability analysis that evaluates a probabilistic constraint is an important part of reliability-based design optimization (RBDO). Inverse reliability analysis evaluates the percentile value of the performance function that satisfies the reliability. To compute the percentile value, analytical methods, surrogate model based methods, and sampling-based methods are commonly used. In case the dimension or nonlinearity of the performance function is high, sampling-based methods such as Monte Carlo simulation, Latin hypercube sampling, and importance sampling can be directly used for reliability analysis since no analytical formulation or surrogate model is required in these methods. The sampling-based methods have high accuracy but require a large number of samples, which can be very time-consuming. Therefore, this paper proposes methods that can improve the accuracy of reliability analysis when the number of samples is not enough and the sampling-based methods are considered to be better candidates. This study starts with the idea of training the relationship between the realization of the performance function at a small sample size and the corresponding true percentile value of the performance function. Deep feedforward neural network (DFNN), which is one of the promising artificial neural network models that approximates high dimensional models using deep layered structures, is trained using the realization of various performance functions at a small sample size and the corresponding true percentile values as input and target training data, respectively. In this study, various polynomial functions and random variables are used to create training data sets consisting of various realizations and corresponding true percentile values. A method that approximates the realization of the performance function through kernel density estimation and trains the DFNN with the discrete points representing the shape of the kernel distribution to reduce the dimension of the training input data is also presented. Along with the proposed reliability analysis methods, a strategy that reuses samples of the previous design point to enhance the efficiency of the percentile value estimation is explained. The results show that the reliability analysis using the DFNN is more accurate than the method using only samples. In addition, compared to the method that trains the DFNN using the realization of the performance function, the method that trains the DFNN with the discrete points representing the shape of the kernel distribution improves the accuracy of reliability analysis and reduces the training time. The proposed sample reuse strategy is verified that the burden of function evaluation at the new design point can be reduced by reusing the samples of the previous design point when the design point changes while performing RBDO.

AN ITERATIVE HDMR APPROACH FOR ENGINEERING RELIABILITY ANALYSIS

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Qian Wang
Keyword(s):  
Reliability Analysis ◽  
Probabilistic Analysis ◽  
Surrogate Models ◽  
Second Order ◽  
High Dimensional Model Representation ◽  
Performance Function ◽  
Reliability Indices ◽  
Reliability Method ◽  
Sample Points ◽  
A Performance

Engineering reliability analysis has long been an active research area. Surrogate models, or metamodels, are approximate models that can be created to replace implicit performance functions in the probabilistic analysis of engineering systems. Traditional 1st-order or second-order high dimensional model representation (HDMR) methods are shown to construct accurate surrogate models of response functions in an engineering reliability analysis. Although very efficient and easy to implement, 1st-order HDMR models may not be accurate, since the cross-effects of variables are neglected. Second-order HDMR models are more accurate; however they are more complicated to implement. Moreover, they require much more sample points, i.e., finite element (FE) simulations, if FE analyses are employed to compute values of a performance function. In this work, a new probabilistic analysis approach combining iterative HDMR and a first-order reliability method (FORM) is investigated. Once a performance function is replaced by a 1st-order HDMR model, an alternate FORM is applied. In order to include higher-order contributions, additional sample points are generated and HDMR models are updated, before FORM is reapplied. The analysis iteration continues until the reliability index converges. The novelty of the proposed iterative strategy is that it greatly improves the efficiency of the numerical algorithm. As numerical examples, two engineering problems are studied and reliability analyses are performed. Reliability indices are obtained within a few iterations, and they are found to have a good accuracy. The proposed method using iterative HDMR and FORM provides a useful tool for practical engineering applications.

A SEQUENTIAL AUGMENTED METAMODELING METHOD FOR ENGINEERING RELIABILITY ANALYSIS

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Qian Wang ◽  
Jun Ji
Keyword(s):  
Sample Size ◽  
Reliability Analysis ◽  
Limit State ◽  
Engineering Systems ◽  
Analysis Method ◽  
Model Accuracy ◽  
Performance Function ◽  
Analysis And Design ◽  
Optimal Sample ◽  
Practical Engineering

Metamodeling methods provide useful tools to replace expensive numerical simulations in engineering reliability analysis and design optimization. The radial basis functions (RBFs) and augmented RBFs can be used to create accurate metamodels; therefore they can be integrated with a reliability analysis method such as the Monte Carlo simulations (MCS). However the model accuracy of RBFs depends on the sample size, and the accuracy generally increases as the sample size increases. Since the optimal sample size used to create RBF metamodels is not known before the creation of the models, a sequential RBF metamodeling method was studied. In each iteration of reliability analysis, augmented RBFs were used to generate metamodels of a limit state or performance function, and the failure probability was calculated using MCS. Additional samples were generated in subsequent analysis iterations in order to improve the metamodel accuracy. Numerical examples from literature were solved, and the failure probabilities based on the RBF metamodels were found to have a good accuracy. In addition, only small numbers of iterations were required for the reliability analysis to converge. The proposed method based on sequential RBF metamodels is useful for probabilistic analysis of practical engineering systems.

scholarly journals An Efficient Reliability Analysis Method Combining Improved EIF Active Learning Mechanism and Kriging Metamodel

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Dawei Zhang ◽  
Xiaohua Wu ◽  
Weilin Li ◽  
Xiaofeng Lv
Keyword(s):  
Active Learning ◽  
Reliability Analysis ◽  
Kriging Model ◽  
Expected Improvement ◽  
Learning Mechanisms ◽  
Learning Mechanism ◽  
Engineering Problems ◽  
Real Performance ◽  
Practical Engineering ◽  
Expected Improvement Function

Complex implicit performance functions widely exist in many engineering problems. The reliability analysis of these problems has always been a challenge. Using surrogate model instead of real performance function is one of the methods to solve this kind of problem. Kriging is one of the surrogate models with precise interpolation technique. In order to make the kriging model achieve higher accuracy using a small number of samples, i.e., improve its practicability and feasibility in practical engineering problems, some active learning equations are wildly studied. Expected improvement function (EIF) is one of them. However, the EIF has a great disadvantage in selecting the added sample point. Therefore, a joint active learning mechanism, J-EIF, is proposed to obtain the ideal added point. The J-EIF active learning mechanism combines the two active learning mechanisms and makes full use of the characters of kriging model. It overcomes the shortcoming of EIF active learning mechanism in the selection of added sample points. Then, using Monte Carlo Simulation (MCS) results as a reference, the reliability of two examples is estimated. The results are discussed showing that the learning efficiency and accuracy of the improved EIF are both higher than those of the traditional EIF.

Reliability Analysis of Subgrade Bearing Capacity of Gravity Foundation of Wind Turbine Based on JC Method

2011 ◽  
Vol 413 ◽  
pp. 314-319
Author(s):  
Zhong Qing Cheng ◽  
Ping Yang ◽  
Hai Bo Jiang
Keyword(s):  
Bearing Capacity ◽  
Wind Turbine ◽  
Reliability Analysis ◽  
Reliability Index ◽  
Maximum Pressure ◽  
Performance Function ◽  
Iterative Calculation ◽  
Reliability Method ◽  
Foundation Base ◽  
Index Effect

The design of foundation of wind turbine should meet the requirement of subgrade bearing capacity. In this paper, reliability method was used to analyze the bearing capacity of gravity foundation of wind turbine. The circular gravity foundation in coral sands is taken as research object. By deriving the expression of maximum pressure at the edge of foundation base under the action of overturning moment, the performance function of subgrade bearing capacity reliability analysis is established. JC method is used to calculate the subgrade bearing capacity reliability index. Effect of foundation size to reliability index is analyzed. Iterative calculation shows that the method proposed in this paper can calculate the reliability index of foundation quickly.

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