Reliability Analysis With Monte Carlo Simulation and Dependent Kriging Predictions

2016 ◽  
Vol 138 (12) ◽  
Author(s):  
Zhifu Zhu ◽  
Xiaoping Du
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Reliability Analysis ◽  
Surrogate Model ◽  
Limit State ◽  
Convergence Criterion ◽  
State Function ◽  
Kriging Method ◽  
Learning Function ◽  
Highly Nonlinear

Reliability analysis is time consuming, and high efficiency could be maintained through the integration of the Kriging method and Monte Carlo simulation (MCS). This Kriging-based MCS reduces the computational cost by building a surrogate model to replace the original limit-state function through MCS. The objective of this research is to further improve the efficiency of reliability analysis with a new strategy for building the surrogate model. The major approach used in this research is to refine (update) the surrogate model by accounting for the full information available from the Kriging method. The existing Kriging-based MCS uses only partial information. Higher efficiency is achieved by the following strategies: (1) a new formulation defined by the expectation of the probability of failure at all the MCS sample points, (2) the use of a new learning function to choose training points (TPs). The learning function accounts for dependencies between Kriging predictions at all the MCS samples, thereby resulting in more effective TPs, and (3) the employment of a new convergence criterion. The new method is suitable for highly nonlinear limit-state functions for which the traditional first- and second-order reliability methods (FORM and SORM) are not accurate. Its performance is compared with that of existing Kriging-based MCS method through five examples.

Mixed Efficient Global Optimization for Time-Dependent Reliability Analysis

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
Zhen Hu ◽  
Xiaoping Du
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Global Optimization ◽  
Reliability Analysis ◽  
Surrogate Model ◽  
Extreme Value ◽  
Time Dependent ◽  
Efficient Global Optimization ◽  
Highly Nonlinear ◽  
Adaptive Kriging

Time-dependent reliability analysis requires the use of the extreme value of a response. The extreme value function is usually highly nonlinear, and traditional reliability methods, such as the first order reliability method (FORM), may produce large errors. The solution to this problem is using a surrogate model of the extreme response. The objective of this work is to improve the efficiency of building such a surrogate model. A mixed efficient global optimization (m-EGO) method is proposed. Different from the current EGO method, which draws samples of random variables and time independently, the m-EGO method draws samples for the two types of samples simultaneously. The m-EGO method employs the adaptive Kriging–Monte Carlo simulation (AK–MCS) so that high accuracy is also achieved. Then, Monte Carlo simulation (MCS) is applied to calculate the time-dependent reliability based on the surrogate model. Good accuracy and efficiency of the m-EGO method are demonstrated by three examples.

Comparison of Monte Carlo Simulation and Response Surface Method by Using ANSYS PDS

2014 ◽  
Vol 578-579 ◽  
pp. 1449-1453
Author(s):  
Chun Xue Song ◽  
Yi Zhang ◽  
Ying Yi Cao
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Probabilistic Analysis ◽  
Limit State ◽  
Design System ◽  
State Function ◽  
Surface Method

Monte Carlo Simulation and Response Surface Method are two very powerful reliability analysis methods. Normally, in the reliability analysis of complex structures, the limit state function often can not be expressed in a closed-form. Usually, the codes for probabilistic analysis need to be combined with finite element models. ANSYS Probabilistic Design System (PDS) has provided a package to conduct probabilistic analysis automatically. This paper is going to compare the performance of these methods through an easy engineering problem in ANSYS. The results are going to be derived to show the feature of applying the corresponding reliability methods.

An Indicator Response Surface-Based Monte Carlo Method for Efficient Component and System Reliability Analysis

2003 ◽  
Author(s):  
Tong Zou ◽  
Zissimos P. Mourelatos ◽  
Sankaran Mahadevan ◽  
Jian Tu
Keyword(s):  
Monte Carlo ◽  
Reliability Analysis ◽  
Response Surface ◽  
Limit State ◽  
Sampling Technique ◽  
Indicator Function ◽  
Computational Method ◽  
State Function ◽  
Engineering Systems ◽  
Highly Nonlinear

Reliability analysis methods are commonly used in engineering design, in order to meet reliability and quality measures. An accurate and efficient computational method is presented for reliability analysis of engineering systems at both the component and system levels. The method can easily handle implicit, highly nonlinear limit-state functions, with correlated or non-correlated random variables, which are described by any probabilistic distribution. It is based on a constructed response surface of an indicator function, which determines the “failure” and “safe” regions, according to the performance function. A Monte Carlo simulation (MCS) calculates the probability of failure based on a response surface of the indicator function, instead of the computationally expensive limit-state function. The Cross-Validated Moving Least Squares (CVMLS) method is used to construct the response surface of the indicator function, based on an Optimum Symmetric Latin Hypercube (OSLH) sampling technique. A number of numerical examples highlight the superior accuracy and efficiency of the proposed method over commonly used reliability methods.

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.

Response surface method strategies coupled with NLFEA for structural reliability analysis of prestressed bridges

2021 ◽  
Author(s):  
Silvia J. Sarmiento Nova ◽  
Jaime Gonzalez-Libreros ◽  
Gabriel Sas ◽  
Rafael A. Sanabria Díaz ◽  
Maria C. A. Texeira da Silva ◽  
...  
Keyword(s):  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Structural Reliability ◽  
Limit State ◽  
Material Behavior ◽  
Nonlinear Material ◽  
State Function ◽  
Surface Method ◽  
Highly Nonlinear

<p>The Response Surface Method (RSM) has become an essential tool to solve structural reliability problems due to its accuracy, efficacy, and facility for coupling with Nonlinear Finite Element Analysis (NLFEA). In this paper, some strategies to improve the RSM efficacy without compromising its accuracy are tested. Initially, each strategy is implemented to assess the safety level of a highly nonlinear explicit limit state function. The strategy with the best results is then identified and used to carry out a reliability analysis of a prestressed concrete bridge, considering the nonlinear material behavior through NLFEA simulation. The calculated value of &#120573; is compared with the target value established in Eurocode for ULS. The results showed how RSM can be a practical methodology and how the improvements presented can reduce the computational cost of a traditional RSM giving a good alternative to simulation methods such as Monte Carlo.</p>

A polynomial chaos meta‐model for non‐linear stochastic magnet variations

2013 ◽  
Vol 32 (4) ◽  
pp. 1211-1218 ◽  
Author(s):  
Peter Offermann ◽  
Kay Hameyer
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Flux Density ◽  
Polynomial Chaos ◽  
Epistemic Uncertainty ◽  
Limit State ◽  
Element Model ◽  
State Function ◽  
Content Type ◽  
Meta Model

PurposeDue to the production process, arc segment magnets with radial magnetization for surface‐mounted permanent‐magnet synchronous machines (PMSM) can exhibit a deviation from the intended ideal, radial directed magnetization. In such cases, the resulting air gap field may show spatial variations in angle and absolute value of the flux‐density. For this purpose, this paper aims to create and evaluate a stochastic magnet model.Design/methodology/approachIn this paper, a polynomial chaos meta‐model approach, extracted from a finite element model, is compared to a direct sampling approach. Both approaches are evaluated using Monte‐Carlo simulation for the calculation of the flux‐density above one sole magnet surface.FindingsThe used approach allows representing the flux‐density's variations in terms of the magnet's stochastic input variations, which is not possible with pure Monte‐Carlo simulation. Furthermore, the resulting polynomial‐chaos meta‐model can be used to accelerate the calculation of error probabilities for a given limit state function by a factor of ten.Research limitations/implicationsDue to epistemic uncertainty magnet variations are assumed to be purely Gaussian distributed.Originality/valueThe comparison of both approaches verifies the assumption that the polynomial chaos meta‐model of the magnets will be applicable for a complete machine simulation.

Sequential Multidisciplinary Design Optimization and Reliability Analysis Using an Efficient Third-Moment Saddlepoint Approximation Method

2015 ◽  
Author(s):  
Debiao Meng ◽  
Hong-Zhong Huang ◽  
Huanwei Xu ◽  
Xiaoling Zhang ◽  
Yan-Feng Li
Keyword(s):  
Reliability Analysis ◽  
Limit State ◽  
Saddlepoint Approximation ◽  
Cumulative Distribution ◽  
Multidisciplinary Design ◽  
Sequential Optimization ◽  
State Function ◽  
Limit State Function ◽  
Highly Nonlinear ◽  
Third Moment

In Reliability based Multidisciplinary Design and Optimization (RBMDO), saddlepoint approximation has been utilized to improve reliability evaluation accuracy while sustaining high efficiency. However, it requires that not only involved random variables should be tractable; but also a saddlepoint can be obtained easily by solving the so-called saddlepoint equation. In practical engineering, a random variable may be intractable; or it is difficult to solve a highly nonlinear saddlepoint equation with complicated Cumulant Generating Function (CGF). To deal with these challenges, an efficient RBMDO method using Third-Moment Saddlepoint Approximation (TMSA) is proposed in this study. TMSA can construct a concise CGF using the first three statistical moments of a limit state function easily, and then express the probability density function and cumulative distribution function of the limit state function approximately using this concise CGF. To further improve the efficiency of RBMDO, a sequential optimization and reliability analysis strategy is also utilized and a formula of RBMDO using TMSA within the framework of SORA is proposed. Two examples are given to show the effectiveness of the proposed method.

Efficient Global Optimization Reliability Analysis (EGORA) for Time-Dependent Limit-State Functions

2014 ◽  
Author(s):  
Zhen Hu ◽  
Xiaoping Du
Keyword(s):  
Monte Carlo Simulation ◽  
Global Optimization ◽  
Surrogate Model ◽  
Limit State ◽  
Time Dependent ◽  
Efficient Global Optimization ◽  
State Function ◽  
Limit State Function ◽  
Extreme Response ◽  
Input Variables

If a limit-state function involves time, the associated reliability is defined within a period of time. The extreme value of the limit-state function is needed to calculate the time-dependent reliability, and the extreme value is usually highly nonlinear with respect to random input variables and may follow a multimodal distribution. For this reason, a surrogate model of the extreme response along with Monte Carlo simulation is usually employed. The objective of this work is to develop a new method, called the Efficient Global Optimization Reliability Analysis (EGORA), to efficiently build the surrogate model. EGORA is based on the Efficient Global Optimization (EGO) method. Different from the current method that generates training points for random variables and time independently, EGORA draws training points for the two types of input variables simultaneously and therefore accounts for their interaction effects. The other improvement is that EGORA only focuses on high accuracy at or near the limit state. With the two improvements, the new method can effectively reduce the number of training points. Once the surrogate model of the extreme response is available, Monte Carlo simulation is applied to calculate the time-dependent reliability. Good accuracy and efficiency of EGORA are demonstrated by three examples.

Local Monte Carlo Simulation for the Reliability Sensitivity Analysis

2011 ◽  
Vol 291-294 ◽  
pp. 2183-2188 ◽  
Author(s):  
Da Wei Li ◽  
Zhen Zhou Lu ◽  
Zhang Chun Tang
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Numerical Technique ◽  
Limit State ◽  
Computational Cost ◽  
Simulation Method ◽  
State Function ◽  
Local Domain ◽  
Monte Carlo Simulation Method ◽  
Reliability Sensitivity

An efficient numerical technique, namely the Local Monte Carlo Simulation method, is presented to assess the reliability sensitivity in this paper. Firstly some samples are obtained by the random sampling, then the local domain with a constant probability content corresponding to each sample point can be defined, finally the conditional reliability and reliability sensitivity corresponding to every local region can be calculated by using linear approximation of the limit state function. The reliability and reliability sensitivity can be estimated by the expectation of all the conditional reliability and reliability sensitivity. Three examples testify the applicability, validity and accuracy of the proposed method. The results computed by the Local Monte Carlo Simulation method and the Monte Carlo method are compared, which demonstrates that, without losing precision, the computational cost by the former method is much less than the later.

The Application of Artificial BP Neural Networks and Monte-Carlo Method for the Reliability Analysis on Frame Structure

2012 ◽  
Vol 204-208 ◽  
pp. 3256-3259 ◽  
Author(s):  
Zhi Cheng Xue ◽  
Hai Jun Wang
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Reliability Analysis ◽  
Limit State ◽  
Frame Structure ◽  
State Function ◽  
Range Data ◽  
Limit State Function ◽  
The Monte Carlo Method ◽  
Wide Range

In order to conduct the reliability analysis of frame structure, the limit state function was first fitted by artificial BP neural network. Then considering the orthogonal array method, sample data was arranged. After that an improved network modes was trained for the probabilistic analysis on a wide range data with the Monte-Carlo method. The mean and standard deviation for the limit state function was easily obtained and the reliability index on the structure can be also calculated. Finally, the example indicated that this method used in the reliability analysis for frame structure was feasible.

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