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.

scholarly journals Structural Reliability Algorithms of Kriging Model Based on Improved Learning Strategy

2020 ◽  
Vol 38 (2) ◽  
pp. 412-419
Author(s):  
Linxiong Hong ◽  
Huacong Li ◽  
Kai Peng ◽  
Hongliang Xiao
Keyword(s):  
Active Learning ◽  
Reliability Analysis ◽  
Structural Reliability ◽  
Learning Strategy ◽  
Limit State ◽  
Surface Region ◽  
Kriging Model ◽  
State Function ◽  
Limit State Function ◽  
Highly Nonlinear

Aiming at the problems of implicit and highly nonlinear limit state function in the process of reliability analysis of mechanical products, a reliability analysis method of mechanical structures based on Kriging model and improved EGO active learning strategy is proposed. For the problem that the traditional EGO method cannot effectively select points in the limit state surface region, an improved EGO method is proposed. By dealing with the predicted values of sample point model with absolute values and assume that the distribution state of response values remains the same, the work focus of active learning selection points is moved to the vicinity, where the points are with larger prediction variance or close to the limit state surface. Three examples show that, compared with the classical active learning method, the proposed method has good global and local search ability, and can estimate the exact failure probability value under the condition of less calculation of the limit state function.

Multidisciplinary reliability design optimization using an enhanced saddlepoint approximation in the framework of sequential optimization and reliability analysis

2016 ◽  
Vol 230 (6) ◽  
pp. 570-578 ◽  
Author(s):  
Rong Yuan ◽  
Debiao Meng ◽  
Haiqing Li
Keyword(s):  
Design Optimization ◽  
Reliability Analysis ◽  
Generating Function ◽  
Multidisciplinary Design Optimization ◽  
Saddlepoint Approximation ◽  
Random Variable ◽  
Multidisciplinary Design ◽  
Sequential Optimization ◽  
Cumulant Generating Function ◽  
Third Moment

For high reliability calculation efficiency and evaluation accuracy, saddlepoint approximation technology has been introduced into design and optimization under uncertainties. When using saddlepoint approximation, there are two prerequisites: all random information is tractable and saddlepoint equations are easy to be solved. However, the above requirements cannot always be met in complex multidisciplinary systems. Random variables sometimes are intractable, or saddlepoint equations are highly nonlinear. To tackle these problems, in this study, an efficient reliability-based multidisciplinary design optimization using the combination method of saddlepoint approximation and third-moment is given. A simplified alternative cumulant generating function can be constructed by saddlepoint approximation and third-moment with the first, second and third moments of a random variable effectively. Then, this cumulant generating function can be utilized to calculate the cumulative distribution function and the probability density function of this random variable approximately. Moreover, to obtain better efficiency, the framework of sequential optimization and reliability analysis is introduced in this study. The corresponding formula of the proposed reliability-based multidisciplinary design optimization is given in detail. Two test problems are solved to show the application of the proposed method.

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>

scholarly journals Gaussian Process-Based Response Surface Method for Slope Reliability Analysis

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Bin Hu ◽  
Guo-shao Su ◽  
Jianqing Jiang ◽  
Yilong Xiao
Keyword(s):  
Gaussian Process ◽  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Failure Probability ◽  
Limit State ◽  
State Function ◽  
Limit State Function ◽  
Surface Method ◽  
Gp Model

A new response surface method (RSM) for slope reliability analysis was proposed based on Gaussian process (GP) machine learning technology. The method involves the approximation of limit state function by the trained GP model and estimation of failure probability using the first-order reliability method (FORM). A small amount of training samples were firstly built by the limited equilibrium method for training the GP model. Then, the implicit limit state function of slope was approximated by the trained GP model. Thus, the implicit limit state function and its derivatives for slope stability analysis were approximated by the GP model with the explicit formulation. Furthermore, an iterative algorithm was presented to improve the precision of approximation of the limit state function at the region near the design point which contributes significantly to the failure probability. Results of four case studies including one nonslope and three slope problems indicate that the proposed method is more efficient to achieve reasonable accuracy for slope reliability analysis than the traditional RSM.

Second-Order Reliability Method With First-Order Efficiency

2010 ◽  
Author(s):  
Xiaoping Du ◽  
Junfu Zhang
Keyword(s):  
Limit State ◽  
Saddlepoint Approximation ◽  
Quadratic Function ◽  
Second Order ◽  
State Function ◽  
Limit State Function ◽  
First Order ◽  
Reliability Method ◽  
Order Of Magnitude ◽  
Univariate Function

The widely used First Order Reliability Method (FORM) is efficient, but may not be accurate for nonlinear limit-state functions. The Second Order Reliability Method (SORM) is more accurate but less efficient. To maintain both high accuracy and efficiency, we propose a new second order reliability analysis method with first order efficiency. The method first performs the FORM and identifies the Most Probable Point (MPP). Then the associated limit-state function is decomposed into additive univariate functions at the MPP. Each univariate function is further approximated as a quadratic function, which is created with the gradient information at the MPP and one more point near the MPP. The cumulant generating function of the approximated limit-state function is then available so that saddlepoint approximation can be easily applied for computing the probability of failure. The accuracy of the new method is comparable to that of the SORM, and its efficiency is in the same order of magnitude as the FORM.

Iterative Algorithm for Structure Reliability Analysis Based on Support Vector Classification Method

2007 ◽  
Vol 353-358 ◽  
pp. 1009-1012
Author(s):  
Chao Ma ◽  
Zhen Zhou Lu
Keyword(s):  
Reliability Analysis ◽  
Iterative Algorithm ◽  
Limit State ◽  
Sampling Procedure ◽  
Support Vector ◽  
State Function ◽  
Limit State Function ◽  
Structure Reliability ◽  
Important Region ◽  
Actual Limit

For reliability analysis of structure with implicit limit state function, an iterative algorithm is presented on the basis of support vector classification machine. In the present method, the support vector classification machine is employed to construct surrogate of the implicit limit state function. By use of the proposed rational iteration and sampling procedure, the constructed support vector classification machine can converge to the actual limit state function at the important region, which contributes to the failure probability significantly. Then the precision of the reliability analysis is improved. The implementation of the presented method is given in detail, and the feasibility and the efficiency are demonstrated by the illustrations.

scholarly journals Hybrid Reliability Analysis for Spacecraft Docking Lock with Random and Interval Uncertainty

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Jianguo Zhang ◽  
Jiwei Qiu ◽  
Pidong Wang
Keyword(s):  
Reliability Analysis ◽  
Structural Reliability ◽  
Limit State ◽  
Random Variables ◽  
Simple Problem ◽  
State Function ◽  
Limit State Function ◽  
Interval Variables ◽  
Reliability Method ◽  
Hybrid Reliability

This paper presents a novel procedure based on first-order reliability method (FORM) for structural reliability analysis with hybrid variables, that is, random and interval variables. This method can significantly improve the computational efficiency for the abovementioned hybrid reliability analysis (HRA), while generally providing sufficient precision. In the proposed procedure, the hybrid problem is reduced to standard reliability problem with the polar coordinates, where an n-dimensional limit-state function is defined only in terms of two random variables. Firstly, the linear Taylor series is used to approximate the limit-state function around the design point. Subsequently, with the approximation of the n-dimensional limit-state function, the new bidimensional limit state is established by the polar coordinate transformation. And the probability density functions (PDFs) of the two variables can be obtained by the PDFs of random variables and bounds of interval variables. Then, the interval of failure probability is efficiently calculated by the integral method. At last, one simple problem with explicit expressions and one engineering application of spacecraft docking lock are employed to demonstrate the effectiveness of the proposed methods.

A Random Field Approach to Reliability Analysis With Random and Interval Variables

2015 ◽  
Vol 1 (4) ◽  
Author(s):  
Zhen Hu ◽  
Xiaoping Du
Keyword(s):  
Random Field ◽  
Reliability Analysis ◽  
Extreme Values ◽  
Limit State ◽  
State Function ◽  
Limit State Function ◽  
Response Variable ◽  
Field Approach ◽  
Reliability Bounds ◽  
Interval Variables

Interval variables are commonly encountered in design, especially in the early design stages when data are limited. Thus, reliability analysis (RA) should deal with both interval and random variables and then predict the lower and upper bounds of reliability. The analysis is computationally intensive, because the global extreme values of a limit-state function with respect to interval variables must be obtained during the RA. In this work, a random field approach is proposed to reduce the computational cost with two major developments. The first development is the treatment of a response variable as a random field, which is spatially correlated at different locations of the interval variables. Equivalent reliability bounds are defined from a random field perspective. The definitions can avoid the direct use of the extreme values of the response. The second development is the employment of the first-order reliability method (FORM) to verify the feasibility of the random field modeling. This development results in a new random field method based on FORM. The new method converts a general response variable into a Gaussian field at its limit state and then builds surrogate models for the autocorrelation function and reliability index function with respect to interval variables. Then, Monte Carlo simulation is employed to estimate the reliability bounds without calling the original limit-state function. Good efficiency and accuracy are demonstrated through three examples.

scholarly journals A New SORM Method for Structural Reliability with Hybrid Uncertain Variables

2020 ◽  
Vol 11 (1) ◽  
pp. 346
Author(s):  
Pidong Wang ◽  
Lechang Yang ◽  
Ning Zhao ◽  
Lefei Li ◽  
Dan Wang
Keyword(s):  
Reliability Analysis ◽  
Structural Reliability ◽  
Limit State ◽  
Random Variables ◽  
State Function ◽  
Strong Nonlinearity ◽  
Limit State Function ◽  
Practical Applications ◽  
Uncertain Variables ◽  
Practical Engineering

(1) Background: in practical applications, probabilistic and non-probabilistic information often simultaneously exit. For a complex system with a nonlinear limit-state function, the analysis and evaluation of the reliability are imperative yet challenging tasks. (2) Methods: an improved second-order method is proposed for reliability analysis in the presence of both random and interval variables, where a novel polar transformation is employed. This method enables a unified reliability analysis taking both random variables and bounded intervals into account, simplifying the calculation by transforming a high-dimension limit-state function into a bivariate state function. The obtained nonlinear probability density functions of two variables in the function inherit the statistic characteristics of interval and random variables. The proposed method does not require any strong assumptions and so it can be used in various practical engineering applications. (3) Results: the proposed method is validated via two numerical examples. A comparative study towards a contemporary algorithm in state-of-the-art literature is carried out to demonstrate the benefits of our method. (4) Conclusions: the proposed method outperforms existing methods both in efficiency and accuracy, especially for cases with strong nonlinearity.

A Nested Extreme Response Surface Approach for RBDO With Time-Dependent Probabilistic Constraints

2012 ◽  
Author(s):  
Zequn Wang ◽  
Pingfeng Wang
Keyword(s):  
Reliability Analysis ◽  
Engineering Design ◽  
Response Surface ◽  
Limit State ◽  
Time Dependent ◽  
Probabilistic Constraints ◽  
State Function ◽  
Limit State Function ◽  
Extreme Response ◽  
Practical Engineering

A primary concern in practical engineering design is ensuring high system reliability throughout a product life-cycle subject to time-variant operating conditions and component deteriorations. Thus, the capability to deal with time-dependent probabilistic constraints in reliability-based design optimization is of vital importance in practical engineering design applications. This paper presents a nested extreme response surface (NERS) approach to efficiently carry out time-dependent reliability analysis and determine the optimal designs. The NERS employs kriging model to build a nested response surface of time corresponding to the extreme value of the limit state function. The efficient global optimization technique is integrated with the NERS to extract the extreme time responses of the limit state function for any given system design. An adaptive response prediction and model maturation mechanism is developed based on mean square error (MSE) to concurrently improve the accuracy and computational efficiency of the proposed approach. With the nested response surface of time, the time-dependent reliability analysis can be converted into the time-independent reliability analysis and existing advanced reliability analysis and design methods can be used. The NERS is integrated with RBDO for the design of engineered systems with time-dependent probabilistic constraints. Two case studies are used to demonstrate the efficacy of the proposed NERS approach.

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