Reliability-Based Design Using Saddlepoint Approximation

2006 ◽  
Author(s):  
Xiaoping Du
Keyword(s):  
Design Optimization ◽  
Reliability Analysis ◽  
Random Variables ◽  
Saddlepoint Approximation ◽  
Sequential Optimization ◽  
Constraint Function ◽  
Deterministic Optimization ◽  
First Order ◽  
Reliability Based Design ◽  
Reliability Method

Reliability-based design optimization is much more computationally expensive than deterministic design optimization. To alleviate the computational demand, the First Order Reliability Method (FORM) is usually used in reliability-based design. Since FORM requires a nonlinear transformation from non-normal random variables to normal random variables, the nonlinearity of a constraint function may increase. As a result, the transformation may lead to a large error in reliability calculation. In order to improve accuracy, a new reliability-based design method with Saddlepoint Approximation is proposed in this work. The strategy of sequential optimization and reliability assessment is employed where the reliability analysis is decoupled from deterministic optimization. The accurate First Order Saddlepoint method is used for reliability analysis in the original random space without any transformation, and the chance of increasing nonlinearity of a constraint function is therefore eliminated. The overall reliability-based design is conducted in a sequence of cycles of deterministic optimization and reliability analysis. In each cycle, the percentile value of the constraint function corresponding to the required reliability is calculated with the Saddlepoint Approximation at the optimal point of the deterministic optimization. Then the reliability analysis results are used to formulate a new deterministic optimization model for the next cycle. The solution process converges within a few cycles. The demonstrative examples show that the proposed method is more accurate and efficient than the reliability-based design with FORM.

scholarly journals A decoupling algorithm with first-order asymptotic integration for reliability-based design optimization

2018 ◽  
Vol 10 (9) ◽  
pp. 168781401879333 ◽  
Author(s):  
Zhiliang Huang ◽  
Tongguang Yang ◽  
Fangyi Li
Keyword(s):  
Design Optimization ◽  
Reliability Analysis ◽  
Optimization Problems ◽  
Asymptotic Integration ◽  
Probabilistic Constraints ◽  
Reliability Based Design Optimization ◽  
First Order Reliability Method ◽  
First Order ◽  
Reliability Based Design ◽  
Reliability Method

Conventional decoupling approaches usually employ first-order reliability method to deal with probabilistic constraints in a reliability-based design optimization problem. In first-order reliability method, constraint functions are transformed into a standard normal space. Extra non-linearity introduced by the non-normal-to-normal transformation may increase the error in reliability analysis and then result in the reliability-based design optimization analysis with insufficient accuracy. In this article, a decoupling approach is proposed to provide an alternative tool for the reliability-based design optimization problems. To improve accuracy, the reliability analysis is performed by first-order asymptotic integration method without any extra non-linearity transformation. To achieve high efficiency, an approximate technique of reliability analysis is given to avoid calculating time-consuming performance function. Two numerical examples and an application of practical laptop structural design are presented to validate the effectiveness of the proposed approach.

Saddlepoint Approximation for Sequential Optimization and Reliability Analysis

2007 ◽  
Vol 130 (1) ◽  
Author(s):  
Xiaoping Du
Keyword(s):  
Reliability Analysis ◽  
High Efficiency ◽  
Saddlepoint Approximation ◽  
Reliability Estimation ◽  
Sequential Optimization ◽  
Probabilistic Constraint ◽  
Reliability Based Design ◽  
Alternative Approach ◽  
Reliability Method ◽  
Normal Transformation

A good balance between accuracy and efficiency is essential for reliability-based design (RBD). For this reason, sequential-loops formulations combined with the first-order reliability method (FORM) are usually used. FORM requires a nonlinear non-normal-to-normal transformation, which may increase the nonlinearity of a probabilistic constraint function significantly. The increased nonlinearity may lead to an increased error in reliability estimation. In order to improve accuracy and maintain high efficiency, the proposed method uses the accurate saddlepoint approximation for reliability analysis. The overall RBD is conducted in a sequence of cycles of deterministic optimization and reliability analysis. The reliability analysis is performed in the original random space without any nonlinear transformation. As a result, the proposed method provides an alternative approach to RBD with higher accuracy when the non-normal-to-normal transformation increases the nonlinearity of probabilistic constraint functions.

Reliability-Based Vehicle Safety Assessment and Design Optimization of Roadway Radius and Speed Limit in Windy Environments

2014 ◽  
Vol 136 (8) ◽  
Author(s):  
Jaekwan Shin ◽  
Ikjin Lee
Keyword(s):  
Design Optimization ◽  
Failure Modes ◽  
Random Variables ◽  
Vehicle Safety ◽  
Speed Limit ◽  
Vehicle Speed ◽  
Bank Angle ◽  
Analysis And Design ◽  
Reliability Based Design ◽  
Reliability Method

This paper presents a reliability-based analysis of road vehicle accidents and the optimization of roadway radius and speed limit design based on vehicle dynamics, mainly focusing on windy environments. The performance functions are formulated as failure modes of vehicle rollover and sideslip and are defined on a finite set of basic variables with probabilistic characteristics, so-called random variables. The random variables are vehicle speed, steer angle, tire–road friction coefficient, road bank angle, and wind speed. The probability of accident was evaluated using the first-order reliability method (FORM) and numerical studies were conducted using a single-unit truck model. The analysis demonstrates that wind is a significant factor when assessing vehicle safety on roads, and probabilistic studies such as reliability-based design optimization (RBDO) are necessarily required to enhance vehicle safety in windy environments. Accordingly, design optimization of roadway radius and speed limit was conducted, and new designs were proposed satisfying the target reliability. This study suggests that probabilistic mechanics and theory can be of value for analysis and design of wind-related vehicle safety.

First-Order Approximation Methods in Reliability-Based Design Optimization

2004 ◽  
Vol 127 (5) ◽  
pp. 851-857 ◽  
Author(s):  
Anukal Chiralaksanakul ◽  
Sankaran Mahadevan
Keyword(s):  
Design Optimization ◽  
Order Approximation ◽  
Mathematical Optimization ◽  
Reliability Based Design Optimization ◽  
First Order ◽  
Reliability Based Design ◽  
Inverse Form ◽  
Numerical Studies ◽  
Reliability Method ◽  
First Order Approximation

Efficiency of reliability-based design optimization (RBDO) methods is a critical criterion as to whether they are viable for real-world problems. Early RBDO methods are thus based primarily on the first-order reliability method (FORM) due to its efficiency. Recently, several first-order RBDO methods have been proposed, and their efficiency is significantly improved through problem reformulation and/or the use of inverse FORM. Our goal is to present these RBDO methods from a mathematical optimization perspective by formalizing FORM, inverse FORM, and associated RBDO reformulations. Through the formalization, their relationships are revealed. Using reported numerical studies, we discuss their numerical efficiency, convergence, and accuracy.

scholarly journals Reliability-Based Multidisciplinary Design Optimization under Correlated Uncertainties

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Huanwei Xu ◽  
Xin Wang ◽  
Wei Li ◽  
Mufeng Li ◽  
Suichuan Zhang ◽  
...  
Keyword(s):  
Design Optimization ◽  
Set Theory ◽  
Multidisciplinary Design Optimization ◽  
Reliability Assessment ◽  
Multidisciplinary Design ◽  
Sequential Optimization ◽  
Engineering System ◽  
First Order ◽  
Reliability Method

Complex mechanical system is usually composed of several subsystems, which are often coupled with each other. Reliability-based multidisciplinary design optimization (RBMDO) is an efficient method to design such complex system under uncertainties. However, the present RBMDO methods ignored the correlations between uncertainties. In this paper, through combining the ellipsoidal set theory and first-order reliability method (FORM) for multidisciplinary design optimization (MDO), characteristics of correlated uncertainties are investigated. Furthermore, to improve computational efficiency, the sequential optimization and reliability assessment (SORA) strategy is utilized to obtain the optimization result. Both a mathematical example and a case study of an engineering system are provided to illustrate the feasibility and validity of the proposed method.

Reliability analysis for a spar-supported floating offshore wind turbine

2017 ◽  
Vol 42 (1) ◽  
pp. 51-65 ◽  
Author(s):  
Abhinav Sultania ◽  
Lance Manuel
Keyword(s):  
Wind Speed ◽  
Wind Turbine ◽  
Reliability Analysis ◽  
Wave Height ◽  
Return Period ◽  
Random Variables ◽  
Environmental Data ◽  
First Order Reliability Method ◽  
First Order ◽  
Reliability Method

The reliability analysis of a spar-supported floating offshore 5-MW wind turbine is the subject of this study. Environmental data from a selected site are employed in the numerical studies. Using time-domain simulations, the dynamic behavior of a coupled platform-turbine system is studied; statistics of tower and rotor loads as well as platform motions are estimated and critical combinations of wind speed and wave height identified. Long-term loads associated with a 50-year return period are estimated using statistical extrapolation based on loads derived from simulations. Inverse reliability procedures that seek appropriate fractile levels for underlying variables consistent with the target load return period are employed; these include use of (1) two-dimensional inverse first-order reliability method where extreme loads, conditional on wind speed and wave height random variables, are selected at median levels and (2) three-dimensional inverse first-order reliability method where variability in the environmental and load random variables is fully represented.

An Improvement of Probabilistic Feasible Region Method for Reliablity-Based Design Optimization

2020 ◽  
pp. 2140004
Author(s):  
Zihao Wu ◽  
Zhenzhong Chen ◽  
Ge Chen ◽  
Xiaoke Li ◽  
Xuehui Gan ◽  
...  
Keyword(s):  
Design Optimization ◽  
Reliability Analysis ◽  
Mathematical Problem ◽  
Sequential Optimization ◽  
Feasible Region ◽  
Boundary Problems ◽  
Reliability Based Design ◽  
Engineering Design Problem ◽  
Highly Nonlinear ◽  
The Common

The decoupled methods for reliability-based design optimization (RBDO) problems are efficient and accurate. Sequential optimization and reliability analysis (SORA) method and probabilistic feasible region (PFR) approach are typical decoupled methods. When there are multiple constraints in RBDO problem, PFR method improves the efficiency of solving this problem by establishing the PFR to reduce the number of unnecessary reliability analysis loops. If the constraint boundary is not fixed in RBDO problem, PFR method may fail to solve and give the wrong result. Based on PFR method, this paper proposed an improvement of PFR method to solve the unfixed constraint boundary problems. The improvement of PFR method may not be efficient as the PFR method in solving the common RBDO problems. But, the improvement of PFR method can solve the RBDO problem with unfixed constraint boundary and has better adaptability. Three applications, a nonlinear mathematical problem, a highly nonlinear mathematical problem and an engineering design problem, are presented to illustrate the accuracy of the improvement of PFR method.

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