A Reliability Approach to Inverse Simulation Under Uncertainty

2012 ◽  
Author(s):  
Xiaoping Du
Keyword(s):  
Reliability Analysis ◽  
High Efficiency ◽  
Probability Distributions ◽  
Random Parameters ◽  
Inverse Simulation ◽  
First Order ◽  
Reliability Method ◽  
Simulation Input ◽  
Input Variables ◽  
Impact Problem

Inverse simulation is an inverse process of a direct simulation. During the process, the simulation input variables are identified for a given set of simulation output variables. Uncertainties such as random parameters may exist in engineering applications of inverse simulation. A reliability method is developed in this work to estimate the probability distributions of unknown simulation input. The First Order Reliability Method is employed and modified so that the inverse simulation is embedded within the reliability analysis algorithm. This treatment avoids the separate executions of reliability analysis and inverse simulation and consequently maintains high efficiency. In addition, the means and standard deviations of unknown input variables can also be obtained. A particle impact problem is presented to demonstrate the proposed method for inverse simulation under uncertainty.

Inverse Simulation Under Uncertainty by Optimization

2013 ◽  
Vol 13 (2) ◽  
Author(s):  
Xiaoping Du
Keyword(s):  
Reliability Analysis ◽  
High Efficiency ◽  
Probability Distributions ◽  
Optimization Method ◽  
Unknown Input ◽  
Random Parameters ◽  
Inverse Simulation ◽  
Reliability Method ◽  
Simulation Input ◽  
Input Variables

Inverse simulation is an inverse process of a direct simulation. During the process, unknown simulation input variables are identified for a given set of known simulation output variables. Uncertainties such as random parameters may exist in engineering applications of inverse simulation. An optimization method is developed in this work to estimate the probability distributions of unknown input variables. The first order reliability method is employed and modified so that the inverse simulation is embedded within the reliability analysis. This treatment avoids the separate executions of reliability analysis and inverse simulation and consequently maintains high efficiency. In addition, the means and standard deviations of the unknown input variables can also be obtained. A particle impact problem is presented to demonstrate the proposed method for inverse simulation under uncertainty.

Some Important Issues on First-Order Reliability Analysis With Nonprobabilistic Convex Models

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
C. Jiang ◽  
G. Y. Lu ◽  
X. Han ◽  
R. G. Bi
Keyword(s):  
Reliability Analysis ◽  
Reliability Index ◽  
Probability Model ◽  
Mean Value ◽  
Convex Model ◽  
First Order ◽  
Reliability Method ◽  
Complex Engineering ◽  
Mean Value Method ◽  
Form Type

Compared with the probability model, the convex model approach only requires the bound information on the uncertainty, and can make it possible to conduct the reliability analysis for many complex engineering problems with limited samples. Presently, by introducing the well-established techniques in probability-based reliability analysis, some methods have been successfully developed for convex model reliability. This paper aims to reveal some different phenomena and furthermore some severe paradoxes when extending the widely used first-order reliability method (FORM) into the convex model problems, and whereby provide some useful suggestions and guidelines for convex-model-based reliability analysis. Two FORM-type approximations, namely, the mean-value method and the design-point method, are formulated to efficiently compute the nonprobabilistic reliability index. A comparison is then conducted between these two methods, and some important phenomena different from the traditional FORMs are summarized. The nonprobabilistic reliability index is also extended to treat the system reliability, and some unexpected paradoxes are found through two numerical examples.

Reliability analysis of corroded pipelines: Novel adaptive conjugate first order reliability method

2019 ◽  
Vol 62 ◽  
pp. 103986 ◽  
Author(s):  
Behrooz Keshtegar ◽  
Mohamed El Amine Ben Seghier ◽  
Shun-Peng Zhu ◽  
Rouzbeh Abbassi ◽  
Nguyen-Thoi Trung
Keyword(s):  
Reliability Analysis ◽  
First Order Reliability Method ◽  
First Order ◽  
Reliability Method

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.

First-Order Reliability Method for Structural Reliability Analysis in the Presence of Random and Interval Variables

2015 ◽  
Vol 1 (4) ◽  
Author(s):  
Umberto Alibrandi ◽  
C. G. Koh
Keyword(s):  
Reliability Analysis ◽  
Structural Reliability ◽  
Limit State ◽  
Computational Cost ◽  
Computational Effort ◽  
Stochastic Dynamic ◽  
First Order Reliability Method ◽  
First Order ◽  
Structural Reliability Analysis ◽  
Reliability Method

This paper presents a novel procedure based on first-order reliability method (FORM) for structural reliability analysis in the presence of random parameters and interval uncertain parameters. In the proposed formulation, the hybrid problem is reduced to standard reliability problems, where the limit state functions are defined only in terms of the random variables. Monte Carlo simulation (MCS) for hybrid reliability analysis (HRA) is presented, and it is shown that it requires a tremendous computational effort; FORM for HRA is more efficient but still demanding. The computational cost is significantly reduced through a simplified procedure, which gives good approximations of the design points, by requiring only three classical FORMs and one interval analysis (IA), developed herein through an optimization procedure. FORM for HRA and its simplified formulation achieve a much improved efficiency than MCS by several orders of magnitude, and it can thus be applied to real-world engineering problems. Representative examples of stochastic dynamic analysis and performance-based engineering are presented.

Probabilistic Inverse Simulation and its Application in Vehicle Accident Reconstruction

2013 ◽  
Author(s):  
Xiaoyun Zhang ◽  
Zhen Hu ◽  
Xiaoping Du
Keyword(s):  
Traffic Accident ◽  
Joint Probability ◽  
Accident Reconstruction ◽  
Direct Simulation ◽  
Inverse Simulation ◽  
Vehicle Accident ◽  
Simulation Output ◽  
Simulation Input ◽  
Input Variables ◽  
Joint Probability Density

Inverse simulation is an inverse process of direct simulation. It determines unknown input variables of the direct simulation for a given set of simulation output variables. Uncertainties usually exist, making it difficult to solve inverse simulation problems. The objective of this research is to account for uncertainties in inverse simulation in order to produce high confidence in simulation results. The major approach is the use of the maximum likelihood methodology, which determines not only unknown deterministic input variables but also the realizations of random input variables. Both types of variables are solved on the condition that the joint probability density of all the random variables is maximum. The proposed methodology is applied to a traffic accident reconstruction problem where the simulation output (accident consequences) is known and the simulation input (velocities of the vehicle at the beginning of crash) is sought.

scholarly journals Framework for evaluating risk of limited sight distance for permitted left-turn movements: case study

2016 ◽  
Vol 43 (4) ◽  
pp. 369-377 ◽  
Author(s):  
Ahmed Osama ◽  
Tarek Sayed ◽  
Said Easa
Keyword(s):  
Reliability Analysis ◽  
Probability Distributions ◽  
Video Data ◽  
Analysis Framework ◽  
Left Turn ◽  
Sight Distance ◽  
Time Gap ◽  
Input Variables ◽  
The City

A reliability analysis framework is used to evaluate the risk of limited sight distance for permitted left-turn movements due to the presence of opposing left-turn vehicles. Two signalized intersection approaches in the city of Surrey were used as case studies for the framework. Geometric and traffic video data was collected and analyzed using a computer vision tool to extract the input variables probability distributions. The data was used in the reliability analysis where first-order and Importance Sampling methods were performed. The analysis showed that the probability of non-compliance was considerable at one approach due to its large left-turn lane offset. The analysis also showed that the probability of non-compliance increased substantially when the obstacle vehicle was a bus rather than a passenger car. Moreover, the time gap had a higher impact on the probability of non-compliance compared to speed. Strategies were suggested to overcome the high probability of non-compliance.

System Reliability Analysis With Second Order Saddlepoint Approximation

2019 ◽  
Author(s):  
Hao Wu ◽  
Xiaoping Du
Keyword(s):  
Normal Distribution ◽  
Reliability Analysis ◽  
System Reliability ◽  
Multivariate Normal Distribution ◽  
High Efficiency ◽  
Saddlepoint Approximation ◽  
Second Order ◽  
Multivariate Normal ◽  
System Reliability Analysis ◽  
Reliability Method

Abstract The second order saddlepoint approximation (SPA) has been used for component reliability analysis for higher accuracy than the traditional second order reliability method. This work extends the second order SPA to system reliability analysis. The joint distribution of all the component responses is approximated by a multivariate normal distribution. To maintain high accuracy of the approximation, the proposed method employs the second order SPA to accurately generate the marginal distributions of component responses; to simplify computations and achieve high efficiency, the proposed method estimates the covariance matrix of the multivariate normal distribution with the first order approximation to component responses. Examples demonstrate the high effectiveness of the second order SPA method for system reliability analysis.

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