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.

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.

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.

High-Dimensional Reliability Method Accounting for Important and Unimportant Input Variables

2021 ◽  
Author(s):  
Jianhua Yin ◽  
Xiaoping Du
Keyword(s):  
Dimension Reduction ◽  
Reliability Analysis ◽  
Limit State ◽  
Physical Models ◽  
Reliability Prediction ◽  
High Dimensional ◽  
Core Element ◽  
Reliability Method ◽  
Input Variables ◽  
Reduced Space

Abstract Reliability analysis is usually a core element in engineering design, during which reliability is predicted with physical models (limit-state functions). Reliability analysis becomes computationally expensive when the dimensionality of input random variables is high. This work develops a high dimensional reliability analysis method by a new dimension reduction strategy so that the contributions of both important and unimportant input variables are accommodated by the proposed dimension reduction method. The consideration of the contributions of unimportant input variables can certainly improve the accuracy of the reliability prediction, especially where many unimportant input variables are involved. The dimension reduction is performed with the first iteration of the first order reliability method (FORM), which identifies important and unimportant input variables. Then a higher order reliability analysis, such as the second order reliability analysis and metamodeling method, is performed in the reduced space of only important input variables. The reliability obtained in the reduced space is then integrated with the contributions of unimportant input variables, resulting in the final reliability prediction that accounts for both types of input variables. Consequently, the new reliability method is more accurate than the traditional method, which fixes unimportant input variables at their means. The accuracy is demonstrated by three examples.

Complementary Intersection Method for System Reliability Analysis

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
Byeng D. Youn ◽  
Pingfeng Wang
Keyword(s):  
Reliability Analysis ◽  
System Reliability ◽  
High Efficiency ◽  
Second Order ◽  
Approximation Formula ◽  
Joint Failure ◽  
System Reliability Analysis ◽  
Reliability Method ◽  
Reliability Methods ◽  
Intersection Method

Although researchers desire to evaluate system reliability accurately and efficiently over the years, little progress has been made on system reliability analysis. Up to now, bound methods for system reliability prediction have been dominant. However, two primary challenges are as follows: (1) Most numerical methods cannot effectively evaluate the probabilities of the second (or higher)–order joint failure events with high efficiency and accuracy, which are needed for system reliability evaluation and (2) there is no unique system reliability approximation formula, which can be evaluated efficiently with commonly used reliability methods. Thus, this paper proposes the complementary intersection (CI) event, which enables us to develop the complementary intersection method (CIM) for system reliability analysis. The CIM expresses the system reliability in terms of the probabilities of the CI events and allows the use of commonly used reliability methods for evaluating the probabilities of the second–order (or higher) joint failure events efficiently. To facilitate system reliability analysis for large-scale systems, the CI-matrix can be built to store the probabilities of the first- and second-order CI events. In this paper, three different numerical solvers for reliability analysis will be used to construct the CI-matrix numerically: first-order reliability method, second-order reliability method, and eigenvector dimension reduction (EDR) method. Three examples will be employed to demonstrate that the CIM with the EDR method outperforms other methods for system reliability analysis in terms of efficiency and accuracy.

Probabilistic Inverse Simulation and Its Application in Vehicle Accident Reconstruction

2013 ◽  
Vol 135 (12) ◽  
Author(s):  
Xiaoyun Zhang ◽  
Zhen Hu ◽  
Xiaoping Du
Keyword(s):  
Probability Density ◽  
Joint Probability ◽  
Accident Reconstruction ◽  
Direct Simulation ◽  
Maximum Probability ◽  
Inverse Simulation ◽  
Vehicle Accident ◽  
Simulation Output ◽  
Simulation Input ◽  
Input Variables

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 probability density function (PDF), 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.

An Investigation of Nonlinearity of Reliability-Based Design Optimization Approaches

2002 ◽  
Author(s):  
Kyung K. Choi ◽  
Byeng D. Youn
Keyword(s):  
Design Optimization ◽  
Reliability Analysis ◽  
Probability Distributions ◽  
Performance Measure ◽  
Probabilistic Constraints ◽  
Random Parameters ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Highly Nonlinear ◽  
Standard Normal

Deterministic optimum designs that are obtained without consideration of uncertainty could lead to unreliable designs, which call for a reliability approach to design optimization, using a Reliability-Based Design Optimization (RBDO) method. A typical RBDO process iteratively carries out a design optimization in an original random space (X-space) and reliability analysis in an independent and standard normal random space (U-space). This process requires numerous nonlinear mapping between X- and U-spaces for a various probability distributions. Therefore, the nonlinearity of RBDO problem will depend on the type of distribution of random parameters, since a transformation between X- and U-spaces introduces additional nonlinearity to reliability-based performance measures evaluated during the RBDO process. Evaluation of probabilistic constraints in RBDO can be carried out in two different ways: the Reliability Index Approach (RIA) and the Performance Measure Approach (PMA). Different reliability analysis approaches employed in RIA and PMA result in different behaviors of nonlinearity of RIA and PMA in the RBDO process. In this paper, it is shown that RIA becomes much more difficult to solve for non-normally distributed random parameters because of highly nonlinear transformations involved. However, PMA is rather independent of probability distributions because of little involvement of the nonlinear transformation.

Interval Reliability Analysis

2007 ◽  
Author(s):  
Xiaoping Du
Keyword(s):  
Reliability Analysis ◽  
Performance Characteristic ◽  
Extreme Values ◽  
Probability Distributions ◽  
Probability Of Failure ◽  
Interval Reliability ◽  
Interval Variables ◽  
Inverse Reliability Analysis ◽  
Reliability Method ◽  
A Performance

Traditional reliability analysis uses probability distributions to calculate reliability. In many engineering applications, some nondeterministic variables are known within intervals. When both random variables and interval variables are present, a single probability measure, namely, the probability of failure or reliability, is not available in general; but its lower and upper bounds exist. The mixture of distributions and intervals makes reliability analysis more difficult. Our goal is to investigate computational tools to quantify the effects of random and interval inputs on reliability associated with performance characteristics. The proposed reliability analysis framework consists of two components — direct reliability analysis and inverse reliability analysis. The algorithms are based on the First Order Reliability Method and many existing reliability analysis methods. The efficient and robust improved HL-RF method is further developed to accommodate interval variables. To deal with interval variables for black-box functions, nonlinear optimization is used to identify the extreme values of a performance characteristic. The direct reliability analysis provides bounds of a probability of failure; the inverse reliability analysis computes the bounds of the percentile value of a performance characteristic given reliability. One engineering example is provided.

System Reliability Analysis With Second-Order Saddlepoint Approximation

2020 ◽  
Vol 6 (4) ◽  
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 (SOSPA) has been used for component reliability analysis for higher accuracy than the traditional second-order reliability method (SORM). This work extends the second-order saddlepoint approximation (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 the 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 the component responses. Examples demonstrate the high effectiveness of the second-order SPA method for system reliability analysis.

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