A Random Field Method for Time-Dependent Reliability Analysis With Random and Interval Variables

2016 ◽  
Author(s):  
Zhangli Hu ◽  
Xiaoping Du
Keyword(s):  
Random Field ◽  
Limit State ◽  
Gaussian Random Field ◽  
Field Method ◽  
Time Dependent ◽  
State Function ◽  
Good Efficiency ◽  
First Order ◽  
Interval Variables ◽  
Reliability Method

In many engineering applications, both random and interval variables exist. Some of the random variables may also vary over time. As a result, the reliability of a component not only decreases with time but also resides in an interval. Evaluating the time-dependent reliability bounds is a challenging task because of the intensive computational demand. This research develops a method that treats a time-dependent random response as a random field with respect to both intervals and time. Consequently, random field methodologies can be used to estimate the worse-case time-dependent reliability. The method employs the first-order reliability method, which results in a Gaussian random field for the response with respect to intervals and time. The Kriging method and Monte Carlo simulation are then used to estimate the worse-case reliability without calling the original limit-state function. Good efficiency and accuracy are demonstrated through examples.

Reliability Methods for Bimodal Distribution With First-Order Approximation1

2018 ◽  
Vol 5 (1) ◽  
Author(s):  
Zhangli Hu ◽  
Xiaoping Du
Keyword(s):  
Probability Density ◽  
Order Approximation ◽  
Limit State ◽  
Random Variables ◽  
Random Variable ◽  
State Function ◽  
First Order ◽  
Reliability Method ◽  
Reliability Methods ◽  
Basic Random Variable

In traditional reliability problems, the distribution of a basic random variable is usually unimodal; in other words, the probability density of the basic random variable has only one peak. In real applications, some basic random variables may follow bimodal distributions with two peaks in their probability density. When binomial variables are involved, traditional reliability methods, such as the first-order second moment (FOSM) method and the first-order reliability method (FORM), will not be accurate. This study investigates the accuracy of using the saddlepoint approximation (SPA) for bimodal variables and then employs SPA-based reliability methods with first-order approximation to predict the reliability. A limit-state function is at first approximated with the first-order Taylor expansion so that it becomes a linear combination of the basic random variables, some of which are bimodally distributed. The SPA is then applied to estimate the reliability. Examples show that the SPA-based reliability methods are more accurate than FOSM and FORM.

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.

In-Plane Creep Stability Design of Concrete Filled Steel Tubular Arches Using Inverse Reliability Method

2013 ◽  
Vol 351-352 ◽  
pp. 1601-1604
Author(s):  
Wei Jiang ◽  
Da Gang Lu
Keyword(s):  
Limit State ◽  
Time Dependent ◽  
Safety Factors ◽  
State Equations ◽  
Stability Range ◽  
Good Efficiency ◽  
Reliability Indices ◽  
Inverse Form ◽  
Dependent Behavior ◽  
Reliability Method

An inverse first order reliability method (FORM) is presented to solve the safety factors for the in-plane creep stability of concrete filled steel tubular (CFST) arches. In the inverse analysis, the safety factors with or without considering the time-dependent behavior of concrete are introduced into limit state equations for the in-plane stability design of CFST arches. For different target reliability indices and steel ratios, the time-independent and time-dependent safety factors are solved. The results show that the inverse FORM is of good efficiency and applicability. The target reliability indices have little effect on the safety factors for the creep stability of CFST arches. The effects of steel ratios are significant which should be considered in design. For the commonly used steel ratios of CFST arches, the in-plane safety factors for creep stability range from 1.17 to 1.43.

Reliability and Sensitivity Analysis of Laminate Using Different Methods

2014 ◽  
Vol 945-949 ◽  
pp. 1159-1162
Author(s):  
Wei Tao Zhao ◽  
Xiao Li ◽  
Feng Guo
Keyword(s):  
Good Accuracy ◽  
Limit State ◽  
Nonlinear Function ◽  
State Function ◽  
Laminate Structure ◽  
First Order Reliability Method ◽  
First Order ◽  
Fiber Properties ◽  
Surface Method ◽  
Reliability Method

Reliability of laminate structure is deeply influenced by uncertainties such as fiber properties, loads and design sizes. It is very difficult to evaluate the reliability and sensitivity of laminate structure because that laminate structure is anisotropic and the limit state function (LSF) is a high nonlinear function. In this paper, reliability and sensitivity are evaluated by using first order reliability method (FORM), response surface method (RSM) and Monte Carlo simulation (MCS). The study aims to find a numerical method to evaluate the reliability and sensitivity of laminate structures efficiently and accurately. An example of laminate with a large number of variables is analyzed. The results obtained by using different methods are compared in terms of efficiency and accuracy. It is shown that FORM is not accuracy, and RSM has a very good accuracy and efficient in terms of reliability, but the accuracy of sensitivity obtained by using RSM is not good enough.

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.

Time-Dependent Reliability Analysis by a Sampling Approach to Extreme Values of Stochastic Processes

2012 ◽  
Author(s):  
Zhen Hu ◽  
Xiaoping Du
Keyword(s):  
Stochastic Processes ◽  
Reliability Analysis ◽  
Extreme Values ◽  
Limit State ◽  
Time Dependent ◽  
State Function ◽  
Limit State Function ◽  
Reliability Method ◽  
Time Invariant ◽  
State Functions

Maintaining high accuracy and efficiency is a challenging issue in time-dependent reliability analysis. In this work, an accurate and efficient method is proposed for limit-state functions with the following features: The limit-state function is implicit with respect to time, and its input contains stochastic processes; the stochastic processes include only general strength and stress variables, or the limit-state function is monotonic to these stochastic processes. The new method employs random sampling approaches to estimate the distributions of the extreme values of the stochastic processes. The extreme values are then used to replace the corresponding stochastic processes, and consequently the time-dependent reliability analysis is converted into its time-invariant counterpart. The commonly used time-invariant reliability method, the First Order Reliability Method, is then applied for the time-variant reliability analysis. The results show that the proposed method significantly improves the accuracy and efficiency of time-dependent reliability analysis.

A Second-Order Reliability Method With First-Order Efficiency

2010 ◽  
Vol 132 (10) ◽  
Author(s):  
Junfu Zhang ◽  
Xiaoping Du
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 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 to identify 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 by a quadratic function. The cumulant generating function of the approximated limit-state function is then available so that saddlepoint approximation can be easily applied in 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.

Reliability Analysis for Multidisciplinary Systems Involving Stationary Stochastic Processes

2015 ◽  
Author(s):  
Zhifu Zhu ◽  
Zhen Hu ◽  
Xiaoping Du
Keyword(s):  
Stochastic Processes ◽  
Reliability Analysis ◽  
Limit State ◽  
Time Dependent ◽  
State Function ◽  
Limit State Function ◽  
Current Time ◽  
Reliability Method ◽  
Stationary Stochastic Processes ◽  
Multidisciplinary System

The response of a component in a multidisciplinary system is affected by not only the discipline to which it belongs, but also by other disciplines of the system. If any components are subject to time-dependent uncertainties, responses of all the components and the system are also time dependent. Thus, time-dependent multidisciplinary reliability analysis is required. To extend the current time-dependent reliability analysis for a single component, this work develops a time-dependent multidisciplinary reliability method for components in a multidisciplinary system under stationary stochastic processes. The method modifies the First and Second Order Reliability Methods (FORM and SORM) so that the Multidisciplinary Analysis (MDA) is incorporated while approximating the limit-state function of the component under consideration. Then Monte Carlo simulation is used to calculate the reliability without calling the original limit-state function. Two examples are used to demonstrate and evaluate the proposed method.

Reliability Estimation of Solder Joint Utilizing Thermal Fatigue Models

2005 ◽  
Vol 297-300 ◽  
pp. 1816-1821
Author(s):  
Ouk Sub Lee ◽  
No Hoon Myoung ◽  
Dong Hyeok Kim
Keyword(s):  
Solder Joint ◽  
Thermal Fatigue ◽  
Failure Probability ◽  
Coefficient Of Thermal Expansion ◽  
Probability Model ◽  
Limit State ◽  
Reliability Estimation ◽  
State Function ◽  
First Order ◽  
Reliability Method

The differences of coefficient of thermal expansion (CTE) of component and FR-4 board connected by solder joint generally cause the dissimilarity in shear strain and failure in solder joint when they are heated. The first order Taylor series expansion of the limit state function (LSF) incorporating with thermal fatigue models is used in order to estimate the failure probability of solder joints under heated condition. Various thermal fatigue models, classified into five categories: categories four such as plastic strain-based, creep strain-based, energy-based, and damage-based except stress-based, are utilized in this study. The effects of random variables such as CTE, distance of the solder joint from neutral point (DNP), temperature variation and height of solder on the failure probability of the solder joint are systematically investigated by using a failure probability model with the first order reliability method (FORM) and thermal fatigue models.

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