A Sampling Approach to Extreme Value Distribution for Time-Dependent Reliability Analysis

2013 ◽  
Vol 135 (7) ◽  
Author(s):  
Zhen Hu ◽  
Xiaoping Du
Keyword(s):  
Stochastic Process ◽  
Reliability Analysis ◽  
Limit State ◽  
Extreme Value ◽  
Time Dependent ◽  
State Function ◽  
Limit State Function ◽  
Reliability Method ◽  
Time Invariant ◽  
Sampling Approach

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. There is only one stochastic process in the input to the limit-sate function. The stochastic process could be either a general strength or a general stress variable so that the limit-state function is monotonic to the stochastic process. The new method employs a sampling approach to estimate the distributions of the extreme value of the stochastic process. The extreme value is then used to replace the corresponding stochastic process. 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 to calculate the probability of failure over a given period of time. The results show that the proposed method significantly improves the accuracy and efficiency of time-dependent reliability analysis.

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.

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.

scholarly journals Second Order Reliability Method for Time-Dependent Reliability Analysis Using Sequential Efficient Global Optimization

2019 ◽  
Author(s):  
Zhangli Hu ◽  
Xiaoping Du
Keyword(s):  
Global Optimization ◽  
Reliability Analysis ◽  
Limit State ◽  
Second Order ◽  
Time Dependent ◽  
Efficient Global Optimization ◽  
State Function ◽  
Limit State Function ◽  
Reliability Problem ◽  
Reliability Method

Abstract Reliability depends on time if the associated limit-state function includes time. A time-dependent reliability problem can be converted into a time-independent reliability problem by using the extreme value of the limit-state function. Then the first order reliability method can be used but it may produce a large error since the extreme limit-state function is usually highly nonlinear. This study proposes a new reliability method so that the second order reliability method can be applied to time-dependent reliability analysis for higher accuracy while maintaining high efficiency. The method employs sequential efficient global optimization to transform the time-dependent reliability analysis into the time-independent problem. The Hessian approximation and envelope theorem are used to obtain the second order information of the extreme limit-state function. Then the second order saddlepoint approximation is use to evaluate the reliability. The accuracy and efficiency of the proposed method are verified through numerical examples.

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 Time-Variant Reliability Analysis Method Based on Stochastic Process Discretization

2014 ◽  
Vol 136 (9) ◽  
Author(s):  
C. Jiang ◽  
X. P. Huang ◽  
X. Han ◽  
D. Q. Zhang
Keyword(s):  
Stochastic Process ◽  
Reliability Analysis ◽  
System Reliability ◽  
Limit State ◽  
Complex Structure ◽  
Random Variable ◽  
State Function ◽  
Analysis Method ◽  
Reliability Problem ◽  
Reliability Method

Time-variant reliability problems caused by deterioration in material properties, dynamic load uncertainty, and other causes are widespread among practical engineering applications. This study proposes a novel time-variant reliability analysis method based on stochastic process discretization (TRPD), which provides an effective analytical tool for assessing design reliability over the whole lifecycle of a complex structure. Using time discretization, a stochastic process can be converted into random variables, thereby transforming a time-variant reliability problem into a conventional time-invariant system reliability problem. By linearizing the limit-state function with the first-order reliability method (FORM) and furthermore, introducing a new random variable, the converted system reliability problem can be efficiently solved. The TRPD avoids the calculation of outcrossing rates, which simplifies the process of solving time-variant reliability problems and produces high computational efficiency. Finally, three numerical examples are used to verify the effectiveness of this approach.

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.

scholarly journals High Dimension Model Representation-Based Response Surface for Reliability Analysis of Tunnel

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Hongbo Zhao
Keyword(s):  
Reliability Analysis ◽  
Response Surface ◽  
Reliability Index ◽  
Limit State ◽  
State Function ◽  
Limit State Function ◽  
Implicit Function ◽  
Surface Method ◽  
Reliability Method ◽  
Rock Tunnel

Uncertainty is an important prosperity to rock tunnel. Reliability analysis is widely used to deal with the uncertainty. But it is difficult to be adopted in rock tunnel using the traditional reliability method because the limit state function is an implicit function. High dimension model representation (HDMR) can approximate the high dimensional, nonlinear, and implicit function using the low dimensional function. In this study, the HDMR method was adapted to approximate the limit state function through combining with response surface method (RSM). A new reliability analysis approach of HDMR-based response surface method, combined with the first-order reliability method (FORM), is developed to calculate the reliability index of tunnel, and implementation of the method is explained briefly. A circular tunnel with analytical solution and horseshoe tunnel with numerical solution are used to demonstrate the proposed method. The obtained reliability index is in excellent agreement with Low and Tang’s (2007) method and traditional RSM. It shows that HDMR-based response surface can approximate well the limit state function, and the proposed method is an efficient and effective approach for reliability analysis in tunnel engineering. It is very useful for reliability analysis of practical large-scale rock engineering.

scholarly journals An Improved Structural Reliability Analysis Method Based on Local Approximation and Parallelization

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 209
Author(s):  
Bolin Liu ◽  
Liyang Xie
Keyword(s):  
Reliability Analysis ◽  
Failure Probability ◽  
Structural Reliability ◽  
Limit State ◽  
Local Approximation ◽  
State Function ◽  
Limit State Function ◽  
Enrichment Technique ◽  
Reliability Method ◽  
Multiple Sample

The Kriging-based reliability method with a sequential design of experiments (DoE) has been developed in recent years for implicit limit state functions. Such methods include the efficient global reliability analysis, the active learning reliability method combining Kriging and MCS Simulations. In this research, a novel local approximation method based on the most probable failure point (MPFP) is proposed to improve such methods. In this method, the MPFP calculated in the last iteration is the center of the next sampling region. The size of the local region depends on the reliability index obtained by the First Order Reliability Method (FORM) and the deviation distance of the standard deviation. The proposed algorithm, which approximates the limit state function accurately near MPFP rather than in the whole design space, can avoid selecting samples in regions that have negligible effects on the reliability analysis results. In addition, a multi-point enrichment technique is also introduced to select multiple sample points in each iteration. After the high-quality approximation of limit state function is obtained, the failure probability is calculated by the Monte Carlo method. Four numerical examples are used to validate the accuracy and efficiency of the proposed method. Results show that the proposed method is very effective for an accurate evaluation of the failure probability.

scholarly journals Time-Dependent Reliability Analysis of Reinforced Concrete Beams Subjected to Uniform and Pitting Corrosion and Brittle Fracture

Materials ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 1820
Author(s):  
Mohamed El Amine Ben Seghier ◽  
Behrooz Keshtegar ◽  
Hussam Mahmoud
Keyword(s):  
Reinforced Concrete ◽  
Brittle Fracture ◽  
Reliability Analysis ◽  
Pitting Corrosion ◽  
Structural Reliability ◽  
Time Dependent ◽  
State Function ◽  
Rc Beams ◽  
Highly Nonlinear ◽  
Reliability Method

Reinforced concrete (RC) beams are basic elements used in the construction of various structures and infrastructural systems. When exposed to harsh environmental conditions, the integrity of RC beams could be compromised as a result of various deterioration mechanisms. One of the most common deterioration mechanisms is the formation of different types of corrosion in the steel reinforcements of the beams, which could impact the overall reliability of the beam. Existing classical reliability analysis methods have shown unstable results when used for the assessment of highly nonlinear problems, such as corroded RC beams. To that end, the main purpose of this paper is to explore the use of a structural reliability method for the multi-state assessment of corroded RC beams. To do so, an improved reliability method, namely the three-term conjugate map (TCM) based on the first order reliability method (FORM), is used. The application of the TCM method to identify the multi-state failure of RC beams is validated against various well-known structural reliability-based FORM formulations. The limit state function (LSF) for corroded RC beams is formulated in accordance with two corrosion types, namely uniform and pitting corrosion, and with consideration of brittle fracture due to the pit-to-crack transition probability. The time-dependent reliability analyses conducted in this study are also used to assess the influence of various parameters on the resulting failure probability of the corroded beams. The results show that the nominal bar diameter, corrosion initiation rate, and the external loads have an important influence on the safety of these structures. In addition, the proposed method is shown to outperform other reliability-based FORM formulations in predicting the level of reliability in RC beams.

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.

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