Effect of Dependent Interval Distribution Parameters on Reliability Prediction

2017 ◽  
Author(s):  
Yao Cheng ◽  
Xiaoping Du
Keyword(s):  
Reliability Analysis ◽  
Limit State ◽  
Distribution Parameter ◽  
State Function ◽  
Simulation And Optimization ◽  
Distribution Parameters ◽  
Reliability Methods ◽  
Input Variables ◽  
Independent Distribution ◽  
Interval Distribution

Distributions of input variables of a limit-state function are required for reliability analysis. The distribution parameters are commonly estimated using samples. If some of the samples are in the form of intervals, the estimated distribution parameters will also be given in intervals. Traditional reliability methodologies assume that interval distribution parameters are independent, but as shown in this study, the parameters are actually dependent since they are estimated from the same set of samples. This study investigates the effect of the dependence of distribution parameters on the accuracy of reliability analysis results. The major approach is numerical simulation and optimization. This study indicates that the independent distribution parameter assumption makes the estimated reliability bounds wider than the true bounds due to interval samples. The reason is that the actual combination of the distribution parameters may not include the entire box-type domain assumed by the independent interval parameter assumption. The results of this study not only reveal the cause of the inaccuracy of the independent distribution parameter assumption, but also demonstrate a need of developing new reliability methods to accommodate dependent distribution parameters.

scholarly journals Toward the Effect of Dependent Distribution Parameters on Reliability Prediction

2018 ◽  
Vol 18 (2) ◽  
Author(s):  
Yao Cheng ◽  
Xiaoping Du
Keyword(s):  
Distribution Parameter ◽  
Reliability Prediction ◽  
Interval Parameter ◽  
Analysis And Design ◽  
Simulation And Optimization ◽  
Reliability Bounds ◽  
Distribution Parameters ◽  
Reliability Methods ◽  
Independent Distribution ◽  
Interval Distribution

Random variables are commonly encountered in engineering applications, and their distributions are required for analysis and design, especially for reliability prediction during the design process. Distribution parameters are usually estimated using samples. In many applications, samples are in the form of intervals, and the estimated distribution parameters will also be in intervals. Traditional reliability methodologies assume independent interval distribution parameters, but as shown in this study, the parameters are actually dependent since they are estimated from the same set of samples. This study investigates the effect of the dependence of distribution parameters on the accuracy of reliability analysis results. The major approach is numerical simulation and optimization. This study demonstrates that the independent distribution parameter assumption makes the estimated reliability bounds wider than the true bounds. The reason is that the actual combination of the distribution parameters may not include the entire box-type domain assumed by the independent interval parameter assumption. The results of this study not only reveal the cause of the imprecision of the independent distribution parameter assumption, but also demonstrate a need of developing new reliability methods to accommodate dependent distribution parameters.

An Efficient Response Surface Method Using Givens Transformation for Structural Reliability Analysis

2012 ◽  
Vol 532-533 ◽  
pp. 408-411
Author(s):  
Wei Tao Zhao ◽  
Yi Yang ◽  
Tian Jun Yu
Keyword(s):  
Response Surface ◽  
Response Surface Method ◽  
Structural Reliability ◽  
Limit State ◽  
State Function ◽  
Limit State Function ◽  
Surface Method ◽  
Mathematical Techniques ◽  
Input Variables ◽  
Improved Accuracy

The response surface method was proposed as a collection of statistical and mathematical techniques that are useful for modeling and analyzing a system which is influenced by several input variables. This method gives an explicit approximation of the implicit limit state function of the structure through a number of deterministic structural analyses. However, the position of the experimental points is very important to improve the accuracy of the evaluation of failure probability. In the paper, the experimental points are obtained by using Givens transformation in such way these experimental points nearly close to limit state function. A Numerical example is presented to demonstrate the improved accuracy and computational efficiency of the proposed method compared to the classical response surface method. As seen from the result of the example, the proposed method leads to a better approximation of the limit state function over a large region of the design space, and the number of experimental points using the proposed method is less than that of classical response surface method.

Response surface method strategies coupled with NLFEA for structural reliability analysis of prestressed bridges

2021 ◽  
Author(s):  
Silvia J. Sarmiento Nova ◽  
Jaime Gonzalez-Libreros ◽  
Gabriel Sas ◽  
Rafael A. Sanabria Díaz ◽  
Maria C. A. Texeira da Silva ◽  
...  
Keyword(s):  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Structural Reliability ◽  
Limit State ◽  
Material Behavior ◽  
Nonlinear Material ◽  
State Function ◽  
Surface Method ◽  
Highly Nonlinear

<p>The Response Surface Method (RSM) has become an essential tool to solve structural reliability problems due to its accuracy, efficacy, and facility for coupling with Nonlinear Finite Element Analysis (NLFEA). In this paper, some strategies to improve the RSM efficacy without compromising its accuracy are tested. Initially, each strategy is implemented to assess the safety level of a highly nonlinear explicit limit state function. The strategy with the best results is then identified and used to carry out a reliability analysis of a prestressed concrete bridge, considering the nonlinear material behavior through NLFEA simulation. The calculated value of &#120573; is compared with the target value established in Eurocode for ULS. The results showed how RSM can be a practical methodology and how the improvements presented can reduce the computational cost of a traditional RSM giving a good alternative to simulation methods such as Monte Carlo.</p>

scholarly journals Semi-Supervised Deep Learning for High-Dimensional Uncertainty Quantification

2020 ◽  
Author(s):  
Zequn Wang ◽  
Mingyang Li
Keyword(s):  
Uncertainty Quantification ◽  
Reliability Analysis ◽  
Supervised Learning ◽  
Dimensional Space ◽  
Limit State ◽  
Failure Surface ◽  
Simulation Method ◽  
High Dimensional ◽  
State Function ◽  
Latent Space

Abstract Conventional uncertainty quantification methods usually lacks the capability of dealing with high-dimensional problems due to the curse of dimensionality. This paper presents a semi-supervised learning framework for dimension reduction and reliability analysis. An autoencoder is first adopted for mapping the high-dimensional space into a low-dimensional latent space, which contains a distinguishable failure surface. Then a deep feedforward neural network (DFN) is utilized to learn the mapping relationship and reconstruct the latent space, while the Gaussian process (GP) modeling technique is used to build the surrogate model of the transformed limit state function. During the training process of the DFN, the discrepancy between the actual and reconstructed latent space is minimized through semi-supervised learning for ensuring the accuracy. Both labeled and unlabeled samples are utilized for defining the loss function of the DFN. Evolutionary algorithm is adopted to train the DFN, then the Monte Carlo simulation method is used for uncertainty quantification and reliability analysis based on the proposed framework. The effectiveness is demonstrated through a mathematical example.

Study on Probabilistic Model of GH4133B for Fatigue-Creep Failure

2009 ◽  
Author(s):  
Dianyin Hu ◽  
Rongqiao Wang
Keyword(s):  
High Temperature ◽  
Reliability Analysis ◽  
Probabilistic Model ◽  
Low Cycle Fatigue ◽  
Limit State ◽  
Interactive Effect ◽  
Creep Damage ◽  
Sensitivity Index ◽  
State Function ◽  
Creep Failure

GH4133B is a nickel-base superalloy which was developed for use in the manufacture of aero-engine turbine disks and other high-temperature components. Since these components are operated at high temperature and under cyclic loading, damage resulting from fatigue-creep interaction is the main factor. The situation is often simulated in laboratories at high temperature low-cycle fatigue. The interactive effect between different loading levels should be considered. The fatigue-creep experiments for alloy GH4133B at 600 Celsius degree have been carried out at continuous cyclic creep (CF) loading to investigate the interaction of creep damage and fatigue damage. Fracture surfaces are examined under the scanning electron microscope (SEM). Then a nonlinear fatigue-creep failure criterion function proposed by Hongyin Mao is employed to fit the experimental data. The probabilistic model of GH4133B under CF loading is established based on the deterministic failure function. Firstly, the random variables influencing the fatigue-creep life and values of the distribution parameters are investigated. Then fatigue-creep damage interaction is discussed and a linear damage accumulation rule is considered, according to which the limit state function used to express the probability of failure is proposed. Lastly, reliability analysis under fatigue-creep failure is proceeded by applying analytical and simulation methods. Furthermore, the random variable with low sensitivity index through the sensitivity analysis can be treated as deterministic parameter during the reliability analysis and reliability design in order to improve the computing efficiency.

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.

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.

scholarly journals Reliability-Based Serviceability Limit State Design of a Jacket Substructure for an Offshore Wind Turbine

Energies ◽  
2019 ◽  
Vol 12 (14) ◽  
pp. 2751 ◽  
Author(s):  
Jianhua Zhang ◽  
Won-Hee Kang ◽  
Ke Sun ◽  
Fushun Liu
Keyword(s):  
Correlation Analysis ◽  
Reliability Analysis ◽  
Limit State ◽  
Statistical Correlation ◽  
Offshore Wind ◽  
Offshore Wind Turbine ◽  
State Function ◽  
Optimized Design ◽  
Foundation Design ◽  
Serviceability Limit State

The development of a structurally optimized foundation design has become one of the main research objectives for offshore wind turbines (OWTs). The design process should be carried out in a probabilistic way due to the uncertainties involved, such as using parametric uncertainties regarding material and geometric properties, and model uncertainties in resistance prediction models and regarding environmental loads. Traditional simple deterministic checking procedures do not guarantee an optimized design because the associated uncertainties are not fully considered. In this paper, a reliability analysis framework is proposed to support the optimized design of jacket foundations for OWTs. The reliability analysis mainly considers the serviceability limit state of the structure according to the requirements of the code. The framework consists of two parts: (i) an important parameter identification procedure based on statistical correlation analysis and (ii) a finite element-simulation-based reliability estimation procedure. The procedure is demonstrated through a jacket structure design of a 3 MW OWT. The analysis results show that the statistical correlation analysis can help to identify the parameters necessary for the overall structural performance. The Latin hypercube sampling and the Monte Carlo simulation using FE models effectively and efficiently evaluate the reliability of the structure while not relying on a surrogate limit state function. A comparison between the proposed framework and the deterministic design shows that the framework can help to achieve a better result closer to the target reliability level.

Fatigue Safety Factors for Flexible Risers Based on Case Specific Reliability Analysis

2005 ◽  
Author(s):  
Bernt J. Leira ◽  
Ragnar T. Igland ◽  
Gro S. Baarholm ◽  
Knut A. Farnes ◽  
Dick Percy
Keyword(s):  
Reliability Analysis ◽  
Limit State ◽  
State Function ◽  
Safety Factors ◽  
Fatigue Lifetime ◽  
Statistical Variation ◽  
Parametric Studies ◽  
Flexible Risers ◽  
Corrosive Environments ◽  
Wave Induced

In the present paper, fatigue safety factors for flexible risers are assessed. A procedure for reliability analysis of wave-induced fatigue is first described. The procedure is based on performing a number of parametric studies with respect to variables that influence the fatigue lifetime. The results of these parametric studies are subsequently combined with models describing the statistical scatter of the same parameters. By application of this procedure, the safety factors which are required in order to reach specific target reliability levels can be computed. Such safety factors are computed for three specific flexible riser configurations. Different SN -curves which correspond to different corrosive environments are considered. The percentwise contribution from each parameter to the total statistical variation of the limit state function is also quantified.

An Efficient Reliability Analysis Method for Structures With Epistemic Uncertainty Using Evidence Theory

2014 ◽  
Author(s):  
Zhe Zhang ◽  
Chao Jiang ◽  
G. Gary Wang ◽  
Xu Han
Keyword(s):  
Reliability Analysis ◽  
Structural Reliability ◽  
Epistemic Uncertainty ◽  
Limit State ◽  
Computational Cost ◽  
Evidence Theory ◽  
State Function ◽  
Limited Information ◽  
Design Point ◽  
Engineering Problems

Evidence theory has a strong ability to deal with the epistemic uncertainty, based on which the uncertain parameters existing in many complex engineering problems with limited information can be conveniently treated. However, the heavy computational cost caused by its discrete property severely influences the practicability of evidence theory, which has become a main difficulty in structural reliability analysis using evidence theory. This paper aims to develop an efficient method to evaluate the reliability for structures with evidence variables, and hence improves the applicability of evidence theory for engineering problems. A non-probabilistic reliability index approach is introduced to obtain a design point on the limit-state surface. An assistant area is then constructed through the obtained design point, based on which a small number of focal elements can be picked out for extreme analysis instead of using all the elements. The vertex method is used for extreme analysis to obtain the minimum and maximum values of the limit-state function over a focal element. A reliability interval composed of the belief measure and the plausibility measure is finally obtained for the structure. Two numerical examples are investigated to demonstrate the effectiveness of the proposed method.

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