Structural Reliability Analysis Using Quadratic Polynomial Response Surface and Finite Element in MATLAB

2016 ◽  
Author(s):  
M. M. A. Wahab ◽  
V. J. Kurian ◽  
M. S. Liew ◽  
Z. Nizamani ◽  
D. K. Kim
Keyword(s):  
Finite Element ◽  
Reliability Analysis ◽  
Response Surface ◽  
Structural Reliability ◽  
Limit State ◽  
Quadratic Polynomial ◽  
System Level ◽  
Approximation Technique ◽  
Reliability Indices ◽  
Polynomial Response Surface

Many aging jacket platforms are being pushed for continued use beyond their design life due to advancement in oil extracting technology and economic reasons. Thus reassessment to determine the platform safety is vital. But no exact guide on methods to assess the safety of the aging platforms is available. Hence, development of reliability analysis methodologies is an active research area. Meanwhile, reassessment deals with numerous uncertainties especially in the load and resistance variables of a jacket platform. Response Surface methodology, a limit state approximation technique was deployed by many in many engineering fields to apprehend inherent uncertainty. Hence in this work, a reliability analysis methodology that combines simple response surface and finite element approach in MATLAB is adopted. The approach assumes a physical transfer function utilizing explicit multivariate expressions and random variables. Also, this avoids large number of finite element simulation required for any probabilistic analysis. The methodology developed allows for reliability analysis to be performed based on easy to program procedures. It also addresses the platform and environmental specific uncertainty variables to distinguish the distinctive characteristics of the cases. Upon execution of multiple finite element simulations, response of components and systems are formulated using quadratic polynomial response surface expressions, which eventually are utilized in the limit state functions. Later using numerical techniques in a separate computational routine the reliability indices are estimated. Utilizing the developed method, component and system level reliability indices are obtained. The developed methodology also has been verified with method currently available in the practice as well as with typical simulation method i.e. Monte Carlo Simulation.

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>

Reliability Analysis of Foundation Pit by Improved Response Surface Method

2011 ◽  
Vol 147 ◽  
pp. 197-202 ◽  
Author(s):  
Jiang Zhou ◽  
Jing Cao ◽  
Yu He ◽  
Jie Song
Keyword(s):  
Reliability Analysis ◽  
Response Surface ◽  
Structural Reliability ◽  
Lateral Displacement ◽  
Limit State ◽  
Uniform Design ◽  
Design Parameters ◽  
State Function ◽  
Foundation Pit ◽  
Improved Response Surface Method

Lacking of explicit limit state function (LSF) will result large quantities of computational efforts for a FEAM based structural reliability analysis. An improved response surface (RS) method is proposed to analyze the failure probability of foundation pit through combining uniform design (UD) and non-parametric regression (NPR). Deferent levels of design parameters are first delicately selected according to UD and then FEAM is used to analysis corresponding pit response parameters including maximum lateral displacement of wall, settlement of ground, safety factor of overall stability, safety factors of against overturning, heave and piping. The RS relationship is then established through NPR based on inputs and responses. At last, a direct Mont Carlo Simulation is carried out to obtain the probability density function of response parameters.

Reliability Analysis of Self-Anchored Suspension Bridge by Improved Response Surface Method

2011 ◽  
Vol 90-93 ◽  
pp. 869-873 ◽  
Author(s):  
Xiao Lin Yu ◽  
Quan Sheng Yan
Keyword(s):  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Structural Reliability ◽  
Limit State ◽  
Suspension Bridge ◽  
Support Vector ◽  
Surface Method ◽  
Reliability Method ◽  
Improved Response Surface Method

The response surface method (RSM) developed in recent years is an effective way to solve the structural reliability problems with implicit performance function. In order to improve the computational efficiency and make RSM suitable well to large and complex engineering structures, the reliability analysis method based on uniform design method (UDM) and support vector machine (SVM) was proposed. UDM is adopted to select training data and SVM is used as response surface. Structural reliability index is calculated in combination with the traditional reliability analysis methods (such as, the first-order reliability method (FORM), the second-order reliability method (SORM) or Monte Carlo simulation method (MCSM)). Numerical examples show that sampled with the UDM can greatly reduce the number of samples required for training by SVM model, and a very good approximation of the limit state surface can be obtained to get the failure probability. The reliability analysis of the under serviceability limit-state of a typical self-anchored suspension bridge——Sanchaji Bridge was carried out with the improved response surface method.

Seismic Reliability Analysis of Complex Structure

2012 ◽  
Vol 446-449 ◽  
pp. 2321-2325
Author(s):  
Zhi Yong Zhang ◽  
Wen Bo Huang ◽  
Yue Fa Zhou ◽  
Tian Shu Song
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Reliability Analysis ◽  
Structural Reliability ◽  
Limit State ◽  
Complex Structure ◽  
State Function ◽  
Limit State Function ◽  
Seismic Reliability ◽  
Element Method

The seismic reliability analysis of complex structure is carried out based on the response surface method and finite element method. Firstly, the appropriate design points are selected based on the mean values and standard deviations of the basic random variables. Secondly, the finite element method is employed to obtain the values of the limit state function of the complex structure. Thirdly, with selected design points and the obtained values of the limit state function of the complex structure, a polynomial function is constructed to approximate the original implicit limit state function. Then, with the established explicit polynomial limit state function and available methods of structural reliability analysis, the seismic reliability of the complex structure is estimated. Numerical analyses show that the established method is simple to use for the evaluation of the reliability analysis of complex structure.

A modified downhill simplex algorithm interpolation response surface method for structural reliability analysis

2019 ◽  
Vol 37 (4) ◽  
pp. 1423-1450
Author(s):  
Hailiang Su ◽  
Fengchong Lan ◽  
Yuyan He ◽  
Jiqing Chen
Keyword(s):  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Structural Reliability ◽  
Limit State ◽  
Simplex Algorithm ◽  
Content Type ◽  
Structural Reliability Analysis ◽  
Surface Method ◽  
Downhill Simplex

Purpose Because of the high computational efficiency, response surface method (RSM) has been widely used in structural reliability analysis. However, for a highly nonlinear limit state function (LSF), the approximate accuracy of the failure probability mainly depends on the design point, and the result is that the response surface function composed of initial experimental points rarely fits the LSF exactly. The inaccurate design points usually cause some errors in the traditional RSM. The purpose of this paper is to present a hybrid method combining adaptive moving experimental points strategy and RSM, describing a new response surface using downhill simplex algorithm (DSA-RSM). Design/methodology/approach In DSA-RSM, the operation mechanism principle of the basic DSA, in which local descending vectors are automatically generated, was studied. Then, the search strategy of the basic DSA was changed and the RSM approximate model was reconstructed by combining the direct search advantage of DSA with the reliability mechanism of response surface analysis. Findings The computational power of the proposed method is demonstrated by solving four structural reliability problems, including the actual engineering problem of a car collision. Compared to specific structural reliability analysis methods, the approach of modified DSA interpolation response surface for structural reliability has a good convergent capability and computational accuracy. Originality/value This paper proposes a new RSM technology based on proxy model to complete the reliability analysis. The originality of this paper is to present an improved RSM that adjusts the position of the experimental points judiciously by using the DSA principle to make the fitted response surface closer to the actual limit state surface.

An Indicator Response Surface Method for Simulation-Based Reliability Analysis

2008 ◽  
Vol 130 (7) ◽  
Author(s):  
Tong Zou ◽  
Zissimos P. Mourelatos ◽  
Sankaran Mahadevan ◽  
Jian Tu
Keyword(s):  
Reliability Analysis ◽  
Response Surface ◽  
Structural Reliability ◽  
Least Squares Method ◽  
Limit State ◽  
Sampling Technique ◽  
Latin Hypercube Sampling ◽  
Simulation Method ◽  
Indicator Function ◽  
Highly Nonlinear

An accurate and efficient Monte Carlo simulation method is presented for limit-state-based reliability analysis at both component and system levels, using a response surface approximation of the failure indicator function. The cross-validated moving least squares method is used to construct the response surface of the indicator function, based on an optimum symmetric Latin hypercube sampling technique. The proposed method can handle problems with complicated limit state(s). Also, it can easily handle implicit, highly nonlinear limit-state functions, with variables of any statistical distributions and correlations. The method appears to be particularly efficient for multiple limit state and multiple design point problems. Three structural reliability examples are used to highlight its superior accuracy and efficiency over traditional reliability methods.

Time-Dependent Reliability Analysis Through Response Surface Method

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Dequan Zhang ◽  
Xu Han ◽  
Chao Jiang ◽  
Jie Liu ◽  
Qing Li
Keyword(s):  
Reliability Analysis ◽  
Response Surface ◽  
Structural Reliability ◽  
Time Dependent ◽  
Gaussian Stochastic Process ◽  
Reliability Indices ◽  
Novel Approach ◽  
Reliability Method ◽  
Optimal Linear ◽  
Uncertain Structures

In time-dependent reliability analysis, the first-passage method has been extensively used to evaluate structural reliability under time-variant service circumstances. To avoid computing the outcrossing rate in this method, surrogate modeling may provide an effective alternative for calculating the time-dependent reliability indices in structural analysis. A novel approach, namely time-dependent reliability analysis with response surface (TRARS), is thus introduced in this paper to estimate the time-dependent reliability for nondeterministic structures under stochastic loads. A Gaussian stochastic process is generated by using the expansion optimal linear estimation (EOLE) method which has proven to be more accurate and efficient than some series expansion discretization techniques. The random variables and maximum responses of uncertain structures are treated as the input and output parameters, respectively. Through introducing the response surface (RS) model, a novel iterative procedure is proposed in this study. A Bucher strategy is adopted to generate the initial sample points, and a gradient projection technique is used to generate new sampling points for updating the RS model in each iteration. The time-dependent reliability indices and probabilities of failure are thus obtained efficiently using the first-order reliability method (FORM) over a certain design lifetime. In this study, four demonstrative examples are provided for illustrating the accuracy and efficiency of the proposed method.

Reliability and reliability-based sensitivity analysis of self-centering buckling restrained braces using meta-models

2021 ◽  
pp. 1045389X2110263
Author(s):  
Seyede Vahide Hashemi ◽  
Mahmoud Miri ◽  
Mohsen Rashki ◽  
Sadegh Etedali
Keyword(s):  
Failure Probability ◽  
Limit State ◽  
Computational Cost ◽  
Sensitivity Analyses ◽  
State Function ◽  
Reliability Indices ◽  
Buckling Restrained Brace ◽  
Polynomial Response Surface ◽  
Nonlinear Dynamic Analyses ◽  
High Computational Cost

This paper aims to carry out sensitivity analyses to study how the effect of each design variable on the performance of self-centering buckling restrained brace (SC-BRB) and the corresponding buckling restrained brace (BRB) without shape memory alloy (SMA) rods. Furthermore, the reliability analyses of BRB and SC-BRB are performed in this study. Considering the high computational cost of the simulation methods, three Meta-models including the Kriging, radial basis function (RBF), and polynomial response surface (PRSM) are utilized to construct the surrogate models. For this aim, the nonlinear dynamic analyses are conducted on both BRB and SC-BRB by using OpenSees software. The results showed that the SMA area, SMA length ratio, and BRB core area have the most effect on the failure probability of SC-BRB. It is concluded that Kriging-based Monte Carlo Simulation (MCS) gives the best performance to estimate the limit state function (LSF) of BRB and SC-BRB in the reliability analysis procedures. Considering the effects of changing the maximum cyclic loading on the failure probability computation and comparison of the failure probability for different LSFs, it is also found that the reliability indices of SC-BRB were always higher than the corresponding reliability indices determined for BRB which confirms the performance superiority of SC-BRB than BRB.

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