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.

An Indicator Response Surface-Based Monte Carlo Method for Efficient Component and System Reliability Analysis

2003 ◽  
Author(s):  
Tong Zou ◽  
Zissimos P. Mourelatos ◽  
Sankaran Mahadevan ◽  
Jian Tu
Keyword(s):  
Monte Carlo ◽  
Reliability Analysis ◽  
Response Surface ◽  
Limit State ◽  
Sampling Technique ◽  
Indicator Function ◽  
Computational Method ◽  
State Function ◽  
Engineering Systems ◽  
Highly Nonlinear

Reliability analysis methods are commonly used in engineering design, in order to meet reliability and quality measures. An accurate and efficient computational method is presented for reliability analysis of engineering systems at both the component and system levels. The method can easily handle implicit, highly nonlinear limit-state functions, with correlated or non-correlated random variables, which are described by any probabilistic distribution. It is based on a constructed response surface of an indicator function, which determines the “failure” and “safe” regions, according to the performance function. A Monte Carlo simulation (MCS) calculates the probability of failure based on a response surface of the indicator function, instead of the computationally expensive limit-state function. The Cross-Validated Moving Least Squares (CVMLS) method is used to construct the response surface of the indicator function, based on an Optimum Symmetric Latin Hypercube (OSLH) sampling technique. A number of numerical examples highlight the superior accuracy and efficiency of the proposed method over commonly used reliability methods.

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.

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.

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.

scholarly journals Structural Reliability Algorithms of Kriging Model Based on Improved Learning Strategy

2020 ◽  
Vol 38 (2) ◽  
pp. 412-419
Author(s):  
Linxiong Hong ◽  
Huacong Li ◽  
Kai Peng ◽  
Hongliang Xiao
Keyword(s):  
Active Learning ◽  
Reliability Analysis ◽  
Structural Reliability ◽  
Learning Strategy ◽  
Limit State ◽  
Surface Region ◽  
Kriging Model ◽  
State Function ◽  
Limit State Function ◽  
Highly Nonlinear

Aiming at the problems of implicit and highly nonlinear limit state function in the process of reliability analysis of mechanical products, a reliability analysis method of mechanical structures based on Kriging model and improved EGO active learning strategy is proposed. For the problem that the traditional EGO method cannot effectively select points in the limit state surface region, an improved EGO method is proposed. By dealing with the predicted values of sample point model with absolute values and assume that the distribution state of response values remains the same, the work focus of active learning selection points is moved to the vicinity, where the points are with larger prediction variance or close to the limit state surface. Three examples show that, compared with the classical active learning method, the proposed method has good global and local search ability, and can estimate the exact failure probability value under the condition of less calculation of the limit state function.

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.

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