AN ITERATIVE HDMR APPROACH FOR ENGINEERING RELIABILITY ANALYSIS

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Qian Wang
Keyword(s):  
Reliability Analysis ◽  
Probabilistic Analysis ◽  
Surrogate Models ◽  
Second Order ◽  
High Dimensional Model Representation ◽  
Performance Function ◽  
Reliability Indices ◽  
Reliability Method ◽  
Sample Points ◽  
A Performance

Engineering reliability analysis has long been an active research area. Surrogate models, or metamodels, are approximate models that can be created to replace implicit performance functions in the probabilistic analysis of engineering systems. Traditional 1st-order or second-order high dimensional model representation (HDMR) methods are shown to construct accurate surrogate models of response functions in an engineering reliability analysis. Although very efficient and easy to implement, 1st-order HDMR models may not be accurate, since the cross-effects of variables are neglected. Second-order HDMR models are more accurate; however they are more complicated to implement. Moreover, they require much more sample points, i.e., finite element (FE) simulations, if FE analyses are employed to compute values of a performance function. In this work, a new probabilistic analysis approach combining iterative HDMR and a first-order reliability method (FORM) is investigated. Once a performance function is replaced by a 1st-order HDMR model, an alternate FORM is applied. In order to include higher-order contributions, additional sample points are generated and HDMR models are updated, before FORM is reapplied. The analysis iteration continues until the reliability index converges. The novelty of the proposed iterative strategy is that it greatly improves the efficiency of the numerical algorithm. As numerical examples, two engineering problems are studied and reliability analyses are performed. Reliability indices are obtained within a few iterations, and they are found to have a good accuracy. The proposed method using iterative HDMR and FORM provides a useful tool for practical engineering applications.

Reliability Analysis of Underground Structures Using Metamodels and FORM

2019 ◽  
Author(s):  
Qian Wang ◽  
Jun Ji
Keyword(s):  
Reliability Analysis ◽  
Alternative Form ◽  
Underground Structures ◽  
Mathematical Functions ◽  
Performance Function ◽  
Reliability Indices ◽  
Nonlinear Responses ◽  
Reliability Method ◽  
Practical Engineering ◽  
Implicit Response

<p>An engineering reliability analysis method of underground structures using metamodels and a first-order reliability method (FORM) was studied. Surrogate models, or metamodels are approximate models that can be constructed to replace implicit response functions that involve finite element analyses. The radial basis functions (RBFs) are suitable for creating metamodels for general linear or nonlinear responses and they are locally and globally adaptive. After a performance function was replaced by an augmented RBF metamodel, an alternative FORM was applied. The method was tested using mathematical functions and applied to a tunnel engineering example. Different numbers of samples were tested and reliability analyses were performed. The failure probabilities and reliability indices were found to have a good accuracy. The proposed method combining RBFs and FORM is useful for practical engineering problems involving expensive response simulations.</p>

ENGINEERING PROBABILISTIC ANALYSIS USING MODEL REDUCTION AND AUGMENTED RADIAL BASIS FUNCTIONS

2020 ◽  
Vol 7 (2) ◽  
Author(s):  
Qian Wang
Keyword(s):  
Model Reduction ◽  
Reliability Analysis ◽  
Radial Basis Functions ◽  
Probabilistic Analysis ◽  
Basis Functions ◽  
Engineering System ◽  
Performance Function ◽  
First Order ◽  
Engineering Problems ◽  
Radial Basis

Probabilistic analysis of practical engineering problems has long been based on traditional sampling-based approaches, such as Monte Carlo Simulations (MCS) and gradient-based first-order and second-order methods. Since the finite element (FE) or other numerical methods are required to evaluate engineering system responses, such as forces or displacements, it is not efficient to directly integrate FE and sampling-based analysis approaches. Over the years, various approximate methods have been developed and applied to the reliability analysis of engineering problems. In this study, an efficient model reduction technique based on high-dimensional model reduction (HDMR) method has been developed using augmented radial basis functions (RBFs). The basic idea is to use augmented RBFs to construct HDMR component functions. The first-order HDMR model only requires sample points along each variable axis. The HDMR model, once created and used to explicitly express a performance function, is further combined with MCS to perform probabilistic calculations. As test problems, a mathematical problem and a 10-bar truss example are studied using the proposed reliability analysis approach. The proposed method works well, and accurate reliability analysis results are found with a small number of original performance function evaluations, i.e., FE simulations.

A Novel Second-Order Reliability Method (SORM) Using Non-Central or Generalized Chi-Squared Distributions

2012 ◽  
Author(s):  
Ikjin Lee ◽  
David Yoo ◽  
Yoojeong Noh
Keyword(s):  
Reliability Analysis ◽  
Linear Combination ◽  
Quadratic Function ◽  
Failure Surface ◽  
Probability Of Failure ◽  
Second Order ◽  
Cumulative Distribution ◽  
State Function ◽  
Reliability Method ◽  
Chi Squared

This paper proposes a novel second-order reliability method (SORM) using non-central or general chi-squared distribution to improve the accuracy of reliability analysis in existing SORM. Conventional SORM contains three types of errors: (1) error due to approximating a general nonlinear limit state function by a quadratic function at most probable point (MPP) in the standard normal U-space, (2) error due to approximating the quadratic function in U-space by a hyperbolic surface, and (3) error due to calculation of the probability of failure after making the previous two approximations. The proposed method contains the first type of error only which is essential to SORM and thus cannot be improved. However, the proposed method avoids the other two errors by describing the quadratic failure surface with the linear combination of non-central chi-square variables and using the linear combination for the probability of failure estimation. Two approaches for the proposed SORM are suggested in the paper. The first approach directly calculates the probability of failure using numerical integration of the joint probability density function (PDF) over the linear failure surface and the second approach uses the cumulative distribution function (CDF) of the linear failure surface for the calculation of the probability of failure. The proposed method is compared with first-order reliability method (FORM), conventional SORM, and Monte Carlo simulation (MCS) results in terms of accuracy. Since it contains fewer approximations, the proposed method shows more accurate reliability analysis results than existing SORM without sacrificing efficiency.

System Reliability Analysis With Second Order Saddlepoint Approximation

2019 ◽  
Author(s):  
Hao Wu ◽  
Xiaoping Du
Keyword(s):  
Normal Distribution ◽  
Reliability Analysis ◽  
System Reliability ◽  
Multivariate Normal Distribution ◽  
High Efficiency ◽  
Saddlepoint Approximation ◽  
Second Order ◽  
Multivariate Normal ◽  
System Reliability Analysis ◽  
Reliability Method

Abstract The second order saddlepoint approximation (SPA) has been used for component reliability analysis for higher accuracy than the traditional second order reliability method. This work extends the second order SPA to system reliability analysis. The joint distribution of all the component responses is approximated by a multivariate normal distribution. To maintain high accuracy of the approximation, the proposed method employs the second order SPA to accurately generate the marginal distributions of component responses; to simplify computations and achieve high efficiency, the proposed method estimates the covariance matrix of the multivariate normal distribution with the first order approximation to component responses. Examples demonstrate the high effectiveness of the second order SPA method for system reliability analysis.

On the Use of Surrogate Models in Reliability-Based Analysis of Dented Pipes

2016 ◽  
Author(s):  
Sherif Hassanien ◽  
Muntaseer Kainat ◽  
Samer Adeeb ◽  
Doug Langer
Keyword(s):  
Finite Element ◽  
Reliability Analysis ◽  
Random Systems ◽  
Probability Of Failure ◽  
Surrogate Models ◽  
Operating Conditions ◽  
Additional Stress ◽  
Internal Stresses ◽  
Stress Risers ◽  
Reliability Method

Pipeline dents lead to changes in the stress/strain state of the pipe body, making it more susceptible to integrity concerns. This susceptibility is especially prevalent in cases where additional stress risers such as crack and/or corrosion features interact with the dented region. While some guidance is available in codes, regulations, and industry best practices, there is substantial room for innovation and improvement to ensure pipeline safety. Existing explicit models are primarily based on experimental correlations and historical findings using simple parameters such as dent depth and location on the pipeline. Moreover, these models are subjected to a substantial uncertainty in both accuracy and precision. This paper presents a state-of-the-art methodology for analyzing dents and dents associated with stress risers through the use of finite element method (FEM) as a mechanical model and reliability analysis to address uncertainties associated with input variables. FEM is used to model the full geometry of dents and any interacting stress risers reported by inline inspection (ILI) to be incorporated into calculations of the internal stresses/strains within the feature. Theoretically, FEM and reliability analysis can be integrated through reliability-based stochastic finite element methodologies due to the absence of closed form mechanical models of dented pipes. However, these methodologies are computationally prohibitive and not suited/designed for frequent integrity analysis. This study aims at further advancing such integration by combining FEM with reliability science to account for pipe properties and measurement uncertainties in order to determine the probability of failure under different operating conditions using surrogate models. This provides the opportunity to more accurately assess the risk posed by ILI reported dent features. Herein, surrogate models refer to the response surface method (RSM) which is considered as a valuable tool for obtaining insight into the behavior of structural random systems at low computational costs. The proposed approach was applied focusing on a plain dent, a dent interacting with a corrosion feature, and a dent interacting with a crack feature. First Order Reliability Method (FORM) is used to evaluate the probability of failure/reliability using the resulting RSM non-linear limit states for each dent feature.

Assessment of time-dependent reliability of reinforced concrete columns with uncertain load eccentricity

2000 ◽  
Vol 27 (3) ◽  
pp. 389-399
Author(s):  
H P Hong ◽  
W Zhou
Keyword(s):  
Reinforced Concrete ◽  
Reliability Analysis ◽  
Axial Load ◽  
Bending Moment ◽  
Time Dependent ◽  
Sensitivity Analyses ◽  
Live Load ◽  
Rc Columns ◽  
Reliability Indices ◽  
Reliability Method

An approach for the time-dependent reliability analysis of reinforced concrete (RC) columns considering the correlation between the axial load and the bending moment or the uncertainty in the load eccentricity is presented. The approach recursively uses the efficient first-order reliability method for the time-dependent reliability analysis. The proposed approach is more efficient than the ones used in the literature for the reliability analysis of RC columns. The proposed approach is used to carry out sensitivity analyses of the reliability of short RC columns to the time-dependent live load effects and to the correlation between the axial load and the bending moment. Results of the analyses suggest that the reliability of RC columns can be sensitive to the correlation between the axial load and the bending moment due to live load. The differences between the reliability indices obtained by considering the live load modeled as a pulse process and as an extreme variate can be large.Key words: reliability, load, time-dependent, time-independent, uncertainty, correlation, concrete, reinforcement, column.

Complementary Intersection Method for System Reliability Analysis

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
Byeng D. Youn ◽  
Pingfeng Wang
Keyword(s):  
Reliability Analysis ◽  
System Reliability ◽  
High Efficiency ◽  
Second Order ◽  
Approximation Formula ◽  
Joint Failure ◽  
System Reliability Analysis ◽  
Reliability Method ◽  
Reliability Methods ◽  
Intersection Method

Although researchers desire to evaluate system reliability accurately and efficiently over the years, little progress has been made on system reliability analysis. Up to now, bound methods for system reliability prediction have been dominant. However, two primary challenges are as follows: (1) Most numerical methods cannot effectively evaluate the probabilities of the second (or higher)–order joint failure events with high efficiency and accuracy, which are needed for system reliability evaluation and (2) there is no unique system reliability approximation formula, which can be evaluated efficiently with commonly used reliability methods. Thus, this paper proposes the complementary intersection (CI) event, which enables us to develop the complementary intersection method (CIM) for system reliability analysis. The CIM expresses the system reliability in terms of the probabilities of the CI events and allows the use of commonly used reliability methods for evaluating the probabilities of the second–order (or higher) joint failure events efficiently. To facilitate system reliability analysis for large-scale systems, the CI-matrix can be built to store the probabilities of the first- and second-order CI events. In this paper, three different numerical solvers for reliability analysis will be used to construct the CI-matrix numerically: first-order reliability method, second-order reliability method, and eigenvector dimension reduction (EDR) method. Three examples will be employed to demonstrate that the CIM with the EDR method outperforms other methods for system reliability analysis in terms of efficiency and accuracy.

scholarly journals A High-Dimensional Reliability Analysis Method for Simulation-Based Design Under Uncertainty

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Mohammad Kazem Sadoughi ◽  
Meng Li ◽  
Chao Hu ◽  
Cameron A. MacKenzie ◽  
Soobum Lee ◽  
...  
Keyword(s):  
Reliability Analysis ◽  
Surrogate Model ◽  
Efficient Estimation ◽  
High Dimensional ◽  
Design Under Uncertainty ◽  
Performance Function ◽  
Simulation Based Design ◽  
Simulation Based ◽  
Computationally Expensive ◽  
Sample Points

Reliability analysis involving high-dimensional, computationally expensive, highly nonlinear performance functions is a notoriously challenging problem in simulation-based design under uncertainty. In this paper, we tackle this problem by proposing a new method, high-dimensional reliability analysis (HDRA), in which a surrogate model is built to approximate a performance function that is high dimensional, computationally expensive, implicit, and unknown to the user. HDRA first employs the adaptive univariate dimension reduction (AUDR) method to construct a global surrogate model by adaptively tracking the important dimensions or regions. Then, the sequential exploration–exploitation with dynamic trade-off (SEEDT) method is utilized to locally refine the surrogate model by identifying additional sample points that are close to the critical region (i.e., the limit-state function (LSF)) with high prediction uncertainty. The HDRA method has three advantages: (i) alleviating the curse of dimensionality and adaptively detecting important dimensions; (ii) capturing the interactive effects among variables on the performance function; and (iii) flexibility in choosing the locations of sample points. The performance of the proposed method is tested through three mathematical examples and a real world problem, the results of which suggest that the method can achieve an accurate and computationally efficient estimation of reliability even when the performance function exhibits high dimensionality, high nonlinearity, and strong interactions among variables.

Reliability Analysis of Subgrade Bearing Capacity of Gravity Foundation of Wind Turbine Based on JC Method

2011 ◽  
Vol 413 ◽  
pp. 314-319
Author(s):  
Zhong Qing Cheng ◽  
Ping Yang ◽  
Hai Bo Jiang
Keyword(s):  
Bearing Capacity ◽  
Wind Turbine ◽  
Reliability Analysis ◽  
Reliability Index ◽  
Maximum Pressure ◽  
Performance Function ◽  
Iterative Calculation ◽  
Reliability Method ◽  
Foundation Base ◽  
Index Effect

The design of foundation of wind turbine should meet the requirement of subgrade bearing capacity. In this paper, reliability method was used to analyze the bearing capacity of gravity foundation of wind turbine. The circular gravity foundation in coral sands is taken as research object. By deriving the expression of maximum pressure at the edge of foundation base under the action of overturning moment, the performance function of subgrade bearing capacity reliability analysis is established. JC method is used to calculate the subgrade bearing capacity reliability index. Effect of foundation size to reliability index is analyzed. Iterative calculation shows that the method proposed in this paper can calculate the reliability index of foundation quickly.

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