Reliability Assessment Of Structural Systems Research Articles

AK-SYS-IE: A novel adaptive Kriging-based method for system reliability assessment combining information entropy

Structural reliability assessment is a popular topic in engineering problems, particularly for the larger and more complex systems with implicit performance functions, also called black-box problems. The reliability assessment for a black-box problem must continuously be computed using simulation models, such as the finite element model, a highly time-consuming process with a high computational cost. The adaptive Kriging has gained considerable attention over the past decade. The Kriging-based reliability assessment method reduces the computational cost to a great extent, on the premise of ensuring the accuracy of reliability assessment. However, many of the currently published system reliability assessment methods, construct adaptive Kriging models by reducing the probability of incorrect prediction of the system state, and do not make full use of the uncertainty of the system state prediction information. To this end, a new Kriging-based method for structural system reliability assessment is proposed in this study. First, the probabilities of incorrect or correct system state predictions were understood from the perspective of information entropy. Second, an active learning strategy is proposed based on information entropy theory. Finally, the advantages of the proposed method are demonstrated and highlighted through several numerical examples. The results show that the proposed method achieves a good balance between the accuracy and computational cost, and the numerical magnitude effect does not affect the computational cost. Moreover, this is an effective method for assessing the reliability of complex systems.

Impact of epistemic and aleatory uncertainties on the seismic reliability assessment of existing structures

Seismic reliability assessment of structural systems is commonly done via the convolution of seismic hazard and structural fragility to get resulting failure rate, and later compute seismic reliability index. Within this frame, many uncertainty sources have to be handled by the risk analyst, who is asked to make some reasonable assumptions in order to carry out his/her seismic safety quantification. However, slight changes in the definition of input parameters and/or the use of different empirical or analytical models can strongly impact the final reliability outcomes. The present work aims therefore to investigate the impact of different sources of uncertainties by comparing together key parameters to be defined in both hazard and fragility analysis, considering a case-study represented by an existing multi-span steel–concrete composite bridge to better understand which of these sources is more impacting on the final estimates. Results show how uncertainties associated to hazard and fragility are as a whole of the same order of magnitude and thus how both uncertainty sources have to be properly considered. In addition, a detailed sensitivity analysis was carried out for ranking the uncertainty sources in relation to their impact on the overall reliability index dispersion. Results showed that the choice of a suitable Ground Motion Prediction Equation (GMPE) model, the non-linear modelling technique and the number of the accelerometric records adopted for the structural analysis seem to be the factors that mostly contribute to the seismic reliability index variability, representing the uncertainty related to these parameters the majority of the overall reliability index dispersion.

Structural system reliability assessment using generalized factorized dimensional reduction method and iterative maximum entropy method

The system reliability analysis of complex engineering structures remains a challenge in the field of reliability. In this work, a high-order moment method using generalized factorized dimensional reduction method (GF-DRM) and iterative maximum entropy method (IMEM) is proposed for structural system reliability assessment. Firstly, the performance functions are described uniformly by equivalent description methods for various system reliability problems. Secondly, a novel point estimation method (PEM) based on GF-DRM is proposed for the high-order moments estimation of the equivalent performance function. Thirdly, the system failure probability of the structures is accurately determined by using the IMEM, which can automatically determine the order of moments. Finally, four examples, including numerical and engineering cases, are investigated to demonstrate the accuracy and efficiency of the proposed method, in which results obtained from the proposed method are compared with some other existing moment methods and Monte Carlo simulation (MCS) method. The results of the examples show the proposed method has fairly high accuracy and efficiency for structural high-order moments estimation and system reliability analysis.

Bayesian networks for disaggregation of structural reliability

Recent developments in theory and solution algorithms have facilitated the application of Bayesian Probabilistic Networks (BPNs) to probabilistic engineering problems. BPNs’ ability to easily perform backward analysis and parameter updating offers advantage over existing methods. This paper attempts to propose a BPN for reliability assessment of structural systems based on their cut-set representation. A five-layer Bayesian network is proposed which includes random variables, component events, failure paths and failure modes to compute the structural probability of failure. Convenient inclusion of parameter dependency or correlation is an advantage of the proposed method. While in existing methods extensive computation or simplifying assumption are used to account for component and mode dependencies, the proposed method utilizes the inherent ability of BPNs to model the joint probability distributions using factors of independent conditional probabilities. This greatly reduces efforts to include parameter dependencies which may significantly affect the output. Application to a real-world example of 4-storey reinforced concrete structure is presented and optimizations to lower the computation costs are reviewed. Also it is described how disaggregation of structural failure and updated distribution of random variables can be obtained using backward inference without any additional recalculations.

An efficient reliability method combining adaptive global metamodel and probability density evolution method

Abstract An efficient reliability method, i.e., AGM-PDEM, is presented which combines the adaptive global metamodel (AGM) and the probability density evolution method (PDEM). The global metamodel is firstly constructed using an adaptive sampling technique and employed to represent the relationship between the equivalent extreme value (EEV) of responses and basic random variables of stochastic systems. The EEVs of representative point sets with enlarged size are approximated by the constructed surrogate model. Reliability of the stochastic systems then can be readily obtained by virtue of the PDEM. To demonstrate the accuracy and efficiency of the proposed method in metamodeling response surface and in assessing system reliability, the global metamodeling of three analytical functions with different nonlinear features, and the reliability analysis of an eight-story shear frame with different random parameters related to the performance level are addressed. A comparative study against the direct Monte Carlo simulation (MCS) with the established metamodel is carried out as well. Numerical results demonstrate that the adaptive sampling technique for global metamodeling is more superior by comparison with the one-stage sampling technique. The AGM-PDEM has a better applicability than the AGM-MCS in dealing with the problems of both moderate and small failure probabilities encountered in engineering structures. Furthermore, both the fidelity of global metamodel and the accuracy of the proposed reliability method can be guaranteed by specifying a moderate stopping condition in the adaptive sampling process. Therefore, the proposed AGM-PDEM exhibits a satisfactory accuracy and a high efficiency for the reliability assessment of structural systems in practice.

Center and Characteristic Seismic Reliability as new indexes for accounting uncertainties in seismic reliability analysis

Seismic reliability analysis is a powerful tool to assess structural safety against ground shaking actions induced by earthquake occurrences. The classic approach for computing seismic reliability of a structural system requires a seismic hazard curve and a fragility function and leads to the estimation of the failure probability of the investigated damage state. However, resulting failure probability is strongly related to the preliminary assumptions in both hazard and fragility analyses, and slight changes in the input model parameters may cause relevant variability of seismic reliability estimates. The present work formalizes a general approach to be followed when dealing with seismic reliability assessment of structural systems, aimed at taking into account the whole uncertainties of the input parameters within hazard and fragility models. In the proposed approach, probability of failure becomes in turn a random variable and therefore new indexes are introduced, namely Expected Failure Rate, Failure Rate Dispersion, Characteristic Failure Rate, Center of Seismic Reliability and Characteristic Seismic Reliability. Lastly, such approach is applied to a case study, where seismic reliability of an existing open-spandrel reinforced concrete arch bridge is analyzed, and results are discussed highlighting some relevant issues.

An adaptive support vector regression method for structural system reliability assessment and its application to a cable-stayed bridge

Engineering structures are most statically indeterminate structures consisting of various types of components and their failure modes exhibit randomness under random loads. A new adaptive support vector regression method is proposed for structural system reliability assessment. Compared with traditional support vector regression, the proposed adaptive support vector regression method involves two updating procedures to estimate structural limit state functions. Three verification examples involving a nonlinear limit state function, a truss bridge structure, and a geometrically nonlinear suspended structure are provided to illustrate the accuracy and the efficiency of the adaptive support vector regression method. A pre-stressed concrete cable-stayed bridge is utilized to demonstrate the applicability of the proposed method. The verification studies show that the proposed adaptive support vector regression method is an efficient method with reasonable accuracy for problems where closed-form failure functions are not available and the failure sequences exist in the structural system. The main failure sequences of the cable-stayed bridge are identified. The application studies of the cable-stayed bridge indicate that (a) the foremost failure sequence is the strength failure of side-span cables followed by the bending failure of towers and (b) the secondary failure sequence is the strength failure of mid-span cables followed by bending failure of mid-span girders.

Reliability assessment of structural systems with interval uncertainties under spectrum-compatible seismic excitations

The paper deals with reliability assessment of linear structures with interval parameters subjected to seismic excitations modeled as stationary spectrum-compatible Gaussian random processes. Under the Vanmarcke assumption that the up-crossings of a specified threshold occur in clumps, an efficient procedure for the evaluation of the bounds of the interval reliability function of the generic response process is presented. The key idea is to view the interval reliability function as depending on the first three interval spectral moments of the structural response rather than on the interval structural parameters. Then, the lower and upper bounds of the interval reliability function are obtained by properly combining the bounds of the interval spectral moments. Such bounds are evaluated in approximate form by applying an approach recently proposed by the authors. Finally, based on the knowledge of the interval reliability function, a method for evaluating the interval survival probability of a structural element with imprecise strength probability density function is developed.

Reliability sensitivity by method of moments

Based on the available methods of moments for structural system reliability assessment and point estimate methods for the first few moments of performance functions, an effective method is proposed to analyze reliability sensitivity of a structural system. The proposed method for analyzing reliability sensitivity includes two steps. Firstly, the reliability sensitivity, usually measured by partial differential of the failure probability P f with respect to distribution parameter θ of the basic random variable is derived according to the moment based reliability assessment. The derived expression of ∂ P f / ∂ θ is related to the derivative of the performance function moment α with respect to θ . Secondly, by using the integral formulation between α and the probability density function (PDF) of the basic random variable, ∂ α / ∂ θ could be derived as an expectation of a transformed performance function, and the expectation could be approximated by the point estimate methods. Through the two steps above, the reliability sensitivity can be obtained easily. The obvious advantages of the proposed method include independence of the explicit expression of the performance function, no limitations on the types of PDF of the basic random variables, wide applicability for multiple failure modes and high efficiency for low and medium dimensional problem, which are illustrated by the given examples. However, the efficiency of this method decreases as the dimension of the basic random variables increase, therefore, it is not suitable for the high dimensional problems.

Hybrid Data Mining/Genetic Shredding Algorithm for Reliability Assessment of Structural Systems

Recent studies have successfully introduced genetic algorithms (GA) to identify the important failure modes of complex structures and quantify their contributions to the reduction of the reliability of structural systems. In these studies, the efficiency of traditional GA techniques was substantially improved by incorporating linkage-learning operators that were used to explore relations among the random variables controlling the safety of a structural system. However, the currently used linkage learning methods were found to be either too complex for easy implementation in routine reliability analyses or too narrowly focused on finding the global optimal solution and thus reduced the capacity of GA to identify local optima. Other techniques especially suitable for exploring relations and linkages among data sets are known as data mining (DM) algorithms. One of the most popular and successful DM tools available in the computer science literature is the a priori algorithm. The purpose of this paper is to propose a hybrid algorithm that would combine the benefits of the pattern identification ability of the a priori DM algorithm to the capability of GA operators to explore new significant search domains. The implementation of the shredding operator and its ability to reduce the computational effort through its self-learning process will further lead to the development of an efficient and robust structural reliability analysis algorithm. This paper will demonstrate that the proposed algorithm will significantly reduce the computational effort associated with determining the probabilistically dominant failure modes of structural systems. Examples are provided to verify the high efficiency and accuracy of the proposed hybrid data mining/genetic shredding algorithm for failure mode exploration, identification, and exploitation.

Linkage-shredding genetic algorithm for reliability assessment of structural systems

The identification of the probabilistically dominant failure modes of complex structures and the estimation of their reliability can be reduced to the solution of an optimization problem in the standardized normal space of the variables that control the random loads applied on the structure and the random strengths of its members. Hence, the ability of genetic algorithms to identify local and global optima makes them especially suitable for solving structural reliability problems. To reduce the known inefficiencies of traditional genetic algorithms, this paper proposes the use of a hybrid genetic search algorithm that is capable of efficiently identifying the dominant failure modes of a structural system and estimating their reliability index values. The proposed algorithm combines the benefits and the efficiency of the linkage learning process of the gene expression messy genetic algorithm (GEMGA) to the ability of the shredding genetic operator to explore new significant search domains. By reducing the dimensionality of the problem through linkage learning, the number of generations needed to reach convergence is greatly reduced. To further ameliorate the GA search’s efficiency, the Shredding operator is used to estimate the value of the reliability index in a given search direction by building and updating a fitness value matrix based on an evolutionary learning process. This will drastically reduce the number of structural analyses that are usually required during the reliability assessment of structural systems. Furthermore, an exploitation process is implemented during the search for the local optima to obtain accurate reliability indexes and quantify the contributions of various variables to the structural failure modes identified during the search process. Thus, the proposed algorithm provides detailed information about a structure’s failure modes that would be helpful for optimizing the design and improving the structure’s safety against local and global failures. Examples are provided to demonstrate the high efficiency and accuracy of the proposed hybrid genetic algorithm.

System Reliability Assessment by Method of Moments

The computational assessment of system reliability of structures has remained a challenge in the field of reliability engineering. Calculation of the failure probability for a system is generally difficult even if the potential failure modes are known or can be identified, because available analytical methods require determination of the sensitivity of performance functions, information on mutual correlations among potential failure modes, and determination of design points. In the present paper, a method based on moment approximations is proposed for structural system reliability assessment that is applicable to both series and nonseries systems. The point estimate method is applied to evaluate the first few moments of the system performance function of a structure from which the moment-based reliability index and failure probability can be evaluated without Monte Carlo simulations. The procedure does not require the computation of derivatives, nor determination of the design point and computation of mutual correlations among failure modes; thus, it should be computationally effective for structural assessment of system reliability.

2110 主成分分析による構造システムの信頼性評価(OS09-2/信頼性設計)(OS09/ロバスト設計・信頼性設計)

2110 主成分分析による構造システムの信頼性評価(OS09-2/信頼性設計)(OS09/ロバスト設計・信頼性設計)

Reliability Assessment of Structural Systems Based on A Directional Vector Approximation Method.

This paper describes a new method for evaluating the probability of structural failure based on a directional vector approximation. Since failure probability is defined by a directional integration of the conditional failure probability evaluated as the upper probability of a chi square distribution in the specified direction, it is evaluated by the summation of the product of the area of the finite element mesh and the upper probability of the chi square distribution corresponding to each element mesh. The directional vectors are detemined by adopting the unit centerline vectors related to finite element meshes allocated regularly on the surface of the unit sphere, which is divided analytically into a specified number of finite element meshes. The proposed method gives good estimates of the structural failure probability. Numerical examples are provided to show the validity of the proposed method.

破損領域重点サンプリング・シミュレーションに基づく構造システムの信頼性解析

This paper is concerned with a reliability assessment of structural systems based on an improved importance sampling simulation, in which the importance sampling density is determined within the limit of the failure region. Basic random variables are assumed to be stochastically independent normal variates and the minimum reliability index β of the system to be known beforehand. The first step of the proposed method is to execute simulations, refered to the preliminary simulations, to get a rough estimate of the failure probability and data about the sample distribution. These data are utilized to determine the importance sampling density as a frequency distribution with respect to radius in polar coordinates. In the second step, the structural failure probabilities are estimated through the importance sampling simulations, samples of which are generated from the estimator of the importance sampling density determined in the first step.The proposed method is compared in a numerical example with the Monte Carlo simulation combined with partition of the region technique and ISPUD for multi mode failure etc. It can be said that the proposed method is effective for the estimation of structural failure probabilities.

Structural system reliability assessment using directional simulation

The theory for the estimation of the reliability of a structural system which is subject to one or more load processes requires knowledge of the surface defining the mechanical response of the system. For many systems this surface may be known only implicitly and defined through a method of structural analysis. In the formulation presented herein, the surface is obtained using an established probabilistic structural analysis technique. The reliability estimation is formulated in the load process space. In this space, directional simulation is employed to estimate the outcrossing rate and the initial (zero time) probability of failure and hence to estimate the probability of failure at any subsequent time. Two examples using discrete rectangular pulse (Poisson) processes are described.

Seismic Risk Analysis of Structural Systems

A methodology for reliability assessment of structural systems subjected to seismic risk is developed. Based on modern concepts of structural reliability theory, structural safety against earthquakes is described through a performance function of ground motion variables. A multivariate risk analysis is then performed to compute the failure probability. The method can be applied to any type of structural system for which a performance function can be formulated. A specific application to linear structures using the response spectrum of ground motion is developed where the performance function is shown to be of quadratic form in terms of spectral ordinates. This application is illustrated through a numerical example for a two-degree-of-freedom structure with multiple failure modes. The example is also used to examine the accuracy of a conventional method that uses marginal probabilities to approximate a joint distribution.