Structural Reliability Problems Research Articles

Evaluation of accuracy and efficiency of some simulation and sampling methods in structural reliability analysis

Numerous simulation and sampling methods can be used to estimate reliability index or failure probability. Some point sampling methods require only a fraction of the computational effort of direct simulation methods. For many of these methods, however, it is not clear what trade-offs in terms of accuracy, precision, and computational effort can be expected, nor for which types of functions they are most suited. This study uses nine procedures to estimate failure probability and reliability index of approximately 200 limit state functions with characteristics common in structural reliability problems. The effects of function linearity, type of random variable distribution, variance, number of random variables, and target reliability index are investigated. It was found that some methods have the potential to save tremendous computational effort for certain types of limit state functions. Recommendations are made regarding the suitability of particular methods to evaluate particular types of problems.

Application of kriging method to structural reliability problems

Approximation methods are widely used to alleviate the computational burden of engineering analyses. For structural reliability analyses, the common approach is to use the response surface method (RSM) based on the least square regression. However, another approximation method based on kriging has gained popularity especially in the field of deterministic optimization. However, the application of the kriging method to structural reliability problems has not been realized until recently. Therefore, this paper investigates the use of the kriging method for structural reliability problems by comparing it with the most common RSM. The effects of the kriging parameters are also examined on the basis of the β computation and fitting behavior. It can be deduced from the results given in this paper that using the most common approach in the literature to find the kriging parameters does not guarantee a good result for the structural reliability problems. As a result, some advantages as well as disadvantages of the kriging method are reported, based on the results obtained from the application of the kriging method to the examples from the literature. Finally, this paper suggests the points for which the kriging model could be improved to get better results for structural reliability problems.

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.

A response surface method based on weighted regression for structural reliability analysis

Approximation methods such as the response surface method (RSM) are widely used to alleviate the computational burden of engineering analyses. For reliability analysis, the common approach in the RSM is to use regression methods based on least square methods. However, for structural reliability problems, RSMs should approximate the performance function around the design point where its value is close to zero. Therefore, in this study, a new response surface called ADAPRES is proposed, in which a weighted regression method is applied in place of normal regression. The experimental points are also selected from the region where the design point is most likely to exist. Examples are given to demonstrate the benefit of the proposed method for both numerical and implicit performance functions.

Comparison of response surface and neural network with other methods for structural reliability analysis

The evaluation of the failure probability and safety levels of structural systems is of extreme importance in structural design, mainly when the variables are eminently random. Some examples of random variables on real structures are material properties, loads and member dimensions. It is necessary to quantify and compare the importance of each one of these variables in the structural safety. Many researchers studied structural reliability problems and nowadays there are several approaches for these problems. Two recent approaches, the Response Surface (RS) and the Artificial Neural Network (ANN) techniques, have emerged attempting to solve complex and more elaborated problems. In this work, these two techniques are presented, and comparison are carried out using the well known First Order Reliability Method (FORM), Direct Monte Carlo Simulation and Monte Carlo Simulation with Adaptive Importance Sampling technique with approximated and exact limit state functions. Problems with simple limit state functions (LSF) and closed form solutions of the failure probability are solved in order to highlight the advantages and shortcomings using these techniques. Some remarks are outlined regarding the fact that RS and ANN techniques have presented equivalent precision levels. It is observed that in problems where the computational cost of structural evaluations (looking for the failure probability and safety levels) is high, these two techniques may turn feasible the evaluation of the structural reliability through simulation techniques.

Structural assessment of existing concrete buildings

AbstractAn approach to the general issue of existing concrete structures safety analysis is presented, referring to the most relevant uncertainties in the process of structural assessment and the various ways of characterizing them. The structural reliability and reliability index concepts and a procedure to measure them probabilistically are presented, as well as the basic problem of structural reliability and a semi‐probabilistic approach to safety compliance.The importance of characterizing the strength properties of structural materials is discussed, and the main related aspects are pointed out. Methods prescribed in some standards and recommendations are presented, emphasizing those suitable for safety analysis of existing structures. The importance of a priori data, the sources normally used in data acquisition and of the inspection and tests planning stages is stressed. The number of tests (sample dimension) needed to infer and statistically validate results is discussed.The importance of characterizing probabilistically actions and effects is stressed. The code criteria for their quantification are presented and the types of probabilistic distribution and variability inherent to each action type are briefly described. Some methods for their quantification in existing structures are pointed out. Special importance is given to the quantification of variable actions, owing to the high associated uncertainties, especially seismic action, in the process of structural safety assessment. Ways of reducing their nominal values or the respective safety factors, depending on the degree of uncertainty involved, namely due to the reduction of the existing structure's expected service life, are pointed out.The probabilistic methodologies developed for structures safety analysis, based on the reliability classical techniques, namely the second moment methods, of First and second order, and those based on the numerical simulation (Monte Carlo) techniques, are discussed, emphasizing the difficulty in its application to case studies of the assessment of existing structures. Copyright © 2003 John Wiley & Sons, Ltd.

Dynamic reliability under random shocks

The theory of dynamic reliability is extended to explicitly incorporate random changes of the state variables at the time points of transition between the discrete states of the Markovian component of the model. It is shown, that this can be used to model random loads induced by external events, a situation often encountered in structural reliability problems. A state model is developed, which represents the behavior of elementary structures degrading, due to aging processes and stochastic environmental loads. Finally, the structural reliability of the basic components of underground water pipe networks is estimated using the proposed framework.

Adaptation of fast Fourier transformations to estimate structural failure probability

Probabilistic analysis with multiple non-normal random variables requires multi-fold integration, for which the closed-form solutions do not exist. Moreover, it is almost impossible to estimate failure probability accurately without the use of numerical integration. A central problem in probabilistic analysis is the computation of the cumulative distribution function of the limit-state. Since the limit-state surface is not available in a closed-form, the convolution theorem is usually thought to be not applicable to the problem. In this paper, a methodology based on function approximations and the convolution theorem is presented to estimate the structural failure probability. The convolution integral is solved efficiently using the fast Fourier transform technique, and the limit-state is approximated using a two-point adaptive nonlinear approximation at the most probable failure point. The proposed technique estimates the failure probability accurately with significantly less computational effort compared to the Monte Carlo simulation. The methodology developed is applicable to structural reliability problems with any number of random variables and any kind of random variable distribution, including normal, log-normal, extreme value, Weibull, etc. The accuracy and robustness of the proposed algorithm is demonstrated by several examples having highly complex, explicit/implicit performance functions.

Model correction factor method for reliability problems involving integrals of non-Gaussian random fields

The model correction factor method (MCFM) is used in conjunction with the first-order reliability method (FORM) to solve structural reliability problems involving integrals of non-Gaussian random fields. The approach replaces the limit-state function with an idealized one, in which the integrals are considered to be Gaussian. Conventional FORM analysis yields the linearization point of the idealized limit-state surface. A model correction factor is then introduced to push the idealized limit-state surface onto the actual limit-state surface. A few iterations yield a good approximation of the reliability index for the original problem. This method has application to many civil engineering problems that involve random fields of material properties or loads. An application to reliability analysis of foundation piles illustrates the proposed method.

Evaluation of Structural Reliability Using a Genetic Algorithm.

To evaluate reliability indices is an important step in the structural reliability analysis. It is, however, difficult to evaluate reliability indices by conventional optimization methods in case local optimal solutions exist or the limit state function is not differentiable. In order to solve these problems, this paper presents genetic algorithm-based optimization methods to evaluate structural reliability indices. Two methods, the penalty function method and the backtracking method, are applied to the GA to deal with constraints. A local GA is also added to the program to accelerate convergence to the optimal solution. Through the application of the developed program to typical structural reliability problems, it is revealed that the GA-based optimization methods can evaluate the reliability indices even when conventional methods fail, and the local GA is quite effective to reduce CPU time and to increase the stability of convergence for both the penalty function method and the backtracking method.

RELIABILITY AND DURABILITY PROBLEMS OF LOAD BEARING CONCRETE STRUCTURES FOR ELECTRIC POWER TRANSMISSION LINES/ELEKTROS TINKLO LAIKANČIŲJŲ GELŽBETONINIŲ KONSTRUKCIJŲ PATIKIMUMO IR ILGALAIKIŠKUMO PROBLEMOS

Experimental and theoretical investigations associated with reliability and durability problems of concrete structures of electric power and communication systems have been carried out by scientists of Vilnius Gediminas Technical University since 1959. An attempt to generalise the accumulated statistical data enabling to evaluate reliability and durability of such structures is presented in this article. It has been determined that concrete pylons of supports of electric power overhead lines under long-term service (over 30 years) are with defects and damages, and the most characteristic of these are vertical cracks close to the longitudinal reinforcing bars, delaminated or fallen down concrete protective cover, naked longitudinal reinforcement which is corroded along 0,5-2 m intervals (not along the whole its length). Cross-sectional area of corroded reinforcement is reduced not substantially, because corrosion becomes slower due to ventilation after opening of a wide crack. Technical state of spun concrete pylons of annular cross-section is better and they are more reliable and durable in comparison with vibrated concrete pylons duringr the same time in service. Reliability and durability of concrete pylons of supports of electric power network are governed by structural solution, condition of manufacture, erection and operation. Durability of concrete pylons can be achieved by using concrete of sufficient density and resistance to aggressive environmental actions. Durability of pylons is very much dependant on concrete structure. Concrete density increases with decrease of v/c ratio. Quality of concrete depends on its mix compaction and hardening conditions. Concrete hardening process should be as mild as possible. Additional effects causing microfracture of concrete should not appear during manufacture, transportation and erection of pylons. Prestressing of concrete during manufacture should be mild-gradual. Durability of pylons is highly influenced by quality of concrete protective cover. The latter should be of adequate thickness. Since it has been established that the cover thickness is not always adequate, sometimes deviations from values specified in design are observed, it was proposed to manufacture pylons with thicker protective concrete cover. Production of vibrated concrete pylons of rectangular cross-section according to new type developed drawings has started in Kaunas factory of concrete pylons. Provision of transverse reinforcement along the whole pylon length is proposed for increasing torsional strength. It is worth discussing whether it is expedient to start again manufacturing more reliable and durable spun concrete pylons of annular cross-section. Full scale tests of concrete pylons in natural conditions indicated that strength to bending about the axis perpendicular to transmission line is sufficient even of pylons in service for 25–30 years. But these pylons are not sufficiently strong to bending in other direction and especially when they are subjected to bending with torsion. Reliability and durability of concrete vibrated pylons are also governed by structural solution, technology of manufacture and conditions of erection and service.

RELIABILITY AND DURABILITY PROBLEMS OF LOAD BEARING CONCRETE STRUCTURES FOR ELECTRIC POWER TRANSMISSION LINES

Summary Experimental and theoretical investigations associated with reliability and durability problems of concrete structures of electric power and communication systems have been carried out by scientists of Vilnius Gediminas Technical University since 1959. An attempt to generalise the accumulated statistical data enabling to evaluate reliability and durability of such structures is presented in this article. It has been determined that concrete pylons of supports of electric power overhead lines under long-term service (over 30 years) are with defects and damages, and the most characteristic of these are vertical cracks close to the longitudinal reinforcing bars, delaminated or fallen down concrete protective cover, naked longitudinal reinforcement which is corroded along 0,5-2 m intervals (not along the whole its length). Cross-sectional area of corroded reinforcement is reduced not substantially, because corrosion becomes slower due to ventilation after opening of a wide crack. Technical state of sp...

Error evaluations for the computation of failure probability in static structural reliability problems

The determination of mathematical reliability in static structures is still a motivating field of research. On one hand, the failure probability values are of greater importance in engineering activities; on the other hand, the determination of this probability remains a time consuming computational task when real problems are examined. To obtain a significant value for the failure probability while preserving a reasonable computation cost is therefore an objective to be considered. One of the necessary conditions to reach this target is to design a method to determine the computational error. Knowing the error will then give the capacity to limit the computation time, in particular by avoiding a too accurate probability evaluation. This paper presents a method allowing one to deal with these factors. The RGMR method, presented at the ICASP'7 meeting (July 1995, Paris) was designed to make such an error evaluation possible. Examples of numerical error computations with the RGMR method, particularly when low significant variables are eliminated, are given. These new developments are a step towards the goal mentioned above.

Equivalent Gaussian process in stochastic dynamics with application to along-wind response of structures

The principle of normal tail approximation, that is, a Gaussian rv equivalent to a non-Gaussian rv, which has been widely applied to structural reliability problems and has been extended by Grigoriu to stochastic processes for calculating the mean upcrossing rate of a non-Gaussian process, is here considered as an approximate tool for solving non-linear dynamical problems, in which the excitation is non-Gaussian. A non-Gaussian excitation is replaced by an equivalent one, so that all methods that are suitable for Gaussian agencies can be used. The method is applied to the study of the SDOF oscillator excited by wind turbulence. The oscillator is assumed to be linear, but an excitation of the form γ[V(t) − x ̇ (t)] 2 introduces a non-linearity; moreover, it is no more Gaussian, even if the turbulence is. The solutions that are obtained using the equivalent Gaussian process for both the cases, in which the term x ̇ (t) is retained or is neglected, are compared with those that are obtained by the use of Monte-Carlo simulation and of stochastic differential calculus. The agreement is satisfactory for engineering purposes.

Structural reliability methods for seismic safety assessment: a review

Recent developments in structural reliability that are relevant to earthquake engineering problems are reviewed. The paper begins with a discussion of types of uncertainties and methods for their quantification and analysis. The mathematical formulation of the structural reliability problem and existing methods for computation of failure probabilities are then reviewed. Included are methods based on first- and second-order approximations, simulation, and various hybrid methods. The topics of reliability sensitivity, updating of reliability, and the treatment of uncertainties in the estimation of reliability are discussed. A brief account of recent developments that combine these probabilistic methods with the finite element method, together with two numerical examples, conclude the paper.

Approximated Evaluation of Failure Probability for Structural System Using Conditional Safety Indices.

This paper deals with the approximated evaluation method for failure probability of structural systems using conditional safety indices. In general, it is difficult to compute an exact solution of the structural reliability problem with correlations of design variables and limit state functions. It is expected that the conditional safety index proposed will be a useful measure for the safety of complicated structural systems. The merit of this new measure is that the characteristics of statistics and geometry are identical on standardized space. Therefore the conditional safety index yields a practical effective interval of system reliability. When the high-order product sets of a failure event is obtained, the new assessment of the bounds for the estimation of failure probability is also significant. However, the evaluation process of conditional safety indices requires a sequential conditional correlation matrix so that it is the complicated process to calculate high-order simultaneous probability. This paper also proposes the method for transforming the vector of original safety indices into the vector of conditional safety indices using cholesky decomposition of the correlation matrix. In addition, it is suggested that the multi-integral can be approximated by the product of simple integrals using conditional safety indices.

知能GAの検討及びその構造信頼性問題への適用 : 遺伝的アルゴリズムによる構造信頼性評価法に関する研究 その2

In this paper, the groth and decay of chromosomes in the process of intelligent GA search is examined using schema theorem of GA and the influences of the probability of crossover and mutation on the evolution process are discussed through a specific computational example. It is found that the problems not only in deciding the length of chromosomes but also in selecting the probability of crossover and mutation can be effectively improved. Based on the examinations above, the application of the intelligent GA to some structural reliability problems is investigated and it is shown that the intelligent GA is applicable to general structural reliability problems through some computational examples.

Structural Reliability Assessment with Ambiguity and Vagueness in Failure

ABSTRACTEngineering projects and designs are commonly developed in a systems framework that includes different types of uncertainty. In general, uncertainty can be of either the ambiguity or vagueness type. The theory of probability and statistics has been extensively used in engineering to deal with the ambiguity type of uncertainty. The theory of fuzzy sets and systems has been used to model the vagueness type of uncertainty in many engineering applications. In this paper, the role of fuzzy sets in engineering systems is described using a selected example area that deals with vagueness in failure definition as used in solving structural reliability problems. The reliability of a structure is commonly based on an explicit definition of failure, making structural reliability dependent on this definition. The vagueness in the perception of damage and failure introduces another class of uncertainty, in addition to the commonly realized and modeled class of uncertainty, i.e., ambiguity. In this study, a methodology for reliability assessment of structures based on a fuzzy definition of failure is developed. The significance of the contribution is in providing the reliability of the structure over a damage spectrum.

Reliability in the context of design

The major purpose of this paper is to formulate the structural reliability problem in the context and objectives of the structural designer. In this formulation, the reliability of the structural system is represented in network form, allowing the designer to control global behavior of the system as a whole through the selection of a critical pathway through this network. This approach differs from that of a member-by-member local optimization scheme in that the selected pathway, representing a particular failure mode, is maximized, within certain bounds, relative to other modes. This type of approach to designing for global behavior is fundamentally old; yet, the reliability computations presented herein are new. Recent developments in object-oriented programming languages provide opportunities for effective computational modeling of these networks.

A fast and efficient response surface approach for structural reliability problems

The reliability analysis of large and complex structural requires approximate techniques in order to reduce computational efforts to an acceptable level. Since it is, from an engineering point of view, desirable to make approximative assumptions at the level of the mechanical rather than the probabilistic modeling, simplifications should be carried out in the space of physically meaningful system- or loading variables. Within the context of this paper, a new adaptive interpolation scheme is suggested which enables fast and accurate representation of the system behavior by a response surface (RS). This response surface approach utilizes elementary statistical information on the basic variables (mean values and standard deviations) to increase the efficiency and accuracy. Thus the RS obtained is independent of the type of distribution or correlations among the basic variables which enables sensitivity studies with respect to these parameters without much computational effort. Subsequently, the response surface is utilized in conjunction with advanced Monte Carlo simulation techniques (importance sampling) to obtain the desired reliability estimates. Numerical examples are carried out in order to show the applicability of the suggested approach to structural systems reliability problems. The proposed method is shown to be superior both in efficiency and accuracy to existing approximate methods, i.e., the first order reliability methods.