On multinormal integrals by Importance Sampling for parallel system reliability

The ability to compute multinormal integrals to any required accuracy is a key issue for an efficient computation of failure probabilities, particular important in context with system reliability analysis. Hence in this paper, an accurate Importance Sampling procedure to compute multinormal integrals in high dimensions is presented. The novel method allows to sample exclusively in the failure domain which substantially increases the efficiency of the Importance Sampling procedure. The proposed approach is extended for slightly non-linear limit state functions which typically result from non-Gaussian distributed input variables and linear limit state functions of the response in linear structural analysis.The suggested procedure is easy to implement, accurate and convenient for practical applications.     

Application of spherical subset simulation method and auxiliary domain method on a benchmark reliability study

This paper addresses a benchmark study designed to evaluate the performance of various methods in calculating the reliability of large systems. In particular, this paper focuses on evaluating two reliability methods recently proposed by the authors, referred to as spherical subset simulation (S³) and auxiliary domain method (ADM). S³ is based on dividing the failure domain into a number of appropriately selected subregions and calculating the failure probability as a sum of the probabilities associated with each of these subregions. The probability of each subregion is calculated as a product of factors. These factors can be estimated accurately by a relatively small number of samples generated according to the conditional distribution corresponding to the particular subregion. The generation of such samples is achieved through Markov Chain Monte Carlo (MCMC) simulations using a MCMC algorithm proposed by the authors. The proposed method is very robust and is suitable for treating general high-dimensional problems such as the given benchmark problems. ADM is applicable to reliability problems involving deterministic dynamic systems subjected to stochastic excitation. The first step in ADM involves the determination of an auxiliary failure domain (AFD). The choice of the AFD is based on preliminary MCMC simulations in the target failure domain. It must be noted that although the AFD is chosen to be specified as a union of linear failure domains, the method does not assume any restriction with respect to the target failure domain, which is assumed to be generally non-linear. Once the AFD is determined, the ADM proceeds with a modified subset simulation procedure where the first step involves the direct simulation of points in the AFD. This is in contrast to standard subset simulation (SSM) where the first step involves standard Monte Carlo Simulations. The number of steps and the computational effort required by ADM, assuming an appropriate AFD is chosen, can be smaller than that required by SSM. Results for the benchmark problems show that both S³ and ADM are efficient for treating high dimensional reliability problems.     

On the reliability-based design of structures including passive energy dissipation systems

This contribution presents a methodology for stochastic design of structures including vibration protection systems. The approach is then used to investigate the effect of uncertain model parameters on the reliability-based optimal design of structures with a class of passive energy dissipation systems. The uncertainty of structural parameters as well as the variability of future excitations are characterized in a probabilistic manner. The optimal design problem is formulated as a non-linear constrained minimization problem involving multiple design requirements, including reliability constraints related to the structural performance. Failure events defined by a large number of random variables are used to characterize the reliability measures. A sequential optimization approach based on global conservative, convex and separable approximations is implemented for solving the optimization problem. The effects of uncertain model parameters on the performance, robustness and reliability of protected systems is illustrated by two example problems that consider multi-story buildings under stochastic ground excitation.     

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.     

Reliability analysis of linear dynamical systems using approximate representations of performance functions

A method to carry out reliability analysis of linear systems with random structural parameters and random excitation is presented. Probability that design conditions are satisfied within a given time period is used as a measure of system reliability. An efficient importance sampling technique is used to estimate the failure probabilities. This technique is combined with high quality approximations of the performance functions in terms of uncertain structural parameters. The number of dynamic analyses required during the estimation process is minimized since the simulations are carried out by evaluating explicit expressions. The explicit quantities correspond to approximate representations of the performance functions in terms of the uncertain structural parameters. A numerical example corresponding to problem 2, sub-case 2 of the benchmark study is presented to illustrate the accuracy and computational efficiency of the proposed computational procedure.     

Strength reduction factor for MDOF soil–structure systems

In most of the seismic design provision, the concept of strength reduction factor has been developed to account for inelastic behavior of structures under seismic excitations. Most recent studies considered soil–structure interaction (SSI) in inelastic response analysis are mainly based on idealized structural models of single degree‐of‐freedom (SDOF) systems. However, an SDOF system might not be able to well capture the SSI and structural response characteristics of real multiple degrees‐of‐freedom (MDOF) systems. In this paper, through a comprehensive parametric study of 21600 MDOF and its equivalent SDOF (E‐SDOF) systems subjected to an ensemble of 30 earthquake ground motions recorded on alluvium and soft soils, effects of SSI on strength reduction factor of MDOF systems have been intensively investigated. It is concluded that generally, SSI reduces the strength reduction factor of both MDOF and more intensively SDOF systems. However, depending on the number of stories, soil flexibility, aspect ratio and inelastic range of vibration, the strength reduction factor of MDOF systems could be significantly different from that of E‐SDOF systems. A new simplified equation, which is a function of fixed‐base fundamental period, ductility ratio, the number of stories, structure slenderness ratio and dimensionless frequency, is proposed to estimate strength reduction factors for MDOF soil–structure systems. Copyright © 2012 John Wiley & Sons, Ltd.     

Structural resistance moments by quadrature

Numerical integration formulas are used to estimate the statistical moments of a function of random variables. Formulas are developed for the special cases of Normal and Lognormal distributed random variables. The moments of the ultimate resistance of two structural systems determined using the quadrature formulas are compared to the results of Monte Carlo simulation. The procedure is convenient to implement and direct use can be made of available deterministic computer programs. The method has applicability to more general problems of second moment reliability.     

Optimization of Earthquake Energy Dissipation System by Genetic Algorithm

Numerous recent studies have assessed the stability and safety of structures furnished with different types of structural control systems, such as viscous dampers. A challenging issue in this field is the optimization of structural control systems to protect structures against severe earthquake excitation. As the safety of a structure depends on many factors, including the failure of structural members and movement of each structural node in any direction, the optimization technique must consider many parameters simultaneously. However, the available literature on optimizing earthquake energy dissipation systems shows that most researchers have considered optimization processes using just one or a few parameters applicable only to simple SDOF or MDOF systems. This article reports on the development of a multiobjective optimization procedure for structural passive control systems based on genetic algorithm; this research focused on systems that would minimize the effects of earthquake based on realistic structural responses considering plastic hinge occurrence in structural elements and three‐directional displacement in all structural nodes. The model was applied to an example of three‐dimensional reinforced concrete framed building and its structural seismic responses were investigated. The results showed that the optimized control system effectively reduced the seismic response of structures, thus enhancing building safety during earthquake excitations.     

Application of subset simulation methods to reliability benchmark problems

This paper presents the reliability analysis of three benchmark problems using three variants of Subset Simulation. The original version of Subset Simulation, SubSim/MCMC, employs a Markov chain Monte Carlo (MCMC) method to simulate samples conditional on intermediate failure events; it is a general method that is applicable to all the benchmark problems. SubSim/Splitting is a variant of Subset Simulation applicable to first-passage problems involving deterministic dynamical systems. It makes use of trajectory splitting for generating conditional samples. Another variant, SubSim/Hybrid, uses a combined MCMC/Splitting strategy and so it has the advantages of MCMC and splitting; it is applicable to uncertain and deterministic dynamical systems. Results show that all three Subset Simulation variants are effective in high-dimensional problems and that some computational efficiency can be gained by exploiting and incorporating system characteristics into the simulation procedure.     

基于结构性能的建筑设计简史

从建筑师的角度来看,基于结构性能的建筑设计的发展过程,按时间顺序可以被划分为三个时代:在静力学图解时代中,由于图解静力学理论的建立和应用,建筑师能够清楚地表达结构概念并试图寻求结构性能的最优方案;在力学建构时代,由于社会经济需求和结构性能设计的发展,高结构性能的特殊结构原型被广泛应用,但由于方法的不可确定性和不可重复性,建筑师亟需新的设计计算工具辅助:在结构性能生形时代,建筑师充分应用电脑计算及模拟技术,为之前的实践方法和理论注入新的血液,更重要的是,建筑师创造了许多更为科学、准确以及创新的设计方法。文章以建筑视角对基于结构性能的建筑设计的发展历史进行梳理,比较和分析目前的结构基于性能的设计方法,并评估其对当下建筑实践的价值。     

Active Saturation Control of Hysteretic Structures

This article presents an analytical approach to estimating the seismic random response of MDOF elastoplastic structural systems with bilinear hysteretic characteristics under saturation control force. Active saturation control is used for both seismic safety and vibration mitigation under severe earthquake excitation. Numerical calculations are carried out for five‐degree-of-freedom systems, and the efficiency of the theoretical saturation control approach is examined from two viewpoints of random seismic response and energy response. Considering the inability to install a saturation control system in actual structural systems, much more realistic nonlinear control systems are developed and examined from the control efficiency viewpoint through simulation analysis based on the earthquake accelerogram recorded during the Hyogo-ken Nanbu earthquake.     

Benchmark study on reliability estimation in higher dimensions of structural systems – An overview

This work is concerned with a Benchmark study on reliability estimation of structural systems. The Benchmark study attempts to assess various recently proposed alternative procedures for reliability estimation with respect to their accuracy and computational efficiency. The emphasis of this study is on systems which include a large number of random variables. For this purpose three sample problems have been selected which cover a wide range of cases of interest in the engineering practice and involve linear and nonlinear systems with uncertainties in the material properties and/or the loading conditions. Here an overview of the Benchmark study is provided.     

Two-step seismic limit state design procedure based on non-linear LRFD and dynamic response analyses

Recently, the limit state design (LSD) or performance-based design have got popularity in the field of building design in Japan as well as in other countries. In the two design methods the structural reliability theory plays an essential role in setting design criteria as well as demonstrating the target reliability level to society. However, the conventional load and resistance factor design (LRFD) has been basically formulated supposing that safety checking is done on the basis of linear assumption of member forces and displacement. Therefore, when applying the LRFD for seismic design, for more accurate treatment of the non-linearity, a new procedure has to be explored especially for the ultimate limit state. Although several procedures for the structural reliability evaluation, treating non-linear displacement responses, have been proposed, they require complex procedures that may not be used in the practical design process. Accordingly, for applying it to a seismic LSD format based on the probabilistic concept, it is essential to manage two important requirements at the same time, accuracy and simplicity of procedure. In the present study, a new design format using the following two-step procedure is proposed to maintain both accuracy and simplicity; (1) a non-linear LRFD formulation, and (2) a formulation based on non-linear dynamic response analysis. Also, two design examples are presented.     

Structural parameter identification and damage detection for a steel structure using a two-stage finite element model updating method

A two-stage eigensensitivity-based finite element (FE) model updating procedure is developed for structural parameter identification and damage detection for the IASC-ASCE structural health monitoring benchmark steel structure on the basis of ambient vibration measurements. In the first stage, both the weighted least squares and Bayesian estimation methods are adopted for the identification of the connection stiffness of beam-column joints and Young’s modulus of the structure; then the damage detection is conducted via the FE model updating procedure for detecting damaged braces with different damage patterns of the structure. Comparisons between the FE model updated results and the experimental data show that the eigensensitivity-based FE model updating procedure is an effective tool for structural parameter identification and damage detection for steel frame structures.     

Dominant failure modes in stochastic structural systems

In an analysis of redundant structural systems in which either or both loading systems and/or member resistances are stochastic variables, all modes of failure are potentially of significance in the calculation of structural reliability. In practice, however, many modes do not contribute very much, and a problem has been to identify those modes which are stochastically dominant.In this paper a general, iterative procedure called the Truncates Enumeration Method [TEM] to determine the most stochastically dominant modes is derived from successive systematic curtailment of the results which would be obtained by complete enumeration. In this way, it is shown that the procedure presented has the capability to produce all dominant modes to within the accuracy of the criteria used for curtailment. The method is similar to that proposed by Murotsu et al.It is also shown that the incremental load method (ILM), proposed by Moses et al., has certain features common to TEM, that both techniques are essentially incremental in nature and that both methods produced the same mode failure probability statement, each using quite distinct procedures. It is finally argued that the methods are not restricted merely to the materials behaviour properties studied thus far by their proponents.     

A Decentralized Control Algorithm for Large‐Scale Building Structures

Abstract: Decentralized control strategy is more suitable for structural control of large‐scale structural systems as it increases in the feasibility of control implementation and decreases the risk on the failure of the control system compared with the conventional centralized control approach. In this article, a decentralized control algorithm is proposed for large‐scale linear building structures. A large‐scale building structure is divided into a set of smaller substructures based on its finite element model. Interconnections between adjacent substructures are treated as disturbances to the individual substructure. Each substructure is controlled by its own local controller using linear quadratic Gaussian control scheme with acceleration measurements as feedback signals. A computational procedure is developed for the recursive estimation of the unknown disturbances to each substructure. Two cases, with substructure interface measurement and without substructure interface measurement respectively, are considered. A numerical example of the decentralized control of the 20‐story Structural Engineers Association of California (SAC) benchmark linear building under seismic excitation is studied to evaluate the performance of the proposed algorithm. Simulation results demonstrate that the decentralized control algorithm has quite good control performance compared with the conventional centralized control approach. Therefore, the proposed decentralized control algorithm is viable for structural control of large‐scale linear structural systems.     

Reliability based optimization of laminated composite structures using genetic algorithms and Artificial Neural Networks

The design of anisotropic laminated composite structures is very susceptible to changes in loading, angle of fiber orientation and ply thickness. Thus, optimization of such structures, using a reliability index as a constraint, is an important problem to be dealt. This paper addresses the problem of structural optimization of laminated composite materials with reliability constraint using a genetic algorithm and two types of neural networks. The reliability analysis is performed using one of the following methods: FORM, modified FORM (FORM with multiple checkpoints), the Standard or Direct Monte Carlo and Monte Carlo with Importance Sampling. The optimization process is performed using a genetic algorithm. To overcome high computational cost it is used Multilayer Perceptron or Radial Basis Artificial Neural Networks. It is shown, presenting two examples, that this methodology can be used without loss of accuracy and large computational time savings, even when dealing with non-linear behavior.     

Simplified multi‐degree‐of‐freedom model for estimation of seismic response of regular wall‐frame structures

A simplified multi‐degree‐of‐freedom (MDOF) model is developed for estimation of seismic response of tall wall‐frame structures. By using the continuum technique for the structure and adopting the bilinear hysteretic model for material properties, procedure for the development of the simplified MDOF model is derived. The numerical study for a 20‐storey reinforced concrete (RC) wall‐frame structure is conducted to investigate the accuracy of seismic response predicted by the proposed model. Results from the nonlinear response history analyses based on the proposed MDOF model and the detailed structural model with member‐by‐member representation are compared and show very good agreement. The proposed simplified MDOF model is shown to provide a simple, efficient and accurate method for estimation of seismic performance of tall wall‐frame structures. Copyright © 2009 John Wiley & Sons, Ltd.     

Displacement estimation of nonlinear structures using the force analogy method

Significant effort has gone toward developing accurate and efficient displacement estimation procedures for the nonlinear multi‐degree‐of‐freedom (MDOF) system. Although the dynamic nonlinear analysis is capable of providing the high computational precision through the step‐by‐step time integration method, the simplified method is still expected and imperative for seismic design practices. The work presented in this paper focuses on the implementation of using the modal superposition method to estimate displacement responses of the nonlinear MDOF system based on the force analogy method (FAM). The current research demonstrated that the equation of motion for the nonlinear MDOF system can be decoupled, but other two governing equations in the FAM about the internal force, such as the moment and force of structural members, are not decomposable. Thus, the FAM is incorporated with the modal pushover analysis (MPA) method to determine the basic parameters of each mode such that the modal superposition method can be suitable for the solution of the nonlinear MDOF system. The procedure presented here is an approximately estimation method due to the application of MPA method. However, the value and potential for the maximum displacement estimation of the nonlinear MDOF system were demonstrated through the application in a framed structure. Copyright © 2014 John Wiley & Sons, Ltd.     

Uncertain linear systems in dynamics: Retrospective and recent developments by stochastic approaches

This paper provides an overview along with a critical appraisal of available methods for uncertainty propagation of linear systems subjected to dynamic loading. All uncertain structural properties are treated as random quantities by employing a stochastic approach. The loading can be either of deterministic or stochastic nature, described by white noise, filtered white noise, and more generally, by a Gaussian stochastic process.The assessment of the variability of the uncertain response in terms of the mean and variance is described by reviewing the random eigenvalue problem and procedures to evaluate the first two moments of the stochastic (uncertain) response. Computational procedures which are efficiently applicable for general FE-models are the focus of this work.Most recent developments for the reliability assessment–besides a retrospective review–are summarized, with particular emphasis on numerical Monte Carlo Simulation approaches. This review comprises methods to assess the first excursion probability directly by efficient numerical methods. General “black box” procedures and approaches applicable only for linear systems are critically discussed. Specific procedures applicable to linear systems subjected to general Gaussian excitation are subsequently addressed. Methods applicable for deterministic structural systems are introduced first. Finally, a procedure to exploit the solutions for deterministic linear systems for stochastic uncertain systems in an efficient manner is described.