Reliability Analysis Of Engineering Structures Research Articles

Stochastic simulation of earthquake ground motions based on improved finite-fault model

In the seismic reliability analysis of engineering structures, it is often necessary to adopt stochastic ground motions as inputs. However, the current methods used to generate stochastic samples, such as the spectral representation method, the spectral transfer method, the dynamic source method, the physical source method, and the comprehensive method, etc., are not very convincing since they do not contain the complete information of seismic occurrence and propagation. In this study, an improved finite-fault model for stochastic simulation of ground motions is proposed. Compared to existing stochastic finite-fault model, the improved model considers the propagation law of phase spectrum, local site effect, and the impact of wave velocity on the arrival time of seismic waves. Besides, identification and statistics of model parameters are carried out based on ground motion records. Reasonable samples of stochastic ground motions are then obtained. In addition, parameter sensitivity analysis is conducted to determine critical random variables, which reduces the complexity of stochastic simulation. Simulation results are compared with recorded accelerograms from the 1999 Chi-Chi earthquake. It is shown that the improved stochastic finite-fault model is reliable, and the acceleration response spectra of simulated samples are consistent with those of station records collected at various site classes and the design spectra.

An electro-mechanical shell model for predicting stochastic vibration behavior of smart piezoelectric structure utilizing the Spectral-Tchebyche method

Random vibration analysis is an important indicator for conducting fatigue analysis as well as reliability analysis of engineering structures. At present, the vibration analysis for plate and shell structures is mostly limited to simple plate and shell structures, while the analysis of random vibration of smart piezoelectric structures is really scarce. In this paper, an electro-mechanical coupling model is proposed to examine the stochastic vibration characteristics of smart piezoelectric structures based on the Spectral-Tchebychev method (S-T), whose type of random excitation is pseudo-excitation method (PEM). By comparing the FEM, the literature and experiments, it is observed that S-T electromechanical coupling model proposed in this paper consumes much less computational time in predicting the stochastic response than the existing methods. Secondly, we focus on the effect of the piezoelectric layer on the stochastic vibration characteristics of the host structure. Then, artificial spring technique is also adopted to simulate the general boundary of the coupled electromechanical model for the random vibration analysis. The research work on the random vibration of piezoelectric smart structures in this paper can provide practical engineering experience for the design and equipment of smart structures.

An efficient approach for evaluating the reliability of engineering structures using support vector machine with clustering algorithm

ABSTRACT An implicit limit state function is predicted with a support vector machine (SVM) for reliability analysis of engineering structures to reduce the number of finite element analyses. The accuracy and predictability of the SVM method are reduced considerably by noise in data. In this paper, density-based spatial clustering of applications with noise (DBSCAN) is applied to reduce the noise in training samples for SVM regression. Then, the SVM model is linked with Monte Carlo simulation (MCS) to find out the reliability of the engineering structures. Four different examples of static and dynamic problems are solved to show acceptability and efficiency of the proposed method. It is observed that the proposed method is suitable for a smaller number of performance function calls. Direct MCS, artificial neural network-based MCS and response surface methods have been used to examine the effectiveness of the algorithm.

Research Methods for Reliability Analysis of Engineering Structures Based on Statistical Theory

With the increasing need for construction engineering projects, the reliability problem of engineering structures has been the focus of public concern.Currently, there is a lack of a systematic summary of structural reliability theory. Therefore, this paper attempts to summarize some basic principles of structural reliability theory. This paper discusses various factors affecting reliability analysis and three typical analysis methods. It is pointed out that multiple factors affecting reliability analysis, such as the applying loads and resistance parameters such as material properties and dimension parameters, can be regarded as random variables and obey specific statistical distribution. First Order Reliability Method presents the most excellent convenience in calculating failure probability, especially for the structure with a relatively small, and the accuracy of this method is acceptable when the nonlinear degree of structural performance function is not significant.The Second Order Reliability Method could provide a relatively accurate solution with a more complicated calculation process. Monte Carlo Simulation is general enough to be applied to all the cases despite the considerable number of simulations resulting from a minuscule failure probability. Researchers are expected to implement improvement measures to simplify analysis methods by combining them with mathematics and computer science. The results of this paper can provide a theoretical reference for the researchers and designers of structural reliability theory.

Reliability analysis of boom of new lifting equipment based on improved wolf swarm algorithm

Aiming at the low accuracy or inability to solve the problem when the traditional reliability optimization method deals with the practical engineering reliability analysis problem, this paper proposes a structural reliability analysis method using the improved wolf swarm algorithm (IWSA). Firstly, the reliability optimization mathematical model is established with the minimum reliability index as the objective function and the limit state equation as the equality constraint. Then the augmented multiplier method is used to transform the constrained optimization mathematical model into an unconstrained optimization mathematical model. Finally, IWSA is used to solve the problem. The proposed method is applied to a numerical example and an engineering example. The computation results of the proposed method in solving the numerical example are compared with the Monte Carlo simulation (MCS), which verifies that the proposed method in this paper has good calculation accuracy. The maximum deformation under the working condition is used as the target to establish a limit state function, and the reliability index is obtained by the proposed method combining with the finite element analysis software, which provides a certain theoretical guiding significance for the reliability analysis of engineering structures.

Accurate Structural Reliability Analysis Using an Improved Line-Sampling-Method-Based Slime Mold Algorithm

Line sampling (LS) is a robust and powerful simulation technique to reduce the computational burden provided by Monte Carlo simulation (MCS) for the reliability analysis of engineering structures. However, when dealing with highly nonlinear and implicit limit-state functions, LS yields instable results as nonconvergence or divergence. In this study, a novel framework that integrates the LS method with the slime mold algorithm (LS-SMA) is proposed to solve complex structural reliability problems. SMA is a new metaheuristic population-based algorithm inspired by the behavior and morphological changes in slime molds that can well solve multivariable optimization problems. In the proposed method, the determination of the important direction of LS is formulated as an unconstrained optimization problem according to the LS theory. Then SMA is employed to solve this optimization problem to decrease the computational cost. Thus, the LS-SMA is able to overcome the drawbacks of LS such as the local convergence and divergence. Seven numerical problems were utilized to investigate the LS-SMA applicability, where its performance was compared with MCS, subset simulation (SS), importance sampling (IS), LS, first-order reliability method (FORM), and first-order control variate method (FOCM). The results demonstrate that the proposed LS-SMA can be applied with high efficiency for solving the reliability problems that involve highly nonlinear or dimensional and complex implicit limit-state functions.

An efficient particle swarm optimization-joint probability distribution optimization method for structural reliability analysis

The performance function of many engineering structures and mechanisms is usually complex, highly nonlinear, and described in the implicit form. The reliability analysis of these structures using common methods requires high cost and time. In this paper, a new approach for reliability analysis of engineering structures and mechanisms by using the particle swarm optimization algorithm is presented. The advantages of this method in comparison with the conventional methods are its simplicity and accuracy. In addition, the limitations of the common previously presented methods are eliminated by the proposed method. This approach is based on a new redefinition of most probable point in the reliability analysis. To evaluate the performance and validity of the proposed method, some examples in the reliability analysis of various functions are employed. Finally, the superiority of the proposed method in performance and accuracy is demonstrated and compared to the conventional methods and it can be used for reliability analysis of complicated engineering structures.

A novel kriging based active learning method for structural reliability analysis

In the reliability analysis of engineering structures, there are usually implict and highly nonlinear performance function problems, which leads to the time-consuming computations. In this paper, a novel Kriging based reliability analysis method combined with the improved efficient global optimization (IEGO) and a secondary point selection strategy is proposed. Based on the IEGO algorithm, the expected improvement function is redefining, which will focus on the points both with large variance and near the limit state surface. Moreover, a secondary point selection strategy is raised to find the point with larger expected improvement and closed to the limit state surface, which can further improve the efficiency of the active learning process. Five examples indicates that the raised method has satisfactory global and local search capability, and can evaluate the probability of failure efficiently.

Physical synthesis method for global reliability analysis of engineering structures

Global reliability analysis is quite essential for safety design and serviceability maintenance of modern engineering structures. Various reliability analysis methods have been proposed though, the issues of combination explosion as well as probabilistic correlation of system failure paths remain challenging. Practical applications of these methods are thus hindered, especially when complex, implicit, and nonlinear performance functions are involved. There isn’t an efficient way out of this dilemma until the emergence of the probability density evolution method (PDEM) combined with the equivalent extreme value event principle in recent years. The governing partial differential equations regarding the probability density evolution of a stochastic dynamical system are decoupled to a one-dimensional generalized probability density evolution equation (GPDEE) by employing the random event description. In conjunction with the PDEM, this paper explores a physical synthesis approach towards the global reliability analysis of actual engineering structures. Evaluation of multiple failure potential is incorporated into the mathematical resolving of the GPDEE for structural response at a representative point. An accurate and efficient solving procedure for the global reliability of probabilistic dissipative systems is presented where no need of seeking the failure paths and their associated probabilities. Numerical applications are examined to illustrate the use of the physical synthesis method as a practical analysis tool.

First order control variates algorithm for reliability analysis of engineering structures

• Indicator of linearized limit state function served as control variates of original indicator. • First order failure probability regulated by control variates technique using few samples. • 50 benchmark reliability problems gathered and solved by proposed method. • Accuracy close to simulations and efficiency close to first order reliability method . • Method is suitable for nonlinear/high-dimensional problems with small probability. This study introduces an efficient method for safety evaluation of the structures with small failure probability. The proposed approach reformulates basic failure probability formula based on control variates method and suggests to firstly substitute the nonlinear limit state function with a linear limit state function for taking the advantages of linear problems during reliability process. Reliability analysis of linear problems would be fully accurate and dimension insensitive. Subsequently, the control variates method imposes the effect of limit state function nonlinearity on the obtained first-order failure probability by using a very small sampling size simulation. The result is a new reliability formulation that is highly suitable for solving nonlinear and high dimension problems. The capabilities of the method examined by solving several benchmarks numerical/engineering problems involving non-normal random variables, complex/noisy limit state functions, and nonlinear high dimension problems. Compared with mainstream reliability methods, for all solved problems, it is demonstrated that the proposed approach presents accuracy close to Monte Carlo simulation while the required number of performance function valuation is close to first-order reliability method.

Fuzzy-based optimised subset simulation for reliability analysis of engineering structures

This paper presents a numerical strategy for the efficient reliability assessment of engineering structures with random variables and fuzzy variables using fuzzy based optimised subset simulation (SS) approach. The proposed method relies on the performance function of the structure, which involves probability distribution functions and fuzzy variables for the modelling of the structural system. The values of the fuzzy variables for every alpha level are first obtained using the membership function. Therefore, the set values of the fuzzy variable bound the reliability of the structure, and this is evaluated using optimisation and efficient SS approach. The rationale behind the proposed strategy is to locate a failure domain or region where the objective function is minimised or maximised and compute the reliability using SS. The proposed algorithm in this study inherits the benefits of direct Monte Carlo approach in propagating the uncertainties associated with structural parameters but also demonstrate more robustness against the latter. The methodology can be applied to any engineering structures, and the applicability is demonstrated here, using a buried pipeline.

Low-cost finite element method-based reliability analysis using adjusted control variate technique

Reliability analysis is used to evaluate the safety of engineering structures subject to uncertainties. Finite element method (FEM) is a popular engineering tool used to evaluate the reliability of complex engineering structures. In general, FEM−based reliability analysis of engineering structures is influenced by the mesh density of the model and the accuracy of the results requires the use of a very fine mesh density in the analysis. However, it is often impractical for reliability analysis complex structures, especially those with low failure probabilities. Hence, a new method is proposed to address this issue, which provides an accurate estimate of the failure probability at low computational cost. In this method, the control variate technique is used in conjunction with the FEM-based reliability analysis, where the failure probability integral is broken down into two separate integral terms. The first term provides a low-cost estimate of the failure probability using a model with coarse mesh density, whereas the second term regulates the failure probability based on fewer finite element analyses with fine mesh density. The adjusted correction factors are also presented in this paper in order to improve the efficiency of the proposed approach. The proposed approach is used to estimate the reliability index of four engineering structures and the results show that the method is efficient and practical for FEM-based reliability analysis of engineering structures.

A method for estimating the reliability of structural systems with moment-matching and copula concept

ABSTRACTIt is aimed to propose a copula based systematic quantitative method for system reliability analysis of engineering structures considering multiple dependent failure modes. The principles of the moment matching method, the copula theory and the bound theory are combined to achieve the purpose. As the very first step, the moment estimation of the limit state function of each component is calculated by anchored ANOVA (Analysis of Variance) expansion. The third moment saddle point approximation is then applied to derive the distribution of each performance function and evaluate the reliability index with obtained moments. By introducing copula functions into the narrow bounds theory, the traditional reliability method is improved. The best-fitting copula function is determined to ensure the accuracy of the joint probabilistic modeling between the dependent failure modes. A novel feature of the proposed method is the use of the copula concept, instead of traditional numerical integration commonly used in the joint failure probability estimation. Examples are presented to illustrate the accuracy and applicability of the presented method.

Reliability analysis with Metamodel Line Sampling

This paper presents an approach for reliability analysis of engineering structures, referred to as Metamodel Line Sampling (MLS). The approach utilizes a metamodel of the performance function, within the framework of the Line Sampling method, to reduce computational demands associated with the reliability analysis of engineering structures. Given a metamodel of the performance function, the failure probability is estimated as a product of a metamodel-based failure probability and a correction coefficient. The correction coefficient accounts for the error in the metamodel estimate of failure probability introduced by the replacement of the performance function with a metamodel. Computational efficiency and accuracy of the MLS approach are evaluated with the Kriging metamodel on analytical reliability problems and a practical reliability problem of a monopile foundation for offshore wind turbine. The MLS approach demonstrated efficient performance in low to medium-dimensional reliability problems.

Reliability Analysis of Engineering Structures

Introduces the concept and content of engineering structural reliability and reliability and reliable indexes, and considering the engineering structure reliability analysis of randomness and fuzziness, the fuzzy random reliability analysis model was established

Artificial Bee Colony Algorithm for Reliability Analysis of Engineering Structures

Artificial bee colony algorithm is a noval optimization method which is inspired by bee colony foraging behavior. Its use in the structure reliability field presents not only the advantage of its facility of implementation, but also the capability to obtain the design point and the failure probability with good accuracy. And by this method, the reliability index of nonlinear and complex limit state function which iteration scheme may fail to converge could be obtained with efficiency. It is demonstrated by four examples that the present method is reliable and accurate in reliability analysis of engineering structures.

Dynamic bounds coupled with Monte Carlo simulations

For the reliability analysis of engineering structures a variety of methods is known, of which Monte Carlo (MC) simulation is widely considered to be among the most robust and most generally applicable. To reduce simulation cost of the MC method, variance reduction methods are applied. This paper describes a method to reduce the simulation cost even further, while retaining the accuracy of Monte Carlo, by taking into account widely present monotonicity. For models exhibiting monotonic (decreasing or increasing) behavior, dynamic bounds (DB) are defined, which in a coupled Monte Carlo simulation are updated dynamically, resulting in a failure probability estimate, as well as a strict (non-probabilistic) upper and lower bounds. Accurate results are obtained at a much lower cost than an equivalent ordinary Monte Carlo simulation. In a two-dimensional and a four-dimensional numerical example, the cost reduction factors are 130 and 9, respectively, where the relative error is smaller than 5%. At higher accuracy levels, this factor increases, though this effect is expected to be smaller with increasing dimension. To show the application of DB method to real world problems, it is applied to a complex finite element model of a flood wall in New Orleans.

Applications of Meta-Models in Finite Element Based Reliability Analysis of Engineering Structures

The problem of reliability analysis of randomly parametered, linear (or) nonlinear, structures Subjected to static and (or) dynamic loads is considered. A deterministic finite element model for the structure to analyze sample realization of the structure is assumed to be available. The reliability analysis is carried out within the framework of response surface methods which involves the construction of surrogate models for performance functions to be employed in reliability calculations. This construction, in the present study, has involved combining space filling optimal Latin hypercube sampling, kriging models and methods from data-based asymptotic extreme value modeling of sequence of random variables. Illustrative examples on numerical prediction of reliability of a ten-bay truss, a W-seal in an aircraft structure, and a nonlinear randomly parametered dynamical system are presented. Limited Monte Carlo simulations are used to validate the approximate procedures developed.