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To research the feasibility in using artificial neural networks (ANN) and response surfaces (RS) techniques for reliability analysis of concrete structures.

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. It is necessary to quantify and compare the importance of each one of these variables in the structural safety. RS and the ANN techniques have emerged attempting to solve complex and more elaborated problems. In this work, these two techniques are presented, and comparisons are carried out using the well‐known first‐order reliability method (FORM), with non‐linear limit state functions. The reliability analysis of reinforced concrete structure problems is specially considered taking into account the spatial variability of the material properties using random fields and the inherent non‐linearity.

It was observed that direct Monte Carlo simulation technique has a low performance in complex problems. FORM, RS and neural networks techniques are suitable alternatives, despite the loss of accuracy due to approximations characterizing these methods.

The examples tested are limited to moderated large non‐linear reinforced concrete finite element models. Conclusions are drawn based on the examples.

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 (computing failure probability and safety levels) is high, these two techniques could improve the performance of the structural reliability analysis through simulation techniques.

This paper is important in the field of reliability analysis of concrete structures specially when neural networks or RS techniques are used.

This paper aims to provide a comprehensive review of uncertainty quantification methods supported by evidence-based comparison studies. Uncertainties are widely encountered in engineering practice, arising from such diverse sources as heterogeneity of materials, variability in measurement, lack of data and ambiguity in knowledge. Academia and industries have long been researching for uncertainty quantification (UQ) methods to quantitatively account for the effects of various input uncertainties on the system response. Despite the rich literature of relevant research, UQ is not an easy subject for novice researchers/practitioners, where many different methods and techniques coexist with inconsistent input/output requirements and analysis schemes.

This confusing status significantly hampers the research progress and practical application of UQ methods in engineering. In the context of engineering analysis, the research efforts of UQ are most focused in two largely separate research fields: structural reliability analysis (SRA) and stochastic finite element method (SFEM). This paper provides a state-of-the-art review of SRA and SFEM, covering both technology and application aspects. Moreover, unlike standard survey papers that focus primarily on description and explanation, a thorough and rigorous comparative study is performed to test all UQ methods reviewed in the paper on a common set of reprehensive examples.

Over 20 uncertainty quantification methods in the fields of structural reliability analysis and stochastic finite element methods are reviewed and rigorously tested on carefully designed numerical examples. They include FORM/SORM, importance sampling, subset simulation, response surface method, surrogate methods, polynomial chaos expansion, perturbation method, stochastic collocation method, etc. The review and comparison tests comment and conclude not only on accuracy and efficiency of each method but also their applicability in different types of uncertainty propagation problems.

The research fields of structural reliability analysis and stochastic finite element methods have largely been developed separately, although both tackle uncertainty quantification in engineering problems. For the first time, all major uncertainty quantification methods in both fields are reviewed and rigorously tested on a common set of examples. Critical opinions and concluding remarks are drawn from the rigorous comparative study, providing objective evidence-based information for further research and practical applications.

The first order reliability method requires optimization algorithms to find the minimum distance from the origin to the limit state surface in the normal space. The purpose of this paper is to develop an improved version of the new metaheuristic algorithm inspired from echolocation behaviour of bats, namely, the bat algorithm (BA) dedicated to perform structural reliability analysis.

Modifications have been embedded to the standard BA to enhance its efficiency, robustness and reliability. In addition, a new adaptive penalty equation dedicated to solve the problem of the determination of the reliability index and a proposition on the limit state formulation are presented.

The comparisons between the improved bat algorithm (iBA) presented in this paper and other standard algorithms on benchmark functions show that the iBA is highly efficient, and the application to structural reliability problems such as the reliability analysis of overhead crane girder proves that results obtained with iBA are highly reliable.

A new iBA and an adaptive penalty equation for handling equality constraint are developed to determine the reliability index. In addition, the low computing time and the ease implementation of this method present great advantages from the engineering viewpoint.

To develop a new computational tool for predicting failure probability of structural/mechanical systems subject to random loads, material properties, and geometry.

High dimensional model representation (HDMR) is a general set of quantitative model assessment and analysis tools for capturing the high‐dimensional relationships between sets of input and output model variables. It is a very efficient formulation of the system response, if higher order variable correlations are weak and if the response function is dominantly of additive nature, allowing the physical model to be captured by the first few lower order terms. But, if multiplicative nature of the response function is dominant then all right hand side components of HDMR must be used to be able to obtain the best result. However, if HDMR requires all components, which means 2^N number of components, to get a desired accuracy, making the method very expensive in practice, then factorized HDMR (FHDMR) can be used. The component functions of FHDMR are determined by using the component functions of HDMR. This paper presents the formulation of FHDMR approximation of a multivariate limit state/performance function, which is dominantly of multiplicative nature. Given that conventional methods for reliability analysis are very computationally demanding, when applied in conjunction with complex finite element models. This study aims to assess how accurately and efficiently HDMR/FHDMR based approximation techniques can capture complex model output uncertainty. As a part of this effort, the efficacy of HDMR, which is recently applied to reliability analysis, is also demonstrated. Response surface is constructed using moving least squares interpolation formula by including constant, first‐order and second‐order terms of HDMR and FHDMR. Once the response surface form is defined, the failure probability can be obtained by statistical simulation.

Results of five numerical examples involving structural/solid‐mechanics/geo‐technical engineering problems indicate that the failure probability obtained using FHDMR approximation for the limit state/performance function of dominantly multiplicative in nature, provides significant accuracy when compared with the conventional Monte Carlo method, while requiring fewer original model simulations.

This is the first time where application of FHDMR concepts is explored in the field of reliability and system safety. Present computational approach is valuable to the practical modeling and design community, where user often suffers from the curse of dimensionality.

The purpose of this study is to improve the efficiency and accuracy of response surface method (RSM), as well as its robustness.

By introducing cut-high-dimensional representation model (HDMR), the delineation of cross terms and the constitution analysis of component function, a new adaptive RSM is presented for reliability calculation, where a sampling scheme is also proposed to help constructing response surface close to limit-state.

The proposed method has a more feasible process of evaluating undetermined coefficients of each component function than traditional RSM, and performs well in terms of balancing the efficiency and accuracy when compared to the traditional second-order polynomial RSM. Moreover, the proposed method is robust on the parameter in a wide range, indicating that it is able to obtain convergent result in a wide feasible domain of sample points.

This study constructed an adaptive bivariate cut-HDMR by introducing delineation of cross-terms and constitution of univariate component function; and a new sampling technique is proposed.

The purpose of this paper is to briefly summarize and review the theories and methods of complex structures’ dynamic reliability. Complex structures are usually assembled from multiple components and subjected to time-varying loads of aerodynamic, structural, thermal and other physical fields; its reliability analysis is of great significance to ensure the safe operation of large-scale equipment such as aviation and machinery.

In this paper for the single-objective dynamic reliability analysis of complex structures, the calculation can be categorized into Monte Carlo (MC), outcrossing rate, envelope functions and extreme value methods. The series-parallel and expansion methods, multi-extremum surrogate models and decomposed-coordinated surrogate models are summarized for the multiobjective dynamic reliability analysis of complex structures.

The numerical complex compound function and turbine blisk are used as examples to illustrate the performance of single-objective and multiobjective dynamic reliability analysis methods. Then the future development direction of dynamic reliability analysis of complex structures is prospected.

The paper provides a useful reference for further theoretical research and engineering application.

In this paper, special emphasis is given to uncertainties in the evaluation of the structural behavior, looking for a better representation of the system characteristics and quantification of the significance of these uncertainties in structural design. The reliability analysis of reinforced concrete structures is performed taking into account the spatial variability of material properties. The finite element method is used to analyze reinforced concrete structures. A multidimensional non‐Gaussian stochastic field generation model (independent of the finite element mesh) is developed and used. The reliability analysis is carried out employing the first order reliability method. Numerical examples are presented to study how to generate correlated non‐Gaussian stochastic fields and determine the reliability of a reinforced concrete structure with respect to a limit state function.

The performance measure approach (PMA) is widely adopted for reliability analysis and reliability-based design optimization because of its robustness and efficiency compared to reliability index approach. However, it has been reported that PMA involves repeat evaluations of probabilistic constraints therefore it is prohibitively expensive for many large-scale applications. In order to overcome these disadvantages, the purpose of this paper is to propose an efficient PMA-based reliability analysis technique using radial basis function (RBF).

The RBF is adopted to approximate the implicit limit state functions in combination with latin hypercube sampling (LHS) strategy. The advanced mean value method is applied to obtain the most probable point (MPP) with the prescribed target reliability and corresponding probabilistic performance measure to improve analysis accuracy. A sequential framework is proposed to relocate the sampling center to the obtained MPP and reconstruct RBF until a criteria is satisfied.

The method is shown to be better in the computation time to the PMA based on the actual model. The analysis results of probabilistic performance measure are accurately close to the reference solution. Five numerical examples are presented to demonstrate the effectiveness of the proposed method.

The main contribution of this paper is to propose a new reliability analysis technique using reconstructed RBF approximate model. The originalities of this paper may lie in: investigating the PMA using metamodel techniques, using RBF instead of the other types of metamodels to deal with the low efficiency problem.

To provide valuable information for scholars to grasp the current situations, hotspots and future development trends of reliability analysis area.

In this paper, recent researches on efficient reliability analysis and applications in complex engineering structures like aeroengine rotor systems are reviewd.

The recent reliability analysis advances of engineering application in aeroengine rotor system are highlighted, it is worth pointing out that the surrogate model methods hold great efficiency and accuracy advantages in the complex reliability analysis of aeroengine rotor system, since its strong computing power can effectively reduce the analysis time consumption and accelerate the development procedures of aeroengine. Moreover, considering the multi-objective, multi-disciplinary, high-dimensionality and time-varying problems are the common problems in various complex engineering fields, the surrogate model methods and its developed methods also have broad application prospects in the future.

For the strong demand for efficient reliability design technique, this review paper may help to highlights the benefits of reliability analysis methods not only in academia but also in practical engineering application like aeroengine rotor system.

The purpose of this paper is to analyze the time-dependent reliability of harmonic drive.

The transient finite element analysis (FEA) of harmonic drive is established to calculate the stress under different loads. Combined with the residual strength model and random variables, the time-dependent reliability model of harmonic drive is deduced by the stochastic perturbation method and Edgeworth series. Based on accelerated life tests, the degradation parameters are estimated by maximizing likelihood function. Under variable load, the key stress from transient FEA is transformed into probability density function by kernel density estimation, and the residual strength model is modified by adding adjustment factors to deal with strength degradation under different loads.

The critical position of stress concentration from transient FEA is consistent with the fatigue fracture position at the accelerated life test sample. Compared with the time-dependent reliability method with equivalent circular-shell static stress or empirical degradation parameters, the proposed method has the smallest prediction error of failure life. Under variable load, the state function should be expanded to second-order series for avoiding error items relevant to variance. The failure life expectation under random variable load is smaller than that under constant load.

The time-dependent reliability method of harmonic drive is firstly proposed under constant and variable load. The transient FEA of harmonic drive is established to calculate the stress for strength analysis. The accelerated life test of harmonic drive is conducted for degradation parameters estimation. The adjustment factor is added to the residual strength model for strength degradation under different loads.