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Optimization of structural systems under reliability‐based performance constraints is an important problem at present receiving too little attention. This problem is investigated in this paper. In developing the reliability‐based optimization approach to the design of framed structures, we review first the general formulation of the deterministic optimization problem and present some of the main features of two general‐purpose deterministic optimization programs. A computer‐automated reliability‐based optimum design procedure is then presented by which the concept of reliability analysis with regard to both serviceability and ultimate performance constraints is combined with that of the minimum weight design to achieve an optimum trade‐off between the global reliability and the total cost. The procedure is feasible for application in system optimization of both steel and reinforced concrete structures.

The paper attempts to establish the connection between structural reliability and structural optimization for the particular case of plastic structures. Along this line, the paper outlines a reliability‐based optimization approach to design plastic structures with uncertain interdependent strengths and acted on by random interdependent loads. The importance of such interdependencies, and of some of the other statistical parameters used as input data in probabilistic computations, is demonstrated by several examples of sensitivity studies on both the probability of collapse failure as well as the reliability‐based optimum solution.

In the last twenty years, the methods for structural system reliability evaluation have evolved considerably. Since these methods are based on different assumptions, it is necessary to evaluate their capabilities. For this reason, a research study was initiated at the University of Colorado at Boulder in order to investigate the accuracy and reliability of various methods for structural system reliability evaluation. This paper emphasizes certain important parametric studies on system reliability methods under uncertainty. The sensitivity of the accuracy of the methods to changes in both strength and load correlations is demonstrated by means of numerical examples.

Structural optimisation and reliability theory are considered, and described. A general reliability‐based structural optimisation problem is formulated, and consideration given to procedures for solving it. Two different examples suggest the efficacy of these procedures. The amount of calculations depends to a great degree on the definition of failure of the structure. In order to reduce this by improving optimisation procedures, more research is needed, and the convergence of the optimisation is very dependent on accurate evaluation of the gradients of the reliability constraints.

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.

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 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.

Modern reliability analyses of large structural system designs require substantial computing times, and need to be repeated frequently in the process of design optimization. In the important case when underlying random variables are not normally distributed, the widely used approximation scheme by Rackwitz and Fiessler further increases the computational requirement by a substantial factor. This paper proposes a simple alternative approximation scheme which requires significantly less computation than the Rackwitz‐Fiessler algorithm, at an acceptable loss of accuracy.

Despite recognizing the significance of risk-based frameworks in fire safety engineering, the usual approach in structural fire design is largely member/component level, wherein effect of uncertainties influencing the fire resistance of structures are not explicitly considered. In this context, a probabilistic framework is presented to investigate the vulnerability of a reinforced concrete (RC) members and structure under fire loading scenario.

The RC structures exposed to fire are modeled in a finite element (FE) platform incorporating material and geometric nonlinearity, in which the transient thermo-mechanical analysis is carried out by suitably incorporating the temperature variation of thermal and mechanical properties of both concrete and steel rebar. The stochasticity in the system is considered in structural resistance, thermal and fire model parameters, and the subsequent fragility curves are developed considering threshold limit state of deflection.

The fire resistance of RC structure is reported to be significantly lower in comparison to the RC members, thereby illustrating the current prescriptive design approaches based on studies of structural member behavior to be crucial from a safety and reliability point of view.

The framework developed for the vulnerability assessment of RC structures under fire hazard through FE analysis can be effectively used to estimate the structural fire resistance for other similar structure to enhance safety and reliability of structures under such extreme threats.

The paper proposes a novel methodology for vulnerability assessment of three-dimensional RC structures under fire hazard through FE analysis and provides comparison of the structural fragility with fragility developed for structural members. Moreover, the research emphasizes to assume 3D behavior of the structure rather than the approximate 2D behavior.

This paper aims to develop a method for evaluating the failure probability and global sensitivity of multiple failure modes based on convex-probability hybrid uncertainty.

The uncertainty information of the input variable is considered as convex-probability hybrid uncertainty. Moment-independent variable global sensitivity index based on the system failure probability is proposed to quantify the effect of the input variable on the system failure probability. Two-mode sensitivity indices are adopted to characterize the effect of each failure mode on the system failure probability. The method based on active learning Kriging (ALK) model with a truncated candidate regions (TCR) is adopted to evaluate the systems failure probability, as well as sensitivity index and this method is termed as ALK-TCR.

The results of five examples demonstrate the effectiveness of the sensitivity index and the efficiency of the ALK-TCR method in solving the problem of multiple failure modes based on the convex-probability hybrid uncertainty.

Convex-probability hybrid uncertainty is considered on system reliability analysis. Moment-independent variable sensitivity index based on the system failure probability is proposed. Mode sensitivity indices are extended to hybrid uncertain reliability model. An effective global sensitivity analysis approach is developed for the multiple failure modes based on convex-probability hybrid uncertainty.