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Most of the previous work on reliability analysis was based on the traditional reliability theory. The calculated results can only reflect the reliability of components at a specific time, which neglects the uncertainty of load and resistance over time. The purpose of this paper is to develop a time-dependent reliability analysis approach based on stochastic process to deal with the problem and apply it to the structural design of railway vehicle components.

First, the parametric model of motor hanger for electric multiple unit (EMU) is established by ANSYS parametric design language, and its structural stress is analyzed according to relevant standards. The Latin hypercube method is used to analyze the sensitivity of the structure, and the uncertainty parameters (sizes and loads) which have great influence on the structural strength are determined. The D-optimal experimental design is carried out to establish the polynomial response surface function, which characterizes the relationship between uncertainty parameters and structural stress. Second, the Poisson stochastic process is adopted to describe the number of loads acting, and the Monte Carlo method is used to obtain the load acting history according to its probability distribution characteristics. The load history is introduced into the response surface function and the uncertainty of other parameters is considered at the same time, and the stress history of the motor hanger is obtained. Finally, the degradation process of structural resistance is described by a Gamma stochastic process, and the time-dependent reliability of the motor hanger is calculated based on the reliability theory.

Time and the uncertainties of parameters have great impact on reliability. The results of reliability decrease with time fluctuation are more reasonable, stable and credible than traditional methods.

In this paper, the proposed method is applied to the structural design of the motor hanger for EMU, which has a good guiding significance for accurately evaluating whether if the design meets the reliability requirements.

The value of this paper is that the method takes both the randomness of load over time and the uncertainty of structural parameters in the design and manufactures process into consideration, and describes the monotonous degradation characteristics of structural resistance. At the same time, the time-dependent reliability of mechanical components is calculated by a response surface method. It not only improves the accuracy of reliability analysis, but also improves the analysis efficiency and solves the problem that the traditional reliability analysis method can only reflect the static reliability of components.

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.

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.

This paper aims to present a novel structural reliability analysis scheme with considering the structural strength degradation for the wing spar of a generic hypersonic aircraft to guarantee flight safety and structural reliability.

A logarithmic model with strength degradation for the wing spar is constructed, and a reliability model of the wing spar is established based on stress-strength interference theory and total probability theorem.

It is demonstrated that the proposed reliability analysis scheme can obtain more accurate structural reliability and failure results for the wing spar, and the strength degradation cannot be neglected. Furthermore, the obtained results will provide an important reference for the structural safety of hypersonic aircraft.

The proposed reliability analysis scheme has not implemented in actual flight, as all the simulations are conducted according to the actual experiment data.

The proposed reliability analysis scheme can solve the structural life problem of the wing spar for hypersonic aircraft and meet engineering practice requirements, and it also provides an important reference to guarantee the flight safety and structural reliability for hypersonic aircraft.

To describe the damage evolution more accurately, with consideration of strength degradation, flight dynamics and material characteristics of the hypersonic aircraft, the stress-strength interference method is first applied to analyze the structural reliability of the wing spar for the hypersonic aircraft. The proposed analysis scheme is implemented on the dynamic model of the hypersonic aircraft, and the simulation demonstrates that a more reasonable reliability result can be achieved.

The aim of this paper is to present a novel multifactor structural optimisation method incorporating reliability performance.

This research addresses structural optimisation problems in which the design is required to satisfy multiple performance criteria, such as strength, stiffness, mass and reliability under multiple loading cases simultaneously. A MOST technique is extended to accommodate the reliability‐related optimisation. Structural responses and geometrical sensitivities are analysed by a FE method, and reliability performance is calculated by a reliability loading‐case index (RLI). The evaluation indices of performances and loading cases are formulated, and an overall performance index is presented to quantitatively evaluate a design.

The proposed method is applicable to multi‐objective, multi‐loading‐case, multi‐disciplinary and reliability‐related optimisation problems. The applications to a star‐like truss structure and a raised‐access floor panel structure confirmed that the method is highly effective and efficient in terms of structural optimisation.

A systematic method is proposed. The optimisation method combines the MOST technique with a RLI (a new alternative route to calculate the reliability index at multiple loading cases) using a parametric FE model.

Considering the randomness of physical parameters of structural material, dynamic characteristic topology optimization mathematical model based on reliability of planar continuum structures is built in this paper. In which topology information variables of the structure are taken as design variables, minimizing the mean value of total structural weight as objective function and satisfying the reliability requirement of structural dynamic characteristic as constraints. In the process of optimization, the ESO method based on probability is adopted as solution strategy. At the same time, distribution function method is utilized to convert the reliability constraints into conventional constraints formally. A square thin plate with four sides fixed is used as an example to demonstrate the rationality and validity of the presented model.

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.

The purpose of this paper is to propose a robust reliability index to characterize the structural safety degree.

On the basis of the interval theory, a new interval reliability analysis method that the structural basic variables are described by the interval lower limit and interval length to characterize the structural uncertainty is proposed in this paper.

A novel structural reliability index solution method is proposed. Besides, both linear and non-linear problem of solving interval non-probabilistic reliability are further discussed in this paper.

Based on interval theory, variables are described by interval lower limit and interval length to characterize the structural uncertainty. A novel structural reliability index solution method is proposed.

Because of the high computational efficiency, response surface method (RSM) has been widely used in structural reliability analysis. However, for a highly nonlinear limit state function (LSF), the approximate accuracy of the failure probability mainly depends on the design point, and the result is that the response surface function composed of initial experimental points rarely fits the LSF exactly. The inaccurate design points usually cause some errors in the traditional RSM. The purpose of this paper is to present a hybrid method combining adaptive moving experimental points strategy and RSM, describing a new response surface using downhill simplex algorithm (DSA-RSM).

In DSA-RSM, the operation mechanism principle of the basic DSA, in which local descending vectors are automatically generated, was studied. Then, the search strategy of the basic DSA was changed and the RSM approximate model was reconstructed by combining the direct search advantage of DSA with the reliability mechanism of response surface analysis.

The computational power of the proposed method is demonstrated by solving four structural reliability problems, including the actual engineering problem of a car collision. Compared to specific structural reliability analysis methods, the approach of modified DSA interpolation response surface for structural reliability has a good convergent capability and computational accuracy.

This paper proposes a new RSM technology based on proxy model to complete the reliability analysis. The originality of this paper is to present an improved RSM that adjusts the position of the experimental points judiciously by using the DSA principle to make the fitted response surface closer to the actual limit state surface.