Application of matrix-based system reliability method in complex slopes

Complex slopes are characterized by large numbers of failure modes,cut sets or link sets,or by statistical dependence between the failure modes.For such slopes,a systematic quantitative method,or matrix-based system reliability method,was described and improved for their reliability analysis.A construction formula of event vector c E was suggested to solve the difficulty of identifying any component E in sample space,and event vector c of system events can be calculated based on it,then the bounds of system failure probability can be obtained with the given probability information.The improved method was illustrated for four copper mine slopes with multiple failure modes,and the bounds of system failure probabilities were calculated by self-compiling program on the platform of the software MATLAB.Comparison in results from matrix-based system reliability method and two generic system methods suggests that identical accuracy could be obtained by all methods if there are only a few failure modes in slope system.Otherwise,the bounds by the Ditlevsen method or Cornell method are expanded obviously with the increase of failure modes and their precision can hardly satisfy the requirement of practical engineering while the results from the proposed method are still accurate enough.

An Uncertainty Analysis and Reliability-Based Multidisciplinary Design Optimization Method Using Fourth-Moment Saddlepoint Approximation

In uncertainty analysis and reliability-based multidisciplinary design and optimization(RBMDO)of engineering structures,the saddlepoint approximation(SA)method can be utilized to enhance the accuracy and efficiency of reliability evaluation.However,the random variables involved in SA should be easy to handle.Additionally,the corresponding saddlepoint equation should not be complicated.Both of them limit the application of SA for engineering problems.The moment method can construct an approximate cumulative distribution function of the performance function based on the first few statistical moments.However,the traditional moment matching method is not very accurate generally.In order to take advantage of the SA method and the moment matching method to enhance the efficiency of design and optimization,a fourth-moment saddlepoint approximation(FMSA)method is introduced into RBMDO.In FMSA,the approximate cumulative generating functions are constructed based on the first four moments of the limit state function.The probability density function and cumulative distribution function are estimated based on this approximate cumulative generating function.Furthermore,the FMSA method is introduced and combined into RBMDO within the framework of sequence optimization and reliability assessment,which is based on the performance measure approach strategy.Two engineering examples are introduced to verify the effectiveness of proposed method.

A Bayesian Updating Method for Non-Probabilistic Reliability Assessment of Structures with Performance Test Data

For structures that only the predicted bounds of uncertainties are available,this study proposes a Bayesianmethod to logically evaluate the nonprobabilistic reliability of structures based on multi-ellipsoid convex model and performance test data.According to the given interval ranges of uncertainties,we determine the initial characteristic parameters of a multi-ellipsoid convex set.Moreover,to update the plausibility of characteristic parameters,a Bayesian network for the information fusion of prior uncertainty knowledge and subsequent performance test data is constructed.Then,an updated multi-ellipsoid set with the maximum likelihood of the performance test data can be achieved.The credible non-probabilistic reliability index is calculated based on the Kriging-based surrogate model of the performance function.Several numerical examples are presented to validate the proposed Bayesian updating method.

Singularity of Some Software Reliability Models and Parameter Estimation Method

According,to the principle, "The failure data is the basis of software reliability analysis", we built a software reliability expert system (SRES) by adopting the artificial intelligence technology. By reasoning out the conclusion from the fitting results of failure data of a software project, the SRES can recommend users "the most suitable model" as a software reliability measurement model. We believe that the SRES can overcome the inconsistency in applications of software reliability models well. We report investigation results of singularity and parameter estimation methods of experimental models in SRES.

Computer System Reliability Allocation Method and Supporting Tool

This paper presents a computer system reliability allocation method that is based on the theory of statistic and Markovian chain,which can be used to allocate reliability to subsystem, to hybrid system and software modules. A relevant supporting tool built by us is introduced.

IMPROVED STRATIFIED SAMPLING MONTE CARLO METHOD TO ANALYZE RELIABILITY OF STRUCTURAL SYSTEMS

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Reliability analysis for aeroengine turbine disc fatigue life with multiple random variables based on distributed collaborative response surface method

The fatigue life of aeroengine turbine disc presents great dispersion due to the randomness of the basic variables,such as applied load,working temperature,geometrical dimensions and material properties.In order to ameliorate reliability analysis efficiency without loss of reliability,the distributed collaborative response surface method(DCRSM) was proposed,and its basic theories were established in this work.Considering the failure dependency among the failure modes,the distributed response surface was constructed to establish the relationship between the failure mode and the relevant random variables.Then,the failure modes were considered as the random variables of system response to obtain the distributed collaborative response surface model based on structure failure criterion.Finally,the given turbine disc structure was employed to illustrate the feasibility and validity of the presented method.Through the comparison of DCRSM,Monte Carlo method(MCM) and the traditional response surface method(RSM),the results show that the computational precision for DCRSM is more consistent with MCM than RSM,while DCRSM needs far less computing time than MCM and RSM under the same simulation conditions.Thus,DCRSM is demonstrated to be a feasible and valid approach for improving the computational efficiency of reliability analysis for aeroengine turbine disc fatigue life with multiple random variables,and has great potential value for the complicated mechanical structure with multi-component and multi-failure mode.

Advanced method to estimate reliability-based sensitivity of mechanical components with strongly nonlinear performance function

Based on the random perturbation technique for reliability sensitivity design,some realistic reliability-based sensitivity issues are discussed,some of which have a structure of high nonlinear performance functions.Combining the related theories of the moment method of the reliability analysis,the matrix differential,and the Kronecker algebra,the reliability-based sensitivity method based on the perturbation method is modified if the first four moments of random variables are given.Meanwhile,a reliability-based sensitivity computation method is proposed.Some examples are used to show that using this method can effectively improve the accuracy of the reliability-based sensitivity computation and offer a reliable theoretic basis in engineering.

Extremum response surface method of reliability analysis on two-link flexible robot manipulator

In order to present a new method for analyzing the reliability of a two-link flexible robot manipulator,Lagrange dynamics differential equations of the two-link flexible robot manipulator were established by using the integrated modal method and the multi-body system dynamics method.By using the Monte Carlo method,the random sample values of the dynamic parameters were obtained and Lagrange dynamics differential equations were solved for each random sample value which revealed their displacement,speed and acceleration.On this basis,dynamic stresses and deformations were obtained.By taking the maximum values of the stresses and the deformations as output responses and the random sample values of dynamic parameters as input quantities,extremum response surface functions were established.A number of random samples were then obtained by using the Monte Carlo method and then the reliability was analyzed by using the extremum response surface method.The results show that the extremum response surface method is an efficient and fast reliability analysis method with high-accuracy for the two-link flexible robot manipulator.

RELIABILITY ASSESSMENT OF ENTROPY METHOD FOR SYSTEM CONSISTED OF IDENTICAL EXPONENTIAL UNITS

The reliability assessment of unit-system near two levels is the most important content in the reliability multi-level synthesis of complex systems. Introducing the information theory into system reliability assessment, using the addible characteristic of information quantity and the principle of equivalence of information quantity, an entropy method of data information conversion is presented for the system consisted of identical exponential units. The basic conversion formulae of entropy method of unit test data are derived based on the principle of information quantity equivalence. The general models of entropy method synthesis assessment for system reliability approximate lower limits are established according to the fundamental principle of the unit reliability assessment. The applications of the entropy method are discussed by way of practical examples. Compared with the traditional methods, the entropy method is found to be valid and practicable and the assessment results are very satisfactory.

An Intelligent Method for Structural Reliability Analysis Based on Response Surface

As water depth increases, the structural safety and reliability of a system become more and more important and challenging. Therefore, the structural reliability method must be applied in ocean engineering design such as offshore platform design. If the performance function is known in structural reliability analysis, the first-order second-moment method is often used. If the performance function could not be definitely expressed, the response surface method is always used because it has a very clear train of thought and simple programming. However, the traditional response surface method fits the response surface of quadratic polynomials where the problem of accuracy could not be solved, because the true limit state surface can be fitted well only in the area near the checking point. In this paper, an intelligent computing method based on the whole response surface is proposed, which can be used for the situation where the performance function could not be definitely expressed in structural reliability analysis. In this method, a response surface of the fuzzy neural network for the whole area should be constructed first, and then the structural reliability can be calculated by the genetic algorithm. In the proposed method, all the sample points for the training network come from the whole area, so the true limit state surface in the whole area can be fitted. Through calculational examples and comparative analysis, it can be known that the proposed method is much better than the traditional response surface method of quadratic polynomials, because, the amount of calculation of finite element analysis is largely reduced, the accuracy of calculation is improved, and the true limit state surface can be fitted very well in the whole area. So, the method proposed in this paper is suitable for engineering application.

Distributed Collaborative Response Surface Method for Mechanical Dynamic Assembly Reliability Design

Because of the randomness of many impact factors influencing the dynamic assembly relationship of complex machinery,the reliability analysis of dynamic assembly relationship needs to be accomplished considering the randomness from a probabilistic perspective.To improve the accuracy and efficiency of dynamic assembly relationship reliability analysis,the mechanical dynamic assembly reliability(MDAR)theory and a distributed collaborative response surface method(DCRSM)are proposed.The mathematic model of DCRSM is established based on the quadratic response surface function,and verified by the assembly relationship reliability analysis of aeroengine high pressure turbine(HPT)blade-tip radial running clearance(BTRRC).Through the comparison of the DCRSM,traditional response surface method(RSM)and Monte Carlo Method(MCM),the results show that the DCRSM is not able to accomplish the computational task which is impossible for the other methods when the number of simulation is more than 100 000times,but also the computational precision for the DCRSM is basically consistent with the MCM and improved by 0.40～4.63%to the RSM,furthermore,the computational efficiency of DCRSM is up to about 188 times of the MCM and 55 times of the RSM under10000 times simulations.The DCRSM is demonstrated to be a feasible and effective approach for markedly improving the computational efficiency and accuracy of MDAR analysis.Thus,the proposed research provides the promising theory and method for the MDAR design and optimization,and opens a novel research direction of probabilistic analysis for developing the high-performance and high-reliability of aeroengine.

RELIABILITY OF ELASTO-PLASTIC STRUCTURE USING FINITE ELEMENT METHOD

A solution of probabilistic FEM for elastic-plastic materials is pre-sented based on the incremental theory of plasticity and a modified initial stressmethod. The formulations are deduced through a direct differentiation scheme. Par-tial differentiation of displacement, stress and the performance function can be it-eratively performed with the computation of the mean values of displacement andstress. The presented method enjoys the efficiency of both the perturbation methodand the finite difference method, but avoids the approximation during the partial dif-ferentiation calculation. In order to improve the efficiency, the adjoint vector methodis introduced to calculate the differentiation of stress and displacement with respectto random variables. In addition, a time-saving computational method for reliabilityindex of elastic-plastic materials is suggested based upon the advanced First OrderSecond Moment (FOSM) and by the usage of Taylor expansion for displacement. Thesuggested method is also applicable to 3-D cases.

STOCHASTIC BOUNDARY ELEMENT METHODS FOR 3－D PROBLEMS WITH CENTRIFUGAL FORCES AND RELIABILITY ANALYSIS

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STOCHASTIC BOUNDARY ELEMENT METHOD FOR RELIABILITY ANALYSIS OF PLATE AND BEAMS COMPOSITE STRUCTURES

In this paper, the reliability of orthotropic plate and beams composite structures,which is under the actions of the stochastic loading and stochastic boundary conditions,have been analyzed by stochastic boundary element method. First, the boundaryintegral equation of orthotropic plate and beams composite structures is given in thispaper. and then based on the stochastic boundary element method, the method forreliability analysis of stochastic structures is establishes and formulas for computationof reliabilily index of orthotropic plate and beams composite structures are obtained.The computed examples show the efficienl of the method used in this paper.

Experimental and Finite Element Method Studies of J-Lead Solder Joint Reliability

A comprehensive experimental and numerical study of solder joints for plastic leaded chip carrier (PLCC) 84-Pin,1.27 mm pitch was carried out. The reliability of solder joints was assessed through accelerated thermal cycling at the temperature range of -55℃～125℃. The samples were taken out to observe the evolution in microstructure, such as grain coarsening, initiation and propagation of cracks. It was found that the Pb-rich phases segregated gradually and formed a continuous layer adjacent to the intermetallic compound (IMC) layer with increasing the number of thermal cycles, resulting in cracks near the solder/lead interface. The response of stress and strain was studied using nonlinear finite element method (FEM), and the results agreed well with the experimental data.

Reliability Analysis of Flexure Hinge Based on Kriging Method

The uncertainty widely exists in the engineering practice.Therefore,it is necessary to research the effect of uncertainty on the structural system. In this paper,the reliability and sensitivity of the flexure hinge, which is the key component of the compliant mechanisms,are investigated. The results of the reliability analysis can effectively guide the engineer to design and optimize the flexure hinge. In order to improve the calculating efficiency,the kriging method is introduced to estimate the failure probability and reliability sensitivity.

Vibration reliability analysis for aeroengine compressor blade based on support vector machine response surface method

To ameliorate reliability analysis efficiency for aeroengine components, such as compressor blade, support vector machine response surface method(SRSM) is proposed. SRSM integrates the advantages of support vector machine(SVM) and traditional response surface method(RSM), and utilizes experimental samples to construct a suitable response surface function(RSF) to replace the complicated and abstract finite element model. Moreover, the randomness of material parameters, structural dimension and operating condition are considered during extracting data so that the response surface function is more agreeable to the practical model. The results indicate that based on the same experimental data, SRSM has come closer than RSM reliability to approximating Monte Carlo method(MCM); while SRSM(17.296 s) needs far less running time than MCM(10958 s) and RSM(9840 s). Therefore,under the same simulation conditions, SRSM has the largest analysis efficiency, and can be considered a feasible and valid method to analyze structural reliability.

AN IMPROVED M-C METHOD AND ITS APPLICATION TO STRUCTURAL RELIABILITY

An improved Monte-Carlo method for the failure calculation of structureis proposed.The present method can determine whether some sample points are in thesafe region without doing structural analysis,so the calculation work is greatly reducedcompared with the ordinary M-C method.Finally,the new M-C method is applied toreliability analysis of frame and the torsional buckling reliability analysis of cylindricalshells.

Study on slope reliability method Response Surface Method based on Morgenstern-Price Method

The combination of Morgenstern-Price Method (MPM) with Response Surface Method (RSM) improves the conventional RSM by replacing Finite-Element Method (FEM) with MPM, which is a type of reliability analysis method--RSM based on MPM, and makes the computing process simpler. The stability of the slope was re-evaluated by use of Monte Carlo method (MCM) and the result contrasted with the fore is the conclusion. The reliability analysis of the artificial slope in Donggang Power Station was carried on, and obtained the reliable characteristics, which provided basis for the project.