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A non-probabilistic reliability topology optimization method based on aggregation function and matrix multiplication considering buckling response constraints
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作者 Lei WANG Yingge LIU +2 位作者 Juxi HU Weimin CHEN Bing HAN 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2024年第2期321-336,共16页
A non-probabilistic reliability topology optimization method is proposed based on the aggregation function and matrix multiplication.The expression of the geometric stiffness matrix is derived,the finite element linea... A non-probabilistic reliability topology optimization method is proposed based on the aggregation function and matrix multiplication.The expression of the geometric stiffness matrix is derived,the finite element linear buckling analysis is conducted,and the sensitivity solution of the linear buckling factor is achieved.For a specific problem in linear buckling topology optimization,a Heaviside projection function based on the exponential smooth growth is developed to eliminate the gray cells.The aggregation function method is used to consider the high-order eigenvalues,so as to obtain continuous sensitivity information and refined structural design.With cyclic matrix programming,a fast topology optimization method that can be used to efficiently obtain the unit assembly and sensitivity solution is conducted.To maximize the buckling load,under the constraint of the given buckling load,two types of topological optimization columns are constructed.The variable density method is used to achieve the topology optimization solution along with the moving asymptote optimization algorithm.The vertex method and the matching point method are used to carry out an uncertainty propagation analysis,and the non-probability reliability topology optimization method considering buckling responses is developed based on the transformation of non-probability reliability indices based on the characteristic distance.Finally,the differences in the structural topology optimization under different reliability degrees are illustrated by examples. 展开更多
关键词 BUCKLING topology optimization aggregation function uncertainty propagation analysis non-probabilistic reliability
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Non-probabilistic fuzzy reliability analysis of pile foundation stability by interval theory 被引量:1
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作者 曹文贵 张永杰 赵明华 《Journal of Central South University of Technology》 EI 2007年第6期864-869,共6页
Randomness and fuzziness are among the attributes of the influential factors for stability assessment of pile foundation. According to these two characteristics, the triangular fuzzy number analysis approach was intro... Randomness and fuzziness are among the attributes of the influential factors for stability assessment of pile foundation. According to these two characteristics, the triangular fuzzy number analysis approach was introduced to determine the probability-distributed function of mechanical parameters. Then the functional function of reliability analysis was constructed based on the study of bearing mechanism of pile foundation, and the way to calculate interval values of the functional function was developed by using improved interval-truncation approach and operation rules of interval numbers. Afterwards, the non-probabilistic fuzzy reliability analysis method was applied to assessing the pile foundation, from which a method was presented for non- probabilistic fuzzy reliability analysis of pile foundation stability by interval theory. Finally, the probability distribution curve of non- probabilistic fuzzy reliability indexes of practical pile foundation was concluded. Its failure possibility is 0.91%, which shows that the pile foundation is stable and reliable. 展开更多
关键词 pile foundation FUZZINESS interval theory interval-truncation approach non-probabilistic fuzzy reliability analysis
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An improved interval model updating method via adaptive Kriging models
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作者 Sha WEI Yifeng CHEN +1 位作者 Hu DING Liqun CHEN 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2024年第3期497-514,共18页
Interval model updating(IMU)methods have been widely used in uncertain model updating due to their low requirements for sample data.However,the surrogate model in IMU methods mostly adopts the one-time construction me... Interval model updating(IMU)methods have been widely used in uncertain model updating due to their low requirements for sample data.However,the surrogate model in IMU methods mostly adopts the one-time construction method.This makes the accuracy of the surrogate model highly dependent on the experience of users and affects the accuracy of IMU methods.Therefore,an improved IMU method via the adaptive Kriging models is proposed.This method transforms the objective function of the IMU problem into two deterministic global optimization problems about the upper bound and the interval diameter through universal grey numbers.These optimization problems are addressed through the adaptive Kriging models and the particle swarm optimization(PSO)method to quantify the uncertain parameters,and the IMU is accomplished.During the construction of these adaptive Kriging models,the sample space is gridded according to sensitivity information.Local sampling is then performed in key subspaces based on the maximum mean square error(MMSE)criterion.The interval division coefficient and random sampling coefficient are adaptively adjusted without human interference until the model meets accuracy requirements.The effectiveness of the proposed method is demonstrated by a numerical example of a three-degree-of-freedom mass-spring system and an experimental example of a butted cylindrical shell.The results show that the updated results of the interval model are in good agreement with the experimental results. 展开更多
关键词 interval model updating(IMU) non-probabilistic uncertainty adaptive Kriging model surrogate model grey number
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Structural Interval Reliability Algorithm Based on Bernstein Polynomials and Evidence Theory
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作者 Xu Zhang Jianchao Ni +1 位作者 Juxi Hu Weisi Chen 《Computer Systems Science & Engineering》 SCIE EI 2023年第8期1947-1960,共14页
Structural reliability is an important method to measure the safety performance of structures under the influence of uncertain factors.Traditional structural reliability analysis methods often convert the limit state ... Structural reliability is an important method to measure the safety performance of structures under the influence of uncertain factors.Traditional structural reliability analysis methods often convert the limit state function to the polynomial form to measure whether the structure is invalid.The uncertain parameters mainly exist in the form of intervals.This method requires a lot of calculation and is often difficult to achieve efficiently.In order to solve this problem,this paper proposes an interval variable multivariate polynomial algorithm based on Bernstein polynomials and evidence theory to solve the structural reliability problem with cognitive uncertainty.Based on the non-probabilistic reliability index method,the extreme value of the limit state function is obtained using the properties of Bernstein polynomials,thus avoiding the need for a lot of sampling to solve the reliability analysis problem.The method is applied to numerical examples and engineering applications such as experiments,and the results show that the method has higher computational efficiency and accuracy than the traditional linear approximation method,especially for some reliability problems with higher nonlinearity.Moreover,this method can effectively improve the reliability of results and reduce the cost of calculation in practical engineering problems. 展开更多
关键词 Structural reliability uncertainty analysis interval problem evidence theory Bernstein polynomial
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MODIFIED SCHEME BASED ON SEMI-ANALYTIC APPROACH FOR COMPUTING NON-PROBABILISTIC RELIABILITY INDEX 被引量:5
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作者 Xuyong Chen Chak-yin Tang +1 位作者 Chi-pong Tsui Jianping Fan 《Acta Mechanica Solida Sinica》 SCIE EI 2010年第2期115-123,共9页
A new computation scheme proposed to tackle commensurate problems is devel- oped by modifying the semi-analytic approach for minimizing computational complexity. Using the proposed scheme, the limit state equations, u... A new computation scheme proposed to tackle commensurate problems is devel- oped by modifying the semi-analytic approach for minimizing computational complexity. Using the proposed scheme, the limit state equations, usually referred to as the failure surface, are obtained from transformation of an interval variable to a normalized one. In order to minimize the computational cost, two algorithms for optimizing the calculation steps have been proposed. The monotonicity of the objective function can be determined from narrowing the scope of interval variables in normalized infinite space by incorporating the algorithms into the computational scheme. Two examples are used to illustrate the operation and computational efficiency of the approach. The results of these examples show that the proposed algorithms can greatly reduce the computation complexity without sacrificing the computational accuracy. The advantage of the proposed scheme can be even more efficient for analyzing sophistic structures. 展开更多
关键词 semi-analytic approach non-probabilistic reliability index interval variable state equation MONOTONICITY
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Combination of structural reliability and interval analysis 被引量:7
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作者 Zhiping Qiu Di Yang Isaac Elishakoff 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2008年第1期61-67,共7页
In engineering applications, probabilistic reliability theory appears to be presently the most important method, however, in many cases precise probabilistic reliability theory cannot be considered as adequate and cre... In engineering applications, probabilistic reliability theory appears to be presently the most important method, however, in many cases precise probabilistic reliability theory cannot be considered as adequate and credible model of the real state of actual affairs. In this paper, we developed a hybrid of probabilistic and non-probabilistic reliability theory, which describes the structural uncertain parameters as interval variables when statistical data are found insufficient. By using the interval analysis, a new method for calculating the interval of the structural reliability as well as the reliability index is introduced in this paper, and the traditional probabilistic theory is incorporated with the interval analysis. Moreover, the new method preserves the useful part of the traditional probabilistic reliability theory, but removes the restriction of its strict requirement on data acquisition. Example is presented to demonstrate the feasibility and validity of the proposed theory. 展开更多
关键词 non-probabilistic reliability interval analysis Parameter estimation
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A Bayesian Updating Method for Non-Probabilistic Reliability Assessment of Structures with Performance Test Data 被引量:5
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作者 Jiaqi He Yangjun Luo 《Computer Modeling in Engineering & Sciences》 SCIE EI 2020年第11期777-800,共24页
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 mo... 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. 展开更多
关键词 Convex model Bayesian method non-probabilistic reliability information fusion
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A Comprehensive Model for Structural Non-Probabilistic Reliability and the Key Algorithms 被引量:2
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作者 Wencai Sun Zichun Yang 《Computer Modeling in Engineering & Sciences》 SCIE EI 2020年第4期309-332,共24页
It is very difficult to know the exact boundaries of the variable domain for problems with small sample size,and the traditional convex set model is no longer applicable.In view of this,a novel reliability model was p... It is very difficult to know the exact boundaries of the variable domain for problems with small sample size,and the traditional convex set model is no longer applicable.In view of this,a novel reliability model was proposed on the basis of the fuzzy convex set(FCS)model.This new reliability model can account for different relations between the structural failure region and variable domain.Key computational algorithms were studied in detail.First,the optimization strategy for robust reliability is improved.Second,Monte Carlo algorithms(i.e.,uniform sampling method)for hyper-ellipsoidal convex sets were studied in detail,and errors in previous reports were corrected.Finally,the Gauss-Legendre integral algorithm was used for calculation of the integral reliability index.Three numerical examples are presented here to illustrate the rationality and feasibility of the proposed model and its corresponding algorithms. 展开更多
关键词 Structural reliability non-probabilistic fuzzy convex set robust reliability volume ratio-based reliability Monte Carlo Gauss-Legendre integral formula
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Interval Motion Accuracy Reliability Analysis of Manipulators Based on Chebyshev Inclusion Polynomial 被引量:1
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作者 Juan Wei Jianguo Zhang Xiaosong Du 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2019年第2期32-40,共9页
Motion accuracy of space manipulators has direct effects on the ability of the systems to perform specified tasks. However, some design variables are inherently interval parameters due to uncertainties in geometric st... Motion accuracy of space manipulators has direct effects on the ability of the systems to perform specified tasks. However, some design variables are inherently interval parameters due to uncertainties in geometric structures, material properties, and so on. This paper presents Chebyshev inclusion function(CIF) for approximating the dynamic responses function of parametrically excited systems. Motion accuracy reliability(MAR) of space manipulators was evaluated based on mechanism reliability analysis methods and interval uncertainty model. To illustrate the accuracy of the proposed method, a two-link manipulator with interval parameters was demonstrated. The results showed that the proposed method required much fewer samples to obtain more accurate reliability compared with the traditional Monte Carlo simulation(MCS). Finally, the sensitivity analysis was performed to facilitate the optimization design by using global sensitivity analysis. 展开更多
关键词 space manipulator motion accuracy reliability(MAR) interval theory CHEBYSHEV INCLUSION function(CIF)
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Interval Estimation for the Stress-Strength Reliability with Bivariate Normal Variables 被引量:1
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作者 Pierre Nguimkeu Marie Rekkas Augustine Wong 《Open Journal of Statistics》 2014年第8期630-640,共11页
We propose a procedure to obtain accurate confidence intervals for the stress-strength reliability R = P (X > Y) when (X, Y) is a bivariate normal distribution with unknown means and covariance matrix. Our method i... We propose a procedure to obtain accurate confidence intervals for the stress-strength reliability R = P (X > Y) when (X, Y) is a bivariate normal distribution with unknown means and covariance matrix. Our method is more accurate than standard methods as it possesses a third-order distributional accuracy. Simulations studies are provided to show the performance of the proposed method relative to existing ones in terms of coverage probability and average length. An empirical example is given to illustrate its usefulness in practice. 展开更多
关键词 BIVARIATE NORMAL Distribution interval Estimation LIKELIHOOD Analysis reliability
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Non-probabilistic Hydraulic Turbine Blade Vibration Reliability Research Based on Fuzzy Failure Criterion
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作者 庞煜 张翔 赖喜德 《Journal of Donghua University(English Edition)》 EI CAS 2016年第2期336-339,共4页
In hydraulic turbine engineering,turbine blade vibration reliability assessment is of great significance. Based on the interval mathematical theory, the variables existing in hydraulic turbine blade are described as i... In hydraulic turbine engineering,turbine blade vibration reliability assessment is of great significance. Based on the interval mathematical theory, the variables existing in hydraulic turbine blade are described as interval variables. Considering the fuzzy failure criterion of turbine blade distancing from resonance and vibration fatigue stress,fuzzy possibilistic reliability is expressed and analyzed qualitatively taking normal bathtub function as the membership function of blade resonance failure and deflection major type function as the membership function of the intensity failure. As a result,hydraulic turbine blade vibration reliability is analyzed based on the fuzziness of variables and failure criterion. A safer working environment is provided under possibility context by comparing with the qualitative conclusions in the past literature. 展开更多
关键词 fuzzy failure criterion interval variable fuzzy reliability membership function
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Application of non-probabilistic reliability on aerostat capsule
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作者 Zhu Zengqing Liu Guoliang 《High Technology Letters》 EI CAS 2018年第4期417-421,共5页
Aerostat capsule is small sample data,so designing reliability is very difficult to be obtained accurately by conventional probabilistic reliability method. Based on the interval non-probabilistic reliability theory,a... Aerostat capsule is small sample data,so designing reliability is very difficult to be obtained accurately by conventional probabilistic reliability method. Based on the interval non-probabilistic reliability theory,an instability mathematics model of envelope structure is studied,and the calculation formula of interval reliability index is put forward. Through the mechanical experiments of three capsule structures,the experimental results of the interval reliability are obtained. By comparing the theoretical and measured values,it is found that the theoretical reliability index is more conservative. Non-probabilistic reliability method can reflect the reliability degree of the capsule body under different loading conditions,which can provide some guidance for engineering application. 展开更多
关键词 non-probabilistic AEROSTAT reliability INDEX CAPSULE
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Reliability Analysis of a Powerloom Plant Using Interval Valued Intuitionistic Fuzzy Sets
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作者 Sanjay Kumar Tyagi 《Applied Mathematics》 2014年第13期2008-2015,共8页
In this paper, we investigate the reliability analysis of a powerloom plant by using interval valued intuitionistic fuzzy sets (IVIFS). Herein, we modeled a powerloom plant as a gracefully degradable system having two... In this paper, we investigate the reliability analysis of a powerloom plant by using interval valued intuitionistic fuzzy sets (IVIFS). Herein, we modeled a powerloom plant as a gracefully degradable system having two units A(n) and B(m) connected in series. The reliability ofncomponents of unitAandmcomponents of unitBis assumed to be an IVIFS defined over the universe of discourse [0, 1]. Thus, the reliability of the system obtained is an IVIFS that covers the inherited uncertainty in data collection and reliability evaluation of a powerloom plant. 展开更多
关键词 reliability interval VALUED Intuitionistic Fuzzy Sets Powerloom PLANT Parallel REDUNDANCY GRACEFUL Degradation
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Comparison of Structural Probabilistic and Non-Probabilistic Reliability Computational Methods under Big Data Condition
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作者 Yongfeng Fang Kong Fah Tee 《Structural Durability & Health Monitoring》 EI 2022年第2期129-143,共15页
In this article,structural probabilistic and non-probabilistic reliability have been evaluated and compared under big data condition.Firstly,the big data is collected via structural monitoring and analysis.Big data is... In this article,structural probabilistic and non-probabilistic reliability have been evaluated and compared under big data condition.Firstly,the big data is collected via structural monitoring and analysis.Big data is classified into different types according to the regularities of the distribution of data.The different stresses which have been subjected by the structure are used in this paper.Secondly,the structural interval reliability and probabilistic pre-diction models are established by using the stress-strength interference theory under big data of random loads after the stresses and structural strength are comprehensively considered.Structural reliability is computed by using various stress types,and the minimum reliability is determined as structural reliability.Finally,the advan-tage and disadvantage of the interval reliability method and probability reliability method are shown by using three examples.It has been shown that the proposed methods are feasible and effective. 展开更多
关键词 Big data STRUCTURE interval reliability probabilistic reliability reliability index
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Time-varying confidence interval forecasting of travel time for urban arterials using ARIMA-GARCH model 被引量:6
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作者 崔青华 夏井新 《Journal of Southeast University(English Edition)》 EI CAS 2014年第3期358-362,共5页
To improve the forecasting reliability of travel time, the time-varying confidence interval of travel time on arterials is forecasted using an autoregressive integrated moving average and generalized autoregressive co... To improve the forecasting reliability of travel time, the time-varying confidence interval of travel time on arterials is forecasted using an autoregressive integrated moving average and generalized autoregressive conditional heteroskedasticity (ARIMA-GARCH) model. In which, the ARIMA model is used as the mean equation of the GARCH model to model the travel time levels and the GARCH model is used to model the conditional variances of travel time. The proposed method is validated and evaluated using actual traffic flow data collected from the traffic monitoring system of Kunshan city. The evaluation results show that, compared with the conventional ARIMA model, the proposed model cannot significantly improve the forecasting performance of travel time levels but has advantage in travel time volatility forecasting. The proposed model can well capture the travel time heteroskedasticity and forecast the time-varying confidence intervals of travel time which can better reflect the volatility of observed travel times than the fixed confidence interval provided by the ARIMA model. 展开更多
关键词 confidence interval forecasting travel time autoregressive integrated moving average and generalized autoregressive conditional heteroskedasticity ARIMA-GARCH) conditional variance reliability
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The AMSAA-BISE Model with Gap Intervals 被引量:1
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作者 Zhou Yuanquan and Weng Zhaoxi(Beijing Institute of Structure and Environment) 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 1990年第1期77-83,共7页
In this paper, the AMSAA-BISE model with missing data is discussed. The ML estimates of model parameters and current MTBF are given, and the chi-squared test and a plot for cumulative number of failures versus cumulat... In this paper, the AMSAA-BISE model with missing data is discussed. The ML estimates of model parameters and current MTBF are given, and the chi-squared test and a plot for cumulative number of failures versus cumulative testing time are used to test the goodness of fit for the model. This paper concludes with a numerical example to verify the model. 展开更多
关键词 reliability growth Gap interval Missing data AMSAA-BISE model.
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Emission Intensity in the Hydrogen Atom Calculated from a Non-Probabilistic Approach to the Electron Transitions 被引量:3
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作者 Stanisƚaw Olszewski 《Journal of Modern Physics》 2016年第8期827-851,共25页
Quantum aspects of the Joule-Lenz law for the transmission of energy allowed us to calculate the time rate of energy transitions between the quantum states of the hydrogen atom in a fully non-probabilistic way. The ca... Quantum aspects of the Joule-Lenz law for the transmission of energy allowed us to calculate the time rate of energy transitions between the quantum states of the hydrogen atom in a fully non-probabilistic way. The calculation has been extended to all transitions between p and s states having main quantum numbers not exceeding 6. An evident similarity between the intensity pattern obtained from the Joule-Lenz law and the corresponding quantum-mechanical transition pro-babilities has been shown. 展开更多
关键词 Time intervals for the Electron Transitions in the Hydrogen Atom non-probabilistic Theory of Energy Emission in the Atom Comparison of the Emission Intensities with the Quantum-Mechanical Transition Probabilities
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Improved Discrete Interval-Valued Stress-Strength Interference Model Based on Extended Universal Generating Function
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作者 高建雄 安宗文 白学宗 《Journal of Donghua University(English Edition)》 EI CAS 2016年第2期305-307,共3页
In practical engineering,sometimes the probability density functions( PDFs) of stress and strength can not be exactly determined,or only limited experiment data are available. In these cases,the traditional stress-str... In practical engineering,sometimes the probability density functions( PDFs) of stress and strength can not be exactly determined,or only limited experiment data are available. In these cases,the traditional stress-strength interference( SSI) model based on classical probabilistic approach can not be used to evaluate reliabilities of components. To solve this issue, the traditional universal generating function( UGF) is introduced and then it is extended to represent the discrete interval-valued random variable.Based on the extended UGF,an improved discrete interval-valued SSI model is proposed, which has higher calculation precision compared with the existing methods. Finally,an illustrative case is given to demonstrate the validity of the proposed model. 展开更多
关键词 reliability universal generating function(UGF) discrete interval-valued stress-strength interference(SSI) model
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Mathematical Modeling and Evaluation of Reliability Parameters Based on Survival Possibilities under Uncertain Environment
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作者 Alhanouf Alburaikan Hamiden Abd El-Wahed Khalifa +2 位作者 Pavan Kumar SeyedaliMirjalili Ibrahim Mekawy 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第3期1943-1956,共14页
In this article,mathematical modeling for the evaluation of reliability is studied using two methods.One of the methods,is developed based on possibility theory.The performance of the reliability of the system is of p... In this article,mathematical modeling for the evaluation of reliability is studied using two methods.One of the methods,is developed based on possibility theory.The performance of the reliability of the system is of prime concern.In view of this,the outcomes for the failure are required to evaluate with utmost care.In possibility theory,the reliability information data determined from decision-making experts are subjective.The samemethod is also related to the survival possibilities as against the survival probabilities.The other method is the one that is developed using the concept of approximation of closed interval including the piecewise quadratic fuzzy numbers.In this method,a decision-making expert is not sure of his/her estimates of the reliability parameters.Numerical experiments are performed to illustrate the efficiency of the suggested methods in this research.In the end,the paper is concluded with some future research directions to be explored for the proposed approach. 展开更多
关键词 reliability function probabilistic function piecewise quadratic fuzzy numbers survival possibility failure rate possibility distribution state function closed interval approximation
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Theoretical analysis of non-probabilistic reliability based on interval model 被引量:2
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作者 Xu-Yong Chen Jian-Ping Fan Xiao-Ya Bian 《Acta Mechanica Solida Sinica》 SCIE EI CSCD 2017年第6期638-646,共9页
The aim of this paper is to propose a theoretical approach for performing the nonprobabilistic reliability analysis of structure.Due to a great deal of uncertainties and limited measured data in engineering practice,t... The aim of this paper is to propose a theoretical approach for performing the nonprobabilistic reliability analysis of structure.Due to a great deal of uncertainties and limited measured data in engineering practice,the structural uncertain parameters were described as interval variables.The theoretical analysis model was developed by starting from the 2-D plane and 3-D space.In order to avoid the loss of probable failure points,the 2-D plane and 3-D space were respectively divided into two parts and three parts for further analysis.The study pointed out that the probable failure points only existed among extreme points and root points of the limit state function.Furthermore,the low-dimensional analytical scheme was extended to the high-dimensional case.Using the proposed approach,it is easy to find the most probable failure point and to acquire the reliability index through simple comparison directly.A number of equations used for calculating the extreme points and root points were also evaluated.This result was useful to avoid the loss of probable failure points and meaningful for optimizing searches in the research field.Finally,two kinds of examples were presented and compared with the existing computation.The good agreements show that the proposed theoretical analysis approach in the paper is correct.The efforts were conducted to improve the optimization method,to indicate the search direction and path,and to avoid only searching the local optimal solution which would result in missed probable failure points. 展开更多
关键词 non-probabilistic reliability interval model Theoretical analysis Probable failure point
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