Traditionally, the calculation of reliability of fuzzy random structures is based on the well-known formulation of probability of fuzzy events. But sometimes the results of this formulation will not indicating the rea...Traditionally, the calculation of reliability of fuzzy random structures is based on the well-known formulation of probability of fuzzy events. But sometimes the results of this formulation will not indicating the real state of safety of fuzzy-random structures. Based on the possibility theory, a computational procedure for the reliability analysis of fuzzy failure problems and random-fuzzy failure problems of mechanical structures that contain fuzzy variables were presented. A procedure for the analysis of structural reliability of problems of fuzzy failure criterion was also proposed. The failure possibility of fuzzy structures and possibility distribution of the probability of failure of fuzzy-random structures can be given by the proposed methods. It is shown that for the hybrid probabilistic and fuzzy reliability problems, the probability of failure should be suitably taken as a fuzzy variable in order to indicate the real safety of system objectively. Two examples illustrate the validity and rationality of the proposed methods.展开更多
To predict the occurrence of the collapse disaster in toppling perilous rock under the action of bidirectional earthquakes,the dynamic stability and fuzzy reliability calculation method of toppling perilous rock under...To predict the occurrence of the collapse disaster in toppling perilous rock under the action of bidirectional earthquakes,the dynamic stability and fuzzy reliability calculation method of toppling perilous rock under the action of bidirectional earthquakes is proposed.First,the mass viscoelasticity model is used to simulate two main control surfaces of toppling perilous rock,the seismic dynamic response model and motion equation of toppling perilous rock are established based on the D'Alembert principle,and the Newmark-β method is used to solve the dynamic motion equation.Then,the instability event of toppling perilous rock is considered a fuzzy event,the membership function expression of the stability coefficient of toppling perilous rock is determined based on the fuzzy failure criterion,the calculation equations of the toppling perilous rock dynamic stability coefficient and fuzzy reliability are established,and the fuzzy reliability evaluation method based on the probability distribution of reliability is proposed.Finally,the influence of different superposition modes of seismic excitation on the fuzzy reliability of toppling perilous rock is analyzed.The calculation results of toppling perilous rock in the engineering case show that the fuzzy reliability calculated after considering the fuzzy failure criterion is reduced by 10.73% to 25.66% compared with the classical reliability.Considering the bidirectional seismic excitation,the fuzzy reliability of toppling perilous rock is reduced by 5.46% to 14.89%.Compared with using the acceleration peak time encounter mode to superpose the seismic excitation,the fuzzy reliability of toppling perilous rock is reduced by 3.4% when the maximum action effect time encounter mode is adopted.展开更多
Slope stability assessment is a geotechnical problem characterized by many sources of uncertainty. In clas- sical reliability analysis, only the randomness of uncertainties is taken into account but the fuzziness of t...Slope stability assessment is a geotechnical problem characterized by many sources of uncertainty. In clas- sical reliability analysis, only the randomness of uncertainties is taken into account but the fuzziness of them is ignored. In this paper, a fuzzy probability approach and a fuzzy JC method are presented for the reliability analysis. The two methods have been applied to stability analysis of a certain slope of permanent ship lock in the Three-Gorges Project. The results obtained from these two methods are basically the same. However, compared with the fuzzy probability means, the fuzzy JC method can reflect the real situation better because it uses a fuzzy-based analysis applied to not only limit state equation but also mechanical parameters.展开更多
Prediction of structural performance is complicated by many uncertainties of random or fuzzy character. This paper presented an initial investigation on reliability theory of structure involved with fuzziness. The mem...Prediction of structural performance is complicated by many uncertainties of random or fuzzy character. This paper presented an initial investigation on reliability theory of structure involved with fuzziness. The membership function of structural safety was established. The calculation methods of fuzzy reliability of structure were also presented, and as an example, the fuzzy reliability of simply supported beam was calculated.展开更多
Conventional fault tree and reliability analysis do not reflect the characteristics of basic events as non stationary and ergodic process. To overcome these drawbacks, theory of fuzzy sets is employed to run fault tre...Conventional fault tree and reliability analysis do not reflect the characteristics of basic events as non stationary and ergodic process. To overcome these drawbacks, theory of fuzzy sets is employed to run fault tree analysis(FTA) of roller oscillating tooth gear drive(ROTGD), the relative frequencies of basic events are considered as symmetrical normal fuzzy numbers, from the logical relationship between different events in the fault tree and fuzzy operators AND and OR, fuzzy probability of top event is solved. Finally, an example is given to demonstrate a real ROTGD system.展开更多
For efficiently estimating the Profust failure probability based on probability input variables and fuzzy-state assumption, a General Performance Function(GPF) expression is established under the strict mathematical d...For efficiently estimating the Profust failure probability based on probability input variables and fuzzy-state assumption, a General Performance Function(GPF) expression is established under the strict mathematical derivation for the Profust reliability model. By constructing the GPF,the calculation of the Profust failure probability can be transformed into the calculation of the traditional failure probability. Then various existing methods for the traditional failure probability can be used to estimate the Profust failure probability. Due to the high efficiency of the Adaptive Kriging(AK) model and the universality of the Monte Carlo Simulation(MCS), AK inserted MCS(abbreviated as AK-MCS) has been proven to be an efficient method for estimating the failure probability. Therefore, the AK-MCS combined with the GPF(abbreviated as AK-MCS + GPF)is proposed for estimating Profust failure probability. The proposed method greatly reduces the computational cost while ensuring the accuracy. Finally, four examples are given to validate the proposed AK-MCS + GPF. The results of the examples show the rationality and the efficiency of the proposed AK-MCS + GPF.展开更多
为满足人机系统概率风险评估的需要,提出一种人为差错概率量化方法。分析技能、规则和知识为基础(skill,rule and knowledge-based,SRK)框架和行为模式的确定方法Hanaman决策树法,指出在确定行为模式的过程中考虑行为模式影响因素的不...为满足人机系统概率风险评估的需要,提出一种人为差错概率量化方法。分析技能、规则和知识为基础(skill,rule and knowledge-based,SRK)框架和行为模式的确定方法Hanaman决策树法,指出在确定行为模式的过程中考虑行为模式影响因素的不确定性是必要的;使用模糊逻辑方法处理行为模式各个影响因素的不确定性,根据Hanaman决策树构建模糊推理规则,利用系统人为行为可靠性程序(systematic human action reliability procedure,SHARP)方法所提供的人为差错概率区间确定人为差错概率的隶属度函数。结果表明:该方法考虑了任务场景的不确定性,可以得到人为差错概率的精确值,满足人机系统概率风险评估的需要。展开更多
The quantum probability theory of fuzzy event is suggested by using the idea and method of fuzzy mathematics, giving the form of fuzzy event path integral, membership degree amplitude, fuzzy field function, Green func...The quantum probability theory of fuzzy event is suggested by using the idea and method of fuzzy mathematics, giving the form of fuzzy event path integral, membership degree amplitude, fuzzy field function, Green function, physical quantity and fuzzy diagram. This theory reforms quantum mechanics, making the later become its special case. This theory breaks unitarity, gauge invariance, probability conservation and information conservation, making these principles become approximate ones under certain conditions. This new theory, which needs no renormalization and can naturally give meaningful results which are in accordance with the experiments, is the proper theory to describe microscopic high-speed phenomenon, whereas quantum mechanics is only a proper theory to describe microscopic low-speed phenomenon. This theory is not divergent under the condition of there being no renormalization and infinitely many offsetting terms, thereby it can become the theoretical framework required for the quantization of gravity.展开更多
文摘Traditionally, the calculation of reliability of fuzzy random structures is based on the well-known formulation of probability of fuzzy events. But sometimes the results of this formulation will not indicating the real state of safety of fuzzy-random structures. Based on the possibility theory, a computational procedure for the reliability analysis of fuzzy failure problems and random-fuzzy failure problems of mechanical structures that contain fuzzy variables were presented. A procedure for the analysis of structural reliability of problems of fuzzy failure criterion was also proposed. The failure possibility of fuzzy structures and possibility distribution of the probability of failure of fuzzy-random structures can be given by the proposed methods. It is shown that for the hybrid probabilistic and fuzzy reliability problems, the probability of failure should be suitably taken as a fuzzy variable in order to indicate the real safety of system objectively. Two examples illustrate the validity and rationality of the proposed methods.
基金financially supported by the National Key Research and Development Program of China(Nos.2021YFB2600604 and 2021YFB2600600)the General Program of Natural Science Foundation of Chongqing(No.cstc2020jcyj-msxm X0218)the Research and Innovation Program for Graduate Students in Chongqing Jiaotong University(No.2022S0021)。
文摘To predict the occurrence of the collapse disaster in toppling perilous rock under the action of bidirectional earthquakes,the dynamic stability and fuzzy reliability calculation method of toppling perilous rock under the action of bidirectional earthquakes is proposed.First,the mass viscoelasticity model is used to simulate two main control surfaces of toppling perilous rock,the seismic dynamic response model and motion equation of toppling perilous rock are established based on the D'Alembert principle,and the Newmark-β method is used to solve the dynamic motion equation.Then,the instability event of toppling perilous rock is considered a fuzzy event,the membership function expression of the stability coefficient of toppling perilous rock is determined based on the fuzzy failure criterion,the calculation equations of the toppling perilous rock dynamic stability coefficient and fuzzy reliability are established,and the fuzzy reliability evaluation method based on the probability distribution of reliability is proposed.Finally,the influence of different superposition modes of seismic excitation on the fuzzy reliability of toppling perilous rock is analyzed.The calculation results of toppling perilous rock in the engineering case show that the fuzzy reliability calculated after considering the fuzzy failure criterion is reduced by 10.73% to 25.66% compared with the classical reliability.Considering the bidirectional seismic excitation,the fuzzy reliability of toppling perilous rock is reduced by 5.46% to 14.89%.Compared with using the acceleration peak time encounter mode to superpose the seismic excitation,the fuzzy reliability of toppling perilous rock is reduced by 3.4% when the maximum action effect time encounter mode is adopted.
文摘Slope stability assessment is a geotechnical problem characterized by many sources of uncertainty. In clas- sical reliability analysis, only the randomness of uncertainties is taken into account but the fuzziness of them is ignored. In this paper, a fuzzy probability approach and a fuzzy JC method are presented for the reliability analysis. The two methods have been applied to stability analysis of a certain slope of permanent ship lock in the Three-Gorges Project. The results obtained from these two methods are basically the same. However, compared with the fuzzy probability means, the fuzzy JC method can reflect the real situation better because it uses a fuzzy-based analysis applied to not only limit state equation but also mechanical parameters.
文摘Prediction of structural performance is complicated by many uncertainties of random or fuzzy character. This paper presented an initial investigation on reliability theory of structure involved with fuzziness. The membership function of structural safety was established. The calculation methods of fuzzy reliability of structure were also presented, and as an example, the fuzzy reliability of simply supported beam was calculated.
文摘Conventional fault tree and reliability analysis do not reflect the characteristics of basic events as non stationary and ergodic process. To overcome these drawbacks, theory of fuzzy sets is employed to run fault tree analysis(FTA) of roller oscillating tooth gear drive(ROTGD), the relative frequencies of basic events are considered as symmetrical normal fuzzy numbers, from the logical relationship between different events in the fault tree and fuzzy operators AND and OR, fuzzy probability of top event is solved. Finally, an example is given to demonstrate a real ROTGD system.
基金supported by the National Natural Science Foundation of China (Nos. NSFC 51475370 and 51775439)
文摘For efficiently estimating the Profust failure probability based on probability input variables and fuzzy-state assumption, a General Performance Function(GPF) expression is established under the strict mathematical derivation for the Profust reliability model. By constructing the GPF,the calculation of the Profust failure probability can be transformed into the calculation of the traditional failure probability. Then various existing methods for the traditional failure probability can be used to estimate the Profust failure probability. Due to the high efficiency of the Adaptive Kriging(AK) model and the universality of the Monte Carlo Simulation(MCS), AK inserted MCS(abbreviated as AK-MCS) has been proven to be an efficient method for estimating the failure probability. Therefore, the AK-MCS combined with the GPF(abbreviated as AK-MCS + GPF)is proposed for estimating Profust failure probability. The proposed method greatly reduces the computational cost while ensuring the accuracy. Finally, four examples are given to validate the proposed AK-MCS + GPF. The results of the examples show the rationality and the efficiency of the proposed AK-MCS + GPF.
文摘为满足人机系统概率风险评估的需要,提出一种人为差错概率量化方法。分析技能、规则和知识为基础(skill,rule and knowledge-based,SRK)框架和行为模式的确定方法Hanaman决策树法,指出在确定行为模式的过程中考虑行为模式影响因素的不确定性是必要的;使用模糊逻辑方法处理行为模式各个影响因素的不确定性,根据Hanaman决策树构建模糊推理规则,利用系统人为行为可靠性程序(systematic human action reliability procedure,SHARP)方法所提供的人为差错概率区间确定人为差错概率的隶属度函数。结果表明:该方法考虑了任务场景的不确定性,可以得到人为差错概率的精确值,满足人机系统概率风险评估的需要。
文摘The quantum probability theory of fuzzy event is suggested by using the idea and method of fuzzy mathematics, giving the form of fuzzy event path integral, membership degree amplitude, fuzzy field function, Green function, physical quantity and fuzzy diagram. This theory reforms quantum mechanics, making the later become its special case. This theory breaks unitarity, gauge invariance, probability conservation and information conservation, making these principles become approximate ones under certain conditions. This new theory, which needs no renormalization and can naturally give meaningful results which are in accordance with the experiments, is the proper theory to describe microscopic high-speed phenomenon, whereas quantum mechanics is only a proper theory to describe microscopic low-speed phenomenon. This theory is not divergent under the condition of there being no renormalization and infinitely many offsetting terms, thereby it can become the theoretical framework required for the quantization of gravity.
