To analyze the effect of basic variable on failure probability in reliability analysis,a moment-independent importance measure of the basic random variable is proposed,and its properties are analyzed and verified.Base...To analyze the effect of basic variable on failure probability in reliability analysis,a moment-independent importance measure of the basic random variable is proposed,and its properties are analyzed and verified.Based on this work,the importance measure of the basic variable on the failure probability is compared with that on the distribution density of the response.By use of the probability density evolution method,a solution is established to solve two importance measures,which can efficiently avoid the difficulty in solving the importance measures.Some numerical examples and engineering examples are used to demonstrate the proposed importance measure on the failure probability and that on the distribution density of the response.The results show that the proposed importance measure can effectively describe the effect of the basic variable on the failure probability from the distribution density of the basic variable.Additionally,the results show that the established solution on the probability density evolution is efficient for the importance measures.展开更多
For structure system with fuzzy input variables as well as random ones, a new importance measure system is presented for evaluating the effects of the two kinds of input variables on the output response. Based on the ...For structure system with fuzzy input variables as well as random ones, a new importance measure system is presented for evaluating the effects of the two kinds of input variables on the output response. Based on the fact that the fuzziness of the output response is determined by that of the input variable, the presented measure system defines the importance measures which evaluate the effect of the fuzzy input variable. And for the random input variable, the importance measure system analyzes its effect from two aspects, i.e. its effect on the central distribution position and that on the fuzzy degree of the membership function of the output response. Taking the effects of the two kinds of input variables on the first moment and second one of the output response into account, the definitions of the importance measures of the input variables are given and their engineering significations are demonstrated. Combining with the advantages of the point estimates of Zhao and Ono, a solution of the proposed importance measures is provided. Several examples show that the proposed measure system is comprehensive and reasonable, and the proposed solution can improve computational efficiency considerably with acceptable precision.展开更多
System reliability optimization problems have been widely discussed to maximize system reliability with resource constraints.Bimbaum importance is a wellknown method for evaluating the effect of component reliability ...System reliability optimization problems have been widely discussed to maximize system reliability with resource constraints.Bimbaum importance is a wellknown method for evaluating the effect of component reliability on system reliability.Many importance measures(IMs)are extended for binary,multistate,and continuous systems from different aspects based on the Bimbaum importance.Recently,these IMs have been applied in allocating limited resources to the component to maximize system performance.Therefore,the significance of Bimbaum importance is illustrated from the perspective of probability principle and gradient geometrical sense.Furthermore,the equations of various extended IMs are provided subsequently.The rules for simple optimization problems are summarized to enhance system reliability by using ranking or heuristic methods based on IMs.The importance-based optimization algorithms for complex or large-scale systems are generalized to obtain remarkable solutions by using IM-based local search or simplification methods.Furthermore,a general framework driven by IM is developed to solve optimization problems.Finally,some challenges in system reliability optimization that need to be solved in the future are presented.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos NSFC1057211, 50875213)New Century Excellent Talents in University of China (Grant No NCET-05-0868)+2 种基金Aviation Science Foundation of China (Grant No 2007ZA53012)National High Technology Research and Development Program of China (Grant No 2007AA04Z401)the Important National Science & Technology Specific Projects (Grant No 2009ZX04014-015-03)
文摘To analyze the effect of basic variable on failure probability in reliability analysis,a moment-independent importance measure of the basic random variable is proposed,and its properties are analyzed and verified.Based on this work,the importance measure of the basic variable on the failure probability is compared with that on the distribution density of the response.By use of the probability density evolution method,a solution is established to solve two importance measures,which can efficiently avoid the difficulty in solving the importance measures.Some numerical examples and engineering examples are used to demonstrate the proposed importance measure on the failure probability and that on the distribution density of the response.The results show that the proposed importance measure can effectively describe the effect of the basic variable on the failure probability from the distribution density of the basic variable.Additionally,the results show that the established solution on the probability density evolution is efficient for the importance measures.
基金supported by the National Natural Science Foundation of China (Grant No. NSFC 50875213)
文摘For structure system with fuzzy input variables as well as random ones, a new importance measure system is presented for evaluating the effects of the two kinds of input variables on the output response. Based on the fact that the fuzziness of the output response is determined by that of the input variable, the presented measure system defines the importance measures which evaluate the effect of the fuzzy input variable. And for the random input variable, the importance measure system analyzes its effect from two aspects, i.e. its effect on the central distribution position and that on the fuzzy degree of the membership function of the output response. Taking the effects of the two kinds of input variables on the first moment and second one of the output response into account, the definitions of the importance measures of the input variables are given and their engineering significations are demonstrated. Combining with the advantages of the point estimates of Zhao and Ono, a solution of the proposed importance measures is provided. Several examples show that the proposed measure system is comprehensive and reasonable, and the proposed solution can improve computational efficiency considerably with acceptable precision.
基金This work was funded by the National Natural Science Foundation of China(GrantNos.71771186,71631001,and 71871181)and the 111 Project(GrantNo.B13044).
文摘System reliability optimization problems have been widely discussed to maximize system reliability with resource constraints.Bimbaum importance is a wellknown method for evaluating the effect of component reliability on system reliability.Many importance measures(IMs)are extended for binary,multistate,and continuous systems from different aspects based on the Bimbaum importance.Recently,these IMs have been applied in allocating limited resources to the component to maximize system performance.Therefore,the significance of Bimbaum importance is illustrated from the perspective of probability principle and gradient geometrical sense.Furthermore,the equations of various extended IMs are provided subsequently.The rules for simple optimization problems are summarized to enhance system reliability by using ranking or heuristic methods based on IMs.The importance-based optimization algorithms for complex or large-scale systems are generalized to obtain remarkable solutions by using IM-based local search or simplification methods.Furthermore,a general framework driven by IM is developed to solve optimization problems.Finally,some challenges in system reliability optimization that need to be solved in the future are presented.
