Research On Structure Reliability Methods Of The Generalized Equivalent Extreme-value Event And Incomplete Probability Information System

Reliability is an important part of structure stochastic analysis, also is the foundation for structure design and performance evaluation. The current methods of reliability analysis mostly base on the complete probability information, while the studies on reliability of incomplete probability information are rarely involved. In addition, system reliability usually takes one of the multiple failure modes as the judgment criterion. And there are no studies about the common-cause failure of multiple structural components and performace reliability, ever. This paper will do some studies on system reliability of the common-cause failure of multiple structural components and reliability of incomplete probability information by the means of theoretical deduction and numerical analysis, simulation.First, in the structural system reliability analysis, reliability analysis of multiple failure modes will be transformed into equivalent of reliability problems of a single failure mode by introducing the equivalent extreme-value event. And, the equivalent extreme-value event can solve the problem of correlation failure in the system reliability effectively, while for the problems of m components failure in l components which called the common-cause failure of multiple structural components and performace reliability, it will encounter the problem of combination explosion. Therefore, in this paper, the generalized equivalent extreme-value event which is equivalent to the equivalent extreme-value event is given by simple and strict mathematical derivation. And the generalized equivalent extreme-value event can overcome the problem of combination explosion efficiently, because it only involves the operation of the sequencing which is easy to implement. At the same time, introducing the probability density evolution method and moment method for the probabilistic structural analysis of the generalized equivalent extreme-value variable, and gives the method of the corresponding reliability problem. The paper finally validates the feasibility of the proposed method by mathematical example and engineering example, also its high efficiency and accuracy is verified by comparing with the Monte Carlo method.Second, for the system involving dependent random variables, the Rosenblatt transformation or the Nataf transformation is usually introduced, to complete an additional normal transformation for the correlated random variables. However, this transformation is complicated and not unique. Besides, the method only works for the system of variables with the known cumulative density function(CDF) or probability density function(PDF), but is not suitable for the system of variables with unknown and partial unknown CDF or PDF. For this, the incomplete information system will be divided into three subclasses in this paper, also the method of calculating the equivalent correlation coefficient has been given. Moreover, a point estimate method of incomplete probability information will be developed. Finally, the methods’ feasibility has been verified by some examples, also the high precision, simple operation, and easy to implement. Then, combining with the practical reliability method for the system with dependent normal variables, the generalized first-order reliability method is proposed, which can be applied to the system of variables with known CDF or PDF as well as variables with unknown CDF or PDF. Besides, a two-step revision technique is also proposed to improve the accuracy of the proposed method because of a possible error brought by the least square method in determine the unknown coefficients of cubic normal transformation model. Also an efficient second-order method has been proposed based on the generalized first-order reliability method. Lastly, comparisons in several examples have been made with the FORM to verify the effectiveness and universality of the proposed method for the reliability evaluation.Finally, for a space grid structure, firstly, this paper builds finite element mold and makes static analysis by ANSYS software, and the results show that the structure has rational design and good performation. Then the paper makes performace reliability analysis at different performance indexes using the realibility analysis methods based on the generalized equivalent extreme-value event, and considering two cases of complete and incomplete probability information. And the results of the analysis show that the proposed method is feasible, and has good precision.Overall, the reliability methods based on the generalized equivalent extreme-value event and the reliability analysis of incomplete probability information have been given in this paper. And the reasonability of these studies has been verified by some mathematical examples and engineering examples, thus the research scope of reliability analysis has been expanded effectively.