Research On The Propagation Of Stochastic Uncertainty And Importance Measure For Complex Structures

For complex practical applications, the outputs of the systems are commonly subjected to the inherent uncertainties deriving from different resource. For the sake of improving the safty performances of the complex practical systems under uncertain circumstances, the importance measure and the methods for uncertainty propagation in the reliability based design are investigated in this work. The detailed contents are summarized as follows.1) The convex model which only needs to know the variation bound of the uncertainty domain is competent to deal with the reliability analysis for the engineering problems lacking sufficient information. However, compared with the researches in solving non-probabilistic reliability index with convex model, the non-probabilistic reliability sensitivity analysis is less available. In this paper, the moment-independent importance measure analysis of the basic variable based on convex-model is performed for investigating the effect of non-probabilistic variable of the structure or system on the dangerous degree in reliability engineering. The proposed s importance measure inherits the advantages of the traditional moment-independent importance measure. For the problems of which the computational cost of the Monte Carlo simulation(MCS) is too high, state dependent parameter(SDP) and active learning Kriging(ALK) solution solution are established to solve the global sensitivity index. Several examples are adopted to illustrate the correctness of this importance measure describing the effect on the reliability of the structure system of the convex model variable, and the applicability and feasibility of the ALK-based solution and SDP-based solution.2) The moment-independent importance measure(IM) on the failure probability is important in system reliability engineering, and it is always influenced by the distribution parameters of inputs. For the purpose of identifying the influential distribution parameters, the parametric sensitivity of IM on the failure probability based on local and global sensitivity analysis technology is proposed. The computational formula of parametric sensitivity is defined as the derivative of statistical quantities with IM on the failure probability to the distribution parameters of inputs. The parametric sensitivity finds out how the IM can be changed by varying the distribution parameters, which provides an important reference to improve or modify the reliability properties. When the sensitivity indicator is larger, the basic distribution parameter becomes more important to the IM. Meanwhile, for the issue that the computational effort of the IM and its parametric sensitivity is usually too expensive, an active learning Kriging(ALK) solution is established in this study. Two numerical examples and two engineering examples are examined to demonstrate the significance of the proposed parametric sensitivity index, as well as the efficiency and precision of the calculation method.3) For the structural with the randomness of parameters and excitation, an important problem in structure reliability analysis is how to reduce the failure probability. We employed a main and total effect indices framework of importance measure on the failure probability. By controlling the uncertainty of input variables with effect indices, the most reduction of failure probability can be obtained. The ALK solution is employed to solve the importance measure, which allows for a strong reduction of the computational cost.Additionally, a dynamic reliability moment-independent importance measure for double random vibration systems is introduced to analyze the effect of the input variables on the dynamic reliability. Based on the expressions of the unconditional dynamic reliability and conditional probability density function(PDF), the importance measure index is numerically obtained. The index can effectively describe the mean effect of the PDF on the dynamic reliability from the distribution density of the basic variable. Then, the SDP method is established to estimate the defined moment-independent importance measure index. Examples are given to illustrate the advantages of the presented method. Compared with the direct Monte Carlo method, the results show that the established solution can considerably improve computational efficiency with acceptable precision and be suitable for non-linear dynamic reliability responses of double random vibration systems.4) To analyze the effects of the different regions within input variables on dynamic reliability and dynamic reliability importance measure, two regional importance measures(RIMs) are firstly proposed, i.e. Contribution to dynamic reliability(CFDR) and Contribution to Dynamic-reliability Main Effect(CDRME),and their properties are analyzed and verified. The proposed RIMs can not only detect the important variables, but also identify regions of the input variable that contribute substantially to dynamic reliability. To calculate the RIM efficiently, its calculation model is transformed, and the highly efficient SDP method and ALK method are introduced.Numerical and engineering examples have demonstrated the effectiveness of the proposed RIM, and the efficiency and accuracy of the established methods.5) Based on the importance measure analysis of aleatory uncertainties, and provided that aleatory-epistemic uncertainties are characterised by non-probabilistic variables, the importance nalysis of the epistemic uncertainties on the output is investigated in detail. First, based on the idea of moment-independent importance analysis, a modified importance measure of non-probabilistic reliability is constructed to identify the most influential epistemic parameters of interval variables. For calculating the non-probabilistic importance measure of the epistemic variables, a computational model is established. And a solution of SDP is employed to improve the computational efficiency and avoid the complex sampling procedure. The numerical examples and engineering examples show that the proposed method of solving the sensitivity measure is reasonable and effective. Second, when all epistemic uncertainties are described by non-probabilistic with convex model, a novel importance measure is proposed to identify the effect of epistemic uncertainties on the failure probability. Based on the uncertainty propagation, the importance measure of each epistemic uncertainty on the failure probability is defined. The computational burden of solving the importance measure may be heavy. In order to circumvent this difficulty, the ALK method is is employed to estimate the importance measure. The importance measures proposed in this paper can give an essential importance sequence of all the epistemic uncertainties and identify key contributing epistemic uncertainties.