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 article, the moment-independent global sensitivity 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 sensitivity index inherits the advantages of the traditional moment-independent global sensitivity index. For the problems of which the computational cost of the Monte Carlo simulation is too high, an active learning Kriging solution is established to solve the global sensitivity index. Several examples are adopted to illustrate the correctness of this global reliability sensitivity describing the effect on the reliability of the structure system of the convex model variable and the applicability and feasibility of the active learning Kriging–based solution.
The aim of this paper is to account for the effect of the epistemic uncertainty of the input variables’ uncertainty in the nonprobabilistic reliability analysis on the safety of the structure system. Based on the idea of moment-independent sensitivity analysis, a modified sensitivity measure of the nonprobabilistic reliability is constructed to identify the most influential epistemic parameters of interval variables. For calculating the nonprobabilistic reliability sensitivity measures of the epistemic variables, a computational model is established. And a solution method with the advantages of the state-dependent parameter model 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. The sensitivity measure of nonprobabilistic reliability proposed in this paper can give an essential importance sequence of all the epistemic uncertainties and identify key contributing epistemic uncertainties. When the sensitivity measure is larger, the epistemic uncertainty variable will become more important and should collect the data to increase knowledge of parameters. The sensitivity measures can provide the availability guidance to reduce the number of epistemic variables.
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. Then the definitions of the parametric sensitivities of IM on the failure probability are given, and their computational formulae are derived. 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.
SUMMARYIn the subject paper, a reliability-based design optimization (RBDO) model with both random and dependent interval uncertainties was proposed based on the First Order Reliability Method. The lower bound of reliability defined in Equation (9) of the subject paper was utilized as the constraint in this RBDO model. The author claimed that it is the minimum reliability with both random and interval variables. However, we prove that it is not the minimum value. It is therefore suggested that the minimum reliability should be used in the RBDO model.
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