To evaluate the safety of casing string is an important task in the oil exploitation. In this paper, the casing string with complex environment is investigated and the global sensitivity analysis (SA) technique is employed to identify the influential factors on the safety. Since the damage of casing string is of different kinds, three failure modes are mainly considered in the analysis. Then, the multivariate global SA technique is employed to identify the influential factors for the three failure modes simultaneously. Due to the full-size FE analysis of casing string which involves contact analysis of tread, being computationally expensive, a simplified model with full constraints are constructed. Then, to compute the multivariate global sensitivity efficiently, the neural network which is used to surrogate the FE model is employed to perform SA.

For the reliability-oriented sensitivity analysis with respect to the parameters of input variables, by introducing the copula function to describe the joint probability distribution with dependent input variables, the reliability-oriented sensitivity can be decomposed into independent sensitivity and dependent sensitivity, which can be used to measure the influence of distribution parameters separately. Since the parameters of multivariate copula function are difficult to be estimated and not flexible in high dimension, the bivariate copulas are preferred in practice. Then the vine copula model is employed to transform the multivariate joint probability density function (PDF) into the product of multiple bivariate copulas and marginal PDF of all variables. Based on copula theory, the computation of reliability-oriented sensitivity with dependent variables can be transformed into the computation of a kernel function for each marginal PDF and the computation of a copula kernel function for each pair-copula PDF involved in the vine factorization. A general numerical approach is proposed to compute the separate sensitivity. Then, some numerical examples and engineering applications are employed to validate the rationality of the proposed method.

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Low-cycle fatigue is typical failure mode of aero-engine turbine disk, traditional reliability analysis method based on the binary state assumption has certain limitations for turbine disk reliability evaluation, because it doesn't consider the change of damage strength parameter caused by loading sequences and the enhanced damage by small load. On the basis of fatigue reliability analysis of the turbine disk, this paper considers the fuzzy state assumption of turbine disk, then select the membership function and indicate fuzzy failure probability of turbine disk, which can be transformed into a series of conventional failure probability by Gaussian quadrature. An active learning Kriging model is used to orderly calculate the failure probability corresponding to different limit state functions and the fuzzy failure probability of turbine disk. A global sensitivity index based on fuzzy failure probability is established to analyze the influence of input variables on the fuzzy failure probability, which is helpful to the reliability design and structural optimization of the turbine disk.

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