Research On Local And Moment-independent Sensitivity Analysis For Structures With Uncertainty

For practical applications, the output performance of the structural systems are commonly subjected to the inherent uncertainties deriving from different resources, such as the inaccuracy of geometry, the variability of material property, the fluctuation of external loads, the errors resulting from the instrument measurement, etc. For the sake of improving the performance of the systems under uncertain circumstances, based on the exsiting researches, local sensitivity, moment-independent sensitivity and reliability analysis are investigated in this paper. The detailed contents are summarized as follows:1. Local sensitivity analysis can reflect how the distribution parameters of input variables affect the failure probability or cumulative distribution function of the output performance function. For employing the commonly used response surface method and Kriging model to solve the local sensitivity analysis, a fourth-moment based analytical local sensitivity computation method is proposed for each emulator model mentioned above respectively. Note that kernel functions play a significant role in getting the sensitivities analytically, the properties of kernel function are extended for the normal distribution, and they are successfully applied to the derivation of analytical expression of local sensitivity. The results of examples well demonstrate the correctness and efficiency of the two proposed emulator model based analytical computation methods for sensitivity, besides, it well shows their good engineering applicability.2. In order to measure how the different distribution parameters of the input variables affect the statistical characteristics of the structure or system output, the mixed sensitivities of failure probability and the statistical moments of the performance function with respect to the distribution parameters of input variables are defined, and the corresponding mixed kernel functions are defined. Then the expressions of the mixed kernel functions for a two-parameter distribution are derived, and the universal properties of the mixed kernel functions are analyzed as well. The analytical expressions of the mixed sensitivity of statistical moments of the performance function are derived. Furthermore, based on the properties of the mixed kernel functions, and by taking a quadratic polynomial without cross-terms as an example of a performance function, the analytical mixed sensitivity results of the failure probability are derived for the normal variables.3. The moment-independent sensitivity analysis indices can comprehensively assess the contribution of uncertainties of input variables to the uncertainties of output performance,without relying on using one of the statistical moments of the output performance to represent the uncertainties. A computational efficiency method is proposed for the moment-independent global sensitivity index proposed by Borgonovo and the regional sensitivity index, respectively. The key tasks for the computation of these two indices are using the fractional moment based maximum entropy to accurately estimate the unconditional probability desnity function(PDF) of the output response, and utilizing the Nataf transformation to estimate the joint PDF of model output and input variable. In the computation of the former global sensitivity index, an improved high-dimensional model representation based dimensional reduction method is adopted to compute the fractional moments of model output, while the sparse grid integration method is applied to calculate the fractional moments in the latter regional sensitivity index. Important input variables can be identified according to the global sensitivity analysis, then the regional sensitivity analysis can be used for the important variables to clearly detect how different ranges of the important variables affect the probabilistic distribution of model output.4. The reliability based moment-independent global sensitivity index can well analyze the effect of input uncertainties on the failure probability of the structure or system. However, compared with the variance-based sensitivity index, there are few accurate and efficient methods for computing this moment-independent one at present. In this context, a highly efficient method to compute the reliability based moment-independent sensitivity index is proposed. The proposed method efficiently estimates the conditional PDF of the model output using the fractional moments and dimonsional reduction method based maximum entropy method, thus the conditional failure probability can be easily obtained by integration. Finally the three-point estimation method is applied to compute the outer variance, namely the reliability based moment-independent global sensitivity. Since the advantages of the maximum entropy method and the three-point estimation method are inherited directly, the proposed method can obtain accurate results under a small number of function evaluations.5. Reliability analysis becomes increasingly difficult when facing the complicated expensive-to-evaluate engineering applications, especially problems involve the implicit finite element models. In order to balance the accuracy and efficiency of implementing reliability analysis, an advanced Kriging method is proposed for efficiently analyzing the reliability. The method starts with an initial Kriging model built from a very small number of samples, then determines the most probable region in the probabilistic viewpoint and chooses the subsequent samples located in this region by employing the probabilistic classification function. Besides, the leave-one-out technique is used to update the current model. By locating samples in the probabilistic most probable region, only a small number of samples are used to build a precise surrogate model in the end, and only a few actual limit state function evaluations are required correspondingly. After the high quality surrogate of the implicit limit state is available by the advanced Kriging model, the Monte Carlo simulation method is employed to implement reliability analysis.