Research On The Method Of Global Sensitivity Analysis For Structures Based On The Optimal Polynomial Model

The sensitivity analysis methods are used to identify the most significant model factors through studying the relationships between the input and the output. Based on the performance of prediction and diagnosis, it is the crucial prerequisite for modeling, model simplification, and optimization analysis. In general, sensitivity analysis methods can be classified as either local or global. The local sensitivity analysis methods include derivation method, finite difference method and perturbation method, and they are usually applied to estimate the sensitivity of a single the input variable affecting the specific model response at some nominal settings. So these methods are only applicable to linear model parameters range is smaller. The global sensitivity analysis methods include regression analysis, variance analysis, screen method and so on. Compared with the local sensitivity analysis methods, global sensitivity analysis methods evaluate the effect of a factor while all other factors varies as well and take into account variation ranges of all the parameters, thus it have been widely used in many fields.Nowdays, global sensitivity analysis involves the evaluation of high-dimensional integral, which are difficult to obtain by the direct integral. Thus, many sampling methods are used to obtain the approximate sensitivity results, such as the Monte Carlo method is used to simulate the Sobol'sensitivity indices, the finite difference method is applied to calculate DGSM indicators, and so on. However, these sampling methods have some drawbacks that their result relies on the stability of the samples, and needed expensive computational cost to obtain large amounts of sample data. In order to overcome the problems, combine global sensitivity analysis methods with the optimal polynomial response surface and they can be more convenient and effective application in practical engineering problems. In addition, some structural random parameters which have a certain probability distribution form exist inevitably in practical structures. Therefore, based on the optimal chaos polynomial response surface and variance decomposition method, a novel global sensitivity analysis method is developed in this paper, which can be used to effectively assess the global sensitivity of probability distribution variables. The work of this thesis is as follow:(1) Based on polynomial structure-selection, a novel global sensitivity analysis method is proposed for conveniently evaluating the sensitivity of complex system parameters. The optimal polynomial response surface used to replace the complex origin model can be constructed by the structure-selection technique based on error reduction ratio. Through the response surface, the SoboP direct integral is conveniently applied to obtain the accurate first order and interaction sensitivity indices. Compared with the traditional SoboF sensitivity analysis, this proposed method improves the efficiency, accuracy and stability. Several numerical examples and engineering applications demonstrate the applicability and effectiveness of this method.(2) Based on the optimal polynomial response surface, a novel global sensitivity analysis method is proposed, which is called derivative-integral sensitivity analysis method. It is made to develop a global sensitivity analysis method through compute the integral for the partial derivatives in the whole domain. The method defines a sensitivity index, named the derivatives-integral global sensitivity index, which can be more convenient to solve through the direct integral computation. Meanwhile, in order to overcome the difficult problem of multidimensional and High-order integral, the optimal polynomial replace surface is applied to replace the complex original model. Because the optimal polynomial replace surface is compendious form of polynomial, the sensitivity indices can be accessible to more efficiently and accurately through the direct integral and partial derivative calculation. In addition, different from variance analysis method, this method effectively decompose the cross effects of groups of input parameters. As a result, the sensitivity result is only the first order sensitivity indices.(3) In order to study the sensitivity of structural random parameters which have a certain probability distribution form, the method of variance decomposition global sensitivity analysis based on the optimal polynomial chaos is researched. Random parameters which have mono-peak probability density functions (PDFs) are approximated through the bounded random variables with A-PDF or their PDFs, which avoids the extremity of random parameters. The response of original model can be expressed as the sum of the series of Gegenbauer polynomial through the structure-selection technique based on error reduction ratio. Through using the weighted orthogonality of these polynomials under under i-PDF weight functions, the sensitivity results of random parameters can be directly obtain via coefficient of the optimal chaos polynomial model. This method avoids the complex computation of multidimensional and high-order integral, and significantly enhances computational efficiency. What is more, it is reliable and effective for random variables which have any unimodal and bounded PDFs.