The Study Of Global Sensitivity Analysis Based On Decomposition For Complex Engineering Problems

Sensitivity analysis is an efficient method to analyze the influence of design variables' change on the output of a system.It can recognize the most important design variables and screen out those trivial or noninfluential ones.Due to the performance of diagnosis and prediction,it is a vital premise for optimization,modelling,uncertainty analysis and robustness analysis in many areas.Sensitivity analysis can be classified into two categories,namely local and global sensitivity analysis,based on the studying region area.Local sensitivity analysis is a method to calculates the partial derivative of an output at the base-line point in the assigned design domain.It includes finite difference,direct differential method,perturbation method and adjoin sensitivity analysis etc.Those methods are suitable for the systems that are linear and monotonous.Global sensitivity analysis is capable of achieving a full evaluation of contributions of input variables in the whole desired domain.Not only this method is able to allow design variables to change at the same time but also has no limitation to model's properties,which makes it more popular than local sensitivity analysis.Global sensitivity analysis includes Partial rank correlation coefficient,Morris method and variance-based global sensitivity analysis and so on.In practical engineering problems,the estimation of sensitivity indexes involves high dimensional integrals which take numerous calculating cost by traditional Monte Carlo or Quasi Monte Carlo methods.The situation turns worse when a system is high-dimensional.To overcome those problems,this study incorporates the random sampling high dimensional model representation(RS-HDMR)theory into global sensitivity analysis by using a Homotopy algorithm,named diffeomorphic modulation under observable response preserving homotopy(D-MORPH).The strength of this algorithm lies in its unnecessity to estimate the high dimensional integrals and cost-saving capacity to acquire accurate sensitivity analysis.The work of this thesis is as follow:(1)In light of high dimensional problems,the performance of several surrogates including Kriging,radial basis function,least square support vector regression and HDMR methods is compared under multiple scenarios.An optimal choice of a surrogate is determined according to different factors that may influence the performance of surrogates,such as sample size,noise and interactions of design variables.(2)Global sensitivity analysis based on D-MORPH-HDMR theory is an efficient method to implement sensitivity analyses for high dimensional problems.The RS-HDMR method can turn high dimensional problems into the sum of a series of component functions and neglect the influence of high cooperation among design variables,thereby leading to the reduction of dimensions.Orthogonal polynomial bases are applied to approximate the component functions in the RS-HDMR expansion to estimate the global sensitivity analysis effectively and efficiently.In addition,D-MORPH regression is utilized to calculate the unknown constants associated with the component functions to obtain a sparse solution.Compared to the traditional global sensitivity analysis based on metamodels,the sensitivity analysis based on D-MORPH-HDMR can obtain a reliable result by taking less sample points.(3)To test the global sensitivity analysis method,four practical engineering problems which include the spring-back analysis of an L-shaped composite part using autoclave process,the buckling analysis of a variable stiffness composite cylinder,structural analysis of a camber beam and a vehicle body.The results have proven that this algorithm is able to obtain the correct global sensitivity results for all problems.It successfully recognizes noninfluential design variables and provides guidance for further studies.