Research On Global Sensitivity Analysis Method Of Structure

Engineering structures parameters are unavoidably subjected to uncertainty.Factors such as material variability,manufacturing and processing errors,and environmental erosion will cause uncertainty to a certain extent.The uncertainty of structural parameters will cause fluctuations in the model response,resulting in a large difference between the real response of the structure and the design value.Neglecting uncertainty will reduce the quality and reliability of engineering structures,and the influence of parameter uncertainties should be considered in structural analysis.Therefore,accurate evaluation of the influence of uncertain parameters on structural response has guiding significance for model construction,analysis,design and optimization of actual engineering structures.Global sensitivity analysis(GSA)has the capability to accurately quantify the effects of individual parameters over their entire space and interaction effects among parameters,and effectively reveal the mechanism of parameter uncertainty affecting model response.This paper takes the GSA as the research object,improves the original traditional method,and explores the application efficiency of the improved method.Finally,the proposed method will be applied to the actual civil engineering structure model.Various Monte Carlo simulation(MCS)methods for structural GSA are studied;analytical method for GSA of structures based on generalized co-Gaussian process model(GC-GPM)is proposed;a structural GSA method considering parameter correlation is proposed.The specific research contents are as follows:(1)Monte Carlo simulation(MCS)has a wide range of applications and is easy to implement.It is very suitable for calculating high-dimensional integrals and is a commonly used GSA method.Various MCS methods for structural global sensitivity analysis are investigated,including Sobol estimation,Saltelli estimation,Mauntz estimation,JanonMonod estimation,Jansen estimation,Mara estimation,Martinez estimation,and Owen estimation.The 2D function,Ishigami function and G function are used as test functions to verify the accuracy of various estimation methods.The results show that the Martinez estimation method is more accurate.Finally,the effect of sample size on the estimation effect of sensitivity indicators is investigated,and the Martinez estimation method is used as an example to compare and analyze the effect of sampling size on the estimation effect of sensitivity indicators.The study found that as the sample size increases,the sensitivity calculation results are closer to the theoretical value and the error decreases.(2)MCS needs to ensure the convergence of sensitivity index calculation through a large number of samples.Large and complex structures are usually simulated as high-precision(refined)finite element models,which leads to a particularly prominent problem of high calculation costs.The surrogate model method replaces the real input-output relationship with a low-dimensional mathematical model,which reduces the computational cost.Gaussian process model(GPM)has a strong ability to simulate complex systems,and is widely used in the GSA of structures.The establishment of the proxy model requires training samples.The higher the accuracy of the training samples,the more accurate the model,and the more complex the corresponding finite element model.Aiming at the high computational cost of high-precision samples and low modeling accuracy of low-precision samples in the GPM,a structural GSA method based on the generalized collaborative Gaussian process model is introduced.In the framework of the generalized co-Gaussian process model(GC-GPM),the high-dimensional integral of the global sensitivity index is successfully transformed into a one-dimensional integral,and the analytical calculation is realized.The effectiveness of the proposed analytical GSA method is verified with borehole function,and the MCS is used for comparison.The calculated results of this method are in good agreement with the results of the MCS.It can be concluded that the GC-GPM based GSA method has advantages of high computational accuracy and efficiency.Finally,the proposed method is applied to the GSA of the stability of a reticulated shell structure.Based on the sensitivity analysis results,the sensitivity(importance)of each structural parameter can be clearly reflected,and the coupling effect between parameters is found to be very significant.(3)Most of GSA methods are aimed at independent random variables.However,there is usually a correlation between parameters in actual engineering,and this correlation may have a greater impact on the importance of parameters.Therefore,it is necessary to study the GSA considering the correlation of variables,so as to accurately evaluate the sensitivity(importance)of the relevant uncertainty parameters.Accurately assess global sensitivity metrics for relevant uncertainty parameters taking into account parameter dependencies.The influence of an uncertainty parameter on the output is divided into non-correlated influence(produced independently by an uncertainty parameter)and correlated influence(produced by a certain uncertainty parameter and related parts of other uncertainty parameters).Through Rosenblatt transformation and Iman-Conover transformation,the correlation input parameters are transformed into independent input parameters.Sensitivity metrics for correlated effects and sensitivity metrics for uncorrelated effects are calculated by MCS.The validity of the test method is verified by linear model and nonlinear model.On this basis,the method is applied to the GSA of a reinforced concrete frame structure.Based on the results,the importance of each structural parameter can be clearly reflected.