Research On Structural Uncertainty Propagation And Computational Inverse Methods Based On Correlation Analysis

Uncertainties widely exist in practical engineering problems.It is an important basis for structural optimization design and analysis to accurately investigate the uncertainty quantification,uncertain forward propagation and uncertain inverse propagation problems.Most of the traditional methods for the above problems were proposed based on the probabilistic model,in which the probability model was applied to describe the uncertainties in structural parameters and responses,and then used the probability density functions or statistical moments to realize the uncertain forward and inverse propagation processes.Generally,constructing an accurate probability model needs to extract a large number of samples according to the known probability density functions.However,due to the limitations of experimental environment and economic conditions,only a few samples can be obtained in practical engineering,which limites the adaptability of the traditional methods.Besides,in practical engineering problems,the uncertainties such as material properties,geometric dimensions and boundary conditions are usually correlated,which may have a great influence on the uncertainty analysis results.For this reason,it is difficult to determine the probability density types and to accurately describe the joint probability density functions of the propagated results,which makes the uncertain forward and inverse propagation analysis methods based on probabilistic model difficult to be widely applied.In recent years,with the emergence and improvement of the non-probabilistic convex model,especially for the ellipsoidal convex model which measures the uncertainties and correlations of the structural parameters under the limited samples,the studies about non-probability uncertain forward and inverse propagations have been widely concerned.At present,there are still many problems in uncertain inverse propagation process should be solved in practical engineering,including the correlation propagation,the global sensitivity analysis of the input correlated parameters,the selection of the optimal sensor positions and the decoupling problem of the non-probabilistic correlation coefficient matrix and intervals.Thus,this paper studies the above problems one by one,and tries to make some effective attempts and explorations in the aspect of structural uncertainty propagation and computational inverse problems.Then,a set of structural inverse method system considering non-probabilistic correlation analysis is established.The research idea of this paper is carried from two aspects of the input parameters and output responses.Firstly,to establish an accurate and compact uncertainty boundary of sturctural responses,the relationship bewteen the non-probability correlation coefficients of structural parameters and responses is discussed,and the correlation propagation equations are newly derived.Secondly,due to the data analysis is usually heavy and the structural model is commonly complex,the importance of the structural parameters should be sorted,so as to ignore the parameters that have little impact on the structural responses,and focus on the parameters that have significant impact on the structural responses.Therefore,the global sensitivity method considering the correlated parameters is studied.Thirdly,in order to overcome the ill-posed problem in the uncertian inverse problem,the optimal sensor placement for stable identification of structural parameter is investigated.Importantly,the coupling problem of uncertainties and correlations of structural parameters to be identified in uncertain inverse problem is also considered,and a sequence interval and correlation inverse strategy is propsoed.Based on the above ideas,the main works of this paper are listed as follows:(1)A correlation propagation method for uncertainty analysis of structures based on the non-probabilistic ellipsoidal model is proposed to propagate the uncertainties and correlations of the structural parameters simultaneously.Aiming at the quantification problem of the uncertainties and correlations of structural parameters with a limited sample,the ellipsoidal convex model is adopted to model their uncertainty boundary.The propagation problem considering correlations and uncertainties is decomposed into an interval propagation problem and a correlation coefficient propagation problem.For the interval propagation problem,a subinterval decomposition analysis method based on the ellipsoidal convex model is developed to evaluate the intervals of the structural responses with a low computational cost.For the correlation propagation problem,the non-probabilistic correlation propagation equations from uncertain parameters to structural responses are newly derived for predicting the correlation coefficient matrix of the responses,which can be expected to extend the n-order Taylor expansion according to the accuracy requirement.(2)A global sensitivity analysis method considering correlation for uncertain structure is proposed to determine the important uncertain parameters.The ellipsoidal convex model is used to quantify the uncertainty boundary of the correlated parameters,and the non-probabilistic variance is defined as a sensitivity index.Importantly,the non-probabilistic variance propagation equations from uncertain structural parameters to responses are derived,and the influence of input parameters on the non-probabilistic variance of output response is decomposed into the independent contribution and correlated contribution.Simultaneously,the total contribution rate,independent contribution rate and correlation contribution rate are defined to accurately estimate the sensitivity of each parameter to the response.(3)An optimal sensor placement method based on maximum independent mean-variance criterion is proposed to ensure the validity of measurement information and the stability of uncertain inverse process.The optimal sensor placement problem for structural parameter identification is transformed into an uncertainty propagation problem,and the maximum independent variance and maximum independent mean-variance criteria are established.The Monte Carlo simulation and the dimension reduction integral method are used to evaluate the maximum independent variance of structural response respectively,and an orthogonal matching pursuit algorithm is developed to determine the positions and the number of sensors.Especially,to ensure the accuracy and stability of the identification results,two-layers Monte Carlo simulation and dimension reduction integral method are developed to achieve the maximum independent mean-variance of the structural responses.(4)A sequence interval and correlation inverse strategy for structural parameter identification is proposed to realize the interval and correlation inverse processes of structural parameters.In practical engineering,considering the non-probabilistic uncertainties and correlations of measured responses,the ellipsoidal convex model is used to quantify their uncertainty boundary.At the same time,the uncertain inverse problem considering correlations is decomposed into the interval inverse problem and correlation inverse problem.For the interval inverse problem,the subinterval decomposition analysis method is adopted to achieve the intervals of the calculated structural responses.For the correlation inverse problem,the correlation coefficient matrix of the structural responses is determined by correlation propagation equations.In this way,the intervals and correlation coefficient matrix of the structural parameters are obtained by using the optimization methods with the help of the measured responses and the calculated responses,so that the uncertainty boundary of the structural parameters can be established by using the ellipsoidal convex model.