Research On Structural Uncertainty Propagation Computational Inverse Methods Based On Clustering Ellipsoid Model

There are various inevitable uncertainties in practical structures,which are commonly associated with material properties,loads,manufacturing errors and boundary conditions,etc.To reasonably model these uncertainties and analyze their effects on structural performance is very important for uncertainty analysis,optimized design and parameter identification.When the experimental sample information is scarce and only the boundary of the uncertainty parameter is obtained,the ellipsoid model is an ideal model to quantify the uncertainty.In the past two decades,the ellipsoid model has advanced significantly,and a series of achievements have been made in this field.However,all the works were based on a single ellipsoidal convex set,and the ellipsoid model is rarely applied to the uncertainty inverse problem.In this paper,a more generalized non-probabilistic ellipsoid model named Cluster Ellipsoid Model(CEM)is proposed by the Gaussian mixed cluster analysis technique to reasonably measure the parameter uncertainties.Then,the CEM will be introduced into the uncertainty propagation with positive and inverse problems.As a result,the following studies are carried out in this dissertation:(1)A novel non-probabilistic uncertain measurement model namely Cluster Ellipsoid Model which can deal with complex sample distribution is proposed.The distribution of uncertainty parameters essentially has a single-peak or multi-peak characteristic,and the scatter plot of the experimental data tend to exhibits the same morphology as the distribution.Firstly,the mixed Gaussian clustering approach is used to investigate the morphologies of the data,and the data of one or more similar properties are clustered to approximate the essential distribution characteristics of the uncertain parameters.Then,the sub-ellipsoid model is modeled by using the Gaussian contour ellipsoid characteristics,and the CEM can be finally assembled by each sub-ellipsoid.By the concept of modeling process,the CEM modeling method takes two advantages of clustering analysis and Gaussian Mixed Model(GMM),which makes it not only to construct single-ellipsoid model but also to construct multi-ellipsoid for the complex sample distribution.More importantly,the mixed Gaussian clustering analysis can achieve the unity of the distribution set and correlation of uncertain parameters,it provide sufficient theoretical basis for ellipsoid modeling.(2)Based on the CEM,two kinds of uncertain propagation methods are studied.Firstly,the CEM is constructed by using mixed Gaussian clustering method for uncertain parameters.Secondly,the uncertain parameter space is transformed into a regularized parameter space,this means that the ellipsoid model is transformed into unit sphere model,then two kinds of uncertain propagation methods are constructed based on this unit sphere model.The first method,the upper and lower bounds fo uncertain response are accurately and efficiently calculated through the performance measure approach(PMA)on the unit spherical shell.The second method,the unit sphere domain is divided into two parts by the first order approximation of the state equation regarding uncertain parameters,then the volume ratio of the divided domain and the whole unit sphere domain can be used to quantify the uncertainty of system response,this ratio namely Pseudo-Cumulative Distribution Function,P-CDF.(3)Based on the CEM,the uncertainty inverse propagation analysis method is studied.Firstly,the uncertainties of input parameters are modeled by CEM.Then,the pseudo-probability measurement approach is introduced into inverse propagation problem.In order to avoid the double-loop process and the computationally expensive,the multi-identification parameters are treated as the design variables,then constructs the variational least squares error optimization of the response to decouple the double-loop process,the boundary and P-CDF of identification parameters are finally computed.