| Uncertainty widely existed in practical engineering problems.Structural uncertainty analysis technology provides an effective way to solve such problems.This makes the research of structural uncertainty analysis methods become the one of the key aspects of reliability verification and cost control and optimization design of engineering structures.The non-probabilistic convex set theory is a common method to deal with structural uncertainty analysis in recent years,which realizes an effective measurement of structural uncertainty under the condition that parameter information is scarce.However,until now,the existing non-probabilistic convex set modeling methods often lack the consideration of the distribution characteristics such as grouping and diversification of parameter sample information,and how to construct a reasonably compact polygonal convex set and analyze it succinctly,how to effectively solve the problem of interval large uncertainties is still difficulty.Therefore,this paper constructs the PCA interval model,the polygonal convex set(PCS)model and the clustering polygonal convex set(CPCS)model by introducing principal component analysis and cluster analysis,and discusses corresponding uncertainty modeling and propagation methods based on the three convex set models respectively.In addition,the constructed PCS model is introduced into the structural reliability analysis problem,and the structural non-probabilistic reliability index based on the PCS model is defined.The main research content of this article can be divided into the following three aspects:(1)Based on principal component analysis(PCA),a new structural uncertainty modeling and propagation method is proposed.Firstly,principal component analysis is performed on the overall information of the uncertain parameters to obtain the orthogonal characteristic vector directions.Then,after a simple linear transformation,the original uncertain parameters are transformed into the direction of the characteristic vector,and the upper and lower bounds of the parameters in the new coordinate space are obtained.Finally,PCA interval model is established based on the new marginal interval and uncertainty modeling coordinate system to realize the measurement of structural uncertainties of parameter.Combined with the sequential quadratic programming algorithm,the solution to the uncertainty of the parameter structure is solved.The model is suitable for the modeling of complex multidimensional uncertainties,and can compactly envelope all sample data.Inaddition,the modeling method can eliminate the correlation between uncertain parameters while the uncertainty modeling was completed,which provides a convenient solution to the following problems such as uncertainty propagation.(2)Structural uncertainty modeling and propagation methods based on PCS model and CPCS model.The non-probabilistic PCS model is constructed by using the coincident domain between the traditional interval model and the PCA interval model.For a structural system with a linearity or a low degree of nonlinearity,classical simplex optimization algorithm can be directly used to solve problems of uncertainty propagation.In addition,the PCS model facilitates the concise analytical expression,which not only retains the advantage that the PCA interval model can eliminate the correlation between parameters,but also its uncertainty domain is more compact and reasonable,and the propagation results are also more accurate.With regard to the problem of interval large uncertainty,by introducing cluster analysis,a new CPCS model was proposed.Firstly,the parameter sample data are divided into several sub-clusters based on the distribution characteristics of the samples.Then a sub-PCS model is constructed in each sub-cluster to implement an effective measure of the uncertainty information of each sub-cluster.Finally,combining the sub-PCS models in all sub-clusters to construct the CPCS model.For the case of higher degree of nonlinearity of the structural system,the response of each sub-cluster can be separately solved by combining the linear Taylor approximation with the classical simplex optimization algorithm.Therefore,the global response interval is obtained by comparing the upper and lower bounds of all sub-cluster responses.In addition,the model can eliminate empty areas without any sample points in the uncertain domain.According to the different distribution characteristics of the parameters,the model are discussed by three different cases of the PCS model separated,PCS model intersected,and the interval large uncertainty.(3)Non-probabilistic reliability analysis method based on PCS model.Based on the proposed PCS model,the structural non-probabilistic reliability analysis method is developed,and the corresponding non-probabilistic reliability index is proposed.Firstly,through the classic HL-RF iterative method,the MPP of the failure surface are obtained,and the failure surface is linearly approximated by Taylor expansion at the MPP;then the simplex optimization algorithm is used to obtain the extreme points of the PCS model.That also can be explained as the first point of intersection between the uncertain domain and the approximate failure surface when the uncertain domain is uniformly extended outwards.And the norm between the center point and theextreme point of the PCS model is determined.Then the direction vector between the center point and the extreme point is constructed.Therefore,the intersected point of the direction vector and the approximate surface can be easily obtained.Finally,based on the simple ratio of the two norm,a non-probabilistic reliability index based PCS model is proposed.The index is a dimensionless quantity,and its degree of structural reliability under three different ranges of values is discussed.When the failure surface gradually moves away from the uncertain domain,the index gradually increases,which means the structure is more secure.Therefore,it can be considered that the index can better quantify the degree of structural reliability. |
PDF Full Text Request