Research On Identification Theories And Methods For Distributed Dynamic Load

In many practical engineering applications,such as the structural strength analysis,dynamic characteristics modification,health detection and fault diagnosis etc.,dynamic load identification technology is a very important indirect means to obtain dynamic load on structures.The research of dynamic load identification has important theoretical value and wide application prospect.At present,scholars at home and abroad have achieved very gratifying achievements in the research of frequency domain and time domain methods for concentrated dynamic load identification,and built the method system and applied it to engineering practice.However,the research on distributed dynamic load identification is still very lacking,and few articles have been reported.Therefore,it is of great significance to research on the theories and methods for distributed dynamic load identification.Different from concentrated dynamic load,the representation of distributed dynamic load requires variables in both time domain and space domain.Consequently,the scale and difficulty of the calculation are greatly increased.This dissertation launches an in-depth study on identification of distributed dynamic load with the help of finite element analysis,modal analysis,regularization,blind source separation,sparse decomposition and interval modeling,which aims to realize the effective identification of time history and spatial distribution of the distributed dynamic load.Firstly,the form of distributed dynamic load is studied,and two cases of time and space independence and time and space coupling are considered.Then,the dynamic equation with distributed dynamic load in physical space is projected to the modal space,and,the load time history recognition and the spatial distribution identification are separated.Afterwards,the principle of vibration problem caused by distributed dynamic load is analyzed in modal space,and mature dynamic load identification method and blind source separation technology are used to realize the identification of time history of the distributed load.Then,the basic function expansion based method and the sparse representation based method are carried out for the load distribution function identification.In addition,the nonlinearity of the structure and the uncertainty of load time history are also considered.The following is the main research work carried out and completed in this dissertation:(1)A distributed dynamic load identification method based on modal analysis and polynomial fitting is developed.It is assumed that the temporal and spatial domai ns of the distributed dynamic load are independent of each other,and the distributed dynamic load can be represented by the time history function and the spatial distribution function.Conducting modal transformation for the dynamic equation in physical space,a series of vibration equations of a single degree of freedom modal system are obtained.The time history function of each order of modal load has the same form as the time history function of the external distributed load,and the different amplitude coefficients are the inner products of the load distribution function and the mode shape functions of the structure.Under the premise of linear time invariant structure,the modal responses are obtained through inverse modal transformation,and the load time history is identified based on Green's kernel function method and regularization.After that,the load distribution function is expressed as a weighted sum of a group of linearly independent basic functions.By fitting the relative amplitude coefficient vector of the modal loads,the weighting coefficients can be computed,and thus the load spatial distribution function is reconstructed.(2)A distributed dynamic load identification method based on blind source separation and sparse decomposition is proposed.For the time and space coupled distributed dynamic load,it can be expressed as the superposition of a series of sub distributed dynamic loads with independent time history functions and space distribution functions by high-dimensional decomposition technique.Currently,the modal load is actually a mixture of the time history functions of each sub distributed dynamic load,and the mixing coefficients are the inner products of each distribution function and modal shape function.Because the physical responses of a structure are normally only composed of the limited low-order modes,so the number of mixing coefficients containing the information of the spatial distribution function of the sub distributed dynamic load is very small.Therefore,the problem of reconstructing the load spatial distribution function based on the mixing coefficients is undetermined,and there will be multiple solutions.By blind source separation,the effective time history functions can be separated from the identified modal loads.By sparse decomposition,the sparse representation of the spatial distribution function of each sub distributed dynamic load can be achieved from the mixing coefficients.Finally,the original continuously distributed dynamic load is equivalently identified as several concentrated dynamic loads acting at the appropriate positions.(3)The distributed dynamic load identification method for locally nonlinear system is studied.The nonlinear elements often cause the change of natural frequencies and mode shapes of the system,which makes it difficult to establish a constant mapping relationship between external loads and structural responses.By substituting the nonlinear components with dynamic load constraints,an equivalent linear system can be obtained.The equivalent system,however,is not only subjected to the external distributed dynamic loads,but also subjected to the equivalent loads of nonlinear elements.On the other hand,for complex nonlinear system,a linear sub system can also be obtained by dividing the original system into several sub systems,and the truncated surface is also equivalently constraint by dynamic loads.Finally,based on the equivalent linear system,the method in the previous chapter can be used to realize the identification of distributed dynamic load.(4)The uncertain distributed dynamic load identification method is explored.The interval process model is introduced and the load uncertainty is described by median value function and radius function.Through K-L expansion,the uncertain distributed dynamic load is expressed as the sum of the median value function part and the uncertain part of the load.Furthermore,the identification of the uncertain distributed dynamic load is converted into two kinds of deterministic problems,i.e.the identification of the median function of the load and the computation of the covariance matrix.The former can be sparsely represented as several concentrated dynamic loads.The latter can be solved by recovering the eigenvectors of the self-covariance matrix of each load.The radius functions of the equivalent concentrated dynamic loads are obtained by the squaring of the diagonal elements of the self-covariance matrix.