Research On The Techniques Of Dynamic Load Identification For Stochastic Structures

It is the crucial prerequisite for structural design and optimization to determineexactly the dynamic loads acting on the engineering structures. The information of thedynamic loads also has great significance for structural health monitoring, parameteridentification, structural fatigue and life estimation and so forth. However, it is alwayspretty difficult to directly measure the dynamic loads acting on the practical structures,but the responses caused by the unknown loads can be obtained easily. In this context,identifying dynamic loads according to the response information of measurementpoints and structural dynamic model has become an important indirect method toobtain dynamic loads.Recently, most traditional techniques of dynamic load identification are limitedin deterministic structures. Nevertheless, randomness exists inevitably in practicalstructures, which leads to hardly adopting traditional deterministic methods to analyzethe problems of dynamic load identification for stochastic structures such asill-posedness and to obtain the time history of dynamic loads. Also, the result ofidentified dynamic loads is not deterministic values but the time history of loadswhich is related to structural random parameters, and this makes the accuracy ofidentified loads hardly be evaluated. As a result, how to identify dynamic loads forstochastic structures and how to estimate and evaluate the effect objectively andaccurately structural randomness has on the identified results of dynamic loads are thekey problems in the research field of inverse problems. In order to resolve theseproblems, on the basis of the existing theories of dynamic load identification fordeterministic structures, this thesis adopts matrix perturbation, orthogonal expansionand evidence theory respectively to research the methods of dynamic loadidentification under stochastic structures aiming at the degree of variation and thedistribution form of structural random parameters. The work of this thesis is asfollows:(1) Aiming at the structures containing the random parameters with little variablecoefficient, the method of dynamic load identification for stochastic structures basedon perturbation theory is investigated. The dynamic loads are expressed as functionsof time and random parameters in time domain and the forward model for dynamicload identification is established through the convolution integral of loads and the corresponding unit-pulse response functions of system. Through the discretization ofconvolution integral, the first-order matrix perturbation on the basis of Taylorexpansion is used to transform the problem of load identification for stochasticstructures into two kinds of certain inverse problems, namely the dynamic loadidentification on the mean value of structures’ random parameters and the sensitivityidentification of dynamic loads to each random parameter. With the measuredresponses containing noise, the modified regularization operator is adopted toovercome ill-posedness of load reconstruction and to obtain the statistics of identifiedloads. When random parameters have little variable coefficients, the identification andassessment of dynamic loads are achieved stably and effectively by this method.(2) In order to consider the effect the form of PDFs has on identified results, themethod of dynamic load identification for stochastic structures based on orthogonalexpansion is researched. Random parameters which have mono-peak probabilitydensity functions (PDFs) are approximated through the bounded random variableswith-PDFs or their PDFs, which avoids the extremity of random parameters.Unknown dynamic loads can be expressed as the sum of the series of Gegenbauerpolynomials with respect to each random parameter, and through using the weightedorthogonality of these polynomials under-PDF weight functions, the problem ofdynamic load identification for stochastic structures is transformed into the problemof corresponding deterministic extended-order system. The extended-order systems inseveral time subintervals are constructed respectively so as to reduce the order ofdeterministic system equations and to enhance computational efficiency. Via solvingthe coefficients of polynomial series, the statistics of identified loads can be obtained.This method avoids the boundedness of choosing the type of orthogonal polynomialsin probability space, and effectively assures the reliability of the identified results.(3) Aiming at the structures containing the random parameters with great variablecoefficient and multimodal PDF, the method of dynamic load identification forstochastic structures on the basis of orthogonal expansion is investigated. Bydiscretizing the PDFs of random parameters, subintervals of PDFs and correspondingpossibility densities can be regarded as the focal elements and their basic probabilityassignments, respectively. Thus, the problem of stochastic structures can betransformed into evidence analysis problem. Through interval opera tion the momentsof evidence variables and of the functions with evidence variables can be obtained.The interval analysis technique is adopted to efficiently compute the mean andstandard deviation of the functions with evidence variables on each focal el ement in order to approximate the actual probability moments of unknown loads. The bounds ofidentified loads can be obtained through defining nominal mean and standarddeviation. This method is free from the limitation of the degree of variation and thedistribution form of structural random parameters, and is able to effectively evaluatethe accuracy of identified loads.