Stochastic Dynamic Load Identification For Uncertain Systems And Its Experimental Verification

Load information of engineering structures is of great significance to structural design and safety assessment.In many cases,the external loads on the structure can not be obtained directly by measurement,so indirect identification method is needed.Therefore,the dynamic load identification technology has attracted the attention of researchers.Traditional dynamic load identification methods usually neglect the uncertainties in the external excitation,the dynamic system and the dynamic response.These methods belong to deterministic methods,which either can not take into account the "uncertainties" in structural system,or identify the random dynamic load on engineering structures.Therefore,it is necessary to develop stochastic dynamic load identification methods considering the "uncertainty" of structural system.In this paper,stochastic dynamic load identification algorithms for structures with uncertain parameters are studied.Research work includes:Firstly,for uncertain dynamic systems,an improved algorithm for stochastic load identification based on spectral stochastic finite element model is presented.Both the force positions and system parameters are assuming known and both the random forces and system parameters obey Gaussian distribution.The stochastic system motion equation is established in which the random system parameters and random response are represented by the K–L expansion and Polynomial Chaos Expansion,respectively.The statistical characteristics of the random dynamic load are determined according to the relationship between the covariance of the response only due to random moving force and the covariance of the response only due to the random system parameters.Numerical simulations on a cantilever beam structure is conducted.Results show that the accuracy of the force variance is greatly improved by using the algorithm based on PCE proposed in this paper instead of existing method and the proposed method maintains good precision when the level of system uncertain increase.Then,for uncertain dynamic systems,a stochastic dynamic load identification algorithm based on perturbation stochastic finite element model is proposed.Both the random forces and system parameters obey Gaussian distribution.The stochastic Green's function is adopted to establish the relationship between the Gaussian excitation and the corresponding response.The stochastic Green's function is expresses by the perturbation expansion in which the Polynomial Chaos bases are adopted to replace the corresponding bases in the Tayler series.The Karhunen–Loève expansion(KLE)and the Polynomial Chaos Expansion(PCE)are used to represent the stochastic dynamic load and g the stochastic system responses,respectively.With the orthogonality of PCE,the stochastic load identification problem on an uncertain dy-namical system is transformed to a problem of stochastic load identification on an equivalent deterministic system.Numerical simulation analysis of a plane truss structure is carried out,and the random dynamic load identification method is validated based on the response samples of the measured points.Numerical simulations and experimental studies on a cantilever beam under a concentrate stochastic force are conducted to estimate the statistical characteristics of the stochastic load from the stochastic structural response samples.Result show that the proposed method has good accuracy in force statistics' identification when the level of uncertainty in system parameters is not small;Large errors may occur in the identified statistics of the stochastic force when the correlation in the random system parameter is neglected.Different correlation length for the random system parameters are investigated to show the effectiveness and accuracy of the proposed method.Finally,existed research works on stochastic dynamic load identification,especially for those considering the uncertainties of the system,are limited to simple structures such as beams or trusses.Stochastic dynamic load identification algorithm based on perturbation stochastic finite element method is redeveloped with commercial software Abaqus and Matlab,which is capable of applying the stochastic load identification algorithm on complex engineering structures.A satellite structure is taken as an example in numerical verification.Results show that the proposed secondary development algorithm can accurately identify the statistical characteristics of random dynamic loads acting on complex uncertain structures.