Investigation Of Dynamic Parametrical Modeling Method On Nonlinear Multi-degree Of Freedom System

The aimbition of system identification is to deduce from the observed data sets,a model or a set of model that can be used for system analysis,controlling and prediction.A mathematical model that based on underlying system is defined by two properties:model structure and the associated parameters.Traditional modeling process of underlying system usually involves only one data set,corresponding to the specific experimental scenario,thus both of the model structure and the associated parameters are fixed.Nevertheless,in the real world,the associated parameters in the established model should be changeable,to meet varing scenarios caused by the changing of either external(temperature)or internal(stiff)parameters.In practice,two types of mathematical models,known as the numerical model and the physical model,are usually used.The physical model is,if possible to achieve,usually expected by engineers because it provides physical relationship between the output response and all related physical parameters.However,in many cases,physical models of complex systems are difficult or even impossible to build.In this case,a data driven numerical model,which can be established by using only input and output data without a-priori knowledge of the system physical properties,is widely applied in engineering practice to investigate the dynamic characteristics of underlying systems.However,the coefficients of these nemerical models don't have any physical meanings,making it difficult to be used in the analysis and design of the underlying system.In order to address these problems,numerical model with design parameters appear explicitly is considered in this paper,to make a further analysis and design of the system,and finally establish a common-structured model,refered as dynamic parametrical model,which based on several data stes correpoding to different experimental scenario.The 'dynamic' means that the current response of the model varies because of past inputs and outputs.This model is different from the conventional parameter-varing models,where process parameters are assumed to be time-varing.Once the common-structured model is obtained,relevant model parameters corresponding to each experimental scenario can be computed based on the available data sets.Not only contribute to make a further analysis and design on underlying system,but can make a prediction under different scenario(stiff,damping),and thus has a fundamental background of engineering application.The paper focus on the following 4 points:(1)Base on the traditional algorithm,establish the dynamic parametrical model of Singe Input Single Output(SISO)system,and verify the prediction accuracy of the modeling method through the simulation and experimental validation.(2)Through the summarization of the problems of traditional algorithm,introduce a new optimal method which applies an iterative process to revise the traditional algorithm and to solve the problems.Through the simulation and experimental validation to demonstrate that the introduced algorithm have advantages over the older one,as a consequence,develop the modeling method.(3)Enlarge the modeling object from SISO system to Singe Input Multiple Output(SIMO)system,and introduce the new algorithm,meanwhile,the assumption about the coupling effect among different outputs may affect the accuracy of prediction will be investigated,and a hypothsis about application of low pass filter on modeling method to improve the accuracy of prediction will be discussed in details.Moreover,a nonlinear system will studied as an example to illustrate the new identification method.Finally,an experiment is conducted to validate the newly proposed modeling algorithm.(4)Summarize the problems of the model terms' selection criterion by using traditional algorithm,base on the referring theory about machine learning,introduce a algorithm based on newly model terms' selection criterion.Through the validations to illustrates its merits.