Research On Nonlinear System Dynamic Response Modeling Method Based On NARX Model

Aiming at the problem that the mechanism of complex nonlinear systems is unclear and it is difficult to establish the mathematical model based on the traditional mechanism method,this paper proposes a modeling method to construct the non-linear Autoregressive with regressive input(NARX)model based on nonlinear system dynamics response.The NARX model is a kind of numerical model with polynomial form.Due to its simple structure,good universality,strong robustness,easy construction and ability to reflect the characteristics of real systems,NARX model has been widely used in many fields such as metallurgy,machinery and medical treatment.Building process of NARX model of nonlinear system is a typical system identification process,which only need to use the reliable identification algorithm to deal with the dynamic response signals of the system including all of the important system characteristics and its corresponding excitation signal.Comparing with the mechanism method,establishing the NARX model through system identification method can avoid to learn lot of theory knowledge before building system model,which simplifies the modeling process,greatly improves the speed of modeling and is suitable to obtain model and analysis system in practical engineering.Using NARX model to analyze nonlinear system often involves data collection,data preprocessing,NARX model building,model validation,model analysis and other steps.Among them,whether the constructed NARX model is close to the original system has a very important impact on the final analysis result.Therefore,aiming at constructing NARX model for nonlinear system,this paper focuses on the modeling method of establishing NARX model.The main contents are as follows:(1)Taking Duffing type single degree of freedom nonlinear vibration system as an example,the method of constructing NARX model based on nonlinear dynamic differential equations(NDE)model is studied.The differences between NARX models obtained by different discrete methods is compared by simulation,and NARX models with discrete errors are constructed theoretically.Through the analysis of the error term,the reason why there is the difference of NARX models obtained by different discrete methods in the aspect of predicting system response is explained,and the optimal discrete method to construct NARX models directly by NDE model is determined.(2)The modeling algorithm of NARX model based on system dynamic response is studied comparatively.By theoretical derivation and simulation study,the paper compares the results of different algorithms,determines the application scope of different modeling algorithms and the advantages of the Forward Regression Orthogonal Least Square(FROLS)algorithm in modeling..(3)Combining the FROLS algorithm and the think of the sliding window(SW),the SWFROLS algorithm is proposed,which can eliminate the data segment affected by greater noise to avoid it influence on the identification results then make the NARX model more similar to the original system.The experimental data of clamp-hollow tube are used to verify this algorithm.The comparison results of the models established by the SW-FROLS algorithm and the FROLS algorithm show the effectiveness of the former algorithm.Finally,NARX model is used to analyze the ideal working interval of the clamp-hollow pipe system from the perspective of frequency response function(4)Aimed at the problem that the random signal can’t be used as the excitation signal due to the limitation of the system structure when the NARX model is built for the rotor system,the harmonic splicing method is proposed to build the excitation and response signals.Through theoretical derivation,when the signals show obvious periodicity,the data order and the number of periods don’t affect the results of the FROLS algorithm identification,and determine the applicable scope of harmonic splicing method.