Research On Nonlinear System Modeling And Frequency Domain Analysis Method Based On NARX Model

The NARX(Nonlinear Auto Regressive with eXogenous inputs)model can describe a large class of nonlinear systems with strong robustness and good prediction ability.It is widely used in nonlinear system identification as a numerical model.System identification is a mathematical modeling method based on input and output data.The aim of system identification is to determine a system model which can describe the system characteristics from a given model space.According to whether the model coefficients have physical meanings,mathematical models can be divided into two categories:the numerical model and the physical model.The physical model is a reasonable simplification of the actual system based on electricity,mechanics,chemistry or other related theories.However,for complex systems such as aero-engines and gas turbines,the nonlinearity of the system is very strong due to the complex nonlinear characteristics such as time-varying stiffness,nonlinear damping,and various coupling faults.Thus it is difficult to establish a physical model based on reasonable assumptions.For these complex systems,it is reasonable to build a numerical model based on system identification.The modeling method based on system identification does not need to know the internal structure of the system.It is often quick and can be made to track changes in the system.These advantages all suggest that system identification is widely used in engineering.The time domain response can be mapped into frequency domain based on discrete NARX model.The frequency response function can reflect the intrinsic dynamic characteristics of the system,making it more convenient of nonlinear system analysis,design,control and fault diagnose in frequency domain.The NARX modeling method is discussed in this paper.Based on the NARX model,the NRSFs(Nonlinear Response Spectrum Functions)is proposed as a feature which can reflect the underlying system characteristics.And fault diagnosis of nonlinear systems is done based on NRSFs.Therefore the propose of modeling,analyzing and diagnosing of complex nonlinear systems id achieved.The main research content of this paper includes the following four parts:(1)For the multi-degree-of-freedom system,the NARX model is established based on the input-output sequence and correlated identification algorithm.And model verification is done to guarantee model accuracy.In traditional,a random signal is selected as the system input in the modeling process to obtain different amplitude frequency response characteristics of the system.However,for complex systems such as rotor systems,random inputs cannot be generated during the operation.Thus,the multi-harmonic input method is proposed to address this problem.(2)Based on the time domain discrete NARX model and combined with the harmonic detection method and the description function method,the concept of NRSFs is proposed.The nonlinear bearing-rotor system is taken as an example.By comparing the NRSFs values of the system under different parameters.The conclusion that the NRSFs are sensitive to system parameter is obtained.Enriched and developed the theory of frequency domain analysis methods for nonlinear systems(3)Combining the NARX-NRSFs frequency domain analysis method with the machine learning algorithm,the NARX-NRSF-SVM method is proposed by using the SVM(Support Vector Machine)as the classifier.It includes the entire nonlinear system analysis process from modeling to feature extraction to fault diagnosis.(4)The results show that the NARX-NRSF-SVM method can identify the different fault states of the system quickly and easily,and can get relative high identification accuracy.Illustrating that the method is feasible and effective.