| This thesis is based on the research work which is the key project of the national defence military measurement Tenth Five-year Plan-"the theory and method research of the high pressure dynamic calibration". The nonlinear system characteristic that is based on the Duffing system is studied. The nonlinear system model is obtained via the input-output data using different methods. It has important significance on the high-pressure dynamic measurement system research.The main results can be summarized as follows:(1) The periodic solution of nonlinear system is obtained using energy method based on the concept of mechanics. The nonlinear model is simulated with the electronic simulation software, and the approaches of building electronic circuit and setting parameters is also presented.(2) The Volterra kernels are deduced through the polynomial activation function, which is poly- fitted from logsig function in artificial neural network model.(3) The transition from nonparametric model (Volterra series model) to more compact parametric model (NARMAX model) is presented using multidimensional Z-transform. The mathematical relation between continuous and discrete nonlinear model is studied and the equivalence relation between them is deduced.(4) The continuous-time transfer function is obtained from Laguerre kernels model, which is convenient for analyzed in frequency field. The order of nonlinear system is then can be deduced.(5) The exponential orthonormal function model of nonlinear system is obtained from the output data and the characteristic function of input data. The input data is characteristic of white noise of which the power spectrum is distributed equably. Characteristic function of input data can be obtained using a technique based on the inverse Fourier transform form PDF estimated of the input data.(6) At last the models mentioned in this thesis are analyzed, in which the effect of modeling and the area of application are summarized.
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