Parameter Recognition Of Harmonic Weak Signal

In this paper,the recognition of weak harmonic signal parameters by nonlinear dynamic system is studied.The dynamic behavior of Duffing system,variable-scale Duffing system and improved Lorenz-like system under the coupling excitation of white Gaussian noise and weak harmonic signal are studied.The main purposes are to analyze the influence of noise intensity on the dynamics of nonlinear systems,which explore the essence of identifying weak harmonic signal parameters by using the sudden change of dynamic behavior of nonlinear systems.In this paper,stochastic Melnikov method is applied to derive the thresholds of stochastic Duffing system under the excitation of white Gaussian noise coupled with weak harmonic signal.The relationship between system control parameters and system thresholds is constructed and used to identify weak harmonic signal parameters.Furthemore,the improved Lorenz-like system is constructed and applied to identify weak harmonic signal parameters.The correctness of the theoretical results is verified by numerical simulation.The effect of noise on the dynamic behavior of nonlinear systems is revealed,and the mechanism of identifying parameters of weak harmonic signal by abrupt change of dynamic behavior of nonlinear systems is explained,which lays the theoretical and experimental foundations for identifying the parameters of practical weak harmonic signal in engineering.The specific content as follows:Chapter one,introduce the research background and significance of this paper.Sketch the identification of weak harmonic signal parameters by nonlinear system,analysis the research status of stochastic Melnikov method at home and abroad.Chapter two,establish the stochastic Duffing system under the excitation of white Gaussian noise coupled with harmonic signal.The chaotic threshold under mean square of stochastic Duffing system is calculated by stochastic Melnikov method.The influence of white Gaussian noise on the dynamics of Duffing system is revealed by the relationship between the intensity of white Gaussian noise and the system threshold.The chaotic threshold under mean square of stochastic Duffing system subjected to the excitation of white Gaussian noise and weak harmonic signal?rcos??t??is calculated by stochastic Melnikov method,and the formula for calculating the amplitude of weak harmonic signal is deduced.Chapter three,construct the variable-scale stochastic Duffing system coupled with white Gaussian noise and weak harmonic signal?rcos??₁t??.The chaotic threshold under mean square of variable-scale stochastic Duffing system is derived by stochastic Melnikov method,which shows the mechanism of identifying the frequency of weak harmonic signal by using the sudden change of dynamic behavior.Under the different frequency relationships between reference signal and weak harmonic signal,the range of reference signal amplitude is limited,so that the dynamic behavior of variable-scale stochastic Duffing system is different.A method of identifying the frequency of weak harmonic signal by using bifurcation diagram of variable-scale stochastic Duffing system is presented.Chapter four,a stochastic Duffing system coupled with white Gaussian noise and weak harmonic signal?rcos??t+???is established.The chaotic threshold under mean square of stochastic Duffing system is derived by stochastic Melnikov method.The relationship between the system threshold and the phase of weak harmonic signal is constructed,which leads to the expression of the phase of weak harmonic signal.The correctness of the conclusion is verified by numerical simulation,which lays the theoretical foundation for identifying the phase of weak harmonic signal in engineering by using phase calculation formula.Chapter five,the improved Lorenz-like system is constructed on the basis of Lorenz-like system.Because the immunity of the improved Lorenz-like system to noise is not absolute,the reliability of the threshold of improved Lorenz-like system after adding white Gaussian noise is used to reveal the effect of white Gaussian noise with different intensities on the sudden change of dynamic behavior of the system.The improved Lorenz-like system bifurcation diagram is applied to identify the amplitude of weak harmonic signals,and a method of identifying the signal frequency by the hollow phenomenon in the system bifurcation diagram is found.The expression of signal phase is derived from the relationship between the reference signal amplitude and the driving force signal amplitude.The numerical simulations under various conditions are established to verify the correctness of the conclusions.Chapter six,the recogonition methods of the harmonic signal?rcos??₁t+???parameters in engineering are detected.Based on the theoretical research and numerical experiments mentioned above,this chapter applies Duffing system to identify the parameters of weak harmonic signal in practical engineering,which establishes the more complete method to identify the parameters of weak harmonic signals in practical engineering.Chapter seven,summary and forecast.The research prospects of identifying the parameters of multi-group weak harmonic signals simultaneously by using nonlinear systems,optimizing the bifurcation diagram algorithms and construction of electronic circuits for nonlinear systems are presented.Briefly describes the advantages and disadvantages of this paper.