The Study Of Weak Signal Detection System Based On Chaos Theory

Chaos is extremely common in nature, and chaotic motion is the typical behavior of many nonlinear systems. Chaos theory has been widely used in many fields, the application of chaos theory in weak signal detection is a pioneering study, because the chaotic detection is extremely sensitive to initial conditions and noise immunity, etc.. So in the detection area, the chaotic system has good prospects for development, the current situation has made great progress. Chaotic oscillator using a common method of detecting weak signals are:the phase trajectory based on the method and system characteristics index method. In this thesis, line voltage electrical insulation in the weak signal detection is based on the change of the phase detection voltage trajectory, the main work of this thesis are:First of all, introducing the basics of chaos theory, including the concept of chaos and the definition of chaos theory, this basic theory give us good understanding, and then introduce the chaos generated ways:the road bifurcation, paroxysmal road, poincare section method, power spectrum analysis, phase space reconstruction, correlation dimension, etc.. And describe the chaos theory in the weak signal detection criterion:melnikov method and the lyapunov index.Secondly, duffing oscillator described in detail the weak signal detection. First, analyzes the characteristics of duffing oscillator, and further analysis of the duffing oscillator detection of weak signals in principle, on this basis, we can use duffing oscillator to detect weak sinusoidal signal to establish a mathematical model or mixed with white noise and colored noise sinusoidal signal model, based on mathematical modeling matlab simulation model, and observe the phase trajectories to determine what state the system, and also apply this method to detect buried in the noise and unknown frequency square wave signal of weak signals.Thirdly, describing the weak signal amplitude estimation method, using floquet characteristic index to discribe features of nonlinear systems, the results show that the periodic state of the floquet index is only concerned with the corresponding periodic orbits, and make further information on the floquet index detection algorithm and characteristic index, the result shows that the relationship between the amplitude of the signal being measured only the amplitude of the signal driving force of the relevant period. At last given maximum likelihood estimation to estimate the magnitude of the signal.Finally, using the constant flow chaotic circuit based on weak voltage signal of pipe insulation, design the appropriate hardware, the hardware circuit control core is the microcontroller, and use software programming to detect weak voltage signal.