Study On Weak Signal Detection Approaches Based On Duffing Chaotic System

The weak signal detection is a new technology, which studies the principle and the method of detecting the weak signal under the strong noise background. Using this kind of technology can detect the weak signal (for example weak light, small displacement, micro vibrationand so on), which the traditional method can not solve. Therefore, this method may be widely used in photics, electricity, magnetism, acoustics, calorifics, biology, mechanics, geology, entironment, medicine, laser, material and so on. Finding the new method of detecting the weak signal and developing new equipment has been the hot topic in the weak signal detecting area.It is the most important to detect the weak sine signal in the multitudinous weak signal detecting methods. As the sine signal's especial structure, it has great significance not only in theoryand, and also in actual project domain, such as: radar, communication, biomedicine and so on.The multitudinous methods of detecting the weak sine signal are mostly based on study the noise's rule (for example the noise's scope, frequency, phase and so on) and analysis the signal's characteristic (for example signal's frequency spectrum, coherence and so on). First, finding the difference between the noise and the signal, then detecting the weak sine signal under the strong noise background by using the electronics, informatics and other physics, mathematics method. At present, the common methods include: filter method, noise counter balance method, correlation method, high step statistic method and so on. But these methods'SNR are all relative high, moreover, there still have some difficulties in processing the non- Gauss noise, such as theα-Stable noise.In view of this, the article unifies the chaos theory and the weak signal detection theory to detect the weak sina signal. This innovative method improved the existing weak signal detecting method, and enhanced the SNR. In a word, this method is effective in processing the weak signal. The main work and conclusion of the paper are as follows:1. Take the Duffing chaos system for example, the paper has analyzed the chaos system'motion, and by the simulation, it discovered that: 1) whether the system comes to the chaotic state has nothing to do with the noise inputed. That means the chaos system is immunity to the noise. 2) When the value of the chaos system'driving forse achieved the critical value, the system will appear the chaos phenomenon, which indicates that by adjusting the chaos system'driving forse value can change the motioning state of the chaos system. Through the two pointsabove, it explained that: when the noise and the weak sine signal inputed to the chaos system, the noise is immune, so it is possible and feasible to detect the weak sine signal from the strong noise background through the chaos system state's change.2. The article discussed several common methods to judge the chaotic system's state: The phase orbit method, Lyapunov method and Melnikov method. The phase orbit method is to judge the system's state by observating the change of the chaos system's phase orbit. This method is simple, direct-viewing, but it often needs very long observational time in certain situations. But if the observational time is not long enough, it will engender false judgement. Therefore, the article discussed two mathematic chaotic criterion: The Lyapunov exponential method and the Melnikov method, which advance two quantificational standard to judge whether the chaos system enteres to the chaotic state, these methods are accuracy, moreover they need not to observe the entire moving process of the chaos system. Actually, we usually uses the phase orbit method cooperated with these two kinds of quantificational standard to judge the chaos system's condition, which enhances the judgement's accuracy.3. The article take the Duffing chaos system as the model, studied the methods of detecting the weak sine signal under the noise background thoroughly. Discussed how to uses the chaos method to detect the weak signal's amplitude under the Gauss or non-Gauss noise background. Compared with the existing weak signal detecting method, the chaos method can detect weaker signal and achieve lower SNR.4. The article associates the correlation theory with the chaos method to detect the weak sine signal. First, make the correlation or the mutual correlation operation with the noise and the weak signal, then sent the signal into the chaos system to detect the weak signal's amplitude. The experiment result has proved that use the method which associate the chaos theory with the correlation theory can lower the SNR. The article has carried on enough simulations to confirme the method is good and effective to detect the weak signal'amplitude.5. The optimization search method is proposed on the base of using chaos principle to detect weak signal. In the article restraint nonlinear plan method is mainly adopt, which combine optimization algorithm with chaos method.Originally, using the sensitivity of chaos system to weak signal can only detect the signal whose frequency is the same with that of driving force. But now, using above method can detect any signal without the frequency restricting. And the former method is only through observing the change of phase orbit manually to judge the system changing to periodic state. While now, through programming andscanning the optimum variance value by computer automatically, and take the variance as detecting criterion which is used to judge whether the system enter into periodic state, then the frequency is detected in turn. This method is simple, convenient, quickly. Meanwhile the simulation experiments show that the optimization search method is not only suitable to white noise but also color noise background, moreover all can achieve very high measuring accuracy. Obviously the above method laid the foundation for the chaos theory used in signal processing and provided a new way and a novel method for weak signal detection.In conclusion, the article uses the chaos theory to detect the weak signal, specially to detect the weak sine signal. Using this method can successfully detect any weak sine signal's frequency and amplitude under either the Gauss noise or the non-Gauss noise background, and can gain very high precision in the extremely low SNR. Through enough simulations, it confirmed that the method is feasible and effective in detecting the weak signal. This innovation method has ameliorated the insufficiency of the existing weak signal detecting methods, and has very high practical value in the actual project application, specially in the heart electrical signal, theradar signal, seismic signal processing,etc.