Research On Some Problems Of Chaos Oscillator Detection And Its Application

An important application of Chaos theory in information science is informationdetection. Chaos system is sensitive to weak signals and immune to noise, whichmeans chaos has a bright future in information detection technique. The methods ofsignal detection using chaos oscillator are divided into two groups: weak signaldetection when the background noise is chaos, and weak signal detection usingchaotic oscillator. In recent years, many scholars have studied the application ofchaotic oscillator in weak signal detection, presented detection models and havedetected weak periodic signal in strong noise successfully. Duffing oscillator is themost widely used detection model. Through the change from chaos state to largescale period state we can detect the weak signal, so we should consider the problemof the judgment of chaos state and large scale period state. There are many methodsto judge chaos, in which the most widely used method is Lyapunov exponent. Untilnow, many scholars have studied the algorithm of Lyapunov exponent. In this paper,the detection model we used is two dimension and the algorithms existed arecomplicated, inefficient and have some trouble in practical application. So it isnecessary to study a fast and efficient algorithm which is used to computeLyapunov exponent of low dimension system. We usually use visual methods tojudge the existence of large scale period state of Duffing equation and nobodypresent the theoretic analysis. So it is necessary to study the problem of theexistence of large scale period state, which in one hand can provide necessarytheoretic supplement to weak signal detection using chaotic oscillator, in anotherhand can provide new method to the frequency detection of weak signal.Chaos theory has been widely used in radar, sonar, and biomedicine and so on.In this paper we use chaos theory to the field of seismic prospecting. With thedeepening of geological exploration, the target area more and more tends todeep-seated structure area. The seismic wave exploded by the source of the earth'ssurface has large attenuation because of the deep of the target layer and reflectionand dispersion in the medium and the non-elasticity effect. So the reflecting signalreceived is very weak. In the background of random noise, the seismic reflectionsignal can not be seen clearly and sometimes is submerged in the noise, so thehyperbolic event is difficult to track. How to derive the weak useful signal fromstrong noise is a very difficult problem in seismic signal processing. If this problemis solved, it will stimulate the development of productivity and bring largeeconomic benefit.According to the analysis above, the following gives the main work of this paperin detail.1. Research on the periodic solution of chaotic oscillator detection technology.We review the development of chaotic oscillator detection system andsummarize the advantage and disadvantage of the detection models. Many scholarshave successfully detected weak periodic signal using Duffing equation, which isthe most widely used model, according to the change of phase space state fromchaotic to periodic. But until now, people only use the visual method to judge theexistence of periodic state of Duffing equation, and nobody present the theoreticanalysis. In this paper, we prove the existence of periodic solution of Duffingequation, which includes nonlinear item x 3 or x 5, and we prove the periodicsolution is exclusive according to the theory of nonlinear differential equation.2. Research on the improved algorithm of Lyapunov exponent.We summarize the existed methods for chaos identification and analyze thequantitative methods. We analyze the development of the Lyapunov exponentalgorithm including Lyapunov exponent of the deterministic system and time series.Then we present a new algorithm to compute the Lyapunov exponent of time series.We apply the Delaunay triangulation to this algorithm. Through the fast algorithmof Delaunay triangulation while searching for the nearest points, the improvedalgorithm can compute Lyapunov exponent quickly. At last, simulation of somelow dimension systems shows the validity of the algorithm and the algorithm isused to chaos identification of Duffing oscillator.3. Research on the application of chaotic oscillator in the process of seismic dataof geophysical exploration.First, we give a necessary introduce to the seismic data model. The preconditionof the application of chaotic oscillator is that the signal to be detected must beperiodic, but in geophysical exploration, we receive multi-channel signal and eachsingle channel signal is not periodic. Without considering the background noise, thereflect signals from the same horizontal are analogical. So we can move the seismicwave of different channel to the same time axes artificially, then detect the seismicsignal using the selected chaotic oscillator. We present research scheme ofdetecting the seismic hyperbolic event. Then we analyze the type of seismic noiseand the methods to suppress noise. When we know the parameters corresponding tothe hyperbolic events, we use multi-channel mean square method to suppress therandom noise of seismic exploration data which is synthesized artificially. At last,we compare the multi-channel mean square method to the τ ?ptransform methodand single channel mean square method.Through our research, we gain the following conclusions: a. Duffing equationcontaining nonlinear item x 3and x 5has periodic solution and the solution isexclusive, so we can use Duffing equation to detect the frequency of weak periodicsignal;b. We present a new algorithm to compute Lyapunov exponent based onDelaunay triangulation, and simulation shows that the improved algorithm cancompute Lyapunov exponent quickly and the precision is equal to the originalalgorithm, also the algorithm can be used to the judgment of chaos;c. Afterknowing the parameters corresponding to the hyperbolic event, multi-channel meansquare method can suppress the random noise of seismic exploration data, and theperformance of the algorithm is better than τ ?ptransform method and singlechannel filtering method.