Weak Pulse Signal Detection Based On Jordan Neural Network In Chaotic Background

In the research of chaotic time series,one of the important research directions is the detection of weak signals in the background of chaotic signals.This problem extends from the problem of mechanical fault diagnosis.For such problems,the characteristics of chaotic signals and the knowledge in statistics are usually used to remove chaotic noise,so as to achieve the purpose of detecting and estimating weak signals in chaotic background.Therefore,the focus of research on this kind of problems is how to fully characterize chaotic background noise.According to the current research,chaos phenomenon is a kind of random phenomenon which is difficult to predict,because it constantly repeats the motion and change state of the previous moment with certain rules.In the chaotic system,the initial value of iteration has a great influence on the whole system,and the term butterfly effect well embodies this chaotic feature.Short-term predictability is another important feature of chaos,and it is the discovery of this feature that makes it necessary to continue this thesis.In this paper,the Jordan neural network with feedback structure is used to detect and estimate the weak pulse signal in chaotic background.First of all,search for relevant data and literature,summarize and analyze the research ideas and methods of relevant data.Secondly,the relevant theories of this paper,such as chaos theory,signal and neural network,are expounded.Then to chaos under the background of weak pulse signal detection problem analysis and modeling,the main steps are: the observation signal phase space reconstruction,the refactoring data set after Jordan neural network model is established to divest chaotic background noise,and then through a step prediction error test whether contain abnormal points to detect the existence and location of the pulse signal.Then,the SP-Jordan neural network model is established to estimate the weak pulse signal in chaotic background,and the pulse signal amplitude is estimated by the section least square method.When the model parameters are estimated by section least squares,the objective function is to minimize the mean square error of the SP-Jordan neural network model.The SP-Jordan neural network estimation model proposed in this paper is simulated.In the experiment,the chaotic background noise is the first component of Lorenz system or the13-month smooth monthly mean value of sunspots.Finally,R software is used to program the simulation experiment.Through simulation experiments,the following conclusions can be drawn :(1)Jordan neural network can fit chaotic time series well,and weak pulse signals can be easily detected from the residual of its fitting.The detection effect of the detection model is evaluated by the accuracy rate,and the evaluation results confirm that the detection effect of the model established in this paper is excellent.(2)The SP-Jordan neural network model,which is combined with the single point jump model and Jordan neural network proposed in this paper,can well extract pulse signals from chaotic background noise and estimate the amplitude of pulse signals,and the absolute error of the estimation is small,and the accuracy is below 0.05.(3)For pulse signals of different intensities,the SNR range that can be estimated by the model established in this paper is from-60 d B to-30 d B.(4)Compared with other neural networks,it is found that the absolute error of the impulse signal amplitude estimated by Jordan neural network is the smallest,which is 0.001952,indicating that it not only has high estimation accuracy but also good stability.