Statistical Detection And Estimation Of Weak Pulse Signal Under Chaotic Noise Interference Based On Deep Learning Model

Weak signal detection is an important issue in modern detection such as machine fault diagnosis.The method principle is to use signal processing theory and probability statistics methods to study the characteristics of the observed signals,analyze the causes of interference or noise,and statistically characterize them,so as to detect and estimate the weak signals drowned in noise.The uniqueness of chaos and the good learning ability of deep learning models provide new ideas and methods for weak signal detection and estimation.Chaos generally exists in nature and social life.Chaos phenomenon is a kind of random effect that the object replicates the state of motion of the previous stage with some rules.The so-called "little difference,lost thousands of miles" is the best annotation of this phenomenon.Chaotic motion is extremely sensitive to initial value,on the one hand,it reflects the strong influence of random system motion trends in non-linear dynamical systems,and on the other hand,it also leads to the unpredictability of long-term behavior of the system.With the continuous development and application of chaos theory,it has become a development trend in the field of weak signal detection and estimation.Deep learning originates from the study of artificial neural networks.Multi-layer perceptrons with multiple hidden layers are a type of deep learning structure.Deep learning is a new field in machine learning research.Its motivation is to build and simulate the neural network of the human brain for analytical learning.It mimics the mechanism of the human brain to interpret data,such as images,sounds,and text.The deep learning model's outstanding learning ability and good nonlinear approximation ability provide a new research direction for improving the accuracy of weak signal detection and estimation.This paper uses deep learning models to study weak pulse signals under chaotic noise interference.First,read a lot of literature to summarize and analyze related research on weak signal detection;second,expound related basic theoretical knowledge such as chaos theory and deep learning;then,we focus on detecting and estimating weak pulse signals based on Elman deep learning neural network.Aiming at the problem of detecting weak pulse signals under chaotic noise,based on the short-term predictability of chaotic signals,the phase space reconstruction of the observed signals is carried out,and an Elman deep learning adaptive detection model(EDAD)is established.Check whether the observation signal contains weak pulse signals from the prediction error..On the problem of estimating weak pulse signals,a single-point jump model for weak pulse signals is established,coupled with the Elman deep learning neural network model,and construct a double-layer Elman deep neural network recovery model(DEDR).With the goal of minimizing the mean square prediction error of the Elman model as the goal to optimize.Because the DEDR model is essentially a semi-parametric model that includes parametric and non-parametric parts,for the problem of weak pulse signals that are difficult to estimate,so we use the profile least square(PLS)method to estimate the parameters of DEDR model.Finally,based on the Lorenz chaotic system,use R software to carry on the simulation experiment to the built model programming.The results show that:(1)The EDAD model constructed can effectively detect weak pulse signals.At the same time,accuracy(ACC)use to evaluate the detection performance of the model,which confirms that the model constructed in this paper has better detection effect.(2)DEDR model can estimate the weak pulse signal under the interference of chaotic noise at a lower operating threshold.The error between the estimated value and the true value is small,and it is basically below 0.002%.(3)For different-intensity pulse signals,the detection and estimation model constructed in this paper can use a smaller amount of data to achieve a lower signal-to-interference ratio working threshold and maintain a higher level of prediction accuracy.(4)Compared the performance with different models,it is found that the advantages of the model in this paper are more obvious: its detection ability is stronger,and the estimation effect is better.