Research On Weak Signal Detection Method Based On Geometric Feature Of Duffing System

With the continuous development of electronic information technology,the complexity of the signal has been greatly improved,and the useful information is often submerged in strong background noise,and it is very difficult to extract useful information.Traditional methods of signal detection and analysis,such as Fourier analysis,time-frequency analysis,and envelope analysis,are generally based on linear transformation and linear filtering,which cannot effectively extract useful information in a strong noise background environment.Nonlinear methods such as empirical mode decomposition,stochastic resonance and wavelet denoising can extract effective information,but cause signal distortion,and it is difficult to achieve quantitative analysis of characteristic signals.Although the weak signal detection technology has made some progress in recent years,the practical problems that can be solved are still very limited.At present,the difficulty of weak signal detection technology is how to detect useful signals under low SNR conditions and minimize signal distortion.In the non-linear detection method,the chaotic vibration system has the characteristics of being sensitive to parameters and immune to noise,and has excellent response characteristics to harmonic signals submerged in noise.Compared with the traditional signal detection method,the detection threshold is greatly reduced,and it has received extensive attention in the field of weak signal detection.Based on the improved high-order double-coupled Duffing system,two geometric features of phase trajectories are extracted to judge the system state and quantized characteristic signal amplitude respectively.A method for detecting unknown frequency signals based on phase trajectory geometric features is proposed.It is applied to the fault detection of high-speed rail bearing signals and the amplitude quantification of the second harmonic of the guided wave signal.The parameters such as parameter sensitivity and noise immunity of the classical Duffing chaotic oscillator are introduced,and the principle of detecting weak signals by chaotic oscillator is expounded.Aiming at the shortcomings of the classic Duffing system with limited noise immunity,the high-order double-coupled Duffing system is further improved.The detection model based on high-order double-coupling system is established,and its feasibility is verified by simulating the bearing fault signal.The phase trajectory geometric feature is used as the basis for judging the state of the system,which greatly reduces the amount of calculation.Based on the classical Duffing system,an unknown frequency signal detection method based on geometric feature polar radius invariant moment is explored.The chaotic vibrator is used to automatically identify the harmonic components in the signal to be tested,and the outliers of the geometric features are used as the basis for determining the characteristic frequency.Compared to the classical chaotic detection method,it is not necessary to use the exact characteristic frequency of the detection as a priori knowledge.In order to demonstrate the universality and versatility of the chaotic detection method,weak signal detection is performed through two different application scenarios.On the one hand,the improved Duffing chaotic oscillator is applied to the weak signal recognition and quantitative analysis of nonlinear ultrasonic guided waves;on the other hand,the fault signal of the rolling bearing in the noise environment is detected,and the detection is performed under the premise of the failure of the traditional method.The effect has been improved.