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CN-117074777-B - Weak harmonic detection method based on Chen system

CN117074777BCN 117074777 BCN117074777 BCN 117074777BCN-117074777-B

Abstract

The invention belongs to the field of weak harmonic signal detection, in particular to a weak harmonic detection method based on a Chen system, which is characterized in that parameters a, b and c of the Chen system and initial values (x 0, y0 and z 0) of the Chen system are set, a critical threshold value of a system control signal is found by adopting a dichotomy according to a bifurcation diagram of a system state variable changing along with a control signal amplitude value f, and an input signal weighting factor A is set according to the critical threshold value. After the Chen system for signal detection is debugged, the control signal and the weighted input signal are input into the system at the same time, a system equation of the Chen system is solved, and a system x-z phase diagram, attractor distribution and state variable time history diagram are drawn. Judging that the system is changed in the position of the fixed point or in the distribution of the attractors, if the system is changed, the harmonic signals to be detected exist, at the moment, reducing the amplitude f of the control signals according to the step length, and recalculating the state of the system until the position of the fixed point or the distribution of the attractors of the system is changed into the initial state, wherein the ratio of the reduced difference value of the amplitude of the control signals of the system to the weighting factor is the amplitude of the harmonic signals to be detected. The signal can be detected without difference under the noise of-60 dB, and the detection error under the noise of-100 dB can be kept below 0.1%.

Inventors

  • SUN SHUQIN
  • QI XIN
  • YUAN ZHENGHAI
  • ZHOU GUANGHAO

Assignees

  • 吉林大学

Dates

Publication Date
20260512
Application Date
20230614

Claims (5)

  1. 1. The weak harmonic detection method based on the Chen system is characterized by comprising the following steps of: Step 1, setting parameters a, b and c of a Chen system and a system initial value x 0 , y 0 ,z 0 ; in the step 2, the bifurcation diagram is a diagram which changes along with nonlinear system parameters and reflects the change of the number of stable points of a system, the approximate range of the critical threshold of the system control signal is determined by observing the shape of the bifurcation diagram of the system state variable which changes along with the amplitude f of the control signal, and a more accurate threshold is obtained in the nearby range by utilizing a dichotomy, and the specific steps are as follows: Step 2-1, drawing a bifurcation diagram of a system state variable along with the change of the control signal amplitude f; Step 2-2, obtaining the approximate range of the critical threshold value of the control signal according to the image of the obtained bifurcation diagram; step 2-3, taking a point at the left side of the critical threshold value as m and a point at the right side as n; step 2-4, assigning the amplitude value of the control signal to be (m+n)/2, and carrying the control signal into a Chen system to draw a phase diagram; Step 2-5, judging the system state, if the system state variable is in a positive-negative alternating state, making m= (m+n)/2, and if the system state variable is continuously a stable positive value, making n= (m+n)/2; step 2-6, judging whether the obtained control signal critical threshold meets the required detection precision, if not, returning to the step 2-4, and if so, ending iteration; Step 3, setting an input signal weighting factor A, and inputting signals into a Chen system; Step 4, solving a system equation of the Chen system, and drawing a system x-z phase diagram, attractor distribution and state variable time history diagram; Step 5, judging that the Chen system has the change of the position of the fixed point or the change of the distribution of attractors, if the Chen system has not changed, modifying the weighting factor A, returning to the step 3, and if the Chen system has changed, entering the step 6; step 6, reducing the control signal amplitude f according to the step length, recalculating the system state, and drawing a system x-z phase diagram, an attractor distribution and a state variable time history diagram; Step 7, judging whether the position of the fixed point or the attractor distribution of the system is changed into an initial state, if not, returning to the step 6 to continuously reduce the control signal amplitude f, and if so, entering the step 8; step 8, the ratio of the system control signal amplitude reduction difference value to the weighting factor is the amplitude of the harmonic signal to be detected; and 9, finishing the operation process after the amplitude calculation of the detected signal is finished.
  2. 2. The Chen system-based weak harmonic detection method according to claim 1, wherein in step 1, the mathematical model of Chen system dynamics is: , wherein x, y and z are state variables of the system, a, b and c are dimensionless system parameters, the Chen system is controlled by adopting a non-resonance parameter control method, and a system model is as follows: , wherein 1+f cos ωt is a control signal, ω is an angular frequency of a periodic component of the control signal, s (t) is a target weak periodic signal, n (t) is noise doped in a signal to be detected, A is a weighting factor of an input signal, and when a Chen system is used for weak signal detection, a state variable x is an output of the system.
  3. 3. The Chen system-based weak harmonic detection method according to claim 1, wherein in step 3, the input signal weighting factor a is set so that Af does not exceed 0.1.
  4. 4. The Chen system-based weak harmonic detection method according to claim 1, wherein in step 4, the system equation of Chen system is solved by using a four-level fourth-order lagrangian method.
  5. 5. The Chen system-based weak harmonic detection method according to claim 1, wherein in step 5, the system change of the stationary point position or the attractor distribution may occur in the quadrant where the phase trajectory is located, and the stationary point coordinates of the system state variable in the stationary state change, i.e., the output of the system is inverted.

Description

Weak harmonic detection method based on Chen system Technical Field The invention belongs to the field of weak harmonic signal detection, and particularly relates to a weak harmonic detection method based on a Chen system. Background In the field of operation and maintenance of power systems, weak harmonic signal detection in a severe noise environment is a big hot spot and difficult point, and particularly has important research value for improving the operation stability of the power systems aiming at blind detection modes with completely unknown signal information. The publication number CN112098723A (2020) discloses a weak harmonic signal detection system and a weak harmonic signal detection method based on the same frequency, and the method has the advantages that the chaotic system is adopted for signal detection, and compared with the traditional detection algorithm, the detection accuracy is higher, and the noise immunity is good. However, in the method, the adopted non-dissipative chaotic system has the defects of inaccurate phase change observation and noise interference of periodic motion, and the detection signal-to-noise ratio is about-69 dB. Disclosure of Invention The invention provides a weak harmonic detection method based on a Chen system, which aims to solve the problems of low detection precision and large error of weak harmonic signals in a severe noise environment. The present invention has been achieved in such a way that, A weak harmonic detection method based on a Chen system comprises the following steps: Step 1, setting parameters a, b and c of a Chen system and a system initial value x 0,y0,z0; Step 2, according to a bifurcation diagram of a system state variable along with the change of the control signal amplitude f, a binary method is adopted to find out a critical threshold value of the system control signal; Step 3, setting an input signal weighting factor A, and inputting signals into a Chen system; Step 4, solving a system equation of the Chen system, and drawing a system x-z phase diagram, attractor distribution and state variable time history diagram; Step 5, judging that the Chen system has the change of the position of the fixed point or the change of the distribution of attractors, if the Chen system has not changed, modifying the weighting factor A, returning to the step 3, and if the Chen system has changed, entering the step 6; Step 6, reducing the control signal amplitude f according to the step length, recalculating the system state, and drawing a system x-z phase diagram, an attractor distribution and a state variable time history diagram; Step 7, judging whether the position of the fixed point or the attractor distribution of the system is changed into an initial state, if not, returning to the step 6 to continuously reduce the control signal amplitude f, and if so, entering the step 8; step 8, the ratio of the system control signal amplitude reduction difference value to the weighting factor is the amplitude of the harmonic signal to be detected; and 9, finishing the operation process after the amplitude calculation of the detected signal is finished. Further, in step 1, the mathematical model of Chen system dynamics is: wherein x, y and z are state variables of the system, a, b and c are dimensionless system parameters, the Chen system is controlled by adopting a non-resonance parameter control method, and a system model is as follows: wherein 1+f cos ωt is a control signal, ω is an angular frequency of a periodic component of the control signal, s (t) is a target weak periodic signal, n (t) is noise doped in a signal to be detected, A is a weighting factor of an input signal, and when a Chen system is used for weak signal detection, a state variable x is an output of the system. In step 2, the bifurcation diagram is a diagram that changes along with the nonlinear system parameter and reflects the change of the number of stable points of the system, the approximate range of the critical threshold of the control signal of the system is determined by observing the shape of the bifurcation diagram that changes along with the amplitude f of the control signal of the system state variable, and a more accurate threshold is obtained by using a dichotomy in the nearby range, and the specific steps are as follows: Step 2-1, drawing a bifurcation diagram of a system state variable along with the change of the control signal amplitude f; Step 2-2, obtaining the approximate range of the critical threshold value of the control signal according to the image of the obtained bifurcation diagram; step 2-3, taking a point at the left side of the critical threshold value as m and a point at the right side as n; step 2-4, assigning the amplitude value of the control signal to be (m+n)/2, and carrying the control signal into a Chen system to draw a phase diagram; Step 2-5, judging the system state, if the system state variable is in a positive-negative alternating state, making m