A weak harmonic detection method based on Chen system

Abstract

The present application belongs to the field of weak harmonic signal detection, and particularly to a weak harmonic detection method based on Chen system. The parameters a, b, c and the initial value (x0, y0, z0) of the system of the Chen system are set, the critical threshold of the control signal of the system is found out by using the dichotomy according to the bifurcation diagram of the system state variable changing with the amplitude f of the control signal, and the input signal weighting factor A is set according to the critical threshold. 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, the system equation of the Chen system is solved, the x-z phase diagram of the system, the attractor distribution and the state variable time history diagram are drawn. The change of the fixed point position or the change of the attractor distribution of the system is judged, if the change occurs, the harmonic signal to be detected exists, at this time, the control signal amplitude f is reduced by a step and the system state is recalculated until the fixed point position or the attractor distribution of the system becomes the initial state, and the ratio of the difference of the control signal amplitude and the weighting factor is the amplitude of the harmonic signal to be detected. The signal can be detected without error under the noise of-60dB, and the detection error under the noise of-100dB can also be kept below 0.1%.

Description

Technical Field

[0001] This invention belongs to the field of weak harmonic signal detection, specifically a weak harmonic detection method based on the Chen system. Background Technology

[0002] In the field of power system operation and maintenance, the detection of weak harmonic signals under harsh noise environments is a major research hotspot and challenge. In particular, blind detection methods for completely unknown signal information have important research value for improving the operational stability of power systems.

[0003] The publication number CN112098723A(2020) discloses a weak harmonic signal detection system and method based on the same frequency. The advantage of this method is that it uses a chaotic system for signal detection, which has higher detection accuracy and better noise resistance compared with traditional detection algorithms.

[0004] However, the non-dissipative chaotic system used in the above method has the defects of inaccurate phase transition observation and periodic motion being affected by noise, and its detection signal-to-noise ratio is about -69dB. Summary of the Invention

[0005] To address the issues of low detection accuracy and large errors in weak harmonic signals under harsh noise environments, this invention provides a weak harmonic detection method based on the Chen system.

[0006] This invention is implemented as follows:

[0007] A method for detecting weak harmonics based on the Chen system, the method comprising the following steps:

[0008] Step 1: Set the parameters a, b, c of the Chen system and the initial system values ​​x0, y0, z0;

[0009] Step 2: Based on the bifurcation diagram of the system state variables as a function of the control signal amplitude f, use the bisection method to find the critical threshold of the system control signal;

[0010] Step 3: Set the input signal weighting factor A and input the signal to the Chen system;

[0011] Step 4: Solve the system equations of the Chen system, and draw the system xz phase diagram, attractor distribution and time history diagram of state variables;

[0012] Step 5: Determine if the fixed point position or attractor distribution of the Chen system has changed. If no change has occurred, modify the weighting factor A and return to step 3. If a change has occurred, proceed to step 6.

[0013] Step 6: Decrease the control signal amplitude f by step size, recalculate the system state, and draw the system xz phase diagram, attractor distribution and state variable time history diagram;

[0014] Step 7: Determine whether the fixed point position or attractor distribution of the system has changed to the initial state. If it has not changed, return to step 6 to continue decreasing the control signal amplitude f. If it has changed, proceed to step 8.

[0015] Step 8: The ratio of the difference in amplitude reduction of the system control signal to the weighting factor is the amplitude of the harmonic signal to be detected;

[0016] Step 9: The amplitude calculation for the detected signal has been completed, and the calculation process ends.

[0017] Furthermore, in step 1, the mathematical model for the dynamic characteristics of the Chen system is:

[0018]

[0019] Where x, y, and z are the system state variables, and a, b, and c are dimensionless system parameters; a non-resonant parameter control method is used to control the Chen system, and the system model is as follows:

[0020]

[0021] Where 1+f cosωt is the control signal, ω is the angular frequency of the periodic component of the control signal, s(t) is the target weak periodic signal, n(t) is the noise doped in the signal to be detected, and A is the weighting factor of the input signal. When the Chen system is used for weak signal detection, the state variable x is the output of the system.

[0022] Further, in step 2, the bifurcation diagram is a graph reflecting the change in the number of stable points of the system as the nonlinear system parameters change. By observing the shape of the bifurcation diagram showing the change of system state variables with the amplitude f of the control signal, the approximate range of the critical threshold of the system control signal is determined, and a more precise threshold is obtained in the vicinity using the bisection method. The specific steps are as follows:

[0023] Step 2-1: Draw a bifurcation diagram of the system state variables as a function of the control signal amplitude f;

[0024] Step 2-2: Obtain the approximate range of the critical threshold of the control signal based on the obtained bifurcation diagram;

[0025] Steps 2-3: Determine a point to the left of the critical threshold as m, and a point to the right as n;

[0026] Steps 2-4: Assign the amplitude of the control signal to (m+n) / 2, substitute it into the Chen system, and draw the phase diagram;

[0027] Steps 2-5: Determine the system state. If the system state variable is in an alternating positive and negative state, let m = (m+n) / 2; if the system state variable is continuously a stable positive value, let n = (m+n) / 2.

[0028] Step 2-6: Determine whether the obtained control signal critical threshold meets the required detection accuracy. If not, return to step 2-4; if it does, end the iteration.

[0029] Furthermore, in step 3, the input signal weighting factor A is set so that Af does not exceed 0.1.

[0030] Furthermore, in step 4, the system equations of the Chen system are solved using the fourth-order Runge-Kutta method.

[0031] Furthermore, in step 5, the change in the fixed point position or the change in the attractor distribution of the system may occur due to the change in the quadrant where the phase trajectory is located, or the change in the fixed point coordinates of the system state variables in the steady state, i.e., the inversion of the system output.

[0032] Compared with the prior art, the beneficial effects of this invention are as follows:

[0033] This invention replaces the "chaotic-chaotic phase transition" or "circular-chaotic phase transition" of non-dissipative systems with "chaotic-chaotic phase transition" as the marker for weak signal detection. It has a detection accuracy and noise resistance that are far superior to those of non-dissipative chaotic systems. It can perform error-free signal detection under -60dB noise and maintain the detection error below 0.1% under -100dB noise. Attached Figure Description

[0034] Figure 1 A flowchart of the method provided in an embodiment of the present invention;

[0035] Figure 2 This invention provides a bifurcation diagram showing the variation of system output x with the amplitude f of the periodic component in an embodiment of the invention.

[0036] Figure 3 The system provides an xz phase trajectory diagram and attractor distribution diagram (f = 0.7014001824) for embodiments of the present invention;

[0037] Figure 4 A time history diagram of the system state variable x (f = 0.7014001824) is provided for embodiments of the present invention;

[0038] Figure 5 The system provides an xz phase trajectory diagram and attractor distribution diagram (f = 0.7014001825) for embodiments of the present invention;

[0039] Figure 6A time history diagram of the system state variable x (f = 0.7014001825) is provided for embodiments of the present invention. Detailed Implementation

[0040] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0041] See Figure 1 This invention discloses a weak harmonic detection method based on the Chen system, which includes the following steps:

[0042] Step 1: Set the parameters a, b, c of the Chen system and the initial system values ​​(x0, y0, z0);

[0043] Including: The mathematical model of the dynamic characteristics of the Chen system is

[0044]

[0045] Where x, y, and z are the system state variables, and a, b, and c are dimensionless system parameters. The Chen system is controlled using a non-resonant parameter control method, and the system model is as follows:

[0046]

[0047] Where 1+fcosωt is the control signal, ω is the angular frequency of the periodic component of the control signal, s(t) is the target weak periodic signal, n(t) is the noise doped in the signal to be detected, and A is the weighting factor of the input signal. When the Chen system is used for weak signal detection, the state variable x is the output of the system.

[0048] Step 2: Based on the bifurcation diagram of the system state variables as a function of the control signal amplitude f, use the bisection method to find the critical threshold of the system control signal;

[0049] This includes: A bifurcation diagram is a graph that reflects the change in the number of stable points of a nonlinear system as its parameters change. By observing the shape of the bifurcation diagram showing the change in system state variables with the amplitude f of the control signal, the range of the critical threshold of the system's control signal can be roughly determined. Then, a more precise threshold can be obtained within this nearby range using the bisection method. The specific steps of this process are as follows:

[0050] Step 2-1: Draw a bifurcation diagram of the system state variables as a function of the control signal amplitude f;

[0051] Step 2-2: Obtain the approximate range of the critical threshold of the control signal based on the obtained image;

[0052] Steps 2-3: Determine a point to the left of the critical threshold as m, and a point to the right as n;

[0053] Steps 2-4: Assign the amplitude of the control signal to (m+n) / 2, substitute it into the Chen system, and draw the phase diagram;

[0054] Steps 2-5: Determine the system state. If the system state variable is in an alternating positive and negative state, let m = (m+n) / 2; if the system state variable is continuously a stationary positive value, let n = (m+n) / 2.

[0055] Step 2-6: Determine whether the obtained control signal critical threshold meets the required detection accuracy. If not, return to step 2-4; if it does, end the iteration.

[0056] Step 3: Set the input signal weighting factor A and input the signal to the system;

[0057] This includes setting the input signal weighting factor A, which must ensure that Af does not exceed 0.1.

[0058] Step 4: Solve the system equations of the Chen system, and draw the system xz phase diagram, attractor distribution and time history diagram of state variables;

[0059] This includes: the system equations of the Chen system can be solved using the fourth-order Runge-Kutta method.

[0060] Step 5: Determine if the fixed point position or attractor distribution of the system has changed. If no change has occurred, modify the weighting factor A and return to step 3. If a change has occurred, proceed to step 6.

[0061] This includes: changes in the fixed point position or attractor distribution of the system, which may occur due to changes in the quadrant where the phase trajectory is located, and changes in the fixed point coordinates of the system's state variables in a stationary state, i.e., the system's output being out of phase.

[0062] Step 6: Decrease the control signal amplitude f by step size, recalculate the system state, and draw the system xz phase diagram, attractor distribution and state variable time history diagram;

[0063] Step 7: Determine whether the fixed point position or attractor distribution of the system has changed to the initial state. If it has not changed, return to step 6 to continue decreasing the control signal amplitude f. If it has changed, proceed to step 8.

[0064] Step 8: The ratio of the difference in amplitude reduction of the system control signal to the weighting factor is the amplitude of the harmonic signal to be detected;

[0065] Step 9: The amplitude calculation for the detected signal has been completed, and the calculation process ends.

[0066] Example 1

[0067] Set the system parameters to a = 38, b = 3, c = 21, and the initial system values ​​to x = 1, y = 1, z = 1. Set the control signal angular frequency ω = 2π × 50Hz. Plot the bifurcation diagram of the system output x as a function of the periodic component amplitude f, as shown below. Figure 2 As shown in the diagram, the critical threshold of the system control signal is around 0.7, as can be seen from the bifurcation diagram.

[0068] To ensure the system has strong noise immunity, the phase transition interval is set within the stationary range after f > 0.7. Through binary iterative experiments, the critical threshold of the system's control signal is found to be 0.7014001824. At this point, the xz phase trajectory diagram and attractor distribution of the system are as follows: Figure 3 As shown in the diagram, the system's fixed point is located in the second quadrant of the xz phase plane, and the phase trajectories are mostly distributed in the second quadrant, with a small portion in the first quadrant. This indicates that the system is currently in a critical state between two chaotic states. The time history diagram of the state variable x is shown below. Figure 4 As shown, the coordinates of the fixed point in equilibrium are (-3.86, 4.99).

[0069] When the amplitude f of the system control signal is changed to 0.7014001825, the phase diagram trajectory and attractor distribution of the system are as follows: Figure 5 As shown, the system's fixed point is located in the first quadrant of the xz phase plane, and the phase trajectory is mostly distributed in the first quadrant, with a small portion in the second quadrant. This indicates that the system has undergone a phase transition from one chaotic state to another. The time history diagram of the state variable x is shown below. Figure 6 As shown, the coordinates of the fixed point in equilibrium are (3.86, 4.99).

[0070] Using weak harmonic signals from the power system

[0071] x(t)=sin(ωt)+0.15sin(2.2ωt)+0.25sin(3ωt)+0.2sin(5ωt)+0.1sin(7ωt)

[0072] As the target signal, where ω = 2π × 50Hz, and the input signal weighting factor A is set to 10. -9 .

[0073] The signal is mixed with Gaussian white noise to make its SNR = -60dB and -100dB, according to

[0074]

[0075] The intensity D of Gaussian white noise can be determined.

[0076] The amplitude of the control signal is reduced step by step until the system returns to its initial state. The difference in the reduction of the control signal amplitude is recorded. The ratio of this difference to the weighting factor of the input signal is the amplitude of the target weak harmonic signal. The detection results under the two signal-to-noise ratios are shown in Table 1.

[0077] Table 1 Critical amplitude of control signal for Chen system under different signal-to-noise ratios

[0078]

[0079] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for detecting weak harmonics based on the Chen system, characterized in that, The method includes the following steps: Step 1: Set the parameters a, b, c of the Chen system and the initial system values ​​x0, y0, z0; Step 2: Based on the bifurcation diagram showing the change of system state variables with the amplitude f of the control signal, the critical threshold of the system control signal is found using the bisection method. In Step 2, the bifurcation diagram is a graph reflecting the change in the number of stable points of the system as the nonlinear system parameters change. By observing the shape of the bifurcation diagram showing the change of system state variables with the amplitude f of the control signal, the approximate range of the critical threshold of the system control signal is determined, and a more precise threshold is obtained in the vicinity using the bisection method. The specific steps are as follows: Step 2-1: Draw a bifurcation diagram of the system state variables as a function of the control signal amplitude f; Step 2-2: Obtain the approximate range of the critical threshold of the control signal based on the obtained bifurcation diagram; Steps 2-3: Determine a point to the left of the critical threshold as m, and a point to the right as n; Steps 2-4: Assign the amplitude of the control signal to (m+n) / 2, substitute it into the Chen system, and draw the phase diagram; Steps 2-5: Determine the system state. If the system state variable is in an alternating positive and negative state, let m = (m + n) / 2; if the system state variable is continuously a stable positive value, let n = (m + n) / 2. Step 2-6: Determine whether the obtained control signal critical threshold meets the required detection accuracy. If not, return to step 2-4; if it does, end the iteration. Step 3: Set the input signal weighting factor A and input the signal to the Chen system; Step 4: Solve the system equations of the Chen system, and draw the system xz phase diagram, attractor distribution and time history diagram of state variables; Step 5: Determine if the fixed point position or attractor distribution of the Chen system has changed. If no change has occurred, modify the weighting factor A and return to step 3. If a change has occurred, proceed to step 6. Step 6: Decrease the control signal amplitude f by step size, recalculate the system state, and draw the system xz phase diagram, attractor distribution and state variable time history diagram; Step 7: Determine whether the fixed point position or attractor distribution of the system has changed to the initial state. If it has not changed, return to step 6 to continue decreasing the control signal amplitude f. If it has changed, proceed to step 8. Step 8: The ratio of the difference in amplitude reduction of the system control signal to the weighting factor is the amplitude of the harmonic signal to be detected; Step 9: The amplitude calculation for the detected signal has been completed, and the calculation process ends.

2. The weak harmonic detection method based on the Chen system according to claim 1, characterized in that, In step 1, the mathematical model for the dynamic characteristics of the Chen system is: ， Where x, y, and z are the system state variables, and a, b, and c are dimensionless system parameters; the Chen system is controlled using a non-resonant parameter control method, and the system model is as follows: ， Where 1+f cosωt is the control signal, ω is the angular frequency of the periodic component of the control signal, s(t) is the target weak periodic signal, n(t) is the noise doped in the signal to be detected, and A is the weighting factor of the input signal. When the Chen system is used for weak signal detection, the state variable x is the output of the system.

3. The weak harmonic detection method based on the Chen system according to claim 1, characterized in that, In step 3, the input signal weighting factor A is set so that Af does not exceed 0.

1.

4. The weak harmonic detection method based on the Chen system according to claim 1, characterized in that, In step 4, the system equations of the Chen system are solved using the fourth-order Runge-Kutta method.

5. The weak harmonic detection method based on the Chen system according to claim 1, characterized in that, In step 5, the system may experience a change in the fixed point position or a change in the attractor distribution. This could be due to a change in the quadrant in which the phase trajectory is located, or a change in the fixed point coordinates of the system's state variables in a steady state, which means that the system's output is out of phase.

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