A weak harmonic detection method based on coupled chaotic system array

Abstract

The present application belongs to the technical field of signal processing and detection, and specifically relates to a weak harmonic detection method based on a coupled chaotic system array, which couples the displacement and nonlinear restoring force of a Duffing system with the displacement and damping force of a Van der pol system to form a new coupled chaotic system for signal detection. The critical driving force of the coupled chaotic system is calculated by using a bifurcation diagram and a bisection method, and then the phase response interval is calculated. According to the size of the phase response interval, the coupled chaotic system array is designed, the to-be-detected signal is input, each subsystem in the array is selected, and it is judged whether the system undergoes a phase transition. If the signal makes the coupled chaotic system jump from a critical chaotic state to a large periodic state, it is indicated that the to-be-detected frequency signal exists. At this time, the amplitude of the harmonic is determined in the manner that the driving force amplitude is gradually reduced by a step size, and it is judged whether the system enters a chaotic state, so as to provide sensitivity and precision of weak harmonic detection.

Description

Technical Field

[0001] This invention belongs to the technical field of signal processing and detection, specifically a method for detecting weak harmonics based on a coupled chaotic system array. 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] Traditional time-frequency domain weak signal detection methods rely on a series of filtering algorithms to improve the signal-to-noise ratio (SNR), with the lowest possible SNR being only -10 dB. Utilizing chaotic systems to estimate weak signals offers superior accuracy and noise immunity compared to traditional time-frequency domain weak signal detection methods.

[0004] CN104965123A (2015) discloses a novel method for the detection and estimation of harmonics and interharmonics in power systems based on chaotic oscillators. The advantages of this method are twofold: first, it integrates variable-scale methods and dual-coupled intermittent chaotic oscillator array methods, proposing a variable-scale dual-coupled intermittent chaotic oscillator. This method possesses high frequency resolution of the signal under test and strong anti-noise interference capability, enabling synchronous and effective detection and high-precision frequency estimation of harmonics and interharmonics under low signal-to-noise ratio conditions; second, it is based on the synchronous estimation of sinusoidal signal amplitude and phase using a phase-jump type dual-coupled chaotic oscillator, achieving high-precision amplitude and phase estimation of harmonics and interharmonics under strong noise interference. However, the effective detection signal-to-noise ratio of the signal processing is -36dB. Although the sensitivity and accuracy are significantly improved compared to traditional algorithms, it still cannot meet the higher precision requirements for detecting weak harmonic signals in harsh noise environments. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a weak harmonic detection method based on a coupled chaotic system array, which solves the problem that the existing technology cannot effectively detect the signal-to-noise ratio, and the sensitivity and accuracy cannot meet the requirements for weak harmonic signal detection.

[0006] This invention is implemented as follows:

[0007] A method for detecting weak harmonics based on a coupled chaotic system array, comprising the following steps:

[0008] Step 1: Set the parameters k, a, b of the Duffing system;

[0009] Step 2: Set the parameters u and ε of the Van der pol system;

[0010] Step 3: Determine the coupling parameter p, and perform system coupling on the Duffing system and Van der Pohl system from Step 1 to obtain a coupled chaotic system;

[0011] Step 4: Determine the critical driving force f of the coupled chaotic system using bifurcation diagrams and the bisection method. d ;

[0012] Step 5: Calculate the phase response interval of the coupled chaotic system;

[0013] Step 6: Design a coupled chaotic system array, and determine the phase parameters of the chaotic system array based on the size of the phase response interval.

[0014] Step 7: Input the signal to be detected;

[0015] Step 8: Select the array subsystem, apply the driving force and the signal to be detected, and draw the phase diagram;

[0016] Step 9: Determine whether a phase transition has occurred in the coupled chaotic system. If no phase transition has occurred, return to step 8; if a phase transition has occurred, proceed to step 10.

[0017] Step 10: Decrease the driving force amplitude f by step size, recalculate the system state, and draw the system phase diagram;

[0018] Step 11: Determine whether the coupled chaotic system has re-entered the chaotic state. If it has not re-entered the chaotic state, return to step 10. If it has re-entered the chaotic state, proceed to step 12.

[0019] Step 12: The ratio of the difference in the amplitude reduction of the system driving force to the scaling factor of the input signal is the amplitude of the detected harmonic signal;

[0020] Step 13: The amplitude calculation for the detected frequency signal has been completed, and the calculation process ends.

[0021] Furthermore, in step 1, the characteristic equation of motion of the Duffing system is:

[0022]

[0023] Where x is the position, k is the damping coefficient, and -ax+bx 3 For nonlinear restoring force, a and b are nonlinear restoring force coefficients, f cosωt is the external linear driving force of the system, f is the driving force amplitude, and ω is the driving force angular frequency.

[0024] Furthermore, in step 2, the characteristic equation of motion of the Van der Pohl system is:

[0025]

[0026] Where u is the damping coefficient and ε is the stiffness coefficient.

[0027] Furthermore, in step 3, the nonlinear restoring force of the Duffing system is coupled with the displacement of the Van der Pohl system, and the damping force of the Van der Pohl system is coupled with the displacement of the Duffing system to form a new coupled chaotic system, whose motion state characteristic equation is:

[0028]

[0029] Where p is the coupling strength.

[0030] Furthermore, the bifurcation diagram is a graph that reflects the change in the number of stable points of the system as the parameters of the nonlinear system change. By observing the shape of the bifurcation diagram, the approximate range of the critical driving force amplitude of the coupled chaotic system can be determined, and a more accurate amplitude can be obtained in the vicinity using the bisection method. The specific steps are as follows:

[0031] Step 4-1: Draw the bifurcation diagram of the displacement and velocity of the coupled chaotic system as a function of the driving force amplitude f;

[0032] Step 4-2: Obtain the approximate range of the driving force amplitude based on the obtained image;

[0033] Step 4-3: Set the point to the left of the critical driving force amplitude as m, and the point to the right as n;

[0034] Step 4-4: Assign the driving force amplitude to (m+n) / 2, substitute it into the coupled chaotic system, and draw the phase diagram;

[0035] Steps 4-5: Determine the system state. If the system is in a chaotic state, let m = (m+n) / 2; if the system is in a large-cycle state, let n = (m+n) / 2.

[0036] Step 4-6: Determine whether the obtained driving force amplitude meets the required detection accuracy. If it does not meet the requirement, return to step 4-4; if it does meet the requirement, end the iteration.

[0037] Further, in step 5, the phase response interval of the coupled chaotic system is calculated, assuming the initial phase of the driving force is... The initial phase of the signal to be detected is θ, and the amplitude of the signal to be detected is A. The driving force and the signal to be detected are sinusoidally superimposed:

[0038]

[0039] Where ξ is a relatively small value, it has little effect on the value of the critical driving force. If the system satisfies the following equation at this time, the weak periodic signal of the input Acos(ωt+θ) can be detected:

[0040]

[0041] Among them, f d Let f be the critical driving force amplitude, and let f be the driving force amplitude. The phase difference satisfies:

[0042]

[0043] Calculate ψ to obtain the phase response interval of the coupled chaotic system as (-ψ, ψ).

[0044] Furthermore, in step 6, the coupled chaotic system array is...

[0045]

[0046] in, For phase parameters, subscript " i The number of "" is sufficient to enable the phase response range of the coupled system array to cover the range from 0° to 360°.

[0047] Furthermore, in step 8, starting from the first subsystem of the coupled chaotic system array, the driving force and the signal to be detected are applied simultaneously, the system phase diagram is drawn, and each subsystem is used for detection one by one.

[0048] Compared with the prior art, the beneficial effects of this invention are as follows:

[0049] This invention couples the displacement and nonlinear restoring force of the Duffing system with the displacement and damping force of the Van der Pohl system to form a new coupled chaotic system for signal detection. The critical driving force of the coupled chaotic system is calculated using a bifurcation diagram and a bisection method. Then, the phase response interval is calculated. Based on the size of the phase response interval, a coupled chaotic system array is designed. The input signal to be detected is used, and each subsystem in the array is selected. It is determined whether a phase transition occurs. If the signal causes the coupled chaotic system to transition from a critical chaotic state to a large-period state, it indicates the presence of the frequency signal to be detected. The amplitude of the harmonic is determined by gradually decreasing the driving force amplitude in increments of a certain step size to determine whether the system has entered a chaotic state, thereby improving the detection accuracy and sensitivity. Attached Figure Description

[0050] Figure 1 A flowchart of the method provided in an embodiment of the present invention;

[0051] Figure 2 A bifurcation diagram of the displacement x of the coupled system as a function of the driving force amplitude f, provided in an embodiment of the present invention;

[0052] Figure 3 A bifurcation diagram of the velocity x of the coupling system as a function of the driving force amplitude f, provided in an embodiment of the present invention;

[0053] Figure 4 A chaotic critical state phase diagram of a coupled system provided in an embodiment of the present invention;

[0054] Figure 5 The large-period phase diagram of the coupled system provided in the embodiments of the present invention. Detailed Implementation

[0055] 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.

[0056] See Figure 1 This invention discloses a weak harmonic detection method based on a coupled chaotic system array, the method comprising the following steps:

[0057] Step 1: Set the parameters k, a, b of the Duffing system;

[0058] Including: The characteristic equation of motion of the Duffing system is

[0059]

[0060] Where x is the position, k is the damping coefficient, and -ax+bx 3 For nonlinear restoring force, a and b are nonlinear restoring force coefficients, f cosωt is the external linear driving force of the system, f is the driving force amplitude, and ω is the driving force angular frequency.

[0061] Step 2: Set the parameters u, ε of the Van der pol system;

[0062] Including: The characteristic equation of motion of the Van der Pohl system is

[0063]

[0064] Where u is the damping coefficient, ε is the stiffness coefficient, and the other parameters have the same meaning as in formula (1).

[0065] Step 3: Determine the coupling parameter p and perform system coupling;

[0066] This includes coupling the nonlinear restoring force of the Duffing system with the displacement of the Vanderpol system, and coupling the damping force of the Vanderpol system with the displacement of the Duffing system to form a new coupled chaotic system, whose characteristic equation of motion is:

[0067]

[0068] Where k, a, b, u, ε, f, ω have the same meaning as in formulas (1) and (2), and p is the coupling strength.

[0069] Step 4: Determine the critical driving force f of the coupled chaotic system using bifurcation diagrams and the bisection method. d ;

[0070] This includes: a bifurcation diagram, which reflects the change in the number of stable points of a nonlinear system as the parameters change. By observing the shape of the bifurcation diagram, the approximate range of the critical driving force amplitude of the coupled chaotic system can be determined, and then a more accurate amplitude can be obtained in the vicinity using the bisection method.

[0071] Step 5: Calculate the phase response interval of the coupled chaotic system;

[0072] This includes: calculating the phase response interval of a coupled chaotic system, assuming the initial phase of the driving force is... The initial phase of the signal to be detected is θ, and the amplitude of the signal to be detected is A. The driving force and the signal to be detected are sinusoidally superimposed:

[0073]

[0074] Where ξ is a relatively small value, its influence on the critical driving force is negligible. If the system can detect the weak periodic signal Acos(ωt+θ) at this point, it must satisfy the following condition:

[0075]

[0076] Among them, f d The critical driving force amplitude is defined by f and A, which have the same meanings as above. Their magnitudes depend on the set system detection accuracy. At this point, the phase difference should satisfy the following conditions.

[0077]

[0078] Since all parameters are known, ψ can be calculated. Therefore, the phase response interval of the coupled chaotic system is (-ψ, ψ).

[0079] Step 6: Design a coupled chaotic system array, and determine the phase parameters of the chaotic system array based on the size of the phase response interval.

[0080] Including: the designed coupled chaotic system array is

[0081]

[0082] in, For phase parameters, subscript " iThe number of "" needs to be sufficient to ensure that the phase response range of the coupled system array can cover the range from 0° to 360°.

[0083] Step 7: Input the signal to be detected;

[0084] Step 8: Select the array subsystem, apply the driving force and the signal to be detected, and draw the phase diagram;

[0085] This includes: after setting up the coupled chaotic system array used for the detection signal, starting from the first subsystem of the coupled chaotic system array, simultaneously applying the driving force and the signal to be detected, and drawing the system phase diagram. Detecting each subsystem one by one ensures that signals with various initial phases can be detected.

[0086] Step 9: Determine whether a phase transition has occurred in the coupled chaotic system. If no phase transition has occurred, return to step 8; if a phase transition has occurred, proceed to step 10.

[0087] Step 10: Decrease the driving force amplitude f by step size, recalculate the system state, and draw the system phase diagram;

[0088] Step 11: Determine whether the system has re-entered the chaotic state. If it has not re-entered the chaotic state, return to step 10. If it has re-entered the chaotic state, proceed to step 12.

[0089] Step 12: The ratio of the difference in the amplitude reduction of the system driving force to the scaling factor of the input signal is the amplitude of the detected harmonic signal;

[0090] Step 13: The amplitude calculation for the detected frequency signal has been completed, and the calculation process ends.

[0091] Example 1

[0092] For the characteristic equation of motion state of the coupled chaotic system described by formula (3), take k = 0.5, a = 1, b = 1, u = 5, ε = 1, p = 0.5. At this time, all system parameters have been set. Draw the bifurcation diagrams of the displacement and velocity of the coupled chaotic system as a function of the driving force amplitude f, as shown below. Figure 2 , Figure 3 As shown, the approximate range of the driving force amplitude obtained from the obtained image is between 12 and 13. Following the bisection method described at the beginning of step 4-3, it can be found that the system is in a chaotic state when f = 12.563100192, and the system phase diagram at this time is as follows. Figure 4 As shown, based on this, the weak signal 10 -9 The cosωt input is given to the system, and the system phase diagram is observed as follows: Figure 5 As shown, the system has now entered a large cycle state.

[0093] This section uses weak harmonic signals from the power system.

[0094]

[0095] The target signal is detected, where ω = 2π × 50Hz. To verify the sensitivity and accuracy of the algorithm, x(t) is subjected to 10... -8 Magnification. Mix the signal with Gaussian white noise to achieve an SNR of -60dB, according to...

[0096]

[0097] The intensity D of Gaussian white noise can be determined.

[0098] After the coupled system array enters the large periodic state, at 10 -9 To reduce the driving force by step size and recalculate the phase trajectory, when the coupled system array re-enters the chaotic critical state, the difference between the current driving force and the initial driving force is increased by 10. 8 By amplifying the signal by a factor of 1, the amplitude of the harmonic signal can be obtained. The results are shown in Table 1 below.

[0099] Table 1

[0100]

[0101] The above description is merely 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 a coupled chaotic system array, characterized in that, The method includes the following steps: Step 1: Set the parameters k, a, b of the Duffing system; Step 2: Set the parameters u and ε of the Van der pol system; Step 3: Determine the coupling parameter p, and couple the Duffing system and Van der Pohl system from Step 1 to obtain a coupled chaotic system. This includes coupling the nonlinear restoring force of the Duffing system with the displacement of the Van der Pohl system, and coupling the damping force of the Van der Pohl system with the displacement of the Duffing system, forming a new coupled chaotic system. Its characteristic equation of motion is: ， Where p is the coupling strength; Step 4: Determine the critical driving force f of the coupled chaotic system using bifurcation diagrams and the bisection method. d ; Step 5: Calculate the phase response interval of the coupled chaotic system. Let the initial phase of the driving force be φ, the initial phase of the signal to be detected be θ, and the amplitude of the signal to be detected be A. Perform sinusoidal superposition of the driving force and the signal to be detected: ， Where ξ is a relatively small value, it has little effect on the value of the critical driving force. If the system satisfies the following equation at this time, the weak periodic signal of the input Acos(ωt+θ) can be detected: ， Among them, f d Let f be the critical driving force amplitude, and let f be the driving force amplitude. The phase difference satisfies: ， Calculate ψ to obtain the phase response interval of the coupled chaotic system as (-ψ, ψ); Step 6: Design a coupled chaotic system array. Based on the size of the phase response interval, determine the phase parameter φ of the chaotic system array. i The coupled chaotic system array is ， Where, φ i For phase parameters, subscript " i The number of "" is such that the phase response range of the coupled system array can cover the range from 0° to 360°; Step 7: Input the signal to be detected; Step 8: Select the array subsystem, apply the driving force and the signal to be detected, and draw the phase diagram; Step 9: Determine whether a phase transition has occurred in the coupled chaotic system. If no phase transition has occurred, return to step 8; if a phase transition has occurred, proceed to step 10. Step 10: Decrease the driving force amplitude f by step size, recalculate the system state, and draw the system phase diagram; Step 11: Determine whether the coupled chaotic system has re-entered the chaotic state. If it has not re-entered the chaotic state, return to step 10. If it has re-entered the chaotic state, proceed to step 12. Step 12: The ratio of the difference in the amplitude reduction of the system driving force to the scaling factor of the input signal is the amplitude of the detected harmonic signal; Step 13: The amplitude calculation for the detected frequency signal has been completed, and the calculation process ends.

2. The weak harmonic detection method based on a coupled chaotic system array according to claim 1, characterized in that, In step 1, the characteristic equation of motion of the Duffing system is: ， Where x is the position, k is the damping coefficient, and -ax+bx 3 For nonlinear restoring force, a and b are nonlinear restoring force coefficients, f cosωt is the external linear driving force of the system, f is the driving force amplitude, and ω is the driving force angular frequency.

3. The weak harmonic detection method based on a coupled chaotic system array according to claim 2, characterized in that, In step 2, the characteristic equation of motion of the Van der Pohl system is: ， Where u is the damping coefficient and ε is the stiffness coefficient.

4. The weak harmonic detection method based on a coupled chaotic system array according to claim 1, characterized in that, The bifurcation diagram is a graph that reflects the change in the number of stable points of the system as the parameters of the nonlinear system change. By observing the shape of the bifurcation diagram, the approximate range of the critical driving force amplitude of the coupled chaotic system can be determined, and a more accurate amplitude can be obtained in the vicinity using the bisection method. The specific steps are as follows: Step 4-1: Draw the bifurcation diagram of the displacement and velocity of the coupled chaotic system as a function of the driving force amplitude f; Step 4-2: Obtain the approximate range of the driving force amplitude based on the obtained image; Step 4-3: Take a point to the left of the critical driving force amplitude as m, and a point to the right as n; Step 4-4: Assign the driving force amplitude to (m+n) / 2, substitute it into the coupled chaotic system, and draw the phase diagram; Steps 4-5: Determine the system state. If the system is in a chaotic state, let m = (m + n) / 2; if the system is in a large-cycle state, let n = (m + n) / 2. Step 4-6: Determine whether the obtained driving force amplitude meets the required detection accuracy. If it does not meet the requirement, return to step 4-4; if it does meet the requirement, end the iteration.

5. The weak harmonic detection method based on a coupled chaotic system array according to claim 1, characterized in that, In step 8, starting from the first subsystem of the coupled chaotic system array, the driving force and the signal to be detected are applied simultaneously, the system phase diagram is drawn, and each subsystem is used for detection one by one.

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