A weak signal detection method based on heterodyne Duffing oscillators

Abstract

This invention discloses a weak signal detection method based on a Duffing oscillator with different frequencies, belonging to the field of weak signal processing. The method is as follows: By distinguishing between the reference frequency and the frequency of the intrinsic dynamic signal of the Duffing oscillator, the system's reference frequency and the amplitude and frequency of the intrinsic dynamic signal are set to obtain the expression for the Duffing oscillator with different frequencies, thus constructing a signal detection model for the Duffing oscillator with different frequencies. The noisy, weak-periodic signal to be measured is mixed and filtered with a reference signal of known frequency to obtain the model input signal. This input signal is then input into the Duffing oscillator model, and the phase trajectory and waveform of the model are output, thus constructing a weak signal detection system for the Duffing oscillator with different frequencies. The reference signal frequency is gradually increased, and the switching of the system state is determined based on the phase trajectory diagram and the amplitude method. The frequency of the reference signal under the critical state of the system is recorded. Based on the relationship between the reference frequency and the frequency of the signal to be measured, the estimated value of the frequency of the signal to be measured is calculated, thus achieving weak signal detection.

Description

Technical Field

[0001] This invention relates to a method for detecting weak signals, and more particularly to a method for detecting weak signals using a Duffing oscillator weak signal detection model, which belongs to the field of weak signal processing. Background Technology

[0002] Since the 1970s, when American scholar Feigenbaum established the universality principle of chaos, pushing qualitative analysis of chaos theory towards quantitative calculation, chaos theory and nonlinear systems have gradually entered the field of application. In 1992, Birx first proposed using the Duffing oscillator for weak signal detection. Subsequently, Wang Guanyu and others from Zhejiang University analyzed the basic principle of signal detection using the Duffing oscillator and improved the Duffing equation to detect periodic signals of different frequencies. Since then, chaos detection technology has attracted the attention of many scholars.

[0003] The research directions of weak signal detection based on chaos are mainly divided into the following three categories: first, extracting useful signals in the background of chaotic noise by predicting chaotic models; second, using chaotic characteristics for high-precision "chaotic" measurement; and third, using the initial value sensitivity and noise immunity of chaotic systems, and using the phase changes of chaotic oscillators as the basis for weak signal detection. The third category is also the current research hotspot in chaotic detection technology. However, because the extended Duffing oscillator signal detection system has an intermittent chaotic state, and traditional chaotic phase discrimination methods mostly use the average motion state of the system over a period of time as the discrimination criterion, Duffing oscillators in an intermittent chaotic state are mostly classified as periodic motion. This leads to the problem of low accuracy and efficiency in the existing chaotic phase discrimination methods when performing phase discrimination and determining the critical threshold. Summary of the Invention

[0004] The main objective of this invention is to provide a weak signal detection method based on a Duffing oscillator with different frequencies. This method distinguishes between the reference frequency of the Duffing oscillator and the frequency of the intrinsic dynamic signal, thus constructing a weak signal detection model based on the Duffing oscillator. By adjusting the reference signal frequency, the Duffing oscillator switches states, and the frequency of the reference signal in the system's critical state is recorded. In other words, the frequency of the weak signal to be measured is calculated based on the weak signal detection model. This invention can achieve frequency detection of weak periodic signals under low signal-to-noise ratio conditions, and has the advantages of high detection accuracy, adjustable frequency resolution, and real-time performance.

[0005] The objective of this invention is achieved through the following technical solution:

[0006] This invention discloses a weak signal detection method based on a different-frequency Duffing oscillator. By distinguishing between the reference frequency and the frequency of the internal driving force signal of the Duffing oscillator, and setting the reference frequency and the amplitude and frequency of the internal driving force of the Duffing oscillator system, a different-frequency Duffing oscillator expression is obtained. A different-frequency Duffing oscillator signal detection model is constructed based on this expression. The noisy, weak-periodic signal to be measured is mixed and filtered with a reference signal of known frequency to obtain the model input signal. This input signal is then fed into the different-frequency Duffing oscillator model, and the phase trajectory and waveform of the model are output, thus constructing a different-frequency Duffing oscillator weak signal detection system. The reference signal frequency is gradually increased to enable the different-frequency Duffing oscillator weak signal detection system to switch between small-period and large-period states. The switching of the system state is determined based on the phase trajectory diagram and the amplitude method. The frequency of the reference signal in the critical state of the system is recorded. Based on the relationship between the reference frequency and the frequency of the signal to be measured, the estimated value of the frequency of the signal to be measured is calculated, thus achieving weak signal detection based on the different-frequency Duffing oscillator.

[0007] This invention discloses a weak signal detection method based on a heterodyne Duffing oscillator, comprising the following steps:

[0008] Step 1: By distinguishing between the reference frequency of the Duffing oscillator and the frequency of the intrinsic dynamic signal, the expression for the heterodyne Duffing oscillator is obtained, and a weak signal detection model based on the heterodyne Duffing oscillator is constructed. Based on this model, the amplitude F = Fint of the intrinsic dynamic signal is taken. c Select the reference frequency ω r The internal dynamic frequency ω = Rω r A weak signal detection system based on a heterodyne Duffing oscillator was constructed. The F... c Based on R and ω rThe bifurcation diagram of the selected heterodyne Duffing oscillator is determined. At this point, the weak signal detection system is in a critical state. If a weak periodic signal with predetermined frequencies Mω and Nω is added to the weak signal detection system, the heterodyne Duffing oscillator system will change from small-period motion to large-scale periodic motion or vice versa. The predetermined frequencies Mω and Nω are determined by the following method: A weak periodic signal of known frequency is input into the selected heterodyne Duffing oscillator system, given the amplitude F and frequency ω of the internal driving force signal. The critical state of the heterodyne Duffing oscillator system is determined by observing the phase trajectory. When the heterodyne Duffing oscillator system switches from a small-period state to a large-scale periodic state, the frequency of the weak periodic signal is set to Mω; when the heterodyne Duffing oscillator system is in a critical state switching from a large-scale periodic state to a small-period state, the frequency of the weak periodic signal is set to Nω.

[0009] The expression for a Holmes-type Duffing oscillator is as follows:

[0010]

[0011] In the formula, x is displacement, t is time, k is damping ratio, and -x+x 3 Fcos(ωt) is the nonlinear restoring force, and Fcos(ωt) is the driving force signal within the period.

[0012] By distinguishing between the reference frequency and the intrinsic dynamic signal frequency of the Duffing oscillator, the expression for the heterodyne Duffing oscillator is obtained as follows:

[0013]

[0014] In the formula, ω r Let ω be the reference frequency of the Duffing oscillator, and ω = Rω. r The frequency of the internal driving force signal.

[0015] Like the Holmes-type Duffing oscillator, the hetero-frequency Duffing oscillator has a wide range of nonlinear dynamic characteristics.

[0016] Let ω = Rω r F = F c Furthermore, the weak periodic signal to be measured and noise are added to the heterodyne Duffing oscillator model to obtain the expression for the heterodyne Duffing oscillator weak signal detection model:

[0017]

[0018] Let F = F cA reference frequency is selected to build a different frequency Duffing oscillator model. At this time, the model is in a critical state. If a weak periodic signal of a specific frequency is added to the model, the state of the different frequency Duffing oscillator model changes from small periodic motion to large-scale periodic motion.

[0019] Step 2: Compare the noisy, weakly periodic signal to be tested with a known frequency ω. a The reference signal is mixed to obtain a signal frequency that is the sum and difference between the frequency of the signal to be measured and the frequency of the reference signal. A low-pass filter is used, with the cutoff frequency set to the reference signal frequency, to filter out signals with frequencies higher than the reference signal frequency. This results in a signal with a frequency difference between the reference signal and the signal to be measured, which is then input into the heterodyne Duffing oscillator signal detection model. The model's phase trajectory and waveform are output, thus constructing a heterodyne Duffing oscillator weak signal detection system. At this point, the heterodyne Duffing oscillator weak signal detection system is in a critical state of transition between small-scale periodic motion and large-scale periodic motion.

[0020] Because the dynamic characteristics of the weak signal detection system using a different frequency Duffing oscillator change when the reference frequency changes, the frequency of the input signal is controlled by setting a reference signal to estimate the frequency of the signal under test.

[0021] The noisy, weakly periodic signal to be measured is mixed with a reference signal of known frequency to obtain the signal frequency, which is the sum and difference of the frequencies of the measured signal and the reference signal. A low-pass filter is then used, with the cutoff frequency set to the reference signal frequency, to filter out signals with frequencies higher than the reference signal frequency, thus obtaining the frequency ω of the input signal. x The frequency difference between the reference signal and the signal under test is input into the weak signal detection system of the Duffing oscillator at different frequencies.

[0022] Step 3: Mix and filter the noisy, weakly periodic signal to be tested with a reference signal of known frequency to obtain the model input signal. When the frequency ω of the input signal... x When the frequency is equal to Mω, the Duffing oscillator system of different frequencies is in a critical state of transitioning from a small-scale periodic state to a large-scale periodic state; when the frequency ω of the input signal is equal to Mω, the system is in a critical state of transitioning from a small-scale periodic state to a large-scale periodic state. x When the value equals Nω, the Duffing oscillator system of different frequencies is in a critical state of switching from a large-scale periodic state to a small-scale periodic state.

[0023] By adjusting the frequency of the reference signal, without affecting the amplitude and frequency of the driving force signal within the heterodyne Duffing oscillator system, only the input signal after the weak periodic signal to be tested and the reference signal are mixed and filtered, so that the state of the heterodyne Duffing oscillator system is switched. The state switching refers to the transition of the heterodyne Duffing oscillator system from a small periodic state to a large periodic state or from a large periodic state to a small periodic state.

[0024] Step 4: Based on the phase plane trajectory and time-domain waveform output by the heterodyne Duffing oscillator system, perform phase state determination on the heterodyne Duffing oscillator system.

[0025] This section describes the phase plane trajectory diagrams of a heterodyne Duffing oscillator system during both small-period and large-scale periodic motions. When F ≤ Fc, the heterodyne Duffing oscillator initially transitions to the vicinity of the outer orbit under the influence of the internal driving force signal. Subsequently, due to insufficient driving force strength, it transitions back to the inner orbit. After a period of time, the heterodyne Duffing oscillator performs stable small-period motions within the inner orbit. The closer F is to Fc, the longer the heterodyne Duffing oscillator spends near the outer orbit. However, as long as F does not exceed a critical threshold, the driving force F only supports a finite number of large-scale periodic motions. When F > Fc, driven by the internal driving force signal, the heterodyne Duffing oscillator performs large-scale periodic motions on the outer orbit after starting from the origin. Therefore, the state of the heterodyne Duffing oscillator system can be determined by analyzing the phase plane trajectory diagrams output by the system.

[0026] This section examines the output time-domain waveforms of a Duffing oscillator operating in both short-period and large-scale periodic motion. Since the phase trajectory and time sequence diagrams of the Duffing oscillator in its short-period and large-scale periodic states differ significantly, and the transition between these states is direct without intermediate states, even using the amplitude judgment method can quickly and accurately determine the phase state of the Duffing oscillator without introducing detection errors due to misjudgment. Amplitude judgment method: If the Duffing oscillator system is undergoing periodic motion, the output is a constant-amplitude signal with a relatively large amplitude; if the system is undergoing chaotic motion, the output signal peak value is relatively small and fluctuates significantly. Therefore, by comparing the amplitude of the peak values ​​of the Duffing oscillator system's output signal, if multiple consecutive peak values ​​exceed the amplitude threshold, the output is determined to be a periodic signal; otherwise, it is a chaotic signal.

[0027] Phase state discrimination is performed on the Duffing oscillator system based on the phase plane trajectory and time-domain waveform output by the system.

[0028] Step 5: Based on the phase state discrimination results of the different frequency Duffing oscillator system in Step 4, record the frequencies ω1 and ω2 of the reference signal in the critical state of the different frequency Duffing oscillator system.

[0029] Because the phase trajectory diagrams and timing diagrams of the heterodyne Duffing oscillator system in small-scale and large-scale periodic states differ significantly, and the transition between the two states is a direct jump without any intermediate transition states, when the frequency of the reference signal is gradually changed, the reference signal frequency ω is recorded when the state discrimination result of the heterodyne Duffing oscillator system changes from a small-scale periodic state to a large-scale periodic state. a =ω1; When the state discrimination result of the heterodyne Duffing oscillator system changes from a large-scale periodic state to a small-scale periodic state, record the reference signal frequency ω at this time. a =ω2.

[0030] Step Six: When the Duffing oscillator system is in a critical state, the frequency ω of the input signal... x There is a relationship with the frequency ω of the internal dynamic signal, that is, when the frequency ω of the input signal... x When the frequency is equal to Mω, the Duffing oscillator system of different frequencies is in a critical state of transitioning from a small-scale periodic state to a large-scale periodic state; when the frequency ω of the input signal is equal to Mω, the system is in a critical state of transitioning from a small-scale periodic state to a large-scale periodic state. x When the frequency equals Nω, the heterodyne Duffing oscillator system is in a critical state transitioning from a large-scale periodic state to a small-scale periodic state. Based on the relationship between the reference frequency and the frequency of the signal under test, the frequency ω of the heterodyne Duffing oscillator input signal at the time of state transition is calculated. x That is, weak signal detection is achieved based on the Duffing oscillator of different frequencies.

[0031] Since the input signal is the result of mixing and filtering the signal to be measured and the reference signal, the frequency ω of the input signal... x Equal to the reference signal frequency ω a Subtract the frequency ω0 of the weak periodic signal to be measured, i.e., ω x =ω a -ω0. Based on the relationship between the reference frequency and the frequency of the signal under test, the estimated value of the frequency ω0 of the weak periodic signal under test is calculated, that is, weak signal detection is realized based on the heterodyne Duffing oscillator system.

[0032] Based on the above relationships and the frequencies ω1, ω2, and ω of the reference signal obtained in step five under the critical state of the system, x =Mω=ω a -ω0, further, we can obtain,

[0033]

[0034] According to formula (4), the estimated values ​​of the frequency ω0 of the signal to be tested when the frequency of the reference signal is ω1 and ω2 are calculated respectively. The average of the estimated values ​​is used to obtain the final estimated frequency of the weak periodic signal to be tested, that is, weak signal detection is realized based on the heterodyne Duffing oscillator system.

[0035] Beneficial effects:

[0036] 1. This invention discloses a weak signal detection method based on a different-frequency Duffing oscillator. The method distinguishes between the reference frequency of the Duffing oscillator and the frequency of the internal dynamic signal to construct a weak signal detection system based on a different-frequency Duffing oscillator. By adjusting the reference signal frequency, the system achieves state switching. An amplitude judgment method is used to determine the phase state of the different-frequency Duffing oscillator, and the frequency of the reference signal under the critical state of the system is recorded. Based on the relationship between the reference frequency and the frequency of the signal to be measured, the frequency of the weak signal to be measured is calculated.

[0037] 2. This invention discloses a weak signal detection method based on a Duffing oscillator with different frequencies. Since the phase trajectory and time series diagrams of the Duffing oscillator in its small-scale and large-scale periodic states differ significantly, and the transition between these two states is direct without intermediate states, even using the amplitude judgment method, the phase state of the Duffing oscillator can be quickly and accurately determined without detection errors caused by phase misjudgment. Therefore, compared to the traditional Duffing oscillator model, this model avoids the occurrence of intermittent chaotic states, making the system phase state determination simpler and more accurate, and preventing detection errors caused by phase misjudgment.

[0038] 3. This invention discloses a weak signal detection method based on a heterodyne Duffing oscillator. Compared to the extended Duffing oscillator weak signal detection method with a frequency detection error of 0.03 ω, the heterodyne Duffing oscillator-based weak signal detection method uses the signal to be measured and a reference signal mixed and filtered as the system input signal. Since the frequency of the reference signal used for mixing and filtering with the weak periodic signal to be measured is adjustable, the signal detection method based on the heterodyne Duffing oscillator has an adjustable frequency resolution, and the frequency resolution is less than or equal to the accuracy of the frequency detection ratio threshold of 0.001 ω. r This significantly improves the frequency detection accuracy of the Duffing oscillator for signals. Attached Figure Description

[0039] Figure 1 This invention discloses a flowchart of a weak signal detection method based on a heterodyne Duffing oscillator;

[0040] Figure 2 Simulation model of a Duffing oscillator signal detection system with different frequencies;

[0041] Figure 3 Simulation model of mixing and filtering between the signal under test and the reference signal;

[0042] Figure 4Reference signal frequency ω a The output signal of the Duffing oscillator at a different frequency around 320MHz; where... Figure 4 a) is ω a At 320MHz, the phase plane trajectory of the Duffing oscillator. Figure 4 b) is ω a The time-domain waveform of the Duffing oscillator at 320MHz. Figure 4 c) is ω a At 321MHz, the phase plane trajectory of the Duffing oscillator. Figure 4 d) is ω a Time-domain waveform of the Duffing oscillator at 321MHz;

[0043] Figure 5 Reference signal frequency ω a The output signal of the Duffing oscillator with different frequencies around 595MHz; where... Figure 5 a) is ω a At 595MHz, the phase plane trajectory of the Duffing oscillator. Figure 5 b) is ω a The time-domain waveform of the Duffing oscillator at 595MHz. Figure 5 c) is ω a At 596MHz, the phase plane trajectory of the Duffing oscillator. Figure 5 d) is ω a The time-domain waveform of the Duffing oscillator at 596MHz. Detailed Implementation

[0044] To better illustrate the purpose and advantages of the present invention, the invention will be further described below with reference to the accompanying drawings.

[0045] Example 1

[0046] To verify the feasibility of the method, a sine wave signal with a frequency of 200MHz and an amplitude of 0.01 was selected and input into the heterodyne Duffing oscillator system for signal detection under the condition of -10dB signal-to-noise ratio and a sampling rate of 1GHz.

[0047] like Figure 1 As shown in the figure, this example discloses a weak signal detection method based on a different frequency Duffing oscillator. The specific implementation steps are as follows:

[0048] Step 1: Construct a reference frequency ω r A Duffing oscillator signal detection system with different frequencies.

[0049] Choose R = 2, that is, let ω = 2ω rBased on the bifurcation diagram of the heterodyne Duffing oscillator at R=2, it was found that the heterodyne Duffing oscillator exhibits significant phase changes around F=0.8, 1.2, and 3.5, which can be used as a basis for signal detection. However, considering that a chaotic oscillator always undergoes a critical chaotic state transition, whether from a chaotic state to a periodic state or from a periodic state to a chaotic state, the critical value F of the heterodyne Duffing oscillator was selected. c =3.53.

[0050] F = F c =3.53, and by adding the weak periodic signal to be measured and noise to the heterodyne Duffing oscillator system, the expression for the heterodyne Duffing oscillator weak signal detection system can be obtained:

[0051]

[0052] Let F = F c A Duffing oscillator system with different frequencies is built by selecting a reference frequency. At this time, the system is in a critical state. If a weak periodic signal of a specific frequency is added to the system, the system will change from small-scale periodic motion to large-scale periodic motion.

[0053] According to expression (4), a heterodyne Duffing oscillator system with a reference frequency of 100MHz, an internal dynamic amplitude of 3.53, and a frequency twice the reference frequency (i.e., 200MHz) is constructed, as follows: Figure 2 As shown.

[0054] Step 2: Mix and filter the signal to be tested with the reference signal and then input it into the heterodyne Duffing oscillator signal detection system.

[0055] The noisy, weakly periodic signal to be tested is mixed with a reference signal of known frequency to obtain a signal frequency that is the sum and difference between the frequencies of the tested signal and the reference signal. A low-pass filter is then used, with the cutoff frequency set to the reference signal frequency, to filter out signals with frequencies higher than the reference signal frequency. The resulting signal, with a frequency difference between the reference signal and the tested signal, is then input into the heterodyne Duffing oscillator signal detection system.

[0056] A sine wave signal with an amplitude of 0.01 and a frequency of 200MHz is selected as the reference signal. After mixing with the signal to be measured, the signal is passed through a low-pass filter, and the cutoff frequency is set to the reference signal frequency. Figure 3 As shown, the filtered signal is input into the heterodyne Duffing oscillator signal detection system to ensure that the reference frequency remains unchanged and the system's dynamic characteristics are not affected.

[0057] Step 3: Adjust the reference signal frequency to enable the different frequency Duffing oscillator to transition from a small periodic state to a large periodic state and from a large periodic state to a small periodic state.

[0058] A weak periodic signal of known frequency is input into a Duffing oscillator system with an internal dynamic signal amplitude F = 3.53 and an internal dynamic signal frequency ω = 200MHz. The critical state of the Duffing oscillator system is determined by observing the phase trajectory. When the Duffing oscillator system switches from a small-scale periodic state to a large-scale periodic state, the frequency of the weak periodic signal is set to 1.21ω. When the Duffing oscillator system is in a critical state of switching from a large-scale periodic state to a small-scale periodic state, the frequency of the weak periodic signal is set to 3.95ω.

[0059] As the reference signal frequency is gradually increased, the frequency of the input signal obtained after mixing and filtering in step two will also gradually increase. When this input signal is fed into the heterodyne Duffing oscillator system, the state of the system will switch. Because the frequency accuracy of the reference signal is adjustable, compared to the 0.03ω frequency detection error of the extended Duffing oscillator weak signal detection method, the heterodyne Duffing oscillator-based signal detection method has adjustable frequency resolution, and this resolution is less than or equal to the accuracy of the frequency detection ratio threshold of 0.001ω. r Therefore, in the process of gradually increasing the reference signal frequency, an appropriate level of precision can be selected and the magnitude of each frequency change can be set according to actual needs.

[0060] By adjusting the frequency of the reference signal, without affecting the amplitude and frequency of the driving force signal within the different frequency Duffing oscillator system, only the input signal is adjusted, thus realizing the transformation of the Duffing oscillator system from a small periodic state to a large periodic state and from a large periodic state to a small periodic state.

[0061] Step 4: Based on the phase plane trajectory and time-domain waveform of the output of the different-frequency Duffing oscillator, perform phase state determination on the different-frequency Duffing oscillator.

[0062] The signal detection theory based on the Duffing oscillator system mainly utilizes the phase transitions of the Duffing oscillator system. Therefore, accurately determining the motion state of the Duffing oscillator system is the key to this type of method. Traditional chaotic phase state discrimination methods mainly include observation methods, analytical methods, neural network methods, and feature-based methods. Observation methods directly observe the phase plane trajectory diagram or time series diagram output by the system to determine the phase state, but these methods are easily affected by external factors such as noise, leading to misjudgments. Analytical methods first transform the system into a two-dimensional mapping, and then derive the existence of chaotic properties in the sense of the Smale horseshoe transform using the Shilnikov method or Melnikov method. However, this method is computationally complex, often failing to meet real-time requirements, and requires known system dynamic equations, thus having certain limitations. Neural network methods mainly utilize neural networks to extract features from the phase plane trajectory diagram or time series diagram under different phase states, and then perform classification and recognition. However, these methods often require a large number of samples for pre-training. Therefore, compared to the first three methods, feature-based methods are more widely used and are the main method adopted in this invention.

[0063] Regarding the distinction between the phase plane trajectories of a different-frequency Duffing oscillator during small-period and large-scale periodic motion: If the different-frequency Duffing oscillator initially jumps to the vicinity of the outer orbit under the influence of the internal driving force signal, and then jumps back to the inner orbit due to insufficient driving force strength, and after a period of time, the phase trajectory performs stable small-period motion on the inner orbit, then the different-frequency Duffing oscillator is in small-period motion. If, driven by the internal driving force signal, the different-frequency Duffing oscillator starts from the origin and gradually moves outward without returning to the middle position, eventually performing large-scale periodic motion on the outer orbit, then the different-frequency Duffing oscillator is in large-scale periodic motion.

[0064] This section examines the output time-domain waveforms of a Duffing oscillator operating in both short-period and large-scale periodic motion. Since the phase trajectory and time series diagrams of the Duffing oscillator in its short-period and large-scale periodic states differ significantly, and the transition between these states is direct without intermediate states, even the simplest amplitude judgment method can quickly and accurately determine the phase state of the Duffing oscillator without introducing detection errors due to misjudgment. Amplitude judgment method: If the Duffing oscillator system is undergoing periodic motion, the output is a constant-amplitude signal with a relatively large amplitude; if the system is undergoing chaotic motion, the output signal peak value is relatively small and varies considerably. Therefore, the peak values ​​of the Duffing oscillator system's output signal can be compared in amplitude. If multiple consecutive peak values ​​exceed the amplitude threshold, the output is considered a periodic signal; otherwise, it is a chaotic signal.

[0065] Based on the phase plane trajectory and time-domain waveform output by the heterodyne Duffing oscillator system, phase state discrimination was performed on the heterodyne Duffing oscillator system. It was found that when the reference signal frequency is 320MHz, the heterodyne Duffing oscillator system is in a small-period state, and when the reference signal frequency is 321MHz, the heterodyne Duffing oscillator system is in a large-period state. Figure 4 As shown. When the reference signal frequency is 565MHz, the heterodyne Duffing oscillator system is in a large-period state; when the reference signal frequency is 566MHz, the heterodyne Duffing oscillator system is in a small-period state. Its phase plane trajectory and time-domain waveform are shown below. Figure 5 As shown.

[0066] Step 5: Based on the phase state discrimination results of the different frequency Duffing oscillator system in Step 4, record the frequencies ω1 and ω2 of the reference signal in the critical state of the different frequency Duffing oscillator system.

[0067] When the state determination result of the Duffing oscillator system changes from a small-scale periodic state to a large-scale periodic state, record the reference signal frequency ω1 = 321MHz; when the state determination result of the Duffing oscillator system changes from a large-scale periodic state to a small-scale periodic state, record the reference signal frequency ω2 = 565MHz.

[0068] Step Six: Based on the relationship between the periodic signal frequency and the reference frequency when the state switch occurs in Step Three, obtain the input signal frequency after the mixed and filtered signal between the signal to be measured and the reference signal. Then, based on the frequency of the reference signal under the critical state of the heterodyne Duffing oscillator system obtained in Step Five, calculate the estimated value of the frequency of the signal to be measured.

[0069] When the frequency of the input signal to the heterodyne Duffing oscillator is 1.21 times and 3.95 times the frequency of the intrinsic dynamic signal, the heterodyne Duffing oscillator system will switch between a small-scale periodic state and a large-scale periodic state. Based on this relationship, the frequency of the input signal to the heterodyne Duffing oscillator when the state switch occurs can be calculated. Since the frequency of the intrinsic dynamic signal ω = 200MHz, the frequency ω of the input signal in the critical state of the filtered heterodyne Duffing oscillator system is... x The frequencies are 121MHz and 395MHz.

[0070] Since the input signal is the signal after mixing and filtering the signal to be measured and the reference signal, and the frequency of the input signal is the frequency difference between the reference signal and the signal to be measured, according to the frequencies ω1 and ω2 of the reference signal in the critical state of the heterodyne Duffing oscillator system obtained in step five, the frequency of the weak periodic signal is equal to the frequency of the reference signal minus the frequency of the input signal in the critical state of the heterodyne Duffing oscillator system. Therefore, the frequency estimation result of the weak periodic signal is 200MHz.

[0071] Compared to the extended Duffing oscillator weak signal detection method with a frequency detection error of 0.03 ω, the signal detection method based on the heterodyne Duffing oscillator has an adjustable frequency resolution, and the frequency resolution is less than or equal to the frequency detection ratio threshold with an accuracy of 0.001 ω. r .

[0072] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for detecting weak signals based on a heterodyne Duffing oscillator, characterized in that: Includes the following steps, Step 1: Determine the reference frequency of the heterodyne Duffing oscillator and the amplitude and frequency of the intrinsic dynamic signal to obtain the heterodyne Duffing oscillator expression and construct a weak signal detection model based on the heterodyne Duffing oscillator; Step 2: Mix and filter the signal to be tested and the reference signal, then input the signal into the Duffing oscillator signal detection model of different frequencies, and output the phase trajectory and waveform of the model to construct the weak signal detection system of the Duffing oscillator of different frequencies; Step 3: Adjust the reference signal frequency to enable the different frequency Duffing oscillators to transition from a small periodic state to a large periodic state or from a large periodic state to a small periodic state respectively; Step 4: Based on the phase plane trajectory and time-domain waveform output by the heterodyne Duffing oscillator system, perform phase state determination on the heterodyne Duffing oscillator system; Step 5: Based on the phase state discrimination results of the Duffing oscillator system in Step 4, record the frequencies ω1 and ω2 of the reference signal in the critical state of the system; Step Six: Based on the relationship between the periodic signal frequency and the reference frequency when the state switch occurs in Step Three, obtain the input signal frequency after the mixed and filtered signal between the signal to be measured and the reference signal. Then, based on the frequency of the reference signal under the critical state of the system obtained in Step Five, calculate the estimated value of the frequency of the signal to be measured. That is, weak signal detection is realized based on the heterodyne Duffing oscillator system.

2. The weak signal detection method based on a heterodyne Duffing oscillator as described in claim 1, characterized in that: The implementation method for step one is as follows: By distinguishing between the reference frequency of the Duffing oscillator and the frequency of the intrinsic dynamic signal, an expression for the heterodyne Duffing oscillator is obtained, and a weak signal detection model based on the heterodyne Duffing oscillator is constructed. Based on this model, the amplitude F = Fc of the intrinsic dynamic signal is taken, and the reference frequency ω is selected. r The internal dynamic frequency ω = Rω r Construct a weak signal detection system based on a heterodyne Duffing oscillator; the Fc is based on R and ω r The bifurcation diagram of the selected heterodyne Duffing oscillator is determined. At this time, the weak signal detection system is in a critical state. If a weak periodic signal with predetermined frequencies Mω and Nω is added to the weak signal detection system, the state of the heterodyne Duffing oscillator system will change from small-period motion to large-scale periodic motion or from large-scale periodic motion to small-period motion. The predetermined frequencies Mω and Nω can be determined by the following method: inputting a weak periodic signal of known frequency into the selected heterodyne Duffing oscillator system with the amplitude F and frequency ω of the internal driving force signal, and using the phase trajectory observation discrimination method to determine the critical state of the heterodyne Duffing oscillator system. When the heterodyne Duffing oscillator system switches from a small-period state to a large-scale periodic state, the frequency of the weak periodic signal is set to Mω; when the heterodyne Duffing oscillator system is in a critical state switching from a large-scale periodic state to a small-period state, the frequency of the weak periodic signal is set to Nω. The expression for a Holmes-type Duffing oscillator is as follows: In the formula, x is displacement, t is time, k is damping ratio, -x+x3 is nonlinear restoring force, and Fcos(ωt) is the driving force signal within the period. By distinguishing between the reference frequency and the intrinsic dynamic signal frequency of the Duffing oscillator, the expression for the heterodyne Duffing oscillator is obtained as follows: In the formula, ω r Let ω be the reference frequency of the Duffing oscillator, and ω = Rω. r The frequency of the internal dynamic signal; Let ω = Rω r F = Fc, and by adding the weak periodic signal to be measured and noise to the Duffing oscillator model of different frequencies, the expression for the weak signal detection model of the Duffing oscillator of different frequencies is obtained: Take F = Fc, select a reference frequency to build a different frequency Duffing oscillator model. At this time, the model is in a critical state. If a weak periodic signal of a specific frequency is added to the model, the state of the different frequency Duffing oscillator model changes from small periodic motion to large-scale periodic motion.

3. The weak signal detection method based on a heterodyne Duffing oscillator as described in claim 2, characterized in that: The second step is implemented as follows: The noisy, weakly periodic signal to be tested is compared with a known frequency ω. a The reference signal is mixed to obtain a signal frequency that is the sum and difference between the frequency of the signal to be measured and the frequency of the reference signal. By using a low-pass filter and setting the cutoff frequency to the reference signal frequency, signals higher than the reference signal frequency are filtered out, resulting in a signal with a frequency difference between the reference signal and the signal to be measured. This signal is then input into the heterodyne Duffing oscillator signal detection model, and the phase trajectory and waveform of the model are output to construct a heterodyne Duffing oscillator weak signal detection system. At this point, the heterodyne Duffing oscillator weak signal detection system is in a critical state of transition between small-period motion and large-scale periodic motion. The frequency of the input signal is controlled by setting a reference signal, thereby estimating the frequency of the signal under test. The noisy, weakly periodic signal to be measured is mixed with a reference signal of known frequency to obtain the signal frequency, which is the sum and difference of the frequencies of the measured signal and the reference signal. A low-pass filter is then used, with the cutoff frequency set to the reference signal frequency, to filter out signals with frequencies higher than the reference signal frequency, thus obtaining the frequency ω of the input signal. x The frequency difference between the reference signal and the signal under test is input into the weak signal detection system of the Duffing oscillator at different frequencies.

4. The weak signal detection method based on a heterodyne Duffing oscillator as described in claim 3, characterized in that: The method for implementing step three is as follows: The noisy, weakly periodic signal to be tested is mixed and filtered with a reference signal of known frequency to obtain the model input signal. When the frequency ω of the input signal... x When the frequency is equal to Mω, the Duffing oscillator system of different frequencies is in a critical state of transitioning from a small-scale periodic state to a large-scale periodic state; when the frequency ω of the input signal is equal to Mω, the system is in a critical state of transitioning from a small-scale periodic state to a large-scale periodic state. x When the value equals Nω, the Duffing oscillator system of different frequencies is in a critical state of switching from a large-scale periodic state to a small-scale periodic state; By adjusting the frequency of the reference signal, without affecting the amplitude and frequency of the driving force signal within the heterodyne Duffing oscillator system, only the input signal after the weak periodic signal to be tested and the reference signal are mixed and filtered, so that the state of the heterodyne Duffing oscillator system is switched. The state switching refers to the transition of the heterodyne Duffing oscillator system from a small periodic state to a large periodic state or from a large periodic state to a small periodic state.

5. The weak signal detection method based on a heterodyne Duffing oscillator as described in claim 4, characterized in that: Step four is implemented as follows: Regarding the distinction between the phase plane trajectory diagrams of a different-frequency Duffing oscillator in small-period and large-scale periodic motion: If the different-frequency Duffing oscillator first jumps to the vicinity of the outer orbit under the action of the internal driving force signal, and then jumps back to the inner orbit due to insufficient driving force strength, and after a period of time, the phase trajectory performs stable small-period motion in the inner orbit, it indicates that the oscillator system is in small-period motion; if, driven by the internal driving force signal, the different-frequency Duffing oscillator starts from the origin and gradually moves outward without returning to the middle position, until it performs large-scale periodic motion on the outer orbit, it indicates that the different-frequency Duffing oscillator is in large-scale periodic motion; For the output time-domain waveforms of the Duffing oscillator at different frequencies, when it is in both small-period and large-scale periodic motion, the phase trajectory diagrams and time-series diagrams of the Duffing oscillator in the small-period and large-scale periodic states are very different, and the transition between the two states is a direct jump without any intermediate transition state. Therefore, even using the amplitude judgment method, the phase state of the Duffing oscillator can still be quickly and accurately determined. Amplitude judgment method: if the Duffing oscillator system has multiple consecutive peaks greater than the amplitude threshold, then the output is determined to be a periodic signal; otherwise, it is a chaotic signal. That is, the phase state of the Duffing oscillator is determined based on the phase plane trajectory and time-domain waveform of the output of the Duffing oscillator.

6. The weak signal detection method based on a heterodyne Duffing oscillator as described in claim 5, characterized in that: Step five is implemented as follows: As the frequency of the reference signal is gradually changed, when the state discrimination result of the heterodyne Duffing oscillator system changes from a small-scale periodic state to a large-scale periodic state, the reference signal frequency ω at this time is recorded. a =ω1; When the state discrimination result of the heterodyne Duffing oscillator system changes from a large-scale periodic state to a small-scale periodic state, record the reference signal frequency ω at this time. a =ω2.

7. The weak signal detection method based on a heterodyne Duffing oscillator as described in claim 6, characterized in that: Step six is ​​implemented as follows: When the Duffing oscillator system of different frequencies is in a critical state, the frequency ω of the input signal... x There is a relationship with the frequency ω of the internal dynamic signal, that is, when the frequency ω of the input signal... x When the frequency is equal to Mω, the Duffing oscillator system of different frequencies is in a critical state of transitioning from a small-scale periodic state to a large-scale periodic state; when the frequency ω of the input signal is equal to Mω, the system is in a critical state of transitioning from a small-scale periodic state to a large-scale periodic state. x When the frequency equals Nω, the heterodyne Duffing oscillator system is in a critical state transitioning from a large-scale periodic state to a small-scale periodic state; based on this relationship, the frequency ω of the heterodyne Duffing oscillator input signal when the state transition occurs can be calculated. x ; Since the input signal is the result of mixing and filtering the signal to be measured and the reference signal, the frequency ω of the input signal... x Equal to the reference signal frequency ω a Subtract the frequency ω0 of the weak periodic signal to be measured, i.e., ω x =ω a -ω0; Based on the relationship between the reference frequency and the frequency of the signal under test, calculate the frequency ω of the input signal of the Duffing oscillator when the state switch occurs. x That is, weak signal detection is achieved based on the Duffing oscillator of different frequencies; Based on the above relationships and the frequencies ω1, ω2, and ω of the reference signal obtained in step five under the critical state of the system, x =Mω=ω a -ω0, therefore, According to formula (4), the estimated values ​​of the frequency ω0 of the signal to be tested when the frequency of the reference signal is ω1 and ω2 are calculated respectively. The average of the estimated values ​​is used to obtain the final estimated frequency of the weak periodic signal to be tested, that is, weak signal detection is realized based on the heterodyne Duffing oscillator system.

Images