Denoising method of non-stationary weak signal of underwater laser light curtain based on EMD and CPSD

Abstract

The present invention relates to the technical field of non-stationary weak signal denoising, and specifically relates to a non-stationary weak signal denoising method for dynamic targets of underwater laser light curtains based on EMD and CPSD, including the following steps: First, build an underwater experimental environment, collect the signal of the underwater target passing through the laser light curtain, and then use empirical mode decomposition (EMD) to decompose the original signal of passing through the curtain to obtain the intrinsic mode function (IMF) i and the residual signal r(t); Secondly, calculate the CPSD of the IMF i and the residual signal r(t) and the original signal of passing through the curtain respectively, and statistically calculate the frequencies corresponding to the peaks of the CPSD amplitudes of the IMF i and the residual signal r(t) and the original signal of passing through the curtain. Take the IMF corresponding to the first minimum frequency when the CPSD amplitude reaches the peak as the boundary IMF k (1 ≤ k ≤ b); Finally, recombine the effective low-frequency components IMF k+1 , IMF k+2 , … IMF b and the residual signal to obtain the denoised signal. The present invention realizes the denoising of non-stationary weak signals, can greatly improve the signal-to-noise ratio, has high robustness, and lays a foundation for the subsequent accurate extraction of the time of passing through the curtain.

Description

Technical Field

[0001] The present invention relates to the technical field of non-stationary weak signal denoising, and particularly relates to a non-stationary weak signal denoising method for underwater laser light curtain based on EMD and CPSD. Background Technique

[0002] The laser light curtain velocity measurement system is an area intercept measurement instrument based on the principle of photoelectric detection. Due to its non-contact, high velocity measurement accuracy, and insensitivity to weather, it is widely used in the velocity measurement of projectiles and fragments in the air. With the increasingly urgent situation of China's offshore defense and far-sea operations, the demand for underwater weapon velocity measurement is particularly prominent. Since the underwater working state and environment are essentially different from conventional tests, and the density of water is 800 times that of air, in an actual underwater laser light curtain velocity measurement system, the target passing curtain signal obtained by the laser light curtain is often submerged in strong noise, with a low signal-to-noise ratio, making it difficult to accurately extract the underwater target passing curtain time and calculate the passing curtain velocity. Therefore, how to improve the signal-to-noise ratio of the passing curtain signal and extract the effective signal from the non-stationary weak signal is the primary problem to be solved.

[0003] For non-stationary weak signals, traditional Fourier transform methods cannot be used for processing. And methods for processing non-stationary signals, such as windowed Fourier transform and wavelet transform methods, cannot scientifically determine the window size or wavelet transform kernel, which brings difficulties to the processing. In the Chinese patent with the patent number CN201810553056.8 and the patent name "Vibration signal denoising method for tap changer based on empirical mode decomposition EMD", the EMD empirical mode decomposition and Savitzky-Golay filter are used to denoise the switch vibration signal (non-stationary weak signal), but this method is prone to introducing high-frequency noise, resulting in difficulty in extracting effective signals. In the Chinese patent with the patent number CN201410823212.X and the patent name "A vibration signal denoising method based on variable step size LMS-EEMD", a variable step size LMS adaptive filter is used in combination with EEMD for denoising. However, in the denoising process of this method, an iterative method is adopted and Gaussian white noise is added multiple times, resulting in a large amount of computation and poor real-time performance. Summary of the Invention

[0004] The present invention provides a non-stationary weak signal denoising method for underwater laser light curtain based on EMD and CPSD to overcome the problems of difficult extraction of effective signals, large amount of computation, and poor real-time performance existing in the prior art.

[0005] In view of this, to achieve the purpose of the present invention, the technical solution provided by the present invention is: a non-stationary weak signal denoising method for underwater laser light curtain based on EMD and CPSD, including the following steps:

[0006] Step 1: Build an underwater experimental environment and collect the original signal of the underwater target passing through the laser light curtain.

[0007] Step 2: Each IMF component satisfies the following two conditions: (1) In the entire sequence, the number of zero-crossing points differs from the number of extreme points by at most 1; (2) The average value of the upper envelope formed by local maxima and the lower envelope formed by local minima is 0. Use empirical mode decomposition (EMD) to decompose the original signal passing through the curtain, and a series of intrinsic mode functions (IMFs) are obtained. i (i = 1, 2, … b, where b is the total number of IMFs) and the residual signal r(t);

[0008] Step 3: Calculate the cross-power spectral density (CPSD) of the IMFs i , the residual signal r(t), and the original signal passing through the curtain respectively, and statistically determine the frequencies corresponding to the peaks of the CPSD amplitudes of the IMFs i , the residual signal r(t), and the original signal passing through the curtain.

[0009] Step 4: Take the IMF corresponding to the first minimum frequency when the CPSD amplitude of the IMFs i , the residual signal r(t), and the original signal passing through the curtain reaches the peak as the boundary IMF k (1 ≤ k ≤ b), IMF1, IMF2,... IMF k are high-frequency noise components, and IMF k+1 , IMF k+2 ... IMF b are low-frequency effective components;

[0010] Step 5: Reconstruct the effective low-frequency components IMF k+1 , IMF k+2 , … IMF b and the residual signal to obtain an effective signal of the target passing through the curtain.

[0011] Furthermore, the original signal U(t) passing through the curtain in Step 1 above can be expressed as:

[0012] U(t) = U s (t) + U n (t) (1)

[0013] where U s (t) is the effective signal of the projectile passing through the curtain, and U n (t) is the noise.

[0014] Furthermore, in Step 2 above, the original signal U(t) passing through the curtain after decomposition is expressed as:

[0015]

[0016] In the formula, b represents the total number of IMF components obtained by decomposition, i represents the order of the IMF components, the IMFs are numbered in sequence from high-frequency components to low-frequency components, that is, IMF1 is the highest-frequency component, IMF2 is the second-highest-frequency component, and so on, and r(t) represents the residual signal.

[0017] Further, in the fifth step described above, the effective over-curtain signal after denoising is expressed as:

[0018]

[0019] In the formula, represents the signal after denoising.

[0020] Compared with the prior art, the advantages of the present invention are as follows:

[0021] 1. In the method of the present invention, after the original over-curtain signal is decomposed by EMD to obtain IMF components, by calculating the first minimum frequency corresponding to the amplitude peak of the CPSD of the IMF component signal, the residual signal and the original over-curtain signal, the boundary IMF of the effective low-frequency components is determined by using the CPSD correlation between the decomposed signal and the original over-curtain signal, and all low-frequency IMFs are scientifically and quickly screened out purposefully. Only the effective low-frequency signals are retained, and they are recombined. When recombining, the effective low-frequency signals are retained to the greatest extent, and the high-frequency noise signals are suppressed. In this way, an effective denoised signal can be extracted from the weak signal. The signal-to-noise ratio of the denoised signal is greatly improved compared with the original over-curtain signal actually collected, providing a guarantee for the accurate extraction of the subsequent over-curtain time and the accurate calculation of the speed.

[0022] 2. By adopting the method of the present invention, there is no need to adopt an iterative method or artificial intervention to adjust parameters. All effective low-frequency signals can be determined by one calculation, and a denoised signal with a greatly improved signal-to-noise ratio can be obtained quickly.

[0023] 3. Wide application range: The method of the present invention is not only limited to denoising the dynamic target signal of the underwater laser light curtain, but also applicable to the processing of other non-stationary weak signals. It has the characteristics of high robustness and no need to adjust parameters during the denoising process. Description of the Drawings

[0024] Figure 1 It is a schematic diagram of an underwater detection light curtain.

[0025] Figure 2 It is a flow chart of the present invention.

[0026] Figure 3 It is the original over-curtain signal of an underwater target passing through the detection light curtain.

[0027] Figures 4a - 4dAll IMFs and residual signals obtained after EMD decomposition of the original passing curtain signal.

[0028] Figure 5 Is the effective passing curtain signal after denoising. Specific implementation manner

[0029] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0030] See Figure 1 , an underwater experimental environment is built, where the light curtains 1 and 2 are parallel detection planes. Each light curtain consists of a light source end and a receiving end, and the light emitted by the light source end is received by the receiving end. The photodetector in the receiving end realizes photoelectric conversion. When the target passes through, due to the change in the light flux, the signal output by the detector changes, thereby realizing the detection of the target.

[0031] See Figure 2 , an underwater laser light curtain non-stationary weak signal denoising method based on empirical mode decomposition (EMD) and cross power spectral density (CPSD) provided by the present invention is as follows:

[0032] The first step: First, use an oscilloscope to collect the original passing curtain signal of the underwater target passing through the detection light curtain. Figure 3 Is the original passing curtain signal when the underwater detection target passes through one of the detection light curtains. The effective signal is submerged in noise. After calculation, the signal-to-noise ratio SNR of this signal is only 3.3 dB. The passing curtain signals of the other detection light curtain have similar characteristics. Therefore, it is very difficult to extract the target passing curtain time from the two passing curtain signals with low signal-to-noise ratio.

[0033] The so-called original passing curtain signal U(t) can be expressed as

[0034] U(t) = U s (t) + U n (t) (1)

[0035] In the formula, U s (t) is the effective signal of the projectile passing through the curtain, and U n (t) is the noise.

[0036] The second step: Perform EMD decomposition on the original passing curtain signal to obtain 17 intrinsic mode functions IMF1-IMF 17 and the residual signal r(t), as Figures 4a - 4d shown.

[0037] When decomposing, each IMF component needs to meet the following two conditions: (1) In the entire sequence, the number of zero-crossing points and the number of extreme points differ by at most 1; (2) The average value of the upper envelope formed by local maxima and the lower envelope formed by local minima is 0.

[0038] After decomposition, the original over-power signal U(t) can be expressed as:

[0039]

[0040] In the formula, b represents the total number of IMF components obtained by decomposition, i represents the order of the IMF component, and the IMFs are numbered in sequence from high-frequency components to low-frequency components, that is, IMF1 is the highest-frequency component, IMF2 is the second-highest-frequency component, and so on. r(t) represents the residual signal.

[0041] Step 3: First, calculate the cross-power spectral density CPSD of the IMF i and the residual signal r(t) with the original over-power signal.

[0042] The cross-power spectral density (CPSD) is the distribution of power per unit frequency and is defined as:

[0043]

[0044] x and y represent two data sequences respectively, and p xy represents the cross-power spectral density at the corresponding positions of the two data sequences.

[0045] The CPSD adopts Welch's averaging and improved period spectral estimation method, and the cross-correlation sequence is defined as:

[0046]

[0047] where x n and y n are both random processes, -∞ < n < ∞, -∞ < m < ∞, E{.} represents the expected value operator, and the CPSD amplitude reaches a peak at the frequency where there is a significant correlation between the signals.

[0048] Then, statistically obtain the frequencies corresponding to the IMF i and the residual signal r(t) and the original over-power signal when the CPSD amplitude reaches a peak. The statistical results are shown in Table 1.

[0049] Table 1 Frequencies corresponding to the IMF i and the residual signal r(t) and the original over-power signal when the CPSD amplitude reaches a peak

[0050]

[0051] Step 4: Take the IMFi The IMF corresponding to the first minimum frequency when the CPSD amplitude of the residual signal r(t) and the original curtain-passing signal reaches the peak is used as the boundary IMF k (1 ≤ k ≤ b).

[0052] That is to say, using the IMF i and the IMF corresponding to the first minimum frequency of the CPSD amplitude peak of the residual signal r(t) and the original curtain-passing signal as the boundary IMF k , so IMF1, IMF2,... IMF k are all high-frequency noise components, IMF k+1 , IMF k+2 ... IMF b are low-frequency effective components. As can be seen from Table 1, the boundary IMF in this embodiment is IMF6.

[0053] Step 5: Recombine the IMF k+1 , IMF k+2 ... IMF b and the residual signal r(t), that is, recombine IMF7 - IMF 17 and the residual signal r(t) to obtain the effective curtain-passing signal.

[0054] The effective curtain-passing signal after denoising can be expressed as:

[0055]

[0056] In the formula, represents the signal after denoising.

[0057] As Figure 5 shown. After calculation, the signal-to-noise ratio SNR of this recombined signal is 8.9 dB, which is 5.6 dB higher than that of the original curtain-passing signal. According to the above steps, the denoising process of non-stationary weak signals can be realized, laying a foundation for extracting the effective curtain-passing signal subsequently, and then accurately extracting the underwater target curtain-passing time and calculating the curtain-passing speed.

[0058] At the same time, to verify the robustness of this method, multiple weak signals in different situations are collected and denoised, and the improvement of the signal ratio is shown in Table 2.

[0059] Table 2 Comparison of signal-to-noise ratios of different original curtain-passing signals for underwater detection light curtain before and after denoising

[0060]

[0061] It can be seen that the signal-to-noise ratios of the recombined signals in all three cases have been greatly improved.

[0062] The content of the present invention is not limited to the examples listed. Any equivalent transformation of the technical solution of the present invention made by those of ordinary skill in the art by reading the specification of the present invention is covered by the claims of the present invention.

Claims

1. An underwater laser light curtain non-stationary weak signal denoising method based on EMD and CPSD, comprising the following steps: The first step: Build an underwater experimental environment and collect the original curtain-passing signal of the underwater target passing through the laser light curtain; Step 2: Each IMF component satisfies the following two conditions: (1) In the entire sequence, the number of zero-crossing points and the number of extreme points differ by at most 1; (2) The average value of the upper envelope formed by local maxima and the lower envelope formed by local minima is 0. The original over-power signal is decomposed using empirical mode decomposition (EMD) to obtain a series of intrinsic mode functions (IMFs). i and the residual signal r(t), where i = 1, 2, …, b, and b is the total number of IMFs; Step 3: Calculate the IMF respectively i , the cross-power spectral density CPSD of the residual signal r(t) and the original overcurtain signal, and statistically calculate the frequencies corresponding to the peaks of the amplitudes of the cross-power spectral density CPSD of the IMF i , the residual signal r(t) and the original overcurtain signal; Step 4: Take the IMF i , the residual signal r(t), and the IMF corresponding to the first minimum frequency when the cross-power spectral density CPSD amplitude reaches the peak of the original over-curtain signal as the boundary IMF k (1 ≤ k ≤ b), IMF1, IMF2,..., IMF k are high-frequency noise components, and IMF k+1 , IMF k+2 , …, IMF b are low-frequency effective components; Step 5: Reconstruct the low-frequency effective components IMF k+1 , IMF k+2 , …, IMF b and the residual signal to obtain an effective target over-screen signal; The original curtain-passing signal U(t) in the first step is expressed as: U(t) = U s (t) + U n (t) (1) where U s (t) is the effective signal of the projectile passing through the screen, and U n (t) is the noise; In the second step, the original curtain-passing signal after decomposition is expressed as U(t): In the formula, b represents the total number of IMF components obtained by decomposition, i represents the order of the IMF components, the IMFs are numbered in sequence from high-frequency components to low-frequency components, that is, IMF1 is the highest-frequency component, IMF2 is the second-highest-frequency component, and so on, and r(t) represents the residual signal.

2. The underwater laser light curtain non-stationary weak signal denoising method based on EMD and CPSD according to claim 1, characterized in that: In the fifth step, the effective curtain-passing signal after denoising is expressed as: In the formula, represents the denoised signal.

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