A valve signal denoising method based on a harvester optimization algorithm optimized wavelet threshold

Abstract

The application provides a signal denoising method based on a dung beetle optimizer (DBO) optimized wavelet threshold, and belongs to the technical field of signal processing. The method comprises the following steps: firstly, performing CEEMDAN decomposition on a signal to obtain a plurality of IMF components; adopting a dung beetle optimizer (DBO) to select an optimal threshold for a wavelet threshold denoising method; for an IMF component with a relatively small correlation coefficient in CEEMDAN decomposition, adopting the threshold selected by the dung beetle optimizer to perform wavelet threshold denoising; and reconstructing signals of the denoised IMF component and other IMF components to obtain a denoised signal. The application has applicability, can effectively solve the problems of threshold selection difficulty and signal noise removal, retains useful information in the signal, and improves the effectiveness of the signal.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology, specifically relating to a valve signal noise reduction method based on wavelet threshold optimization using the dung beetle optimization algorithm. Background Technology

[0002] The Dung Beetle Optimization Algorithm (DBO) is inspired by the dung beetle's ball-rolling, dancing, foraging, stealing, and reproductive behaviors. In general, this algorithm balances global exploration and local exploitation, exhibiting strong optimization capabilities, fast convergence speed, and high solution accuracy. Furthermore, in terms of Wilcoxon rank-sum tests and Friedman tests, the DBO algorithm demonstrates significant superiority over other currently popular swarm intelligence optimization algorithms.

[0003] Valve signals often contain a large amount of noise, which seriously affects the assessment and prediction of valve health status. Therefore, denoising methods are needed to remove noise from valve signals. Existing valve signal noise filtering methods can be roughly divided into the following categories according to their signal processing algorithms: First, traditional signal denoising methods based on Fourier transform; second, Empirical Mode Decomposition (EMD) methods and derived related decomposition algorithms, such as Ensemble Empirical Mode Decomposition (EEMD), Complementary Ensemble Empirical Mode Decomposition (CEEMD) algorithm, and Fully Adaptive Noise Ensemble Empirical Mode Decomposition (CEEMDAN) algorithm; and third, wavelet thresholding denoising methods and wavelet packet thresholding denoising methods.

[0004] The Fully Adaptive Noise Ensemble Empirical Mode Decomposition (CEEMDAN) algorithm, as an adaptive signal decomposition method, offers convenient parameter selection in practical applications. Compared to similar signal processing methods such as wavelets and short-time Fourier transforms, it does not require the selection of basis functions, largely avoiding poor signal analysis results caused by parameter selection. It also solves the problems of mode aliasing and residual noise in EMD algorithms. However, CEEMDAN decomposition presents the problem of selecting multiple IMF components, which can easily lead to the loss of effective information. To retain the effective information in the signal, it is necessary to analyze and process multiple IMF components.

[0005] The essence of wavelet thresholding denoising is the process of suppressing useless parts of a signal and enhancing useful parts. The wavelet thresholding denoising process is as follows:

[0006] (1) Decomposition process, that is, selecting a wavelet to perform n-level wavelet decomposition on the signal;

[0007] (2) Thresholding process, that is, thresholding the coefficients of each decomposed layer to obtain the estimated wavelet coefficients;

[0008] (3) Reconstruction process: Based on the denoised wavelet coefficients, wavelet reconstruction is performed to obtain the denoised signal.

[0009] However, wavelet thresholding denoising methods face the challenge of threshold selection. An inappropriate threshold will fail to reflect the adaptability of the original signal; an excessively large threshold will result in signal loss, while an excessively small threshold will lead to incomplete denoising. Therefore, effective threshold selection is necessary to obtain a better denoised signal.

[0010] Therefore, this invention proposes a valve signal denoising method based on the dung beetle optimization algorithm to optimize the wavelet threshold, which achieves the retention of effective signal information and the removal of invalid information. Summary of the Invention

[0011] The purpose of this invention is to propose a valve signal denoising method based on the dung beetle optimization algorithm to optimize the wavelet threshold. This method can solve the problem of selecting multiple IMF components after CEEMDAN decomposition and can select the optimal wavelet threshold to improve the signal denoising capability, thereby achieving noise removal of valve signals.

[0012] To achieve the above objectives, the technical solution adopted by the present invention is characterized by comprising the following steps:

[0013] The noise signal is decomposed using the fully adaptive noise ensemble empirical mode decomposition (CEEMDAN) algorithm. The algorithm steps are as follows.

[0014] Step S101: Set the iteration number N, and add N pairs of positive and negative Gaussian white noise to the original signal x(t), resulting in a total of N new signals. The new signal after the j-th addition of Gaussian white noise is:

[0015]

[0016] In the formula, x(t) is the original signal; ε0 is the standard deviation of the noise, dB; ω j It is the j-th Gaussian white noise that satisfies the standard normal distribution.

[0017] Step S102: Let E(·) be the EMD decomposition, then the j-th IMF1 component can be obtained through j decompositions:

[0018]

[0019] In the formula For the j-th IMF1 component; r j (t) represents the j-th residual component.

[0020] Step S103: Sum and average the N IMF1 components obtained from the above decomposition to obtain the final IMF1(t):

[0021]

[0022] Step S104: Calculate the first residual component r1(t):

[0023] r1(t)=x(t)-IMF1(t) (4)

[0024] Step S105: Add the N groups of auxiliary noise from step 1, which are respectively applied to the paired positive and negative Gaussian white noise using EMD decomposition, to r1(t). Let E i (·) represents the i-th modal component after EMD decomposition. Then, the new signal after the j-th addition of auxiliary noise is:

[0025]

[0026] Through the Performing j decompositions yields the j-th IMF2 component, with the following decomposition result:

[0027]

[0028] Then, the N IMF2 values ​​are summed and averaged to obtain the final IMF2(t):

[0029]

[0030] Calculate the second residual component r2(t):

[0031] r2(t)=r1(t)-IMF2(t) (8)

[0032] Step S106: Repeat step S105 until the obtained residual components cannot be further decomposed into EMD components, at which point the algorithm ends. Let the number of IMF components obtained at this point be k, then the original signal x(t) is decomposed into:

[0033]

[0034] The steps for using the Dung Beetle Optimization (DBO) algorithm are as follows:

[0035] Step S201: First, initialize the population: randomly generate a certain number of dung beetle individuals, each of which has a set of random initial positions.

[0036] Step S202: Calculate fitness: Calculate the fitness value of each dung beetle based on its location. The higher the fitness value, the better the individual.

[0037] Step S203: Update location: Update the location of each dung beetle individual based on its fitness value and location information.

[0038] Step S204: Update fitness: Recalculate the fitness value of each dung beetle individual based on the new location information.

[0039] Step S205: Update the optimal solution: Record the dung beetle individual with the highest fitness value in the current population as the global optimal solution.

[0040] Step S206: Determine the termination condition: If the preset termination condition is met (such as the number of iterations, the fitness value reaching a certain threshold, etc.), then stop the algorithm and output the optimal solution.

[0041] The steps of the wavelet threshold denoising method are as follows:

[0042] Step S301: After selecting the optimal wavelet threshold using the Dung Beetle Optimization (DBO) algorithm, select an appropriate threshold function for noise reduction.

[0043] Step S302: Reconstruct the denoised IMF component with other IMF components to obtain the denoised signal. The reconstruction formula is:

[0044]

[0045] In the formula, IMF n (t) represents the nth IMF component, R(t) represents the residual component, and x(t) represents the denoised signal;

[0046] Step S303: Verify the simulation results using the signal-to-noise ratio (SNR) and root mean square error (RMSE); SNR formula:

[0047]

[0048] In the formula, Ps is the signal power, Pm is the noise power, x(t) is the useful signal, m(t) is the noise signal, and SNR is the signal-to-noise ratio.

[0049] The formula for calculating the root mean square error is:

[0050]

[0051] In the formula, N is the signal length, x i For a noisy signal, y i This is the noise-reducing signal. A higher signal-to-noise ratio (SNR) indicates a better noise reduction effect; conversely, a lower root mean square error (RMSE) indicates a better noise reduction effect.

[0052] The present invention has the following beneficial effects:

[0053] (1) The parameters are highly adaptable, easy to adjust, and convenient to operate;

[0054] (2) The valve signal denoising method based on the dung beetle optimization algorithm to optimize the wavelet threshold has a smaller signal-to-noise ratio and a higher denoising effect compared with the traditional valve signal denoising method, and can more effectively remove invalid information in the signal. Attached Figure Description

[0055] Figure 1 This is a flowchart of the CEEMDAN algorithm of this invention.

[0056] Figure 2 This is a bar chart showing the correlation coefficients of various IMF components in a specific embodiment of the present invention.

[0057] Figure 3 This is a schematic diagram of the noisy and denoised signals of CEEMDAN according to a specific embodiment of the present invention.

[0058] Figure 4 This is a flowchart of the Dung Beetle Optimization Algorithm (DBO) of this invention.

[0059] Figure 5 This is a schematic diagram of wavelet hard thresholding denoising according to a specific embodiment of the present invention.

[0060] Figure 6 This is a schematic diagram of wavelet fixed threshold denoising according to a specific embodiment of the present invention.

[0061] Figure 7 This is a schematic diagram of the combined noise reduction method according to a specific embodiment of the present invention.

[0062] Figure 8 This is a schematic diagram comparing the SNR (signal-to-noise ratio) of various methods in specific embodiments of the present invention.

[0063] Figure 9 This is a schematic diagram comparing the root mean square error (RMSE) of various methods in specific embodiments of the present invention.

[0064] Figure 10 This is a flowchart of the wavelet threshold denoising algorithm optimized by combining CEEMDAN and DBO in this invention. Detailed Implementation

[0065] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solution of this invention will be specifically described below with reference to the accompanying drawings and examples. A valve signal denoising method based on wavelet threshold optimization using a dung beetle optimization algorithm is provided, comprising the following steps:

[0066] S1. Simulate the collected valve signals and compare the simulation results by adding noise signals.

[0067] S2, Figure 1The flowchart of the CEEMDAN algorithm of this invention is shown, and the specific steps are as follows:

[0068] The original signal is decomposed, and the first-order IMF component obtained from the decomposition can be expressed as shown in Equation 1:

[0069]

[0070] After obtaining the first-order IMF component, the residual signal component is calculated as shown in Equation 2:

[0071] r1(n)=x(n)-IMF1(n) (2)

[0072] In the N decomposition processes, the same input signal is decomposed each time, and all the above steps are repeated. The algorithm terminates when the residual signal has no more than two extreme points. The entire decomposition process yields K-order IMF components, and the k-th IMF component is shown in Equation 3:

[0073]

[0074] S3. Calculate the correlation coefficient CC of each IMF component after the fully adaptive noise ensemble empirical mode decomposition (CEEMDAN). The correlation coefficient CC is shown in Formula 4:

[0075]

[0076] In the formula, r represents the IMF component; x represents the original signal; and n represents the number of IMF components. The correlation coefficient can be used to describe the degree of correlation between the IMF component and the original data. The closer the correlation coefficient is to 1, the stronger the correlation between the component and the original data. A larger absolute value of the correlation coefficient CC indicates a stronger correlation between r and x; a smaller absolute value of the correlation coefficient CC indicates a weaker correlation between r and x. The histogram of the correlation coefficients of each IMF component calculated in this embodiment is shown below. Figure 2 As shown in the figure, the fully adaptive noise ensemble empirical mode decomposition (CEEMDAN) algorithm decomposes the noise signal into 12 IMF components. Among them, the IMF components with a threshold of 0.3 are IMF1-IMF8, and the IMF components with a threshold of 0.3 are IMF9-IMF12. Therefore, IMF9-IMF12 have weak correlation and contain a lot of noise and irrelevant information, so they need to be processed.

[0077] To highlight the advantages of this invention, simulations will be performed to compare the CEEMDAN algorithm, wavelet hard thresholding, wavelet fixed thresholding, and the joint denoising method of this invention. A schematic diagram of the noisy signal and the denoised signal from the CEEMDAN denoising algorithm is shown below. Figure 3As shown in the figure, the noise reduction effect of using the CEEMDAN denoising algorithm alone is not good, with a signal-to-noise ratio (SNR) of only 2.3171.

[0078] S4, Dung Beetle Optimization Algorithm Flowchart as follows: Figure 2 As shown, the population is first initialized by randomly generating a certain number of dung beetle individuals, each with a set of random initial positions.

[0079] Fitness calculation: The fitness value of each dung beetle is calculated based on its location. The higher the fitness value, the better the individual.

[0080] Location Update: The location of each dung beetle is updated based on its fitness value and location information. The algorithm divides the population into four subpopulations, based on dung beetle behaviors such as rolling, dancing, foraging, stealing, and breeding. During the rolling process, there are two modes: one with obstacles and one without. The location update formula for the unobstructed mode is as follows:

[0081]

[0082] Where t represents the current iteration number, This represents the position of the i-th dung beetle in the population during the t-th iteration. α is a number taking the value -1 or 1; k is a random number in (0, 0.2] (assigned the value 0.1 in the code); b is a constant taking the value (0, 1) (assigned the value 0.3 in the code); It is the worst position for the dung beetle in the entire map.

[0083] The position update formula for obstacle-prone mode is as follows:

[0084]

[0085] Because when When the value is π, tan(θ) is 0 or meaningless, so the dung beetle's position will not be updated.

[0086] During dung beetle reproduction, the formulas for the upper and lower boundaries are as follows:

[0087]

[0088] Where R = (lt) / T, and T is the maximum number of iterations; This represents the global optimal position for the current population. The breeding position is dynamically adjusted with the number of iterations, as shown in the following formula:

[0089]

[0090] in Let b1 and b2 be the positions at the t-th iteration, and let b1 and b2 be two independent random vectors of size 1·D, where D represents the dimension of the optimization problem.

[0091] During the dung beetle's foraging process, the formulas for the upper and lower boundaries are as follows:

[0092]

[0093] Where R = (1-t) / T, and T is the maximum number of iterations; This represents the global optimal position for the current population. The foraging position is dynamically adjusted with the number of iterations, as shown in the following formula:

[0094]

[0095] Where C1 is a random number that follows a normal distribution, and C2 is a random vector of 1·D between (0, 1).

[0096] During the dung beetle's theft, its position is dynamically adjusted with the number of iterations, and the formula is updated as follows:

[0097]

[0098] Where g represents a random vector of size 1·D that follows a normal distribution; S represents a constant value.

[0099] Update fitness: Recalculate the fitness value for each dung beetle individual based on the new location information.

[0100] Update the optimal solution: Record the dung beetle individual with the highest fitness value in the current population as the global optimal solution.

[0101] Determine the termination condition: If the preset termination condition is met (such as the number of iterations, the fitness value reaching a certain threshold, etc.), the algorithm stops and the optimal solution is output.

[0102] Selecting a new population: Based on the fitness value of each dung beetle individual, a new population is selected with a certain probability.

[0103] Repeat steps 2-7 until the termination condition is met, and select the optimal threshold.

[0104] S5. The principle of wavelet thresholding denoising is as follows: Wavelet decomposition is used to decompose the acquired signal into various scales, and then an appropriate threshold and threshold function are selected to process the signal, achieving a denoising effect. After selecting the optimal wavelet threshold using the Dung Beetle Optimization (DBO) algorithm, the wavelet threshold is substituted and a hard thresholding function is selected for denoising. A schematic diagram of wavelet hard thresholding denoising is shown below. Figure 5As shown in the figure, the methods are heuristic hard threshold denoising, Stein unbiased risk hard threshold denoising, and maximum-minimum criterion hard threshold denoising, with a signal-to-noise ratio (SNR) of 10.6005.

[0105] S6. Wavelet decomposition is used to decompose the acquired signal into various scales. Then, by selecting an appropriate threshold and threshold function, the signal is processed to achieve denoising. After selecting the optimal wavelet threshold using the Dung Beetle Optimization (DBO) algorithm, the wavelet threshold is substituted into the function and a fixed threshold function is selected for denoising. A schematic diagram of wavelet fixed threshold denoising is shown below. Figure 6 As shown in the figure, the fixed hard threshold denoising and fixed soft threshold denoising have signal-to-noise ratios (SNR) of 8.9875 and 15.3868, respectively.

[0106] S7. Reconstruct the denoised IMF9-IMF12 components with other IMF1-IMF8 components to obtain the denoised signal. The reconstruction formula is shown in Formula 5:

[0107]

[0108] In the formula, IMF n (t) represents the nth IMF component, R(t) represents the residual component, and x(t) represents the denoised signal; a schematic diagram of CEEMDAN combined with DBO to optimize wavelet threshold denoising is shown below. Figure 7 As shown in the figure, the CEEMDAN combined with DBO optimized wavelet threshold denoising method proposed in this invention has a higher denoising effect, with a signal-to-noise ratio (SNR) of 21.0527.

[0109] S8. Verify the simulation results using the signal-to-noise ratio (SNR) and root mean square error (RMSE). Signal-to-noise ratio (SNR) is the ratio of signal to noise in an electronic device or system. The signal refers to the electronic signal from outside the device that needs to be processed by it. Noise refers to irregular extraneous signals (or information) generated after passing through the device that are not present in the original signal and do not change with the original signal. SNR is a ratio, or a multiple. In communications and electronic engineering, a higher SNR is generally preferred. SNR formula:

[0110]

[0111] In the formula, Ps is the signal power, Pm is the noise power, x(t) is the useful signal, m(t) is the noise signal, and SNR is the signal-to-noise ratio.

[0112] The formula for calculating the root mean square error is:

[0113]

[0114] In the formula, N is the signal length, x i For a noisy signal, y i The signal-to-noise ratio (SNR) is the noise reduction signal. A higher SNR indicates a better denoising effect; conversely, a lower RMSE indicates a better denoising effect. A comparative diagram of the SNR of the CEEMDAN algorithm, wavelet hard thresholding, wavelet fixed thresholding, and the joint denoising method of this invention is shown below. Figure 8 As shown in the figure, the CEEMDAN combined with DBO optimized wavelet threshold denoising method proposed in this invention has a higher denoising effect and a significantly higher signal-to-noise ratio (SNR) than other methods; the comparison diagram of the root mean square error of RMSE is shown in the figure. Figure 9 As shown in the figure, the CEEMDAN combined with DBO optimized wavelet threshold denoising method proposed in this invention achieves higher denoising performance, with a significantly smaller root mean square error (RMSE) than other methods. The flowchart of the combined CEEMDAN and DBO optimized wavelet threshold denoising algorithm is shown below. Figure 10 As shown.

[0115] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0116] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

[0117] The above description is merely an 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 valve signal denoising method based on the optimization of wavelet threshold by the algorithm of dung beetle, characterized in that: The method comprises the following steps: S1, collecting noise-free leakage signal data and noise-containing leakage signal data of the valve at different leakage rates, and establishing original signal data set M and noise-containing signal data set N; S2, performing complete ensemble empirical mode decomposition (CEEMDAN) on the noise-containing signal to obtain a first-order IMF component IMF1(n), calculating a unique residual component r1(n) after obtaining the first-order component, obtaining a second-order IMF2(n) by re-decomposing r1(n), and calculating a unique residual component r2(n), repeating the above steps until the number of extreme points of the residual signal is not more than two: E(x j (t)) = IMF j (n) + r j (n) (1) where IMF j (n) is the jth IMF component; r j (n) is the jth residual component; S3, calculating the correlation coefficient CC of each IMF component after complete ensemble empirical mode decomposition (CEEMDAN): In the formula, r is the IMF component; x is the original signal; n is the number of IMF components; the correlation coefficient can be used to describe the correlation degree of the IMF component and the original data, and the closer the correlation coefficient is to 1, the stronger the correlation of the component with the original data is; the greater the absolute value of the correlation coefficient CC is, the stronger the correlation of r and x is; the smaller the absolute value of the correlation coefficient CC is, the weaker the correlation of r and x is; S4, using the DBO algorithm to select the optimal threshold value for the wavelet threshold denoising method, inputting the range of the threshold value a first; then randomly generating an initial value as an initial population; calculating the fitness value according to the position of each individual; updating the position of each individual according to the fitness value and the position information; recalculating the fitness value according to the new position information; recording the dung beetle individual with the highest fitness value in the current population as the global optimal solution; judging whether the maximum fitness value is reached; and finally outputting the optimal threshold value a solution: S5, for the IMF component with a small correlation coefficient CC calculated after complete ensemble empirical mode decomposition (CEEMDAN), since the correlation coefficient CC is small, it indicates that the correlation of the component with the original signal is weak and the noise is more, so the wavelet threshold selected by the DBO algorithm is used for wavelet threshold denoising; S6, reconstructing the denoised IMF component and other IMF components to obtain a denoised signal, and the reconstruction formula is: where IMF n (t) is the nth IMF component, R(t) is the residual component, and x(t) is the denoised signal. S7, using the values of the signal-to-noise ratio SNR and the root mean square error RMSE to verify the simulation effect; the signal-to-noise ratio formula is: In the formula, Ps is the signal power, Pm is the noise power, x(t) is the useful signal, m(t) is the noise signal, and SNR is the signal-to-noise ratio; The root mean square error calculation formula is: In the formula, N is the signal length, x i is a noisy signal, y i is a denoised signal; the greater the SNR value, the better the denoising effect; on the contrary, the smaller the RMSE value, the better the denoising effect.

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