Water supply pipe network data quality control method coupling multi-scale decomposition and independent noise reduction

Abstract

The invention discloses a water supply network data quality control method coupling multi-scale decomposition and independent noise reduction. The method comprises the following steps: (1) decomposing a monitoring data sequence and determining a noisy IMF component; (2) carrying out independent noise reduction on the noisy IMF component based on Gaussian filtering; and (3) reconstructing a monitoring data sequence. The method can improve the noise reduction effect of the monitoring data sequence of the water supply network, has robustness on the noise reduction of the monitoring data in leakage scenes with different leakage intensities, and is an important way for the quality control of the real-time monitoring data of the water supply network; technical support is provided for achieving pipe network real-time hydraulic model construction and data analysis driven pipe network intelligent management and control, and the method has great significance in improving the comprehensive performance of a water supply pipe network intelligent system.

Description

Technical Field

[0001] The present invention belongs to the technical field of urban water supply pipe networks, and in particular relates to a water supply pipe network data quality control method that couples multi-scale decomposition and independent noise reduction. Background Art

[0002] In recent years, with the continuous development of the Internet of Things and sensor network technology, the real-time monitoring system of the water supply network constructed by sensors distributed in the water supply network can record monitoring data online, such as node pressure and pipeline flow in the water supply network. There is inevitably some noise in the monitoring data, and it gradually increases as the equipment ages. Due to the development of data transmission and storage technology, the amount of data has exploded, and the quality problem of large-scale data has become increasingly prominent. Controlling data quality is the basis for realizing data analysis and model-driven intelligent management and control of water supply networks.

[0003] As a whole system, the real monitoring data of the water supply network, especially the pressure monitoring data, often changes synchronously with the fluctuation of water consumption. Therefore, the real pressure data is often linearly correlated, while the noise is usually considered to be an independent and unrelated stationary time series. This significant difference between noise and real monitoring data can provide a new idea for noise reduction of water supply network monitoring data.

[0004] Since independent noise reduction will increase the complexity of the data structure, and the independent noise reduction process changes the relative position of each sample point of the original data. If multi-scale decomposition technology is used later, it will affect the decomposition results to a certain extent, resulting in unstable noise reduction results. Using a combination of multiple data quality control technologies and integrating independent noise reduction into the multi-scale decomposition process to process data can effectively reduce data distortion and is more suitable for pipe network data quality management. Therefore, before massive monitoring data sequences are applied to the intelligent management and control of water supply pipe networks, it is urgent to realize real-time monitoring data quality control at the theoretical and technical levels.

[0005] In view of this, the present invention proposes a multi-scale decomposition technology based on fusion independent denoising to meet the quality control needs of water supply network monitoring data. ICEEMDAN is combined with Gaussian filtering, and the demarcation point is determined by the modified CMSE criterion. The correlation coefficient, signal-to-noise ratio, root mean square error and permutation entropy are used as evaluation indicators to characterize the denoising performance for data reconstruction. Finally, the denoised monitoring data sequence is obtained, which effectively improves the denoising effect of the water supply network monitoring data sequence. Summary of the invention

[0006] The present invention aims to provide a water supply network data quality control method that couples multi-scale decomposition and independent noise reduction. To achieve the above purpose, the present invention takes the following steps: (1) Decompose the monitoring data series and determine the noisy IMF components; (2) Independently denoise the noisy IMF components based on Gaussian filtering; (3) Reconstruct the monitoring data sequence.

[0007] Furthermore, the step 1 is specifically as follows: 1.1 Obtain different IMF components based on ICEEMDAN time series decomposition: To monitor time series Add to i Gaussian white noise with submean 0 , while adding the amplitude of the noise ,form i Sequence to be decomposed ,in i =1,2,3…,n: ; To the top i Perform EMD decomposition on the sequence and find i local means, the original signal Minus this i The average of the local means, the first IMF component is found: ; Where: is the local mean function; The second IMF component is: ; Repeat the above steps until the final remainder is a monotonic function or a constant; 1.2 Determine whether the IMF component is noisy by using the modified CMSE criterion: After the data sequence is decomposed by ICEEMDAN, we get m IMF components sorted from high to low frequency and a residual res ; Based on the CMSE criterion, the demarcation point between the noisy IMF component and the non-noisy IMF component is determined by the following calculation method:

[0008] ; In the formula x is the original signal, N is the signal length, k is the number of decomposition layers; Since the noise is high frequency, the energy of the noise gradually decreases with the decomposition of ICEEMDAN, and the global minimum value of the IMF component energy is used as the dividing point j , see formula: ; This method modifies the above formula. When there is a local minimum before the global minimum is calculated using the CMSE criterion, the cutoff point j The number corresponding to the first local minimum plus 1 should be taken, which is the formula: ; The IMF components before the dividing point are noisy components and require further independent noise reduction; the IMF components after the dividing point are noise-free components, that is, data sequences composed of valid information.

[0009] Furthermore, the step 2 is specifically as follows: Gaussian filtering is applied to each noisy IMF component obtained in step 1.2 above to perform independent noise reduction. The one-dimensional expression of the Gaussian filtering is: ; Among them, σ is the standard deviation of the function, the standard deviation range is 0.2-0.65, and the interval is 0.05. Each component will produce 10 sets of filtering results under different parameters.

[0010] Furthermore, the step 3 is specifically as follows: 3.1 Assumptions k IMF components are reconstructed, and a set of data is selected from the independent denoising results of each component, totaling Group data, The data is reconstructed with the noise-free IMF component to obtain The monitoring data after noise reduction; 3.2 The correlation coefficient CORR, signal-to-noise ratio SNR, root mean square error RMSE and permutation entropy are selected as the evaluation indicators of denoising performance; 3.3 Calculate the correlation coefficient between the denoised data and the original data. The closer the value is to 1, the more similar the denoised data is to the original data, that is, the better the denoising effect is. The formula is as follows: ; in, is the original signal, is the signal after noise reduction; 3.4 Calculate the signal-to-noise ratio of the denoised data. The higher the signal-to-noise ratio, the better the denoising performance of the algorithm. The calculation formula is as follows: ; In the formula, N is the data length, is the original signal, is the signal after noise reduction; 3.5 Calculate the root mean square error between the denoised data and the original data. The smaller the value, the better the denoising effect. The calculation formula is as follows: ; 3.6 Sorting Entropy Calculate the permutation entropy of the denoised data. The larger the value, the more noise is removed and the better the denoising effect. The steps for calculating the permutation entropy are as follows: 3.6.1 Given length N Time series data , by arranging these data to obtain different sequences, for length N time series, can be generated N There are different arrangements, each of which corresponds to a new sequence.

[0011] 3.6.2 For each arrangement, the entropy formula in information theory is used to calculate its entropy value. The Shannon entropy is calculated by calculating the frequency distribution of each arrangement and its entropy value, and then averaging the entropy values ​​of all arrangements to obtain the arrangement entropy as the entropy value of the entire time series data. The calculation formula is as follows: ; in, represents the total number of permutations, Indicates i The probability of the arrangement; 3.7 Characterization based on the above evaluation indicators The denoising performance of the data sequence reconstructed under different parameters is evaluated, and the best set of parameters and its corresponding reconstructed data are determined, and finally the denoised monitoring data sequence is obtained.

[0012] The present invention implements the above technical solution and has the following technical effects or advantages: Due to the development of data transmission and storage technology, the amount of water supply network data has exploded, and data noise has caused data quality to decline, which has greatly hindered the implementation of data-driven intelligent management and control methods for water supply networks. Multi-scale decomposition and noise reduction can reduce the complexity of data, but at the same time, some real data are eliminated, while independent noise reduction will increase the complexity of data structure and reduce data stability. The water supply network data quality control method based on multi-scale decomposition fused with independent noise reduction integrates independent noise reduction into the multi-scale decomposition process to process data, which can effectively reduce data distortion and improve the noise reduction effect of water supply network monitoring data series. It has robustness in monitoring data quality control under leakage scenarios with different leakage intensities, which is of great significance to improving the comprehensive performance of intelligent water supply network systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 Flow chart of the water supply network data quality control method for coupling multi-scale decomposition and independent noise reduction; Figure 2 This is a schematic diagram of the water supply network in J City; Figure 3 It is the IMF component waveform diagram; Figure 4 It is the IMF continuous mean square error curve; Figure 5 It is the root mean square error curve of the IMF component denoising result; Figure 6 (a) shows the correlation coefficient of the denoising results of Gaussian filtering, coupled multi-scale decomposition and independent denoising methods ( ); Figure 6 (b) shows the signal-to-noise ratio of the denoising results of Gaussian filtering, coupled multi-scale decomposition and independent denoising methods ( ); Figure 6 (c) shows the root mean square error of the denoising results of Gaussian filtering, coupled multi-scale decomposition and independent denoising methods ( ); Figure 7 (a) shows the correlation coefficient of the denoising results of the coupled multi-scale decomposition and independent denoising methods ( ); Figure 7 (b) shows the signal-to-noise ratio of the denoising results of the coupled multi-scale decomposition and independent denoising methods ( ); Figure 7 (c) shows the root mean square error of the denoising results of the coupled multi-scale decomposition and independent denoising methods ( ); Figure 8 (a) shows the correlation coefficient of the denoising results of the coupled multi-scale decomposition and independent denoising methods (leakage condition and normal condition); Figure 8 (b) is the signal-to-noise ratio diagram of the denoising results of the coupled multi-scale decomposition and independent denoising methods (leakage condition and normal condition); Figure 8 (c) shows the root mean square error diagram of the denoising results of the coupled multi-scale decomposition and independent denoising methods (leakage condition and normal condition). DETAILED DESCRIPTION

[0014] The present invention aims to propose a water supply network data quality control method that couples multi-scale decomposition and independent noise reduction (hereinafter collectively referred to as "the present invention"). The implementation method of the present invention is further described in detail below with reference to the accompanying drawings and examples. Figure 1 The process of the water supply network data quality control method that couples multi-scale decomposition and independent noise reduction is given. The specific steps are as follows: Construct a hydraulic model of the water supply network and obtain the data sequence monitored by the water supply network monitoring system; like Figure 2The figure shows a real medium-sized urban water supply network. City J has three water plants supplying water, 491 water demand nodes and 640 pipe sections, in which 20 pressure sensors have been arranged ( n s =20).

[0015] Establish a node water demand prediction model to predict the future in real time b The node water demand in each period; t The predicted value of water demand at the water demand node at each moment is used as the input of the hydraulic model of the water supply network. The pressure value of the monitoring point (pressure sensor) is simulated using EPANET software (DDA) to obtain t Momentary pressure prediction vector , unit is meter (m), the formula is as follows: ; in, for t Moment Pressure prediction data of each pressure sensor, is the number of pressure sensors; for Column vector of rows; Table 1 t = Predicted water demand at water demand node at time 1 Node Number 1 2 … 240 … 490 491 Water requirement (CMH) 6.83 7.31 … 42.52 … 23.07 36.71 ; Will As model input, simulated Real-time pressure monitoring data , the formula is as follows: ; in, is the pressure prediction data at the first moment, which is a column vector of 20 rows. In the present invention, the data of 240 moments are simulated, and finally data, that is, the data of 20 monitoring points at 240 moments. Here is the simulated pressure value matrix of 20 monitoring points at 240 moments:

[0016] ; The simulated pressure value is affected by the pressure measurement disturbance and the water demand disturbance. The following is an example of adding a disturbance value: Add pressure measurement disturbance to the simulated pressure value to simulate the real data. The error of pressure measurement disturbance follows the standard normal distribution. The noise intensity is given below Example of a pressure vector when : ; Add water demand disturbance to the simulated pressure value. The error of water demand disturbance follows the standard normal distribution N(0, σ ), ; In the formula, σ is the standard deviation of the added disturbance, p is the disturbance ratio, μ is the predicted value of water demand at the water demand node. Here the water demand disturbance is given , Noise intensity Example of adding a water demand disturbance pressure vector: .

[0017] The embodiment of the present invention provides a water supply network data quality control method that couples multi-scale decomposition and independent noise reduction, comprising the following steps: (1) Decompose the monitoring data series and determine the noisy IMF components.

[0018] Step (1) specifically includes: (1.1) Different IMF components are obtained based on ICEEMDAN time series decomposition: To monitor time series Add to i Gaussian white noise with submean 0 , while adding the amplitude of the noise ,form i Sequence to be decomposed ,in i =1,2,3…,n: ; To the top i Perform EMD decomposition on the sequence and find i local means, the original signal Minus this i The average of the local means, the first IMF component is found: ; Where: is the local mean function; The second IMF component is: ; Repeat the above steps until the final remainder is a monotonic function or a constant; Figure 3 This is the decomposition result when adding pressure disturbance to the simulated pressure value. The original data is decomposed into 5 IMF components (IMF1 to IMF5) with high to low frequencies and a remainder. res .

[0019] (1.2) The modified CMSE criterion is used to determine whether the IMF component is noisy: After the data sequence is decomposed by ICEEMDAN, we get m IMF components sorted from high to low frequency and a residual res ; Based on the CMSE criterion, the demarcation point between the noisy IMF component and the non-noisy IMF component is determined by the following calculation method:

[0020] ; In the formula, x is the original signal, N is the signal length, k is the number of decomposition layers; Since the noise is high frequency, the energy of the noise gradually decreases with the decomposition of ICEEMDAN, and the global minimum value of the IMF component energy is used as the dividing point j , see formula: ; This method modifies the above formula. When there is a local minimum before the global minimum is calculated using the CMSE criterion, the cutoff point j The number corresponding to the first local minimum plus 1 should be taken, which is the formula: ; The IMF components before the dividing point are noisy components and require further independent noise reduction; the IMF components after the dividing point are noise-free components, that is, data sequences composed of valid information.

[0021] First calculate the correlation coefficient between each IMF component and the original data. The formula is as follows: ; in, Indicates K IMF components at time t The value of h(t) Represents the original data at time t The value of N Represents the length of the data sequence. The correlation coefficient between the IMF component and the original data is as follows Figure 4 As shown in the figure, when the IMF sequence number is 3, the IMF continuous mean square error curve has the first extreme point. According to the correlation coefficient criterion, the IMF when the first correlation coefficient takes the minimum value is taken as the dividing point. , so IMF1, IMF2 and IMF3 are noisy data, and IMF4 and IMF5 are noise-free data. (2) Independent denoising of the noisy IMF components is performed based on Gaussian filtering.

[0022] Step (2) specifically includes: The one-dimensional expression of Gaussian filtering is: ; Among them, σ is the standard deviation of the function, the standard deviation range is 0.2-0.65, and the value is taken at an interval of 0.05. Gaussian filtering is performed on the noisy IMF component, and each component produces 10 sets of independent denoising results under different parameters.

[0023] Use Gaussian filtering to reduce the noise of each noisy IMF component, with the parameters of Gaussian filtering σ Taking the value range of 0.2-0.65 (interval 0.05) as an example, each noisy IMF component (IMF1, IMF2 and IMF3) produces corresponding 10 denoised components, and a total of 1000 (10^3 = 1000) sets of denoised data sequences are obtained.

[0024] (3) Reconstruct the monitoring data sequence.

[0025] Step (3) specifically includes: (3.1) Assume that k IMF components are reconstructed, and a set of data is selected from the independent denoising results of each component, totaling Group data, The data is reconstructed with the noise-free IMF component to obtain The monitoring data after noise reduction; (3.2) The correlation coefficient CORR, signal-to-noise ratio SNR, root mean square error RMSE and permutation entropy are selected as the evaluation indicators of noise reduction performance; (3.3) Calculate the correlation coefficient between the denoised data and the original data. The closer the value is to 1, the more similar the denoised data is to the original data, that is, the better the denoising effect is. The formula is as follows: ; in, is the original signal, is the signal after noise reduction; (3.4) Calculate the signal-to-noise ratio of the denoised data. The higher the signal-to-noise ratio, the better the denoising performance of the algorithm. The calculation formula is as follows: ; In the formula, N is the data length, is the original signal, is the signal after noise reduction; (3.5) Calculate the root mean square error between the denoised data and the original data. The smaller the value, the better the denoising effect. The calculation formula is as follows: .

[0026] Reconstruct the 1000 denoised data sequences with the remaining IMF4 and IMF5 to obtain 1000 denoised data sets. Calculate the CORR, SNR and RMSE of the denoised data and the original data, as shown in Figure 5 As shown, taking the calculation of RMSE as an example, the RMSE value of the data with 233 groups is the smallest, and the corresponding standard deviations are 0.4, 0.45, and 0.25, respectively. That is, the data with 233 groups has the best denoising effect.

[0027] Based on the above method, the data sequence of 20 monitoring points is traversed, and the noise reduction performance evaluation index is calculated to obtain a set of parameters with the best noise reduction performance and its corresponding reconstructed data. The larger the CORR, the more similar the noise-reduced data is to the data without noise, that is, the more noise is removed. SNR represents the ratio of real data to noise in the data. The larger the SNR, the less noise in the data. RMSE is the square root of the average degree of difference between the noise-reduced data and the original data without noise. The smaller the RMSE, the better the noise reduction effect. Figure 6 (a) to Figure 6 (c) show the noise intensity when the noise intensity is The noise reduction results of using only Gaussian filtering and using the technology of the present invention are compared. The average CORR of the Gaussian filtering method is 0.995475, the average SNR is 43.5782, and the average RMSE is 0.197428. The average CORR of ICEEDMAN combined with the Gaussian filtering method is 0.996323, the average SNR is 44.9861, and the average RMSE is 0.187623. The data of the three evaluation indicators all show that the noise reduction effect of the technology of the present invention is better.

[0028] (3.6) Sorting entropy Calculate the permutation entropy of the denoised data. The larger the value, the more noise is removed and the better the denoising effect. The steps to calculate the permutation entropy are as follows: (3.6.1) Given the length N Time series data , by arranging these data to obtain different sequences, for length N time series, can be generated N There are different arrangements, each of which corresponds to a new sequence; (3.6.2) For each arrangement, the entropy formula in information theory is used to calculate its entropy value. The Shannon entropy is calculated by calculating the frequency distribution of each arrangement and calculating its entropy value; then the entropy values ​​of all arrangements are averaged to obtain the arrangement entropy as the entropy value of the entire time series data. The calculation formula is as follows: ; in, represents the total number of permutations, Indicates i The probability of the arrangement; Calculate the permutation entropy of the two sets of filter residuals. The permutation entropy can reflect the disorder and randomness of the data. The larger the permutation entropy, the more chaotic the data is, indicating that more noise is removed. The noise intensity is given here. The sorting entropy of the two sets of filter residuals in the case of .

[0029] As shown in Table 2, the average permutation entropy of the Gaussian filter residuals of the 20 monitoring points is 0.9491, and the average permutation entropy of the ICEEMDAN combined with the Gaussian filter residuals is 0.9577, that is, the present invention achieves more noise removal and has better noise reduction performance.

[0030] Table 2. Permutation entropy of denoising residuals based on two algorithms Monitoring point number Gaussian filter permutation entropy ICEEMDAN combined with Gaussian filtering permutation entropy 1 0.9479 0.9543 2 0.9518 0.9527 3 0.9523 0.9649 4 0.9469 0.9531 5 0.9507 0.9587 6 0.9454 0.9642 7 0.9520 0.9629 8 0.9473 0.9538 9 0.9455 0.9496 10 0.9522 0.9586 11 0.9490 0.9529 12 0.9488 0.9642 13 0.9481 0.9491 14 0.9530 0.9638 15 0.9491 0.9545 16 0.9507 0.9634 17 0.9467 0.9537 18 0.9497 0.9621 19 0.9481 0.9639 20 0.9485 0.9538 (3.7) Based on the above evaluation indicators The denoising performance of the data sequence reconstructed under different parameters is evaluated, and the best set of parameters and its corresponding reconstructed data are determined, and finally the denoised monitoring data sequence is obtained.

[0031] Experimental results: Figures 7(a) to 7(c) show the water demand disturbances when , noise intensity The noise reduction results of the present invention are shown in Figure 2. The average CORR of the original data is 0.9948, the average SNR is 42.8184, and the average RMSE is 0.1987. After noise reduction, the average CORR increases by 0.0006, the average SNR increases by 0.4013, and the average RMSE decreases by 0.0089. The data of the three evaluation indicators all show that the present invention maintains good noise reduction performance in the water demand disturbance scenario.

[0032] Table 3 gives the noise intensity , the water demand disturbances are When the water demand disturbance ratio increases, the average permutation entropy decreases continuously, that is, the real components filtered out increase continuously. This shows that the water demand disturbance ratio will affect the noise reduction performance of the technology of the present invention.

[0033] Table 3. Denoising residual permutation entropy based on multi-scale decomposition technology integrating independent denoising ( ) Monitoring point number #timg#=5% #timg#=10% 1 0.9368 0.9304 2 0.9451 0.9332 3 0.9443 0.9299 4 0.9389 0.9317 5 0.9467 0.9306 6 0.9461 0.9338 7 0.9354 0.9308 8 0.9361 0.9291 9 0.9419 0.9346 10 0.9396 0.9321 11 0.9515 0.9322 12 0.9468 0.9307 13 0.9426 0.9323 14 0.9472 0.9328 15 0.9489 0.9298 16 0.9518 0.9336 17 0.9342 0.9325 18 0.9347 0.9313 19 0.9475 0.9302 20 0.9363 0.9296 FIG8 (a) to FIG8 (c) show the CORR, SNR and RMSE indicators after noise reduction of the present invention under leakage conditions and normal conditions. leakage) accompanied by noise intensity ( ) as an example, the CORR, SNR and RMSE of the denoised data under normal working conditions and leakage working conditions are generally close, the three indicators of normal working conditions of some nodes are slightly higher than those of leakage conditions, and the three indicators of leakage conditions of some nodes are slightly higher than those of normal working conditions. This shows that the present invention is suitable for quality control of monitoring data in leakage scenarios, and the present invention has a certain robustness in denoising data related to leakage control of water supply pipe networks.

Claims

1. A water supply network data quality control method that couples multi-scale decomposition and independent noise reduction, characterized in that: The steps include: (1) Decompose the monitoring data series and determine the noisy IMF components; (2) Independently denoise the noisy IMF components based on Gaussian filtering; (3) Reconstruct the monitoring data sequence.

2. The water supply network data quality control method of coupled multi-scale decomposition and independent noise reduction as claimed in claim 1 is characterized in that: The step (1) is specifically as follows: (1.1) Different IMF components are obtained based on ICEEMDAN time series decomposition: To monitor time series Add to i Gaussian white noise with submean 0 , while adding the amplitude of the noise ,form i Sequence to be decomposed ,in i =1,2,3…,n: ； To the top i Perform EMD decomposition on the sequence and find i local means, the original signal Minus this i The average of the local means, the first IMF component is found: ； Where: is the local mean function; The second IMF component is: ； Repeat the above steps until the final remainder is a monotonic function or a constant; (1.2) The modified CMSE criterion is used to determine whether the IMF component is noisy: After the data sequence is decomposed by ICEEMDAN, we get m IMF components sorted from high to low frequency and a residual res ; Based on the CMSE criterion, the demarcation point between the noisy IMF component and the non-noisy IMF component is determined. The calculation method is as follows: ； In the formula, x is the original signal, N is the signal length, k is the number of decomposition layers; Since the noise is high frequency, the energy of the noise gradually decreases with the decomposition of ICEEMDAN, and the global minimum value of the IMF component energy is used as the dividing point j , see formula: ； This method modifies the above formula. When there is a local minimum before the global minimum is calculated using the CMSE criterion, the cutoff point j The number corresponding to the first local minimum should be taken plus 1, which is the formula: ； The IMF components before the dividing point are noisy components and require further independent noise reduction; the IMF components after the dividing point are noise-free components, that is, data sequences composed of valid information.

3. The water supply network data quality control method of coupled multi-scale decomposition and independent noise reduction as claimed in claim 1 is characterized in that: The step (2) is specifically as follows: The one-dimensional expression of Gaussian filtering is: ； Among them, σ is the standard deviation of the function, the standard deviation range is 0.2-0.65, and the value is taken at an interval of 0.

05. Gaussian filtering is performed on the noisy IMF component, and each component produces 10 sets of independent denoising results under different parameters.

4. The water supply network data quality control method of coupled multi-scale decomposition and independent noise reduction as claimed in claim 1 is characterized in that: The step (3) is specifically as follows: (3.1) Assume that k IMF components are reconstructed, and a set of data is selected from the independent denoising results of each component, totaling Group data, The data is reconstructed with the noise-free IMF component to obtain The monitoring data after noise reduction; (3.2) The correlation coefficient CORR, signal-to-noise ratio SNR, root mean square error RMSE and permutation entropy are selected as the evaluation indicators of noise reduction performance; (3.3) Calculate the correlation coefficient between the denoised data and the original data. The closer the value is to 1, the more similar the denoised data is to the original data, that is, the better the denoising effect is. The formula is as follows: ； in, is the original signal, is the signal after noise reduction; (3.4) Calculate the signal-to-noise ratio of the denoised data. The higher the signal-to-noise ratio, the better the denoising performance of the algorithm. The calculation formula is as follows: ； In the formula, N is the data length, is the original signal, is the signal after noise reduction; (3.5) Calculate the root mean square error between the denoised data and the original data. The smaller the value, the better the denoising effect. The calculation formula is as follows: ； (3.6) Sorting entropy Calculate the permutation entropy of the denoised data. The larger the value, the more noise is removed and the better the denoising effect. The steps to calculate the permutation entropy are as follows: (3.6.1) Given the length N Time series data , by arranging these data to obtain different sequences, for length N time series, can be generated N There are different arrangements, each of which corresponds to a new sequence; (3.6.2) For each arrangement, the entropy formula in information theory is used to calculate its entropy value. The Shannon entropy is calculated by calculating the frequency distribution of each arrangement and calculating its entropy value; then the entropy values ​​of all arrangements are averaged to obtain the arrangement entropy as the entropy value of the entire time series data. The calculation formula is as follows: ； in, represents the total number of permutations, Indicates i The probability of the arrangement; (3.7) Based on the above evaluation indicators The denoising performance of the data sequence reconstructed under different parameters is evaluated, and the best set of parameters and its corresponding reconstructed data are determined, and finally the denoised monitoring data sequence is obtained.

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