Industrial process parameter denoising method based on segmented ICEEMDAN reconstructed component distribution

Abstract

The application belongs to the technical field of signal processing, and particularly relates to an industrial process parameter denoising method based on segmented ICEEMDAN reconstructed component distribution, which comprises the following steps: performing average segmentation on an original signal based on maximum inter-segment difference; respectively performing empirical mode decomposition on the subsegments after average segmentation; sequentially superimposing and reconstructing the IMF components of each subsegment from high to low frequency; calculating the average Manhattan distance between the empirical probability distributions of the reconstructed components of each subsegment at the same reconstruction position; dividing the IMF components of each subsegment into noise components, signal-to-noise mixed components and signal components based on the change rule of the average Manhattan distance; performing adaptive interval threshold denoising on the signal-to-noise mixed components; reconstructing the signal components, residuals and the signal-to-noise mixed components after denoising; splicing the reconstructed subsegments in chronological order to obtain a final denoised signal. The application can retain the key trends and detailed information of the signal.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology, specifically relating to a method for denoising industrial process parameters based on segmented ICEEMDAN reconstructed component distribution. Background Technology

[0002] Industrial signal denoising is a key technology for improving the accuracy of industrial process monitoring and control. In complex industrial environments, signals acquired by sensors often contain a large amount of nonlinear and non-stationary noise, which traditional linear analysis methods such as Fourier transform are difficult to effectively process. Improved Adaptive Noise Complete Ensemble Empirical Mode Decomposition (ICEEMDAN), as an advanced signal processing method, can adaptively decompose the original signal into multiple intrinsic mode functions (IMFs) and a residual. The IMF components are arranged in descending order of frequency, and the residual reflects the signal's trend information. Denoising methods based on ICEEMDAN typically first decompose the signal, then classify the IMF components using entropy values ​​(such as fuzzy entropy or permutation entropy), dividing them into three categories: noise components, signal-noise mixture components, and signal components. For the signal-noise mixture components, methods such as wavelet thresholding are typically used for further denoising. Finally, the final denoised signal is obtained by reconstructing the signal components, the residual, and the denoised signal-noise mixture components. The core of this method lies in quantifying the noise characteristics of the IMF components through entropy values, thereby achieving effective noise identification and removal.

[0003] However, existing IMF classification methods still have significant limitations in practical applications. First, these methods typically require a fixed entropy threshold to distinguish noise from valid signals. The threshold setting often relies on experience or extensive experimental parameter tuning, lacking adaptability. This fixed threshold approach easily leads to overfitting or underfitting, affecting denoising performance. Second, the entropy distributions of noise and signal components may overlap, especially in mid-frequency signal-noise mixtures. Relying solely on a single entropy metric (such as fuzzy entropy or permutation entropy) is insufficient for accurate classification, potentially leading to valid signals being misclassified as noise and removed. Furthermore, entropy calculation itself is affected by parameters such as embedding dimension and time delay; improper parameter settings can significantly reduce classification reliability. These issues render existing methods inadequate for generalization in complex and dynamic industrial scenarios, making it difficult to meet the demands of high-precision denoising. Summary of the Invention

[0004] As mentioned above, industrial process parameters (such as blast furnace temperature and pressure) are affected by electromagnetic interference and thermal noise during the acquisition process, resulting in low signal-to-noise ratio and strong nonlinearity and non-stationarity. Traditional denoising methods (such as EMD, ICEEMDAN-FE-AITD, etc.) suffer from problems such as mode mixing, strong subjectivity in threshold selection, noise residue or signal distortion, making it difficult to adaptively separate noise from effective signals. Therefore, this invention provides an industrial process parameter denoising method based on segmented ICEEMDAN reconstructed component distribution. This invention mainly improves the screening accuracy of IMF components in the ICEEMDAN-based denoising process by first adaptively segmenting the signal based on the maximum inter-segment difference, and then comparing the similarity of each sub-segment with the improved adaptive noise complete set empirical mode decomposition (ICEEMDAN). This effectively suppresses noise while retaining key trend information, providing a high-precision adaptive solution for industrial process parameter processing. It achieves robust identification of global noise in non-stationary industrial signals, adaptive classification of IMF components, and effective preservation of local signal features while suppressing noise.

[0005] The technical means employed in this invention are as follows:

[0006] A method for denoising industrial process parameters based on piecewise ICEEMDAN reconstructed component distribution includes the following steps:

[0007] Obtain the raw data containing noise;

[0008] The original data is divided into several segments on an average basis. The average absolute error between segments is calculated under different numbers of segments. The number of segments corresponding to the maximum mean absolute error is found. Based on the number of segments corresponding to the maximum mean absolute error, the original data is divided into segments on an average basis to obtain the segments after average segmentation.

[0009] Empirical mode decomposition is performed on each of the sub-segments after average segmentation to obtain the IMF components and residuals of each sub-segment;

[0010] The IMF components of each segment are reconstructed by stacking them up in descending order of frequency, generating several reconstructed components at different reconstructed positions in each segment.

[0011] Calculate the average Manhattan distance between the empirical probability distributions of the reconstructed components at the same reconstruction position for each segment. Based on the variation law of the average Manhattan distance, divide the IMF component of each segment into noise component, signal-noise mixture component and signal component.

[0012] Adaptive interval threshold denoising is performed on the signal-to-noise mixture components;

[0013] The signal components, the residual, and the denoised signal-noise mixture components are reconstructed to obtain the reconstructed segments. The reconstructed segments are then spliced ​​together in time sequence to obtain the final denoised signal.

[0014] Further, the calculation of the average Manhattan distance between the empirical probability distributions of the reconstructed components of each segment at the same reconstructed location includes:

[0015] The empirical probability distribution of the reconstruction components of each segment at each reconstruction location is calculated based on the histogram method.

[0016] For the same reconstruction location, calculate the Manhattan distance of the empirical probability distribution between all pairs of segments, and take the average value to obtain the average Manhattan distance of that reconstruction location. The formula for calculating the Manhattan distance is:

[0017]

[0018] in, For Manhattan distance, Let J be the empirical probability distribution of the j-th reconstructed component in the p-th segment. Let be the empirical probability distribution of the j-th reconstructed component in the q-th segment. B The number of intervals in the histogram. b For histogram interval index, j To reconstruct the location, the formula for calculating the average Manhattan distance is:

[0019]

[0020] in, Let j be the average Manhattan distance. k For the number of segments, p For the p-th segment, q This is the q-th segment.

[0021] Furthermore, based on the variation law of the average Manhattan distance, the IMF component of each segment is divided into a noise component, a mixed signal-noise component, and a signal component, including:

[0022] Traverse all reconstruction locations, find the minimum average Manhattan distance, and classify the IMF components contained in the reconstruction component corresponding to the minimum average Manhattan distance as noise components.

[0023] Calculate the relative rate of change of the average Manhattan distance at each reconstruction location. The reconstruction location corresponding to the point with the maximum relative rate of change is determined as the starting location of the signal component. IMF components following the starting location of the signal component are classified as signal components, while IMF components between the noise component and the starting location of the signal component are classified as mixed signal-noise components. The formula for calculating the relative rate of change of the average Manhattan distance is:

[0024]

[0025] in, Let j be the average Manhattan distance. For the (j+1)th average Manhattan distance, This represents the relative rate of change of the average Manhattan distance. j To reconstruct the location, m This represents the total number of IMF components.

[0026] Further, the adaptive interval threshold denoising of the signal-to-noise mixture includes:

[0027] For each IMF component in the signal-noise mixture, it is divided into multiple local intervals based on its zero-crossing point;

[0028] The threshold for each local interval is dynamically determined based on the noise energy estimate of the IMF component.

[0029] An extreme value correlation shrinkage function is used to adaptively adjust the extreme values ​​in each local interval based on the dynamically determined threshold, so as to suppress noise and preserve signal characteristics.

[0030] Furthermore, the calculation formula for the threshold of each local interval is as follows:

[0031]

[0032] in, Let be the threshold of the i-th local interval. This is the threshold adjustment constant. Let i be the energy of the i-th IMF component. Let be the length of the IMF component, and the formula for calculating the energy of the i-th IMF component is:

[0033]

[0034] in, For the first signal-to-noise mixing IMF component, i This is the index number of the signal-to-noise hybrid IMF component. The energy of the first signal-to-noise mixing IMF component. The energy decay coefficient, The power exponent of energy decay. It is the median operator.

[0035] Furthermore, the formula for calculating the extreme value-related adaptive shrinkage function is as follows:

[0036]

[0037] in, For the j-th interval where the i-th IMF component is thresholded, Let be the original value of the i-th IMF component in the j-th interval. For shrinkage strength parameters, This is the local threshold scaling factor. Let be the extreme value of the i-th IMF in the j-th interval. Let be the threshold for the i-th local interval, and the formula for calculating the local threshold scaling factor is:

[0038] .

[0039] Furthermore, the formula for calculating the mean absolute error is as follows:

[0040]

[0041] in, The mean absolute error, The number of midpoints in the sub-segment. For the i-th data point in the first sub-segment, This is the i-th data point in the second sub-segment.

[0042] Furthermore, the formulas for calculating the IMF components and residuals of each segment are as follows:

[0043]

[0044] in, The sub-segments are the result of equal segmentation. For IMF components, For residuals, The number of IMF components obtained from the decomposition. This is the first index variable.

[0045] Furthermore, the calculation formula for the reconstructed components is as follows:

[0046]

[0047] in, To reconstruct the components, For IMF components, j To reconstruct the location, l This is the second index variable.

[0048] Further, the reconstructed signal component, the residual, and the denoised signal-to-noise mixture component are combined to obtain the reconstructed sub-segment, including:

[0049] Based on the signal components, the IMF component, the denoised signal-to-noise mixture component, and the corresponding residual are linearly superimposed to obtain the reconstructed sub-segment. The calculation formula for the reconstructed sub-segment is as follows:

[0050]

[0051] in, For the reconstructed sub-segment, For signal components, For signal-to-noise mixing components, For IMF components, This refers to the signal-to-noise mixture component after denoising. It represents the residual.

[0052] Compared with the prior art, the present invention has the following advantages:

[0053] 1. This invention divides the signal into segments with significant trend differences by maximizing the mean absolute error (MAE) between segments, thus avoiding misclassification of IMF components caused by the high similarity of the real signals within each segment.

[0054] 2. This invention reconstructs the segmented IMF components from high frequency to low frequency, calculates the Manhattan distance similarity of the reconstructed component distributions at the same location between different segments, and adaptively classifies them into noise components, signal-noise mixture components, and signal components. This avoids the subjective bias of manual thresholding and improves the objectivity of noise component identification; through the analysis of the extreme points of the Manhattan distance, it accurately separates high-frequency noise from low-frequency effective signals.

[0055] 3. This invention employs an extreme value correlation contraction function for the signal-noise mixture component, combined with noise energy estimation to dynamically adjust the threshold, achieving interval-level denoising. It preserves local signal characteristics and reduces waveform distortion; by suppressing residual noise through adaptive thresholding, it balances the accuracy of noise suppression and signal preservation.

[0056] In metallurgical production, this method can be applied to denoising key blast furnace parameters (such as oxygen enrichment, temperature, pressure, and flow rate). By suppressing high-frequency interference such as electromagnetic interference and thermal noise, it retains key trends and detailed information of the signal, providing high signal-to-noise ratio data support for precise furnace condition analysis and production control. Furthermore, its adaptive characteristics can be extended to fields such as chemical process parameter monitoring, mechanical vibration signal analysis, and environmental noise suppression, providing technical support for the precise analysis of complex industrial data and production optimization. Through segmented decomposition and distribution similarity comparison, the screening accuracy of IMF components in the ICEEMDAN-based denoising process is improved, effectively suppressing noise while retaining key trend information, providing a high-precision adaptive solution for industrial process parameter processing.

[0057] For the reasons stated above, this invention can be widely applied in fields such as signal processing. Attached Figure Description

[0058] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0059] Figure 1 This is a schematic diagram of the process flow of the present invention, which is a method for denoising industrial process parameters based on the segmented ICEEMDAN reconstructed component distribution.

[0060] Figure 2 This is a flowchart illustrating the division of noise components, mixed signal-noise components, and signal components in this invention.

[0061] Figure 3 This is a diagram showing the denoising result of the simulated signal in Embodiment 1 of the present invention.

[0062] Figure 4 This is a denoising result diagram of the measured data of oxygen enrichment in a blast furnace in Example 2 of the present invention. Detailed Implementation

[0063] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0064] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0065] The purpose of this invention is to design an industrial parameter adaptive denoising method based on segmented ICEEMDAN reconstructed component distribution similarity IMF classification, in order to solve the problems of strong threshold dependence and inaccurate screening in the IMF component classification of denoising methods based on ICEEMDAN decomposition.

[0066] In industrial process parameters, noise components oscillate at higher frequencies than the true signal components. The high-frequency IMF components obtained from signal decomposition contain a significant amount of noise, which gradually decreases as the IMF component frequency decreases. This type of noise is typically unaffected by the true signal components, exhibiting additive white Gaussian noise. It is prevalent in various industrial production processes, displaying similar distribution characteristics across different time periods, and is stationary noise independent of the operating conditions. Therefore, if a combination of IMF components with a similar distribution pattern is found within a range where the original signal fluctuation trend changes significantly, it can be considered a combination of additive noise commonly present in the signal. Conversely, combinations of IMF components with lower distribution similarity contain more of the true signal components.

[0067] First, the signal is divided into segments with significant trend differences by maximizing the inter-segment differences, and each segment is decomposed using ICEEMDAN. Next, the IMF components of each segment are reconstructed from high frequency to low frequency. Based on the Manhattan distance similarity of the component distribution at the same reconstruction position in different segments, the IMF is adaptively classified into noise, signal-noise mixture, and signal components. Finally, adaptive interval threshold denoising (AITD) is applied to the signal-noise mixture components, and the final denoised signal is obtained by reconstructing the signal components, residuals, and denoised signal-noise mixture components.

[0068] like Figure 1 As shown, this invention provides a method for denoising industrial process parameters based on piecewise ICEEMDAN reconstructed component distribution, the specific steps of which are as follows:

[0069] S1. Obtain the raw data containing noise. X .

[0070] S2. Divide the original data into several segments on an average basis, calculate the mean absolute error (MAE) between segments under different numbers of segments, find the number of segments corresponding to the maximum mean MAE, and divide the original data into segments on an average basis based on the number of segments corresponding to the maximum mean absolute error, to obtain the segments after average segmentation.

[0071] Specifically, the number of candidate segments is set to 2~10. The mean of MAE between all pairs of segments is calculated. The number of segments k that maximizes the mean MAE is selected as the optimal number of segments. The original data is then divided into S1, S2, ..., S... k .

[0072] The formula for calculating the mean absolute error is:

[0073]

[0074] in, The mean absolute error, The number of midpoints in the sub-segment. For the i-th data point in the first sub-segment, This is the i-th data point in the second sub-segment.

[0075] S3. Perform improved adaptive noise complete set empirical mode decomposition (ICEEMDAN) on each of the sub-segments after average segmentation to obtain the IMF components and residuals of each sub-segment.

[0076] The formulas for calculating the IMF components and residuals for each segment are as follows:

[0077]

[0078] in, The sub-segments are the result of equal segmentation. For IMF components, For residuals, The number of IMF components obtained from the decomposition. This is the first index variable.

[0079] S4. The IMF components of each sub-segment are reconstructed by stacking them up in descending order of frequency, generating several reconstructed components at different reconstructed positions of each sub-segment.

[0080] The formula for calculating the reconstructed components is:

[0081]

[0082] in, The reconstructed component contains the reconstructed components of the first j components of the i-th segment. l This is the second index variable. The formula represents a method of reconstructing the data by progressively stacking frequencies from high to low.

[0083] S5. Calculate the average Manhattan distance between the empirical probability distributions of the reconstructed components at the same reconstruction position for each sub-segment. Based on the variation law of the average Manhattan distance, divide the IMF component of each sub-segment into noise component, signal-noise mixture component and signal component.

[0084] S5 specifically refers to:

[0085] S51. Calculate the empirical probability distribution of the reconstruction components of each segment at each reconstruction position based on the histogram method.

[0086] Among them, the number of histogram intervals B The optimal value is 20~50, for the j-th reconstructed component of the i-th segment. The empirical probability distribution is obtained as follows: , .

[0087] S52. For the same reconstruction location, calculate the Manhattan distance of the empirical probability distribution between all pairs of segments, and take the average value to obtain the average Manhattan distance of that reconstruction location. The formula for calculating the Manhattan distance is:

[0088]

[0089] in, For Manhattan distance, Let J be the empirical probability distribution of the j-th reconstructed component in the p-th segment. Let be the empirical probability distribution of the j-th reconstructed component in the q-th segment. B The number of intervals in the histogram. b For histogram interval index, j To reconstruct the location, the formula for calculating the average Manhattan distance is:

[0090]

[0091] in, Let j be the average Manhattan distance. k For the number of segments, p For the p-th segment, q This is the q-th segment.

[0092] S53. Iterate through all reconstruction locations, find the minimum average Manhattan distance, and extract the IMF component contained in the reconstruction component corresponding to the minimum value. Classified as noise components, the set of noise components is The formula for calculating the reconstruction location corresponding to the minimum Manhattan distance is:

[0093]

[0094] in, This represents the reconstructed location corresponding to the minimum mean Manhattan distance.

[0095] S54. Calculate the relative rate of change of the average Manhattan distance at each reconstruction location, and determine the reconstruction location corresponding to the point with the maximum relative rate of change as the starting location of the signal component. The IMF components after the starting location of the signal component... Classified as a signal component, the IMF component lies between the noise component and the starting position of the signal component. Classified as signal-to-noise mixture components, the set of signal-to-noise mixture components is: The formula for calculating the relative rate of change of the average Manhattan distance is:

[0096]

[0097] in, Let j be the average Manhattan distance. For the (j+1)th average Manhattan distance, This represents the relative rate of change of the average Manhattan distance. j To reconstruct the location, m This represents the total number of IMF components.

[0098] The formula for calculating the maximum point of the relative rate of change is:

[0099]

[0100] in, This is the point where the relative rate of change reaches its maximum.

[0101] The relevant discussions for S1~S5 are as follows: Figure 2 As shown.

[0102] S6. Perform adaptive interval threshold denoising on the signal-noise mixture components.

[0103] S6 specifically refers to:

[0104] S61. For each IMF component in the signal-noise mixture, it is divided into multiple local intervals based on its zero-crossing point.

[0105] S62. Based on the noise energy estimate of the IMF components, dynamically determine the threshold for each local interval. The calculation formula for the threshold of each local interval is:

[0106]

[0107] in, Let be the threshold of the i-th local interval. This is the threshold adjustment constant, with a value ranging from 0.6 to 0.8. Let i be the energy of the i-th IMF component. Let be the length of the IMF component, and the formula for calculating the energy of the i-th IMF component is:

[0108]

[0109] in, For the first signal-to-noise mixing IMF component, i This is the index number of the signal-to-noise hybrid IMF component. The energy of the first signal-to-noise mixing IMF component. The energy decay coefficient is 0.719. The energy decay exponent is 2.01. It is the median operator.

[0110] S63. An extreme value correlation shrinkage function is used to adaptively adjust the extreme values ​​in each local interval based on a dynamically determined threshold in order to suppress noise and preserve signal characteristics.

[0111] The formula for calculating the extreme value-related adaptive contraction function is:

[0112]

[0113] in, For the j-th interval of the i-th IMF that has already been thresholded, This represents the original value of the j-th interval of the i-th IMF. This is a shrinkage strength parameter, typically set to 5. This is the local threshold scaling factor. Let be the extreme value of the i-th IMF in the j-th interval. Let be the threshold value for the i-th local interval.

[0114] The formula for calculating the local threshold scaling factor is:

[0115] .

[0116] S7. Reconstruct the signal components, residuals, and denoised signal-noise mixture components to obtain the reconstructed segments, and then concatenate the reconstructed segments in time sequence to obtain the final denoised signal.

[0117] Specifically, S7 is as follows: Based on the signal components, the IMF component, the denoised signal-to-noise mixture component, and the corresponding residual are linearly superimposed to obtain the reconstructed sub-segment. The calculation formula for the reconstructed sub-segment is:

[0118]

[0119] in, For the reconstructed sub-segment, For signal components, For signal-to-noise mixing components, For IMF components, This is the signal-to-noise mixture component after denoising.

[0120] Example 1

[0121] A simulated signal was generated, comprising a high-amplitude low-frequency signal (0.1Hz), a frequency-modulated signal (5-15Hz), and an amplitude-modulated signal (20Hz). The sampling frequency was 1000Hz, the duration was 5 seconds, and 5000 sampling points were generated. Gaussian white noise with a signal-to-noise ratio of 10dB was superimposed on the simulated signal to obtain a noisy signal. The noisy data was optimized to have 3 segments by maximizing the mean of the mean (MAE). The three segments were decomposed: the first and second segments yielded 8 IMF components, and the third segment yielded 9 IMF components. Based on the decomposition criteria, IMF1-IMF5 of the three segments were classified as noise components, IMF8 of the first and second segments as signal components, IMF8 and IMF9 of the third segment as signal components, and IMF6 and IMF7 of the three segments as mixed signal-to-noise components. Then, adaptive threshold denoising is performed on the mixed signal-noise component data. Finally, the denoised mixed signal-noise component is reconstructed with the signal component and residual, and the denoised data of each segment is concatenated in time sequence to obtain the final denoised signal. The original signal, the denoised signal, and the denoised signal results of the method of this invention are as follows: Figure 3 As shown, the signal-to-noise ratio (SNR) after denoising reaches 28.66 dB, and the root mean square error (RMSE) is as low as 0.147.

[0122] Example 2

[0123] Measured oxygen enrichment data from Liuzhou Iron and Steel Group's No. 2 blast furnace were obtained, with a sampling interval of 30 seconds and a duration of 48 hours, totaling 5760 data points. The optimal number of segments was determined to be 2 using the MAE (Mean Average Estimated Value) maximization principle. Each segment was decomposed into 10 IMF (Integrated Motion Component) components. Based on the division criteria, IMF1-IMF6 were classified as noise components, IMF8-IMF10 as signal components, and IMF7 as a mixed signal-noise component. Adaptive threshold denoising was performed on the mixed signal-noise component data. Finally, the denoised mixed signal-noise component was reconstructed with the signal component and residual, and then the denoised data from each segment was concatenated in time sequence to obtain the final denoised signal. The original oxygen enrichment signal and the denoised signal results are shown below. Figure 4 As shown, the noise reduction method of the present invention can effectively suppress noise while avoiding the loss of useful information.

[0124] The sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0125] In the above embodiments of the present invention, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0126] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for denoising industrial process parameters based on piecewise ICEEMDAN reconstructed component distribution, characterized in that, Includes the following steps: Obtain raw data containing noise, wherein the raw data is the measured data of oxygen enrichment in the blast furnace; The original data is divided into several segments on an average basis. The average absolute error between segments is calculated under different numbers of segments. The number of segments corresponding to the maximum mean absolute error is found. Based on the number of segments corresponding to the maximum mean absolute error, the original data is divided into segments on an average basis to obtain the segments after average segmentation. Empirical mode decomposition is performed on each of the sub-segments after average segmentation to obtain the IMF components and residuals of each sub-segment; The IMF components of each segment are reconstructed by stacking them up in descending order of frequency, generating several reconstructed components at different reconstructed positions in each segment. Calculate the average Manhattan distance between the empirical probability distributions of the reconstructed components at the same reconstruction position for each segment. Based on the variation law of the average Manhattan distance, divide the IMF component of each segment into noise component, signal-noise mixture component and signal component. The signal-to-noise mixture is divided into multiple local intervals for adaptive interval threshold denoising. The signal components, the residual, and the denoised signal-noise mixture components are reconstructed to obtain the reconstructed segments. The reconstructed segments are then spliced ​​together in time sequence to obtain the final denoised signal.

2. The method for denoising industrial process parameters based on piecewise ICEEMDAN reconstructed component distribution according to claim 1, characterized in that, The calculation of the average Manhattan distance between the empirical probability distributions of the reconstructed components of each segment at the same reconstructed location includes: The empirical probability distribution of the reconstruction components of each segment at each reconstruction location is calculated based on the histogram method. For the same reconstruction location, calculate the Manhattan distance of the empirical probability distribution between all pairs of segments, and take the average value to obtain the average Manhattan distance of that reconstruction location. The formula for calculating the Manhattan distance is: in, For Manhattan distance, Let J be the empirical probability distribution of the j-th reconstructed component in the p-th segment. Let be the empirical probability distribution of the j-th reconstructed component in the q-th segment. B The number of intervals in the histogram. b For histogram interval index, j To reconstruct the location, the formula for calculating the average Manhattan distance is: in, Let j be the average Manhattan distance. k For the number of segments, p For the p-th segment, q This is the q-th segment.

3. The method for denoising industrial process parameters based on piecewise ICEEMDAN reconstructed component distribution according to claim 1, characterized in that, Based on the variation law of the average Manhattan distance, the IMF component of each sub-segment is divided into a noise component, a mixed signal-noise component, and a signal component, including: Traverse all reconstruction locations, find the minimum average Manhattan distance, and classify the IMF components contained in the reconstruction component corresponding to the minimum average Manhattan distance as noise components. Calculate the relative rate of change of the average Manhattan distance at each reconstruction location. The reconstruction location corresponding to the point with the maximum relative rate of change is determined as the starting location of the signal component. IMF components following the starting location of the signal component are classified as signal components, while IMF components between the noise component and the starting location of the signal component are classified as mixed signal-noise components. The formula for calculating the relative rate of change of the average Manhattan distance is: in, Let j be the average Manhattan distance. For the (j+1)th average Manhattan distance, This represents the relative rate of change of the average Manhattan distance. j To reconstruct the location, m This represents the total number of IMF components.

4. The method for denoising industrial process parameters based on piecewise ICEEMDAN reconstructed component distribution according to claim 1, characterized in that, The step of dividing the signal-to-noise mixture into multiple local intervals and performing adaptive interval threshold denoising includes: For each IMF component in the signal-noise mixture, it is divided into multiple local intervals based on its zero-crossing point; The threshold for each local interval is dynamically determined based on the noise energy estimate of the IMF component. An extreme value correlation shrinkage function is used to adaptively adjust the extreme values ​​in each local interval based on the dynamically determined threshold, so as to suppress noise and preserve signal characteristics.

5. The method for denoising industrial process parameters based on piecewise ICEEMDAN reconstructed component distribution according to claim 4, characterized in that, The calculation formula for the threshold of each local interval is as follows: in, Let be the threshold of the i-th local interval. This is the threshold adjustment constant. Let i be the energy of the i-th IMF component. Let be the length of the IMF component, and the formula for calculating the energy of the i-th IMF component is: in, For the first signal-to-noise mixing IMF component, i This is the index number of the signal-to-noise hybrid IMF component. The energy of the first signal-to-noise mixing IMF component. The energy decay coefficient, The power exponent of energy decay. It is the median operator.

6. The method for denoising industrial process parameters based on piecewise ICEEMDAN reconstructed component distribution according to claim 4, characterized in that, The formula for calculating the extreme value-related contraction function is as follows: in, For the j-th interval where the i-th IMF component is thresholded, Let be the original value of the i-th IMF component in the j-th interval. For shrinkage strength parameters, This is the local threshold scaling factor. Let be the extreme value of the i-th IMF in the j-th interval. Let be the threshold for the i-th local interval, and the formula for calculating the local threshold scaling factor is: 。 7. The method for denoising industrial process parameters based on piecewise ICEEMDAN reconstructed component distribution according to claim 1, characterized in that, The formula for calculating the mean absolute error is: in, The mean absolute error, The number of midpoints in the sub-segment. For the i-th data point in the first sub-segment, This is the i-th data point in the second sub-segment.

8. The method for denoising industrial process parameters based on piecewise ICEEMDAN reconstructed component distribution according to claim 1, characterized in that, The formulas for calculating the IMF components and residuals of each segment are as follows: in, The sub-segments are the result of equal segmentation. For IMF components, For residuals, The number of IMF components obtained from the decomposition. This is the first index variable.

9. The method for denoising industrial process parameters based on piecewise ICEEMDAN reconstructed component distribution according to claim 1, characterized in that, The formula for calculating the reconstructed components is: in, To reconstruct the components, For IMF components, j To reconstruct the location, l This is the second index variable.

10. The method for denoising industrial process parameters based on piecewise ICEEMDAN reconstructed component distribution according to claim 1, characterized in that, The reconstructing of the signal component, the residual, and the denoised signal-to-noise mixture component yields a reconstructed sub-segment, including: Based on the signal components, the IMF component, the denoised signal-to-noise mixture component, and the corresponding residual are linearly superimposed to obtain the reconstructed sub-segment. The calculation formula for the reconstructed sub-segment is as follows: in, For the reconstructed sub-segment, For signal components, For signal-to-noise mixing components, For IMF components, This refers to the signal-to-noise mixture component after denoising. It represents the residual.

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