A method and system for filling missing data in industrial sensors based on EEMD

Abstract

This invention relates to a method and system for filling in missing data in industrial sensors based on EEMD. The method includes the following steps: Step 1, collecting process data from the equipment and performing preprocessing; Step 2, decomposing continuous data based on EEMD; Step 3, filling in missing values ​​in discontinuous subsequences; Step 4, obtaining complete sensor data after filling, thus realizing the method for filling in missing data in industrial sensors. This invention also relates to a system for filling in missing data in industrial sensors based on EEMD, the system including a computer module for running the method. This invention can decompose industrial sensor data into a number of constrained intrinsic mode functions, reflecting local characteristics at different time scales and frequencies. This invention analyzes and processes different frequency components separately, taking into account the changing trends of signal components at different frequencies, to achieve the filling in of missing data in industrial sensors.

Description

Technical Field

[0001] This invention belongs to the field of industrial data analysis and processing technology, specifically relating to a method and system for filling missing data in industrial sensors based on EEMD. Background Technology

[0002] With the continuous upgrading of sensor equipment and communication technologies, acquiring industrial data has become increasingly easier. System control, fault diagnosis, process monitoring, and intelligent operation and maintenance based on big data analytics have become hot research topics. In real-world operations, factors such as the complex structure of industrial equipment, long operating times, external environmental interference, packet loss during data transmission, and malfunctions in sensing and measurement elements can directly or indirectly lead to varying degrees of data loss during acquisition and storage. However, big data analytics is highly dependent on data; the quality of the raw data directly affects the performance of the analysis. Therefore, employing appropriate methods to fill in missing values ​​in industrial sensor data and improve data quality is of great significance for subsequent analysis.

[0003] Currently, missing value handling can be divided into direct deletion and missing value imputation. Direct deletion is only suitable for cases with a small amount of missing data, but it can lead to data loss and the loss of some useful information. Missing value imputation methods use known information as an aid to find suitable replacement values, and can be divided into simple imputation and multiple imputation. Simple imputation calculates missing values ​​by using the mean, mode, linear relationship, and nearest neighbor of known values. Multiple imputation obtains multiple complete datasets through multiple imputation steps, and then obtains the imputation result according to certain criteria. Simple imputation fills in fixed values, which cannot reflect the uncertainty of the original data and causes significant bias; multiple imputation requires obtaining the internal relationships in the data, making the analysis process more complex.

[0004] When filling in missing data from industrial sensors, traditional processing methods that analyze the signal as a whole often fail to take into account the characteristics of signals at different frequencies, leading to information loss. Therefore, there is an urgent need for an EEMD-based method and system for filling in missing industrial sensor data, capable of effectively filling in missing data from a completeness perspective, ensuring it conforms to the characteristics of the signal in different frequency bands. Summary of the Invention

[0005] This invention addresses the shortcomings of existing technologies by proposing a method and system for filling in missing data in industrial sensors based on EEMD, thereby improving data quality and laying the foundation for subsequent data analysis.

[0006] This invention relates to a method for filling in missing data in industrial sensors based on EEMD, comprising the following steps:

[0007] Step 1: Collect process data from the equipment and perform preprocessing;

[0008] Step 2: Decompose the continuous data based on EEMD;

[0009] Step 3: Impute missing values ​​in non-continuous subsequences;

[0010] Step 4: Obtain the complete sensor data after filling, realizing the method for filling missing data in industrial sensors.

[0011] Furthermore, in step 1, the process data of the industrial equipment during operation is collected using sensors, the missing values ​​in the data are analyzed, the coordinates of the missing values ​​are recorded, the missing data parts are deleted, and the data is merged into a continuous data segment.

[0012] Further, in step 2, for the continuous data segment merged in step 1, the intrinsic mode function components and residual components are obtained by EEMD decomposition. The intrinsic mode function components are divided into three parts: high-frequency components, low-frequency components, and trend components according to the number of zero crossings. The components in each part are accumulated to obtain three component signals: high-frequency component, low-frequency component, and trend component, as well as one residual component signal.

[0013] Furthermore, in step 2, the method for decomposing continuous data based on EEMD is as follows:

[0014] Step 2-1: Assume the signal to be decomposed is x(t), the time is t, the total average frequency is m, the noise figure is α, and the IMF constraint parameter is N;

[0015] Step 2-2: When performing the i-th decomposition process on the signal x(t), add white noise ni(t) with a standard normal distribution to obtain the signal to be decomposed in the i-th step as x. i (t)=x(t)+α×n i (t), where i = 1, 2, 3, ..., m;

[0016] Steps 2-3, for x i (t) Perform EMD processing to obtain a set of n intrinsic mode function components c ij (t) and a residual component r i (t), then we have Where n≤N, j=1,2,3,…,n;

[0017] Step 2-4: Repeat steps 2-2 and 2-3 a total of m times to obtain m sets of IMF components obtained from EMD decomposition and residual terms. Then, using the EEMD approach, perform a ensemble average on the corresponding IMF components and residual components, as shown in the following formula:

[0018]

[0019]

[0020]

[0021] Steps 2-5: Obtain the eigenmode function components and residual components through EEMD decomposition; for the eigenmode functions obtained by EEMD decomposition, count the number of zero crossings q for each component. j Calculate the average of all zero-crossing times. This is used as the dividing threshold; based on the number of times each component crosses zero, it is divided into three parts: high-frequency components, low-frequency components, and trend components, as follows:

[0022]

[0023] By accumulating each combination to obtain the corresponding component, the original signal, after EEMD decomposition, yields four continuous subsequences: high-frequency component, low-frequency component, trend component, and residual component.

[0024] Furthermore, in step 3, missing values ​​are inserted into the high-frequency components, low-frequency components, trend components, and residual components obtained in step 2 according to the missing value coordinates recorded in step 1, resulting in four non-continuous subsequences with missing values.

[0025] Furthermore, in step 3, missing values ​​of discontinuous subsequences are filled according to different components of the signal. The filling methods for high-frequency components and residual components are as follows: First, median filling is performed to make the missing data conform to the distribution of the original data to the greatest extent. Second, third-order spline filling is performed on the two parts of data to make the missing data conform to the data change trend to the greatest extent. The average value of the data obtained by the two filling methods is calculated as the filling data for high-frequency components and residual components.

[0026] Furthermore, in step 3, the filling method for low-frequency components and trend components is as follows: perform third-order spline filling on low-frequency components and trend components to obtain the filled data of low-frequency components and trend components.

[0027] Furthermore, in step 4, the complete high-frequency components, low-frequency components, trend components, and residual components obtained in step 3 are reconstructed to obtain the filled complete signal.

[0028] The present invention also relates to a system for an EEMD-based method for filling missing data in industrial sensors, the system comprising a computer module for running the EEMD-based method for filling missing data in industrial sensors.

[0029] Beneficial effects

[0030] The present invention provides an EEMD-based method for filling in missing data in industrial sensors. This method decomposes industrial sensor data into a constrained number of intrinsic mode functions (IMFs), reflecting local characteristics at different time scales and frequencies. The invention analyzes and processes different frequency components separately, taking into account the changing trends of signal components at different frequencies, thereby achieving the filling of missing data in industrial sensors. Attached Figure Description

[0031] Figure 1 This is an overall flowchart of the missing data filling method for industrial sensors based on EEMD according to the present invention;

[0032] Figure 2 This refers to the engine speed signal without any missing data collected in this embodiment of the invention.

[0033] Figure 3 This refers to the rotational speed signal with missing values ​​after random missing value processing in an embodiment of the present invention.

[0034] Figure 4a The intrinsic mode function (IMF1) is obtained by decomposing continuous data with missing values ​​removed in the example using EEMD.

[0035] Figure 4b The intrinsic mode function (IMF2) is obtained by decomposing continuous data with missing values ​​removed in the example using EEMD.

[0036] Figure 4c The intrinsic mode function (IMF3) is obtained by decomposing continuous data with missing values ​​removed in the example using EEMD.

[0037] Figure 4d The intrinsic mode function (IMF4) is obtained by decomposing continuous data with missing values ​​removed in the example using EEMD.

[0038] Figure 4e The intrinsic mode function (IMF5) is obtained by decomposing continuous data with missing values ​​removed in the example using EEMD.

[0039] Figure 4f The intrinsic mode function (IMF6) is obtained by decomposing continuous data with missing values ​​removed in the example using EEMD.

[0040] Figure 4g The intrinsic mode function (IMF7) is obtained by decomposing continuous data with missing values ​​removed in the example using EEMD.

[0041] Figure 4h The residual component Res is obtained by decomposing continuous data with missing values ​​removed in the example using EEMD.

[0042] Figure 5a The high-frequency components of the missing values ​​are inserted in the examples;

[0043] Figure 5b The examples show the low-frequency components with missing values ​​inserted.

[0044] Figure 5c This is a trend component for inserting missing values ​​in the examples;

[0045] Figure 5d This refers to the residual component of the inserted missing values ​​in the example;

[0046] Figure 6a This is the complete subsequence after filling in the high-frequency components with missing values ​​in the example;

[0047] Figure 6b This is the complete subsequence after filling in the low-frequency components with missing values ​​in the example;

[0048] Figure 6c This is the complete subsequence after imputing the trend components with missing values ​​in the example;

[0049] Figure 6d This is the complete subsequence after imputing the residual components with missing values ​​in the example;

[0050] Figure 7 The complete data obtained after filling in the missing industrial sensor data in the embodiment using the method of the present invention. Detailed Implementation

[0051] The following combination Figures 1 to 7 This implementation method will be described in detail.

[0052] This invention relates to a method for filling in missing data in industrial sensors based on EEMD, comprising the following steps:

[0053] Step 1: Collect process data from the equipment and perform preprocessing.

[0054] Sensors are used to collect process data during the operation of industrial equipment. The system analyzes the missing values ​​in the data and records their coordinates. Based on this, the missing data segments are deleted, and the data is merged into a single continuous data segment.

[0055] Step 2: Decompose the continuous data based on EEMD (Ensemble Empirical Mode Decomposition).

[0056] For the continuous data segments merged in step 1, EEMD decomposition is used to obtain intrinsic mode function (IMF) components and residual components. Based on the number of zero-crossing points of the IMF components, they are divided into three parts: high-frequency components, low-frequency components, and trend components. The components in each part are accumulated to obtain three component signals: high-frequency component, low-frequency component, and trend component, as well as one residual component signal. The specific implementation method is as follows:

[0057] Step 2-1: Assume the signal to be decomposed is x(t), the time is t, the total average frequency is m, the noise figure is α, and the IMF (Intrinsic Mode Function) constraint parameter is N.

[0058] Step 2-2: When performing the i-th decomposition process on the signal x(t), add white noise ni(t) with a standard normal distribution to obtain the signal to be decomposed in the i-th step as x. i (t)=x(t)+α×n i (t), where i = 1, 2, 3, ..., m.

[0059] Steps 2-3, for x i (t) Perform EMD (Empirical Mode Decomposition) processing to obtain a set of n intrinsic mode function components c. ij (t) and a residual component r i (t), then we have Where n≤N, j=1,2,3,…,n.

[0060] Step 2-4: Repeat steps 2-2 and 2-3 a total of m times to obtain m sets of IMF components obtained from EMD decomposition and residual terms. Then, using the EEMD approach, perform a ensemble average on the corresponding IMF components and residual components, as shown in the following formula:

[0061]

[0062]

[0063]

[0064] Steps 2-5: Obtain the eigenmode function components and residual components through EEMD decomposition; for the eigenmode functions obtained by EEMD decomposition, count the number of zero crossings q for each component. j Calculate the average of all zero-crossing times. This is used as the dividing threshold; based on the number of times each component crosses zero, it is divided into three parts: high-frequency components, low-frequency components, and trend components, as follows:

[0065]

[0066] By accumulating each combination to obtain the corresponding component, the original signal, after EEMD decomposition, yields four continuous subsequences: high-frequency component, low-frequency component, trend component, and residual component.

[0067] Step 3: Impute missing values ​​in non-continuous subsequences.

[0068] According to the missing value coordinates recorded in step 1, insert null values ​​into the high-frequency component, low-frequency component, trend component and residual component obtained in step 2 to obtain 4 non-continuous subsequences with missing values; among them, the high-frequency component and residual component change more drastically, while the low-frequency component and trend component have relatively smooth waveforms.

[0069] Missing values ​​in discontinuous subsequences are filled according to different components of the signal. The filling method is as follows: For high-frequency components and residual components, median filling is performed first to make the missing data conform to the distribution of the original data as much as possible. Then, third-order spline filling is performed on the two parts of data to make the missing data conform to the data change trend as much as possible. The average value of the data obtained by the two filling methods is calculated as the filling data for high-frequency components and residual components.

[0070] Third-order spline filling is performed on the low-frequency and trend components to obtain the filled data of the low-frequency and trend components.

[0071] Step 4: Obtain the complete sensor data after filling, realizing the method for filling missing data in industrial sensors.

[0072] The complete high-frequency components, low-frequency components, trend components, and residual components obtained in step 3 are reconstructed to obtain the filled complete signal.

[0073] The present invention also relates to a system for an EEMD-based method for filling missing data in industrial sensors, the system comprising a computer module for running the EEMD-based method for filling missing data in industrial sensors.

[0074] Example:

[0075] Figure 1 This is an overall flowchart of the missing data filling method for industrial sensors based on EEMD according to the present invention.

[0076] Step 1: Collect process data from the equipment and perform preprocessing.

[0077] The engine speed signal of an industrial device during operation is collected using a speed sensor. The signal length is 300. The original complete signal is as follows: Figure 2 As shown. To verify the effectiveness of this invention, the original signal was randomly delimited, resulting in 43 missing values. The incomplete data containing these missing values ​​is shown below. Figure 3 As shown.

[0078] Analyze the missing values ​​in the data and record their coordinates. Then, delete the missing data segments and merge the data into a single continuous data segment.

[0079] Step 2: Decompose the continuous data based on EEMD.

[0080] Let x(t) be the continuous data segment obtained in step 1 after removing missing values. In this embodiment, the overall average number of iterations of the EEMD method is m = 10, the noise figure is α = 0.98, and the IMF constraint parameter is N = 8. The intrinsic mode function components obtained after EEMD decomposition total 7, such as... Figures 4a-4g As shown, and one residual component, as Figure 4h As shown, the intrinsic mode function components are divided into three parts according to the number of zero crossings: high-frequency components, low-frequency components, and trend components. The components in each part are accumulated to obtain four continuous subsequences: high-frequency components, low-frequency components, trend components, and a residual component signal.

[0081] Step 3: Impute missing values ​​in non-continuous subsequences.

[0082] By inserting null values ​​into the high-frequency components, low-frequency components, trend components, and residual components obtained in step 2 according to the missing value coordinates recorded in step 1, four discontinuous subsequences with missing values ​​are obtained, such as... Figures 5a-5d As shown, the high-frequency components and residual components exhibit more dramatic changes, while the low-frequency components and trend components show relatively gentle changes.

[0083] Missing values ​​in discontinuous subsequences are imputed according to different signal components. For high-frequency components and residual components, median imputation is performed first to ensure the missing data closely matches the distribution of the original data. Then, third-order spline imputation is performed on both parts of the data to ensure the missing data closely matches the data trend. The average of the two imputation methods is calculated as the imputed data for high-frequency components and residual components. Figure 6a , 6d As shown.

[0084] Third-order spline imputation is performed on the low-frequency and trend components to obtain the imputed data for the low-frequency and trend components, such as... Figure 6b , 6c As shown.

[0085] Step 4 is executed to obtain the complete sensor data after filling, thus realizing the method for filling missing data in industrial sensors.

[0086] The complete high-frequency components, low-frequency components, trend components, and residual components obtained in step 3 are reconstructed to obtain the filled-in complete signal, such as... Figure 7 As shown.

[0087] The above description of the present invention is only a preferred embodiment of the present invention and is not intended to limit the implementation of the present invention. Those skilled in the art can easily make corresponding modifications or alterations based on the main concept and spirit of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of protection claimed in the claims.

Claims

1. A method for filling missing data in industrial sensors based on EEMD, characterized in that, Includes the following steps: Step 1: Collect process data from the equipment and perform preprocessing; The process data of industrial equipment operation is collected by sensors, the missing values ​​in the data are analyzed, the coordinates of the missing values ​​are recorded, the missing data parts are deleted, and the data is merged into a continuous data segment. Step 2: Decompose the continuous data based on EEMD; For the continuous data segments merged in step 1, EEMD decomposition yields intrinsic mode function (IMF) components and residual components. Based on the number of zero-crossing points of the IMF components, they are divided into three parts: high-frequency components, low-frequency components, and trend components. The components in each part are accumulated to obtain three component signals: high-frequency component, low-frequency component, and trend component, as well as one residual component signal. Step 2-1: Assume the signal to be decomposed is x(t), the time is t, the overall average frequency is m, and the noise figure is... The IMF constraint parameter is N; Step 2-2: When performing the i-th decomposition process on the signal x(t), add white noise with a standard normal distribution. n i (t), the signal to be decomposed in the i-th iteration is obtained as , where i = 1, 2, 3, ..., m; Steps 2-3, for x i (t) Perform EMD processing to obtain a set of n intrinsic mode function components c ij (t) and a residual component r i (t), then we have , where n≤N, j=1, 2, 3,…, n; Step 2-4: Repeat steps 2-2 and 2-3 a total of m times to obtain m sets of IMF components obtained from EMD decomposition and residual terms. Then, using the EEMD approach, perform a ensemble average on the corresponding IMF components and residual components, as shown in the following formula: Steps 2-5: Obtain the eigenmode function components and residual components through EEMD decomposition; for the eigenmode functions obtained by EEMD decomposition, count the number of zero crossings q for each component. j Calculate the average of all zero-crossing times. This is used as the threshold for division; based on the number of times each component crosses zero, it is divided into three parts: high-frequency components, low-frequency components, and trend components, as follows: By accumulating each combination to obtain the corresponding component, the original signal, after EEMD decomposition, yields four continuous subsequences: high-frequency component, low-frequency component, trend component, and residual component. Step 3: Impute missing values ​​in non-continuous subsequences; According to the missing value coordinates recorded in step 1, insert null values ​​into the high-frequency components, low-frequency components, trend components and residual components obtained in step 2 to obtain 4 discontinuous subsequences with missing values. Fill in the missing values ​​of the discontinuous subsequences according to the different components of the signal. Step 4: Obtain the complete sensor data after filling, realizing the method for filling missing data in industrial sensors; The complete high-frequency components, low-frequency components, trend components, and residual components obtained in step 3 are reconstructed to obtain the complete sensor data after filling, thus realizing the method for filling missing data in industrial sensors.

2. The method for filling missing data in industrial sensors based on EEMD according to claim 1, characterized in that, In step 3, the high-frequency components and residual components are filled in as follows: First, median imputation is performed to make the missing data conform to the distribution of the original data to the greatest extent. Second, third-order spline imputation is performed on the two parts of data to make the missing data conform to the data change trend to the greatest extent. The average value of the data obtained by the two imputation methods is calculated as the imputation data for the high-frequency components and residual components.

3. The method for filling missing data in industrial sensors based on EEMD according to claim 1, characterized in that, In step 3, the filling method for low-frequency components and trend components is as follows: perform third-order spline filling on low-frequency components and trend components to obtain the filled data of low-frequency components and trend components.

4. A system for implementing the EEMD-based missing data filling method for industrial sensors according to any one of claims 1 to 3, characterized in that, The system includes a computer module for running an EEMD-based method for filling in missing data in industrial sensors.

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