A non-intrusive real-time monitoring method for industrial production and pollution control equipment status

Abstract

The present invention provides a non-invasive real-time monitoring method for the status of industrial production and pollution control equipment, which belongs to the field of non-contact measurement technology of electricity, and includes the following steps: S1, measuring non-invasive voltage; S2, measuring non-invasive current; S3, identifying the operating status based on the power characteristic model method; S4, performing matching evaluation on production equipment and pollution control equipment. The present invention adopts the above-mentioned non-invasive real-time monitoring method for the status of industrial production and pollution control equipment, which can analyze and calculate the real-time power data of the equipment, effectively identify whether the equipment is in standby, faulty or pollution control mismatching states, and then comprehensively evaluate the operating status of the equipment. It solves the shortcomings of traditional monitoring technology in terms of real-time, safety and accuracy, helps to eliminate potential risks and environmental impacts in industrial production, and promotes the intelligent and green development of industrial production.

Description

Technical Field

[0001] The present invention relates to the technical field of non-contact measurement of electric power, and in particular to a non-invasive real-time monitoring method for the status of industrial production and pollution control equipment. Background Art

[0002] With the rapid development of industrial production, environmental protection and the improvement of resource utilization efficiency have become urgent global challenges. In this context, it is particularly important to ensure that pollution in the industrial production process is effectively controlled and the equipment status is monitored in real time. However, existing monitoring methods mostly rely on invasive detection, which may not only interfere with the production process, but also bring safety hazards.

[0003] In order to solve these problems, non-invasive monitoring technologies based on magnetic field, TMR electric field and space capacitance voltage division principle have gradually been developed in this field. These technologies use capacitive sensors made of flexible circuits, TMR sensors and capacitance voltage division principle, combined with Biot-Savart law, etc., to achieve real-time and accurate monitoring of the equipment operation status without interrupting the production process.

[0004] Despite this, non-intrusive monitoring technology still faces many challenges in practical applications. The complexity and variability of industrial environments require monitoring systems to be highly adaptable and robust. At the same time, the exponential growth of data volume places higher demands on data processing and analysis capabilities. In addition, the security and privacy of monitoring data are also issues that cannot be ignored in the development of technology.

[0005] In order to overcome these challenges, the present invention proposes an innovative non-invasive real-time monitoring method for the status of industrial production and pollution control equipment. Summary of the invention

[0006] The purpose of the present invention is to provide a non-invasive real-time monitoring method for the status of industrial production and pollution control equipment, which can analyze and calculate the real-time power data of the equipment, effectively identify whether the equipment is in standby, faulty or pollution control mismatched states, and then comprehensively evaluate the operating status of the equipment. It solves the shortcomings of traditional monitoring technology in terms of real-time, safety and accuracy, helps to eliminate potential risks and environmental impacts in industrial production, and promotes the intelligent and green development of industrial production.

[0007] To achieve the above object, the present invention provides a non-invasive real-time monitoring method for the status of industrial production and pollution control equipment, comprising the following steps:

[0008] S1, measure non-invasive voltage;

[0009] S2, measure non-invasive current;

[0010] S3, identifying the operating status based on the power characteristic model method;

[0011] S4. Conduct matching assessment on production equipment and pollution control equipment.

[0012] Preferably, in step S1, measuring the non-invasive voltage includes the following sub-steps:

[0013] S11. When performing non-contact voltage measurement, the probe clamps the circuit to be tested at the center of the insulating elastic material, and the probe mounting shell is buckled so that the probe contains the circuit to be tested. Each pair of electrode plates in the probe couples with the circuit to be tested to form two different parasitic capacitors, which then sense the electric field signal generated by the voltage radiation of the circuit to be tested together with the sampling capacitor C loaded between the pair of electrode plates, thereby obtaining the voltage U of the circuit to be tested. i ;

[0014] The voltage of the line to be measured obtained by the branch where the nth pair of electrode plates is located is Where N is the total number of electrode plates; a voltage equal to the circuit voltage to be measured is obtained at both ends of the sampling capacitor C. The associated differential voltage signal Then the differential voltage signal Input to the signal processing module for processing;

[0015] S12, the signal processing module includes 2N filter circuits, the positive input ends of the 2N filter circuits are respectively connected to 2N plates through protruding conductive parts, and the negative input ends are connected to the shielding ground layer through protruding conductive parts. Each pair of electrode plates obtains the differential voltage signal of the branch input. Then the differential voltage signal After amplification and filtering, the analog differential voltage signal U is obtained. o(n) , and finally input to the analog-to-digital conversion module through the output port;

[0016] S13, the analog-to-digital conversion circuit converts the simulated differential voltage signal U o(n) Converted into digital signals and then input into the MCU data processing module;

[0017] S14, the MCU data processing module calculates the voltage of the line to be tested based on the 2N digital differential voltage signals and the corresponding N different transfer function equations:

[0018]

[0019] Wherein, d represents the distance between the electrode plate and the circuit to be measured; is the voltage of the Nth circuit to be tested; U oN is the Nth simulated differential voltage signal; coefficient Where G is the amplification factor; ε is the dielectric constant of the medium between the plates; S is the area facing the capacitor plates; k1 is the electrostatic force constant; C is the size of the sampling capacitor;

[0020] S15. Calculate the voltage of the circuit to be tested as:

[0021]

[0022] Preferably, in step S2, measuring the non-invasive current includes the following sub-steps:

[0023] S21, constructing a TMR sensor array;

[0024] S22, each TMR sensor is set at a measuring point position r away from the center of the conductor, and the TMR sensor is used to measure the magnetic flux density of the magnetic field generated by the current-carrying conductor at the measuring point position;

[0025] S23. The current to be measured (current-carrying conductor current) is obtained by solving the following formula:

[0026]

[0027] Among them, μ0 is the magnetic permeability; r is the distance between the center of the current-carrying conductor to be measured and the measuring point; B is the magnetic flux density; I is the current to be measured.

[0028] Preferably, in step S3, identifying the operating state based on the power characteristic model method includes the following sub-steps:

[0029] S31, calculating power data according to the voltage and current of the circuit to be tested measured in step S1 and step S2:

[0030] P=IU i

[0031] S32, preprocessing the power data by using a limiting filtering algorithm to remove abnormal values ​​in the power data and retain the reliability and accuracy of the data;

[0032] S33, extracting time domain features of the preprocessed power data and establishing a power feature model;

[0033] S34, using the time domain features as feature vectors of each operating state to form a feature information matrix;

[0034] The feature information matrix is ​​normalized so that the value is within the range of 0 to 2 to eliminate the differences in dimensions and numerical ranges between different features;

[0035] S35. Calculate the contribution rate of each time domain feature to the power data by using principal component analysis (PCA);

[0036] S36, state recognition through KNN classification algorithm;

[0037] The KNN classification algorithm sets a status flag for each state, 1 for standby, 2 for normal operation, and 0 for shutdown;

[0038] S37. When there is correlation between power data of different scales or features, the Mahalanobis distance is calculated, and the formula is:

[0039]

[0040] Among them, D M (y i ,y j ) is the Mahalanobis distance to be calculated; M is the covariance matrix of the data, y i and j is the sample point;

[0041] S38. Calculate the distance between the point to be classified and all other points, and select the K points with the closest distance as the nearest neighbors. According to the categories of the K nearest neighbors, determine the category of the point to be classified by weighted voting: the closer the neighbor, the greater the voting weight.

[0042] Weighted voting formula:

[0043]

[0044] Among them, Vote(y i ) is the category y i The total number of weighted votes; k is the number of categories considering the nearest neighbors, that is, the K value; c = 1, 2, ..., K; d (q, x c ) is the new instance q and its neighbor x c The distance between them; p is the weighting index.

[0045] Preferably, in step S35, before performing principal component analysis, the calculated power data is first standardized, and the standardization formula is as follows:

[0046]

[0047] Among them, Z ij is the normalized power data matrix; x ij is the element in the original power data matrix; μ j is the mean of the jth variable; σ j is the standard deviation of the jth variable;

[0048] Calculate the covariance matrix or correlation coefficient matrix of the standardized data to determine the linear relationship between the variables. The calculation formula of the covariance matrix is ​​as follows:

[0049]

[0050] Where Σ is the covariance matrix; z i is the normalized power data vector; is the sample mean vector of power data; β is the number of samples; i = 1, 2, 3…, β;

[0051] Perform eigendecomposition on the covariance matrix Σ to obtain the eigenvalue λ and eigenvector v:

[0052] Σv=λv

[0053] Arrange the eigenvalues ​​λ in descending order, and the corresponding eigenvectors v are the principal components; usually only the first few largest eigenvalues ​​and their corresponding eigenvectors are retained, and these eigenvectors form the basis of the new space. Project the original power data onto these principal components to obtain a new power data set, that is, the power data after dimensionality reduction:

[0054] t=zV

[0055] Among them, t is the transformed power data, that is, the principal component score; V is the eigenvector matrix, and its columns are the obtained eigenvectors.

[0056] Preferably, in step S4, the compatibility assessment of the production equipment and the pollution control equipment includes the following sub-steps:

[0057] S41. Check whether the pollution control equipment is in normal working condition during the operation of the production equipment;

[0058] Compare the operating status of production equipment and pollution control equipment to assess whether the two are synchronized;

[0059] S42. Calculate the energy efficiency ratio of pollution control equipment and evaluate its energy consumption per unit of pollutant to be treated;

[0060] Evaluate whether the performance of pollution control equipment meets the expected goals based on the removal rate and emission level of pollutants;

[0061] S43. Analyze the changing trend of power data over time and predict the possible future status changes of production equipment and pollution control equipment;

[0062] S44. Set alarm thresholds to promptly alarm when production equipment and pollution control equipment are in abnormal operating conditions;

[0063] Regularly generate operating status reports for production equipment and pollution control equipment to provide a basis for maintenance and optimization.

[0064] S45. Continuously collect the voltage, current and power data of the line to be tested, and optimize the alarm threshold according to the latest operating status.

[0065] Therefore, the present invention adopts the above-mentioned non-invasive real-time monitoring method for industrial production and pollution control equipment status, and the technical effects are as follows:

[0066] (1) The present invention uses a capacitive sensor made of a flexible circuit and the principle of capacitive voltage division to achieve non-invasive voltage measurement of pollution control equipment, and uses a TMR sensor and Biot-Savart law to achieve non-invasive current measurement of the equipment, thereby ensuring the accuracy and precision of monitoring and solving the problem that the traditional invasive monitoring system needs to interrupt the production process for sensor installation and maintenance;

[0067] (2) The present invention calculates the real-time power data of the equipment operation and adopts the sewage treatment and pollution control equipment operation status recognition technology based on deep learning, identifies the problems of equipment standby, failure and mismatch between sewage treatment and pollution production equipment, and realizes the effective evaluation of the equipment operation status. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 This is a design diagram of the flexible circuit capacitive sensor in the present invention;

[0069] Figure 2 This is a schematic diagram of the TMR sensor measuring current in the present invention;

[0070] Figure 3 To visualize the results of principal component analysis (PCA) calculations;

[0071] Figure 4 This is the result scatter plot of KNN operation when K=4;

[0072] Figure 5 The monitoring status of pollution control equipment and pollution producing equipment; Figure 5 (a) is a grinding machine; Figure 5 (b) in the figure is the central dust removal fan; Figure 5 (c) in the figure is a VOC treatment fan; Figure 5 (d) in it is a planer;

[0073] Figure 6 This is a flow chart for real-time monitoring of the status of non-intrusive industrial production and pollution control equipment. DETAILED DESCRIPTION

[0074] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0075] Unless otherwise defined, technical or scientific terms used in the present invention shall have the common meanings understood by one having ordinary skills in the field to which the present invention belongs.

[0076] Embodiment 1

[0077] like Figure 6 The figure shows a flow chart of real-time monitoring of the status of non-invasive industrial production and pollution control equipment.

[0078] In the voltage measurement stage, the electrode plate adopts a flexible PCB board, the top layer of which is 2N electrode plates symmetrically distributed in an array. The free area of ​​the top layer is connected to the bottom layer through a "via" to form a grounding layer for shielding interference; each array-type symmetrically distributed electrode plate and the grounding layer form a pair of electrode plates, forming a total of 2N pairs of electrode plates; there is an insulating layer between the array-type electrode plate and the grounding layer, the purpose of which is to obtain the voltage signal of the line to be measured, because the radiation electric field generated by the voltage of the line to be measured will generate induced charges on the electrode plate, and at the same time, a coupling capacitor is formed between the electrode plate and the line to be measured, thereby generating a current signal;

[0079] In this embodiment, each pair of electrode plates in the multi-level plate differential probe is coupled with the device line to be measured to form two unequal parasitic capacitors, such as Figure 1 , denoted as the first parasitic capacitor CP1 and the second parasitic capacitor CP2, and the line voltage U to be measured is obtained based on the first parasitic capacitor CP1, the second parasitic capacitor CP2 and the sampling capacitor C loaded between each pair of electrode plates i .

[0080] Since the voltage signal of the line to be measured U i is an AC voltage. Therefore, according to the physical properties of the capacitor, the change in the current direction of the circuit to be tested (equivalent to one electrode of the parasitic capacitor) will cause the current of the other electrode of the parasitic capacitor to change. Therefore, the differential detection module converts the voltage U i It is input into the system in the form of electric current for processing by the signal processing module.

[0081] The signal processing module includes 2N filter circuits with the same structure and an amplification function. The positive input ends of the 2N filter circuits are respectively connected to 2N plates through protruding conductive parts, and the negative input ends are connected to the shielding ground layer through protruding conductive parts to obtain the differential voltage signal U input to the module. c , then the differential voltage signal U c After amplification and filtering, a voltage signal Uo with good waveform is obtained, which is finally input to the analog-to-digital conversion module through the output port;

[0082] Generally, the signal output by the signal processing module is an analog signal. To facilitate the processing by the MCU data processing module, an analog-to-digital conversion module is connected to the output end of the signal processing module to convert the output analog signal into a digital signal. In this embodiment, an analog-to-digital converter ADC is used to digitize the analog signal. For the nominal 50Hz input signal of the measuring device, for the convenience of sampling, the ADC can sample the output signal from the signal processing circuit at a sampling frequency of 10.24KHz to provide 1024 samples in 100ms to be ready for processing by FFT.

[0083] The MCU data processing module obtains the digital signal output by the digital-to-analog conversion module, transmits it to the computer cloud through the data transmission line, and constructs an equation based on the circuit transfer function and writes a computer program to solve the voltage to be measured, thereby solving the voltage value of the line to be measured.

[0084] In the current measurement stage, a TMR sensor array is installed at a suitable location on the transmission line, such as Figure 2 The distance between the sensor and the wire is 1 cm, or 0.01 m.

[0085] The magnetic flux density B measured by the TMR sensor array is 1.2×10 -7 Tesla (T). This data is directly read by the sensor's built-in analog-to-digital converter (ADC). Since the output signal of the TMR sensor is very weak, it needs to be amplified by a high-gain amplifier. Then, digital signal processing techniques (filtering and averaging) are used to reduce noise and improve signal quality.

[0086] The current is calculated using Biot-Savart's law. Considering that the sensor measures the tangential component of the magnetic field, the following formula is used:

[0087]

[0088] Where μ0 is the magnetic permeability (μ0 = 4π×10 -7 ), substituting the measured value:

[0089] I=(1.2×10 -7 ) / (4π×0.01)=9.549(A)

[0090] The results show that the current in the transmission line is about 9.5 amps. This result can be verified by comparing with the line design parameters or historical data. In addition, the TMR sensor needs to be calibrated regularly using a standard current source to ensure measurement accuracy. During the calibration process, the sensor's amplification gain or signal processing algorithm is adjusted to eliminate any long-term drift or deviation.

[0091] According to the power calculation formula P = IUi The power data is calculated and the outliers in the sampled power data are eliminated through the limiting filtering algorithm, including but not limited to abnormal fluctuations in the data caused by electromagnetic interference or other types of noise, errors that may occur in the process of transmitting data from the acquisition system to the processing system, operators' misoperation or deliberate tampering with data, and outliers in the data due to random fluctuations. The preprocessed data is obtained: X = [1.0, 2.0, 0.0; 1.5, 1.8, 2.4; 0.8, 1.6, 2.5; 1.2, 2.1, 3.0; 1.9, 2.0, 2.1], which contains 3 observations and 12 variables.

[0092] The time domain features of the preprocessed power data are extracted to establish a power feature model. These time domain features are used as the feature vectors of each operating state [0.0815, 0.9660, -0.245, -0.0317, 0.2487, 0.9681, 0.9962, -0.0712, 0.0509] to form a feature information matrix. The feature information matrix is ​​normalized so that the values ​​are within the range of 0 to 2 to eliminate the differences in dimensions and numerical ranges between different features. The principal component analysis (PCA) method is used to calculate the contribution rate of each time domain feature to the data. The PAC result visualization is shown in Figure 3 .

[0093] The obtained data is used to identify the equipment operation status through the KNN classification algorithm. The KNN classification algorithm sets a status flag for each state, 1 for standby, 2 for normal operation, and 0 for shutdown. The Mahalanobis distance measurement method is selected to calculate the distance between the point to be classified and all other points, and the K points with the closest distance are selected as the nearest neighbors. According to the categories of the K nearest neighbors, the category of the point to be classified is determined by weighted voting. The closer the neighbor, the greater the voting weight. The weighted index is between 1 and 2. The final result uses a scatter plot to distinguish different categories, such as Figure 4 .

[0094] In the process of production / pollution control equipment matching evaluation, four devices, namely, VOC treatment fan, central dust removal fan, grinder and planer, were selected for data monitoring and evaluation, and the energy efficiency ratio of production and pollution control equipment, that is, the ratio of the energy consumed to the amount of pollutants treated, was calculated. At the same time, pollutant online monitoring equipment (CEMS) was used to monitor the removal rate and emission level of pollutants in real time, analyze the time series of boiler and purification system power data, and use time series analysis or machine learning models to predict future state changes, such as Figure 5 .

[0095] At the same time, a series of alarm thresholds are set according to needs, and the thresholds are based on the data range when the equipment is operating normally. When the monitored data exceeds these thresholds, the system will trigger an alarm and notify maintenance personnel in time. At the same time, a pollution control equipment operation status report is regularly generated, including performance indicators, energy consumption data and predictive analysis, to provide a basis for equipment maintenance and optimization.

[0096] Therefore, the present invention adopts the above-mentioned non-intrusive real-time monitoring method for the status of industrial production and pollution control equipment, which uses advanced sensor technology, signal processing algorithms and intelligent diagnosis models to monitor the status of equipment in real time and accurately, and timely warn of potential failures and pollution risks. At the same time, the design of the device takes into account the special needs of the industrial environment, ensuring the stability and reliability of the monitoring process.

[0097] It not only improves the monitoring efficiency and accuracy of industrial production and pollution control equipment, but also provides strong technical support for the green, intelligent and sustainable development of industrial production. Through the application of non-invasive measurement technology, interference with the production process is avoided and the safety and reliability of monitoring are improved. The introduction of deep learning technology improves the accuracy and intelligence level of equipment status identification. Real-time power data analysis and equipment matching evaluation provide strong data support for equipment maintenance and optimization. Continuous data collection and model optimization realize continuous improvement and upgrading of the monitoring system.

[0098] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A non-invasive real-time monitoring method for industrial production and pollution control equipment status, characterized in that: The following steps are involved: S1, measure non-invasive voltage; S2, measure non-invasive current; S3, identifying the operating status based on the power characteristic model method; S4. Conduct matching assessment on production equipment and pollution control equipment; In step S3, the operating state is identified based on the power characteristic model method, including the following sub-steps: S31, calculating power data according to the voltage and current of the circuit to be tested measured in step S1 and step S2: P=IU i S32, preprocessing the power data by using a limiting filtering algorithm to remove abnormal values ​​in the power data; S33, extracting time domain features of the preprocessed power data and establishing a power feature model; S34, using the time domain features as feature vectors of each operating state to form a feature information matrix; Normalize the feature information matrix so that the value is within the range of 0 to 2; S35. Calculate the contribution rate of each time domain feature to the power data using the principal component analysis method; S36, state recognition through KNN classification algorithm; The KNN classification algorithm sets a status flag for each state, 1 for standby, 2 for normal operation, and 0 for shutdown; S37. When the power data have different scales or there is correlation between features, the Mahalanobis distance is calculated, and the formula is: Among them, D M (y i ,y j ) is the Mahalanobis distance to be calculated; M is the covariance matrix of the data, y i and j is the sample point; S38. Calculate the distance between the point to be classified and all other points, and select the K points with the closest distance as the nearest neighbors. According to the categories of the K nearest neighbors, determine the category of the point to be classified by weighted voting: Weighted voting formula: Among them, Vote(y i ) is the category y i The total number of weighted votes; k is the number of categories considering the nearest neighbors, that is, the K value; c = 1, 2, ..., K; d (q, x c ) is the new instance q and its neighbor x c The distance between them; p is the weighted index; In step S4, the compatibility of production equipment and pollution control equipment is evaluated, including the following sub-steps: S41. Check whether the pollution control equipment is in normal working condition during the operation of the production equipment; S42. Calculate the energy efficiency ratio of pollution control equipment and evaluate its energy consumption per unit of pollutant to be treated; S43. Analyze the changing trend of power data over time and predict the possible future status changes of production equipment and pollution control equipment; S44. Set alarm thresholds to promptly alarm when production equipment and pollution control equipment are in abnormal operating conditions; S45. Continuously collect the voltage, current and power data of the line to be tested, and optimize the alarm threshold according to the latest operating status.

2. A non-invasive real-time monitoring method for industrial production and pollution control equipment status according to claim 1, characterized in that: In step S1, non-invasive voltage is measured, including the following sub-steps: S11. When performing non-contact voltage measurement, the probe clamps the circuit to be tested at the center of the insulating elastic material, and the probe mounting shell is buckled so that the probe contains the circuit to be tested. Each pair of electrode plates in the probe couples with the circuit to be tested to form two different parasitic capacitors, which then sense the electric field signal generated by the voltage radiation of the circuit to be tested together with the sampling capacitor C loaded between the pair of electrode plates, thereby obtaining the voltage U of the circuit to be tested. i ; The voltage of the line to be measured obtained by the branch where the nth pair of electrode plates is located is Where N is the total number of electrode plates; a voltage equal to the circuit voltage to be measured is obtained at both ends of the sampling capacitor C. The associated differential voltage signal Then the differential voltage signal Input to the signal processing module for processing; S12, the signal processing module includes 2N filter circuits, the positive input ends of the 2N filter circuits are respectively connected to 2N plates through protruding conductive parts, and the negative input ends are connected to the shielding ground layer through protruding conductive parts. Each pair of electrode plates obtains the differential voltage signal of the branch input. Then the differential voltage signal After amplification and filtering, the analog differential voltage signal U is obtained. o(n) , and finally input to the analog-to-digital conversion module through the output port; S13, the analog-to-digital conversion circuit converts the simulated differential voltage signal U o(n) Converted into digital signals and then input into the MCU data processing module; S14, the MCU data processing module calculates the voltage of the line to be tested based on the 2N digital differential voltage signals and the corresponding N different transfer function equations: Wherein, d represents the distance between the electrode plate and the circuit to be measured; is the voltage of the Nth circuit to be tested; U oN is the Nth simulated differential voltage signal; coefficient Where G is the amplification factor; ε is the dielectric constant of the medium between the plates; S is the area facing the capacitor plates; k1 is the electrostatic force constant; C is the size of the sampling capacitor; S15. Calculate the voltage of the circuit to be tested as:

3. A non-invasive real-time monitoring method for industrial production and pollution control equipment status according to claim 2, characterized in that: In step S2, non-invasive current is measured, including the following sub-steps: S21, constructing a TMR sensor array; S22, each TMR sensor is set at a measuring point position r away from the center of the conductor, and the TMR sensor is used to measure the magnetic flux density of the magnetic field generated by the current-carrying conductor at the measuring point position; S23. The current to be measured is obtained by solving the following formula: Among them, μ0 is the magnetic permeability; r is the distance between the center of the current-carrying conductor to be measured and the measuring point; B is the magnetic flux density; I is the current to be measured.

4. A non-invasive real-time monitoring method for industrial production and pollution control equipment status according to claim 3, characterized in that: In step S35, before performing principal component analysis, the calculated power data is first standardized, and the standardization formula is as follows: Among them, Z ij is the normalized power data matrix; x ij is the element in the original power data matrix; μ j is the mean of the jth variable; σ j is the standard deviation of the jth variable; Calculate the covariance matrix or correlation coefficient matrix of the standardized data to determine the linear relationship between the variables. The calculation formula of the covariance matrix is ​​as follows: Where Σ is the covariance matrix; z i is the normalized power data vector; is the sample mean vector of power data; β is the number of samples; i = 1, 2, 3…, β; Perform eigendecomposition on the covariance matrix Σ to obtain the eigenvalue λ and eigenvector v: Σv=λv Arrange the eigenvalues ​​λ in descending order, and the corresponding eigenvectors v are the principal components; project the original power data onto these principal components to obtain a new power data set, that is, the power data after dimensionality reduction: t=zV Among them, t is the transformed power data, that is, the principal component score; V is the eigenvector matrix, and its columns are the obtained eigenvectors.

Images