Carrier module intelligent detection system based on artificial intelligence analysis
The carrier module detection system, which utilizes artificial intelligence analysis, solves the problems of missing and inaccurate fault data filling in carrier module detection. It achieves fast and accurate fault data filling and correlation analysis, supporting fault judgment and prediction.
Patent Information
- Application Number
- CN202510702442.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2025-05-28
- Publication Date
- 2025-10-28
- Estimated Expiration
- 2045-05-28
AI Technical Summary
Existing technologies for carrier module detection suffer from missing fault data due to sensor failures, communication interruptions, and other reasons. Furthermore, the missing data is not accurately filled in, which affects the overall assessment of the fault and the analysis of its development trend.
It employs an AI-based fault data basic filling module, fault correlation cross-analysis module, fault relationship precise analysis module, and precise fault data repair module. Through data filling method, cross-analysis method, partial correlation analysis method, and linear regression model, it accurately fills and analyzes fault data.
It can quickly fill in missing data, reduce computing resource consumption, improve data processing efficiency, accurately identify fault correlations, and support fault analysis and prediction.
Smart Images

Figure CN120498960B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of intelligent detection technology, and more specifically, to an intelligent detection system for carrier modules based on artificial intelligence analysis. Background Technology
[0002] In today's digital communication era, the stable operation of carrier communication systems plays a crucial role in ensuring the efficient and accurate transmission of information. As the core component of carrier communication systems, the performance of carrier modules directly affects the reliability of the entire system.
[0003] The carrier module detection system aims to ensure the stable operation of the carrier communication system. To this end, in practical applications, the fault data of the carrier module will be recorded for a long time to form a historical fault database containing information such as the time of fault occurrence, fault characteristic data and fault content. The historical fault data is usually indexed by timestamps, and each timestamp contains detection data of multiple equidistant time nodes, presenting a complex structure of multiple dimensions and multiple time series.
[0004] However, during data acquisition and recording, due to various reasons (such as sensor failure, communication interruption, data storage errors, etc.), it is inevitable that fault data will be missing. After the missing fault data is lost, existing technologies usually fill in the missing data by analyzing the changing trends of the fault data, and then analyze the correlation between different fault data. However, if the overall distribution pattern of the data and the complex correlation between multiple variables are not fully considered during data filling, the missing data filling will be inaccurate. As a result, when staff view the filled historical fault data, it is difficult to accurately grasp the whole picture of the fault and judge the development trend of the fault due to inaccurate data. In view of this, we propose a carrier module intelligent detection system based on artificial intelligence analysis. Summary of the Invention
[0005] The purpose of this invention is to solve the problem that during data acquisition and recording, fault data is often missing due to sensor failure, communication interruption, etc. Existing technologies often fill in the missing data by analyzing data change trends and then analyzing the correlation of fault data. However, if the overall data distribution and complex correlation of multiple variables are not fully considered during the filling process, the filling is prone to inaccuracy. This makes it difficult for staff to accurately grasp the whole picture of the fault and judge the development trend when viewing the filled historical fault data.
[0006] To achieve the above objectives, this invention provides an intelligent carrier module detection system based on artificial intelligence analysis, comprising a fault data basic filling module, a fault correlation cross-analysis module, a fault relationship precise analysis module, and a precise fault data repair module, wherein:
[0007] The fault data basic filling module uses a data filling method to calculate and fill in missing historical fault data. The fault correlation cross-analysis module uses a cross-analysis method to calculate the correlation coefficient between historical fault data. When there is a correlation between two fault data, the correlation relationship is determined based on the timestamp of the fault data. When there is a correlation between multiple fault data, the fault relationship precise analysis module uses a biased correlation analysis method to calculate the partial correlation coefficient between each pair of fault data. The precise fault data repair module uses a fusion filling method and a linear regression model established by the partial correlation coefficient to calculate supplementary data and replace the filled data.
[0008] As a further improvement to this technical solution, the fault data base filling module senses the historical fault data of the carrier module. The historical fault data includes multiple fault occurrence timestamps, and each timestamp corresponds to multiple fault data detected at equidistant time nodes.
[0009] As a further improvement to this technical solution, the data filling method in the fault data basic filling module retrieves the timestamp of the missing data, senses two other non-missing data points adjacent to the corresponding time node, determines a straight line through the two other non-missing data points, and uses the trend of the straight line to calculate and fill the missing data.
[0010] The beneficial effects of adopting the above-mentioned further solution are that the filling method in this invention is relatively simple and direct, based on the basic mathematical principle (two points determine a straight line), and does not require complex calculations and model construction. This enables the missing data to be filled quickly during the data processing process, reducing the time cost and computational resource consumption of data processing, improving the efficiency of data processing, and ensuring that the filled fault data can meet the basic requirements of subsequent analysis methods for data integrity, so that the fault correlation cross-analysis module and the fault relationship precise analysis module can be carried out smoothly.
[0011] Based on the above technical solution, the present invention can be further improved as follows.
[0012] As a further improvement to this technical solution, the fault correlation cross-analysis module senses fault data. , Fault data and fault data If the detection data are from the same time point, then the correlation coefficient is:
[0013] ;
[0014] in for The mean, for The mean of the correlation coefficient is set; a correlation coefficient threshold is set, and if the absolute value of the correlation coefficient is less than or equal to the correlation coefficient threshold, then the data is considered faulty. and fault data There is no correlation between them; if the absolute value of the correlation coefficient is greater than the correlation coefficient threshold, then the data is considered faulty. and fault data There is a correlation between them; retrieve fault data. and fault data Corresponding timestamp , If timestamp Earlier than the timestamp Then the fault data and fault data The correlation between them is the fault data → Fault Data .
[0015] The beneficial effect of adopting the above-mentioned further solution is that, by calculating the correlation coefficient between different fault data at the same time point, the present invention aims to find the potential correlation between fault data. During the operation of the carrier module, multiple faults may occur simultaneously or sequentially, and there may be causal relationships or common factors among the fault data. The fault correlation cross-analysis module accurately identifies the correlation between fault data through quantitative methods, so as to gain a deeper understanding of the fault occurrence mechanism and clarify the sequential relationship of fault occurrence through correlation, which facilitates the analysis of the propagation path and root cause of fault data.
[0016] Based on the above technical solution, the present invention can be further improved as follows.
[0017] As a further improvement to this technical solution, the fault correlation cross-analysis module calculates fault data. and fault data Correlation coefficient between Then, calculate the fault data. and fault data Correlation coefficient between ,like >correlation coefficient threshold, and If the correlation coefficient threshold is reached, fault data will be calculated immediately. and fault data Correlation coefficient between If the correlation coefficient is calculated If the correlation coefficient threshold is exceeded, then a determination is made. , and There are correlations between them, and the correlation relationship of the fault data is determined based on the corresponding timestamps.
[0018] The beneficial effect of adopting the above-mentioned further solution is that, considering that among a large number of fault data, if a comprehensive pairwise correlation coefficient calculation is performed on all fault data, the amount of calculation will increase exponentially with the increase in the number of fault data. The fault correlation cross-analysis module adopts a cross-calculation method to first determine the correlation between some fault data pairs, and then calculate the correlation coefficient of other fault data pairs in a targeted manner based on the results, thus avoiding blind calculation.
[0019] Based on the above technical solution, the present invention can be further improved as follows.
[0020] As a further improvement to this technical solution, the biased correlation analysis method in the fault relationship precision analysis module is used to calculate fault data. and fault data Controlling fault data Partial correlation coefficient under the influence And calculate fault data and fault data Controlling fault data Partial correlation coefficient under the influence ;like > When that happens, determine the fault data. The impact is greatest;
[0021] As a further improvement to this technical solution, the calculation formula of the biased correlation analysis method is as follows: Perceived fault data , and Control fault data Under the influence of fault data and fault data Partial correlation coefficient between for: .
[0022] The beneficial effect of adopting the above-mentioned further solution is that the partial correlation coefficient of the present invention can more accurately represent the degree of linear relationship between two fault data after controlling for other factors. Compared with the simple correlation coefficient, the partial correlation coefficient eliminates the interference of other factors and can better reflect the intrinsic relationship between variables, further helping to analyze the causal relationship between faults. By controlling different variables and observing the changes in the partial correlation coefficient, it is possible to determine which fault data is the cause and which is the effect, or whether there are common influencing factors.
[0023] Based on the above technical solution, the present invention can be further improved as follows.
[0024] As a further improvement to this technical solution, the fusion filling method in the precise fault data repair module detects multiple fault data that are correlated with the missing fault data, retrieves the partial correlation coefficients between the multiple fault data and the missing fault data, and establishes multiple linear regression models respectively: ;in To supplement the data, For fault data that is relevant to supplementary data, For regression coefficients, This is the intercept.
[0025] As a further improvement to this technical solution, the regression coefficient Calculated using the partial correlation coefficient: ,in For fault data and fault data The partial correlation coefficient between them and Fault data and fault data Standard deviation;
[0026] intercept ,in and Fault data and fault data The mean.
[0027] As a further improvement to this technical solution, the precise fault data repair module calculates multiple supplementary data, retrieves the most frequent supplementary data, selects the one with the highest frequency of occurrence as the final supplementary data, and replaces the filling data.
[0028] The beneficial effect of adopting the above-mentioned further solution is that, in the fault data basic filling module of the present invention, the data filling method may be inaccurate. The fusion filling method of the accurate fault data repair module establishes a more accurate linear regression model by considering multiple fault data related to the missing fault data and the partial correlation coefficient between them, thereby improving the accuracy of missing data filling. When performing fault diagnosis, analyzing the correlation between faults and predicting the development trend of faults, staff can make more accurate judgments and decisions based on accurate fault data.
[0029] In addition to the objectives, features, and advantages described above, the present invention has other objectives, features, and advantages. The invention will now be described in further detail with reference to the figures. Attached Figure Description
[0030] Figure 1 This is a schematic diagram of the overall module of the present invention;
[0031] Figure 2 This is a flowchart illustrating the working principle of the fault data basic filling module of the present invention.
[0032] Figure 3 This is a flowchart illustrating the working principle of the correlation coefficient in the fault correlation cross-analysis module of this invention.
[0033] Figure 4 This is a flowchart illustrating the working principle of the cross-calculation method in the fault correlation cross-analysis module of this invention.
[0034] Figure 5 This is a flowchart illustrating the working principle of the fault relationship precision analysis module of the present invention.
[0035] Figure 6 This is a flowchart illustrating the working principle of the precise fault data repair module of the present invention.
[0036] The meanings of the labels in the diagram are as follows:
[0037] 100. Fault data basic filling module; 200. Fault correlation cross-analysis module; 300. Fault relationship precise analysis module; 400. Precise fault data repair module. Detailed Implementation
[0038] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. 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 are within the scope of protection of the present invention.
[0039] Example 1, Reference Figures 1-6 As shown, the intelligent carrier module detection system based on artificial intelligence analysis includes a fault data basic filling module 100, a fault correlation cross-analysis module 200, a fault relationship precise analysis module 300, and a precise fault data repair module 400, wherein:
[0040] The historical fault data of the 100 sensing carrier module, which is used to fill in basic fault data, includes data such as fault occurrence time, fault characteristic data, and fault content. The historical fault data includes multiple fault occurrence timestamps, each corresponding to fault data detected at multiple equidistant time nodes.
[0041] Fault occurrence timestamp Time Node Fault characteristic data 1 Fault characteristic data 2 ... Fault details [Date] 1 Data value 1 Data value 2 ... Fault Description 1 [Date] 2 Data value 3 Missing data value 4 ... Fault Description 2 [Date] 3 Data value 5 Data value 6 ... Fault Description 3 ... ... ... ... ... ... [Date] 1 Data value 7 Data value 8 ... Fault Description 4 [Date] 2 Data value 9 Data value 10 ... Fault Description 5 [Date] 3 Data value 11 Data value 12 ... Fault Description 6 ... ... ... ... ... ...
[0042] In the table above:
[0043] The "Fault Occurrence Timestamp" column records the specific time when the fault occurred;
[0044] The "Time Node" column represents the equidistant time nodes under each fault occurrence timestamp;
[0045] The "Fault Characteristic Data" column contains various characteristic fault data related to the fault;
[0046] The "Fault Details" column describes in detail the fault conditions detected at each time point.
[0047] The fault data basic filling module 100 detects missing fault data in historical fault data and uses a data filling method to fill in the missing fault data. The data filling method retrieves two other non-missing data points adjacent to the corresponding time node in the timestamp of the missing data, uses these two other non-missing data points to determine a straight line, and uses the trend of the straight line to calculate and fill in the missing data. The corresponding expression is as follows: The time node for detecting missing data is... Its preceding non-missing data point is The next non-missing data point is According to the principle that two points determine a straight line, the slope of the straight line... for Then the missing data points Fill value at Calculated using the following formula: .
[0048] In the actual fault data recording process, due to various reasons such as sensor failure and communication interruption, data loss is inevitable. The fault data basic filling module 100 supplements these missing fault data through data filling methods, making the historical fault data complete. This provides a more comprehensive data foundation for subsequent fault analysis and processing, and provides preliminary data support for the fault correlation cross-analysis module 200 and the fault relationship precise analysis module 300 to calculate the correlation between fault data and determine the root cause of the fault.
[0049] refer to Figure 3 As shown, the fault correlation cross-analysis module 200 uses the cross-analysis method to calculate the correlation coefficient between multiple historical fault data within the same timestamp: perceived fault data , Fault data and fault data For detection data at the same time point, the correlation coefficient is... ;
[0050] in for The mean, for The mean of the correlation coefficient is used to measure the degree of association between fault data. Its value typically ranges from -1 to 1. A positive correlation coefficient indicates a positive correlation between the two variables; a negative correlation coefficient indicates a negative correlation. A correlation coefficient threshold is set; if the absolute value of the correlation coefficient is less than or equal to the threshold, the fault data is considered... and fault data There is no correlation between them; if the absolute value of the correlation coefficient is greater than the correlation coefficient threshold, then the data is considered faulty. and fault data There is a correlation between them, and fault data is retrieved. and fault data Corresponding timestamp , If timestamp Earlier than the timestamp Then the fault data and fault data The correlation between them is the fault data → Fault Data .
[0051] For example, if the correlation coefficient between carrier signal strength fault data and data transmission fault data is found to be greater than the correlation coefficient threshold, it indicates that there is an inherent connection between the two faults, which are caused by the same underlying cause, or that the occurrence of one fault will trigger the other fault. To determine the relationship between the faults, the magnitude of the correlation coefficient is used to further determine the degree of closeness between the two fault data. The closer the correlation coefficient of two correlated fault data is to 1, the stronger the positive correlation between the two variables; the closer it is to -1, the stronger the negative correlation.
[0052] When fault data occurs, the root cause of the fault can be located more quickly based on the correlation between the fault data. For example, if it is known that a certain fault is related to several other faults, then during the troubleshooting process, the fault data that may appear at the next time stamp can be predicted based on the correlation coefficient and correlation relationship between different fault data.
[0053] Historical fault data contains a large amount of fault data, and different fault data may have complex relationships. If a comprehensive pairwise correlation coefficient calculation is performed on all fault data randomly, the computational workload will increase exponentially with the increase in the number of fault data. Therefore, to avoid blind calculation when calculating correlation coefficients, a reference is made... Figure 4 As shown, the fault correlation cross-analysis module 200 uses the cross-analysis method to calculate the correlation coefficient. The specific working principle is as follows: Calculate the fault data... and fault data Correlation coefficient between Then, calculate the fault data. and fault data Correlation coefficient between ,like >correlation coefficient threshold, and If the correlation coefficient threshold is reached, fault data will be calculated immediately. and fault data Correlation coefficient between If the correlation coefficient is calculated If the correlation coefficient threshold is exceeded, then a determination is made. , and There are correlations between them, and the correlation relationship of the fault data is determined based on the corresponding timestamps;
[0054] Fault correlation cross-analysis module 200 calculates fault data. and fault data Fault data and fault data There is a correlation between them, in order to avoid , and The interaction of multiple factors leads to the fault correlation cross-analysis module 200 calculating fault data. and fault data Correlation coefficient between When, the correlation coefficient Received fault data Due to the influence of fault relationships, the fault relationship precision analysis module 300 uses biased correlation analysis to calculate fault data. and fault data Controlling fault data Partial correlation coefficient under the influence And calculate fault data and fault data Controlling fault data Partial correlation coefficient under the influence ;
[0055] like > When that happens, determine the fault data. The impact is greatest when the fault correlation cross-analysis module 200 outputs the correlation between fault data, and simultaneously outputs the degree of influence of different fault data to assist staff in determining the fault data that needs to be repaired.
[0056] Partial correlation analysis is a method for analyzing the linear relationship between two fault data points while controlling for the linear effects of other fault data. It uses the partial correlation coefficient to represent the strength of this relationship, thereby eliminating interference from other factors and calculating the fault data. and fault data Correlation coefficient between To avoid "spurious correlations," the specific calculation formula is as follows: Perceived fault data , and Control fault data Under the influence of fault data and fault data Partial correlation coefficient between for: ;
[0057] Calculate fault data and fault data Partial correlation coefficient between Afterwards, the key influencing factors between different fault data can be identified, which helps staff to fundamentally solve fault problems and reduce the probability of fault recurrence.
[0058] Example 2, based on Example 1, aims to avoid inaccuracies in the data filling method used by the fault data basic filling module 100 when filling missing data due to missing fault data. It also considers that the missing data filled by the fault data basic filling module 100 will not affect the calculation of the correlation coefficient in the fault correlation cross-analysis module 200 (the correlation coefficient is a statistical indicator used to measure the strength and direction of the linear relationship between two variables. Its calculation is mainly based on the relative position and trend of data points, rather than the specific value of a single data point. Although the specific values may have errors after filling, the relative position of the filled data in the dataset and its relationship with other variables are determined based on the overall characteristics of the original data. Therefore, when calculating the correlation coefficient, the filled data can be integrated into the overall data relationship and will not significantly affect the calculation result). However, inaccurate filled data may still interfere with the staff's viewing and in-depth analysis of historical fault data, thus affecting their ability to view and analyze historical fault data.
[0059] refer to Figures 4-6 As shown, this embodiment differs from Embodiment 1 in that: the precise fault data repair module 400 comprehensively perceives historical fault data, accurately locates missing fault data, and then processes it using a fusion filling method. The fusion filling method perceives multiple fault data points correlated with the missing fault data, retrieves the partial correlation coefficients between these multiple fault data points and the missing fault data, establishes multiple linear regression models, calculates multiple supplementary data points, retrieves the most frequent supplementary data, and selects the most frequently occurring supplementary data point as the final supplementary data point to replace the filled data. The fusion filling method, based on the fault data... Calculate supplementary data The calculation formula is as follows:
[0060] The partial correlation coefficient between each known fault data point and the missing data is determined. The fault data is considered as a variable influencing the missing data. A positive partial correlation coefficient indicates a positive correlation between the two variables, meaning that an increase in one variable tends to increase the other; a negative coefficient indicates a negative correlation. A linear regression model is then established. ;in To supplement the data, For fault data that is relevant to supplementary data, For regression coefficients, The intercept is calculated using the partial correlation coefficient: ,in For fault data and fault data The partial correlation coefficient between them reflects and The direction and degree of linear correlation between them; and Fault data and fault data standard deviation The correlation was scaled to adjust the regression coefficients. Able to accurately represent When changing by one unit The average change;
[0061] Calculate the intercept ;in and Fault data and fault data Mean, intercept For when hour The estimated value ensures that the regression line passes through the mean point of the sample data. .
[0062] The fusion filling method in the accurate fault data repair module 400 considers the partial correlation coefficient during the calculation process, which can eliminate the interference of other factors and accurately reflect the relationship between fault data. For example, when analyzing the fault of the carrier module in the communication system, accurate filling data can help the staff to accurately judge whether the relationship between different fault characteristics (such as signal strength, bit error rate, etc.) is a real causal relationship or a false relationship caused by inaccurate data, thus providing a reliable basis for subsequent fault diagnosis by workers.
[0063] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely preferred examples and are not intended to limit the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.
Claims
1. A carrier module intelligent detection system based on artificial intelligence analysis, characterized in that, It includes a fault data basic filling module (100), a fault correlation cross-analysis module (200), a fault relationship precise analysis module (300), and a precise fault data repair module (400), among which: The fault data basic filling module (100) uses the data filling method to calculate and fill in the missing historical fault data. The fault correlation cross-analysis module (200) uses the cross-analysis method to calculate the correlation coefficient between historical fault data. When there is a correlation between two fault data, the correlation relationship is determined according to the timestamp of the fault data. When there is a correlation between multiple fault data, the fault relationship precise analysis module (300) uses the biased correlation analysis method to calculate the biased correlation coefficient between the two fault data one by one. The precise fault data repair module (400) uses the fusion filling method and the biased correlation coefficient to establish a linear regression model to calculate supplementary data and replace the filled data. The fusion-filling method in the precise fault data repair module (400) detects multiple fault data that are correlated with the missing fault data, retrieves the partial correlation coefficients between the multiple fault data and the missing fault data, and establishes multiple linear regression models respectively: ;in To supplement the data, For fault data that is relevant to supplementary data, For regression coefficients, The intercept; The regression coefficients Calculated using the partial correlation coefficient: ,in For fault data and fault data The partial correlation coefficient between them and Fault data and fault data Standard deviation; intercept ,in and Fault data and fault data The mean.
2. The intelligent carrier module detection system based on artificial intelligence analysis according to claim 1, characterized in that: The fault data base filling module (100) senses the historical fault data of the carrier module. The historical fault data includes multiple fault occurrence timestamps, and each timestamp corresponds to multiple fault data detected at equidistant time nodes.
3. The intelligent carrier module detection system based on artificial intelligence analysis according to claim 2, characterized in that: The data filling method in the fault data basic filling module (100) retrieves the timestamp of the missing data, senses two other non-missing data points adjacent to the corresponding time node, determines a straight line through the two other non-missing data points, and uses the straight line trend to calculate and fill the missing data.
4. The intelligent carrier module detection system based on artificial intelligence analysis according to claim 3, characterized in that: The fault correlation cross-analysis module (200) senses fault data. , Fault data and fault data If the detection data are from the same time point, then the correlation coefficient is: ; in for The mean, for The mean; Set a correlation coefficient threshold; if the absolute value of the correlation coefficient is less than or equal to the correlation coefficient threshold, then the data is considered faulty. and fault data There is no correlation between them; If the absolute value of the correlation coefficient is greater than the correlation coefficient threshold, then the data is considered faulty. and fault data There is a correlation between them; retrieve fault data. and fault data Corresponding timestamp , If timestamp Earlier than the timestamp Then the fault data and fault data The correlation between them is the fault data → Fault Data .
5. The intelligent carrier module detection system based on artificial intelligence analysis according to claim 4, characterized in that: The fault correlation cross-analysis module (200) calculates the fault data. and fault data Correlation coefficient between Then, calculate the fault data. and fault data Correlation coefficient between ,like >correlation coefficient threshold, and If the correlation coefficient threshold is reached, fault data will be calculated immediately. and fault data Correlation coefficient between If the correlation coefficient is calculated If the correlation coefficient exceeds the threshold, then a determination is made. , and There are correlations between them, and the correlation relationship of the fault data is determined based on the corresponding timestamps.
6. The intelligent carrier module detection system based on artificial intelligence analysis according to claim 5, characterized in that: The biased correlation analysis method in the fault relationship precision analysis module (300) is used to calculate fault data. and fault data Controlling fault data Partial correlation coefficient under the influence And calculate fault data and fault data Controlling fault data Partial correlation coefficient under the influence ;like > When that happens, determine the fault data. The impact is greatest.
7. The intelligent carrier module detection system based on artificial intelligence analysis according to claim 6, characterized in that: The calculation formula for the biased correlation analysis method is as follows: Perceived fault data , and Control fault data Under the influence of fault data and fault data Partial correlation coefficient between for: .
8. The intelligent carrier module detection system based on artificial intelligence analysis according to claim 1, characterized in that: The precise fault data repair module (400) calculates multiple supplementary data, retrieves the most frequent supplementary data, selects the one with the highest frequency of occurrence as the final supplementary data, and replaces the filling data.
Citation Information
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