A method for quickly locating a water leakage point of a pipeline

By analyzing the RGB values ​​and temperature zones of pipe leaks using a thermal imaging detector, the problem of inaccurate leak location in existing technologies has been solved, enabling rapid and accurate location of leaks and identification of leak types.

CN119533780BActive Publication Date: 2025-10-24BEIJING SHOUHUA CONSTR OPERATION CO LTD
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Patent Information

Application Number
CN202411523463.6
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2024-10-29
Publication Date
2025-10-24
Estimated Expiration
2044-10-29

AI Technical Summary

Technical Problem

In existing technologies, the process of locating pipe leaks cannot pinpoint the exact type of pipe that is leaking, resulting in insufficient accuracy.

Method used

The pipeline is thermally imaged using a thermal imaging detector. The RGB values ​​of the thermal images are analyzed to identify abnormal areas. Vertical correlation lines are constructed to divide the area into zones. Temperature variance processing is used to lock the temperature zone with the largest deviation, generating a ring area. Warm or cool color zones are confirmed by sorting by temperature mean, and a leakage signal is generated.

Benefits of technology

It enables rapid and accurate location of leaks and can distinguish between leaks in hot and cold water pipes, providing timely repair guidance.

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Patent Text Reader

Abstract

The application discloses a kind of pipeline water leakage point fast positioning method, the present application relates to pipeline water leakage positioning technical field, solve the original positioning process, and cannot be accurate to which kind of pipeline exists water leakage situation Problem, the present application is confirmed from the temperature difference maximum subzone, by the relevant ring set is carried out ring subarea, again based on the specific ring area divided, lock the associated temperature mean value of corresponding ring area, then corresponding temperature mean value is sorted, based on the specific numerical characteristics of sorting, the specific confirmation of color tone subarea is carried out, based on confirmation result, generate corresponding water leakage signal, not only can effectively complete the relevant positioning of water leakage point, but also lock which kind of pipeline exists water leakage situation, and timely show, for external personnel to check, timely maintenance, make response measures.
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Description

TECHNICAL FIELD

[0001] The application relates to the technical field of pipeline water leakage positioning, and particularly relates to a pipeline water leakage point rapid positioning method. BACKGROUND

[0002] For the related processing procedure of pipeline water leakage positioning, a thermal imager is generally used to scan a pipeline area; the temperature around a water leakage point is different from that of a normal pipeline part, and temperature differences are displayed on the thermal imager; the water leakage point can be quickly positioned by analyzing the temperature distribution in the thermal imaging image.

[0003] An application with the publication number CN115183157A discloses a pipeline water leakage positioning and detection method, system, intelligent terminal and storage medium, and belongs to the technical field of pipeline detection. The application comprises the following steps: acquiring the position of a water leakage quantity detection device and the detected water leakage quantity; screening out a water leakage quantity detection device corresponding to the maximum water leakage quantity, and defining the water leakage quantity detection device corresponding to the maximum water leakage quantity as a center detection device; determining an offset ratio according to the ratio of the water leakage quantities detected by the water leakage quantity detection devices on both sides of the center detection device; acquiring offset information according to the corresponding relationship between the preset offset information and the offset ratio, wherein the offset information comprises offset direction information and offset quantity information relative to the center detection device, and generating water leakage point axial position information according to the offset information and the position of the center detection device; and sending the water leakage point axial position information to a background terminal. The application has the effect of more accurately acquiring the position of a pipeline water leakage point.

[0004] When the pipeline internal water leakage point is detected and positioned, the corresponding abnormal area is generally recognized based on the corresponding thermal imager, and the abnormal area is displayed for external personnel to view, so that the corresponding positioning process is completed. However, the original positioning process cannot accurately determine which type of pipeline has a water leakage condition, and only abnormal conditions are simply recognized. Therefore, the original water leakage abnormality recognition method needs to be strengthened. SUMMARY

[0005] In view of the defects of the prior art, the application provides a pipeline water leakage point rapid positioning method, which solves the problem that the original positioning process cannot accurately determine which type of pipeline has a water leakage condition.

[0006] To achieve the above object, the application is implemented by the following technical scheme: a pipeline water leakage point rapid positioning method, comprising the following steps:

[0007] Step one, based on a thermal imaging detector, a wall internal water pipeline is subjected to thermal imaging processing, and a thermal imaging image generated by the water pipeline is subjected to numerical analysis. Based on the numerical checking result, an abnormal area is determined. The specific sub-steps are as follows:

[0008] S11, based on the specific thermal imaging processing procedure of the water delivery pipeline, confirming the thermal imaging image of the entire water delivery pipeline, confirming the RGB value associated with each pixel point in the thermal imaging image, and marking the confirmed RGB value as R i , wherein i represents different pixel points;

[0009] S12, R i , the RGB value associated with each pixel point in the thermal imaging image is confirmed, and the confirmed RGB value is marked as R i , the RGB value associated with each pixel point in the thermal imaging image is confirmed, and the confirmed RGB value is marked as R i , the RGB value associated with each pixel point in the thermal imaging image is confirmed, and the confirmed RGB value is marked as R

[0010] S13, based on the determined same type area in the thermal imaging image, marking other areas not divided into the same type area as abnormal areas;

[0011] Step two, based on the determined center point of the abnormal area, constructing two groups of associated vertical lines, rotating the two groups of associated vertical lines according to the center point, and analyzing the temperature data of the area between adjacent associated vertical lines based on each rotation process, based on the analysis result, locking the maximum deviation temperature area, the specific sub-steps are:

[0012] S21, based on the edge contour of the abnormal area, placing the edge contour in a two-dimensional coordinate system, and confirming the point coordinates of the internal points of the edge contour from the two-dimensional coordinate system, performing mean value processing on the point coordinates of the internal points, determining the mean value point, and marking the mean value point in the edge contour as the center point of the abnormal area;

[0013] S22, based on the determined center point, constructing two groups of associated vertical lines perpendicular to each other, and the vertical points of the two groups of associated vertical lines coincide with the center point, so that the end points of the associated vertical lines fall on the edge contour of the abnormal area, the constructed associated vertical lines divide the abnormal area into four groups of micro areas, and the temperature data of the internal different points of each group of micro areas is confirmed and marked as WD k , wherein k represents different points, and the confirmed temperature data WD k , the standard deviation Fc is confirmed by variance processing;

[0014] S23, make the constructed correlation vertical line rotate along the center point to the corresponding correlation vertical line re-rotate to the initial position, and the standard deviation of the corresponding micro region is confirmed by variance processing of the different micro region temperature data generated in each group of rotation processes. Based on the different standard deviations generated by different micro regions in each different rotation process, the maximum value is selected from the several standard deviations, the rotation process associated with this maximum value is marked as the standard process, and the micro region associated with this maximum value in this standard process is marked as the maximum deviation temperature zone;

[0015] Step three, based on the determined maximum deviation temperature zone, diffuse from the center point to the outside, generate equidistant annuli in turn, and confirm the mean temperature of each annular region. The mean temperature sequence is determined by sorting the several mean temperatures in the order of the center point to the outside, and the mean temperature sequence is analyzed to confirm whether the abnormal region belongs to the warm color tone partition or the cold color tone partition;

[0016] Step four, based on the marked warm color tone partition, generate a hot water pipe leakage signal and simultaneously display the abnormal region, and based on the marked cold color tone partition, generate a cold water pipe leakage signal and simultaneously display the abnormal region, in specific ways:

[0017] S31, based on the determined maximum deviation temperature zone and the center point of the abnormal region, the center point is taken as the center of the circle to construct a circle, the radius of the initial circle is Y2, the radius of the second group of circles is 2Y2, the radius of the third group of circles is 3Y2, and so on, until the constructed circle does not intersect with the maximum deviation temperature zone and the circle is deleted, wherein Y2 is a preset value. The region between adjacent circles and located inside the maximum deviation temperature zone is marked as a circular ring region, and the region between the first group of circles or the last group and the maximum deviation temperature zone is also marked as a circular ring region;

[0018] S32, based on the several groups of temperature data included in the annular region, the several groups of temperature data are processed by mean value to determine the temperature mean value belonging to the corresponding annular region, and then the several temperature mean values are sorted in the order of the center point to the outside to determine the mean temperature sequence belonging to the maximum deviation temperature zone;

[0019] S33, compare the adjacent temperature mean values in the mean temperature sequence, if the current group of temperature mean values < the next group of temperature mean values, assign value 1, if the current group of temperature mean values > the next group of temperature mean values, assign value 0, and if the adjacent temperature mean values are equal, do not assign any value;

[0020] When the number of assigned values 1 is greater than the number of assigned values 0, the abnormal region is divided into a warm color tone partition;

[0021] When the number of assigned values 1 is less than the number of assigned values 0, the abnormal region is divided into a cold color tone partition.

[0022] When the number of assignment 1 is equal to the number of assignment 0, an error signal is generated, and the mean temperature sequence is displayed for external personnel to view.

[0023] The application provides a pipeline water leakage point rapid positioning method. Compared with the prior art, the application has the following advantages

[0024] Beneficial effects:

[0025] The application confirms the thermal imaging image, and based on the RGB values associated with different pixel points in the thermal imaging image, analyzes the RGB value changes of adjacent points, determines the same type of region, locks the abnormal region in the image based on the determined same type of region, confirms the center point of the abnormal region, constructs the corresponding related vertical line, partitions the abnormal region, divides the abnormal region into multiple micro-zones, changes the region contained in the micro-zone by rotating, determines the micro-zone with the largest temperature difference based on the specific process of temperature variance processing, and confirms the partition.

[0026] From the confirmed partition with the largest temperature difference, the application divides the ring area by the set related ring, locks the associated temperature mean value of the corresponding ring area based on the divided specific ring area, sorts the corresponding temperature mean value, confirms the specific confirmation of the color tone partition based on the specific numerical characteristics of the sorting, generates the corresponding water leakage signal based on the confirmation result, effectively completes the positioning of the water leakage point, locks which type of pipeline has the water leakage condition, and timely displays for external personnel to view, timely repairs, and takes countermeasures. BRIEF DESCRIPTION OF DRAWINGS

[0027] Figure 1 The figure is a method flowchart of the application;

[0028] Figure 2 The figure is a micro-zone adjustment and determination schematic diagram of the application;

[0029] Figure 3 The figure is a ring area determination schematic diagram of the application. DETAILED DESCRIPTION

[0030] The technical solutions in the embodiments of the application will be clearly and completely described below with reference to the drawings in the embodiments of the application. Obviously, the described embodiments are only part of the embodiments of the application, rather than all the embodiments of the application. Based on the embodiments in the application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the application.

[0031] First embodiment

[0032] Please refer to Figure 1 The application provides a pipeline water leakage point rapid positioning method, comprising the following steps:

[0033] Step one, based on the thermal imaging detector, the water supply pipeline inside the wall is subjected to thermal imaging processing, and the thermal imaging image generated by the water supply pipeline is subjected to numerical analysis, based on the numerical checking result, the abnormal area is determined, specifically, for the water leakage analysis and processing of the water supply pipeline, generally, the imaging analysis is carried out by using the related thermal imager, and the abnormal area is confirmed by human observation, the human observation is not accurate for subtle changes, therefore, the RGB value of the imaging point of the corresponding area is analyzed to confirm the related abnormal area, so as to lock the abnormal area;

[0034] Among them, the specific sub-step of determining the abnormal area is:

[0035] S11, based on the specific thermal imaging processing process of the water supply pipeline, the thermal imaging image of the entire water supply pipeline is confirmed, the RGB value associated with each pixel point in the thermal imaging image is confirmed, and the confirmed RGB value is marked as R i , wherein i represents different pixel points;

[0036] S12, the R i of adjacent pixel points is compared, and the same type area is locked by numerical comparison: Based on the R i associated with two adjacent pixel points, after difference processing and taking the absolute value JD, the determined absolute value JD is compared with the preset value Y1, if JD≤Y1, the two adjacent pixel points are divided into the same type point, and the area covered by the same type point is marked as the same type area, wherein Y1 is a preset value, and its specific value is determined by the operator according to experience, if JD>Y1, the same type point is not marked, for example: Y1 is set to 5, there are three points A, B and C, the RGB value of A is 21, the RGB value of B is 22, and the RGB value of C is 27, based on the determination process of adjacent pixel points, A and B belong to the same type point, B and C belong to the same type point, therefore, the area covered by A, B and C belongs to the same type area;

[0037] S13, based on the same type area determined in the thermal imaging image, other areas not divided into the same type area are marked as abnormal areas, the points in the abnormal area and the same type points do not belong to the same type, and the abnormal area exists because the corresponding color tone is inconsistent with the color tone of other areas, therefore, the corresponding abnormal area can be directly determined;

[0038] Step two, based on the determined abnormal area, the center point of the abnormal area is determined preferentially, two groups of associated vertical lines are constructed based on the determined center point, the two groups of associated vertical lines are rotated according to the center point, and the temperature data of the area between adjacent associated vertical lines is analyzed based on each rotation process, based on the analysis result, the maximum deviation temperature zone is locked, specifically, in order to achieve more accurate evaluation, it is necessary to lock the temperature area with the largest temperature difference in the determined abnormal area, and data analysis is performed on the temperature area, and it is evaluated whether the abnormal area belongs to the warm color tone area or the cold color tone area;

[0039] Wherein, the specific sub-step of locking the maximum deviation temperature zone is:

[0040] S21, based on the edge contour of the abnormal area, the edge contour is placed in a two-dimensional coordinate system, and the point coordinates of the internal point positions of the edge contour are confirmed from the two-dimensional coordinate system, the point coordinates of the internal point positions are processed by mean value, the mean value point is determined, and the mean value point is marked in the edge contour to determine the center point of the abnormal area;

[0041] S22, based on the determined center point, two groups of associated vertical lines perpendicular to each other are constructed, and the vertical points of the two groups of associated vertical lines coincide with the center point, so that the end points of the associated vertical lines fall on the edge contour of the abnormal area, the associated vertical lines divide the abnormal area into four groups of micro areas, the temperature data of different internal point positions of each group of micro areas is confirmed, and marked as WD k , wherein k represents different point positions, and the temperature data WD k of the same group of micro areas is processed by variance to confirm the standard variance Fc;

[0042] S23, the constructed associated vertical lines are rotated along the center point to the corresponding associated vertical lines, and the rotation is stopped at the initial position, the variance of the temperature data of different micro areas generated in each rotation process is processed, and the standard variance of the corresponding micro area is confirmed, based on the different standard variances generated by different micro areas in each different rotation process, a maximum value is selected from the several standard variances, the rotation process associated with the maximum value is marked as the standard process, and the micro area associated with the maximum value in the standard process is marked as the maximum deviation temperature zone;

[0043] Combined Figure 2, based on the determined abnormal area, locking the center point of the abnormal area based on the overall edge contour line of such abnormal area, based on the confirmed center point, constructing two sets of associated perpendicular lines perpendicular to each other, both end points of the associated perpendicular lines are located on the edge contour of the abnormal area, based on the specific rotation direction, the associated perpendicular lines are rotated, and the end points of the associated perpendicular lines are still located on the corresponding edge contour during the rotation, that is, the length of the associated perpendicular line is real-time changing, so the range of the micro area contained by the associated perpendicular line is also changing during the rotation, based on the specific change process, the standard deviation associated with the corresponding micro area can be locked, based on the specific rotation analysis process, the corresponding maximum deviation temperature zone can be locked from the specific rotation analysis process, thereby facilitating subsequent temperature analysis to determine the related confirmation of cold color tone and warm color tone.

[0044] Second embodiment

[0045] The embodiment is mainly used for confirming the related confirmation of the warm color tone and the cold color tone partition of the temperature zone;

[0046] Step three, based on the determined maximum deviation temperature zone, the center point is diffused outward, and a series of equidistant annuli are generated in turn, and the mean temperature of each annular region is confirmed, a series of mean temperatures are sorted in a center-out order, a mean temperature sequence is determined, and the mean temperature sequence is analyzed to confirm whether the abnormal area belongs to the warm color tone partition or the cold color tone partition. Specifically, the mean temperature arrangement of the corresponding partition has a corresponding arrangement feature, that is, the corresponding change process of the temperature, when the temperature gradually decreases, it represents that the region belongs to the cold color tone partition, when the corresponding temperature gradually rises, it represents that the region belongs to the warm color tone partition, and the temperature gradually rises outward, the warm color tone partition belongs to hot water pipe leakage, then a warm color tone partition is generated, the cold color tone partition belongs to cold water pipe leakage, and when the water droplets fall downward, a corresponding cold color tone partition is generated. The specific sub-steps for confirmation are:

[0047] S31, based on the determined maximum deviation temperature zone and the center point of the abnormal area, the center point is taken as the center to construct a circle, the radius of the initial circle is Y2, the radius of the second set of circles is 2Y2, the radius of the third set of circles is 3Y2, and so on, until the constructed circle does not intersect with the maximum deviation temperature zone and the circle is deleted, wherein Y2 is a preset value, the specific value is determined by the operator according to experience, the region between adjacent circles and located in the maximum deviation temperature zone is marked as an annular region, and the region between the first set of circles or the last set of circles and the maximum deviation temperature zone is also marked as an annular region, such as Figure 2As shown, the area between the annular rings belongs to the annular region, the area between the first group of annular rings and the center point also belongs to the annular region, and the area between the last group of annular rings and the maximum deviation temperature zone also belongs to the corresponding annular region;

[0048] S32, based on the several groups of temperature data included in the annular region, the several groups of temperature data are mean processed to determine the temperature mean value belonging to the corresponding annular region, and then the several temperature mean values are sorted in the order of the center point outward to determine the mean temperature sequence belonging to the maximum deviation temperature zone;

[0049] S33, compare the adjacent temperature mean values in the mean temperature sequence, if the previous group of temperature mean values < the next group of temperature mean values, assign 1, if the previous group of temperature mean values > the next group of temperature mean values, assign 0, and if the adjacent temperature mean values are equal, do not assign any value;

[0050] When the number of assigned 1 is greater than the number of assigned 0, the abnormal area is divided into a warm color tone partition;

[0051] When the number of assigned 1 is less than the number of assigned 0, the abnormal area is divided into a cold color tone partition;

[0052] When the number of assigned 1 is equal to the number of assigned 0, an error signal is generated, and the mean temperature sequence is displayed for external personnel to view, and external personnel can determine the color tone partition based on the specific change process between the temperatures based on the related temperatures displayed in the mean temperature sequence.

[0053] Step four, based on the calibrated warm color tone partition, a hot water pipe leakage signal is generated, and the abnormal area is displayed synchronously, based on the calibrated cold color tone partition, a cold water pipe leakage signal is generated, and the abnormal area is displayed synchronously.

[0054] Specifically, based on the determined warm color tone partition, the temperature of such a warm color tone partition belongs to an increasing state from inside to outside, so it belongs to a hot water pipe leakage situation, so a corresponding hot water pipe leakage signal is directly generated, and the temperature of the corresponding cold color tone partition belongs to a decreasing state from inside to outside, so it belongs to a cold water pipe leakage situation, so a corresponding cold water pipe leakage signal is directly generated.

[0055] Third embodiment

[0056] In the specific implementation process of this embodiment, all the implementation processes of the above two embodiments are included.

[0057] Some data in the above formula are dimensionless numerical calculations, and the contents not described in detail in the specification all belong to the prior art known to those skilled in the art.

[0058] The above examples are only used to illustrate the technical method of the present application but not limit the present application. Although the present application is described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical method of the present application can be modified or equivalently replaced without departing from the spirit and scope of the technical method of the present application.

Claims

1. A method for quickly locating a water leakage point in a pipe, characterized in that, The method comprises the following steps: Step one, based on the thermal imaging detector, the water pipeline inside the wall is processed by thermal imaging, and the thermal imaging image generated by the water pipeline is analyzed by numerical value. Based on the numerical checking result, the abnormal area is determined; Step two, based on the abnormal area, the center point of the abnormal area is determined, two groups of associated vertical lines are constructed based on the center point, the two groups of associated vertical lines are rotated based on the center point, and the temperature data of the area between the adjacent associated vertical lines is analyzed based on each rotation process to lock the maximum deviation temperature zone: S21, based on the edge profile of the abnormal area, the edge profile is placed in a two-dimensional coordinate system, and the point coordinates of the internal points of the edge profile are confirmed from the two-dimensional coordinate system. The point coordinates of the internal points are processed by mean value to determine the mean value point, and the mean value point is calibrated in the edge profile to determine the center point of the abnormal area; S22, based on the center point, two sets of mutually perpendicular associated perpendicular lines are constructed, and the perpendicular points of the two sets of associated perpendicular lines coincide with the center point, so that the two end points of the associated perpendicular line fall on the edge contour of the abnormal area, the associated perpendicular line divides the abnormal area into four groups of micro areas, and the temperature data of different points in each group of micro areas are confirmed and marked as WD k , wherein k represents different points, and a plurality of temperature data WD k in the same group of micro areas are subjected to variance processing to confirm the standard variance Fc; S23, make the associated vertical line rotate along the center point to the corresponding associated vertical line, and stop rotating to the initial position. The standard deviation of the different micro areas generated in each rotation process is confirmed by variance processing of the several temperature data of the different micro areas. Based on the different standard deviations generated by different micro areas in each different rotation process, the maximum value is selected from the several standard deviations. The maximum value associated with the rotation process is calibrated as the standard process, and the micro area associated with the maximum value in the standard process is calibrated as the maximum deviation temperature zone; Step three, based on the maximum deviation temperature zone, the center point is diffused outward to generate equidistant annuli in turn, and the mean temperature of each annular area is confirmed. The mean temperature sequence is determined by sorting the several mean temperatures in the order of the center point outward, and the abnormal area is analyzed to determine whether it belongs to the warm color tone partition or the cold color tone partition; Step four, based on the calibrated warm color tone partition, a hot water pipe leakage signal is generated, and the abnormal area is displayed synchronously. Based on the calibrated cold color tone partition, a cold water pipe leakage signal is generated, and the abnormal area is displayed synchronously.

2. The method of claim 1, wherein, In step one, the specific sub-step for determining the abnormal area is: S11, based on the specific thermal imaging processing procedure of the water delivery pipeline, confirming the thermal imaging image of the entire water delivery pipeline, confirming the RGB value associated with each pixel point in the thermal imaging image, and marking the confirmed RGB value as R i where i represents different pixel points; S12, R i S13, the absolute value JD of the difference value is determined, and the determined absolute value JD is compared with a preset value Y1. If JD≤Y1, the two adjacent pixel points are divided into the same type of points, and a region covered by a plurality of same type of points is marked as a same type of region, where Y1 is a preset value. i S13, the absolute value JD of the difference value is determined, and the determined absolute value JD is compared with a preset value Y1. If JD≤Y1, the two adjacent pixel points are divided into the same type of points, and a region covered by a plurality of same type of points is marked as a same type of region, where Y1 is a preset value. S13, based on the same type of area determined in the thermal imaging image, other areas not divided into the same type of area are calibrated as abnormal areas.

3. The method of claim 2, wherein, In step S12, if JD>Y1, no related calibration of the same type of point is performed.

4. The method of claim 1, wherein, In step three, the specific way to determine that the abnormal area belongs to the warm color tone partition is: S31, based on the determined maximum deviation temperature zone and the center point of the abnormal area, the center point is taken as the center of the circle to construct a circle. The radius of the initial circle is Y2, the radius of the second group of circles is 2Y2, the radius of the third group of circles is 3Y2, and so on, until the constructed circle does not intersect with the maximum deviation temperature zone and the circle is deleted. Y2 is a preset value. The area between adjacent circles and located in the maximum deviation temperature zone is calibrated as a circular ring area, and the area between the first group of circles or the last group and the maximum deviation temperature zone is also calibrated as a circular ring area. S32, based on the several groups of temperature data included in the annular region, the several groups of temperature data are processed by mean value, the temperature mean values belonging to the corresponding annular region are determined, and then the several temperature mean values are sorted according to the outward ordering of the center point, so as to determine the mean temperature sequence belonging to the maximum deviation temperature region; S33, the adjacent temperature mean values in the mean temperature sequence are compared, if the previous group of temperature mean values is less than the next group of temperature mean values, the value is 1, if the previous group of temperature mean values is greater than the next group of temperature mean values, the value is 0; When the number of value 1 is greater than the number of value 0, the abnormal region is divided into a warm color tone partition.

5. The method of claim 4, wherein, In the step S33, when the number of value 1 is less than the number of value 0, the abnormal region is divided into a cold color tone partition.

6. The method of claim 4, wherein, In the step S33, when the number of value 1 is equal to the number of value 0, an error signal is generated, and the mean temperature sequence is displayed for external personnel to view.

7. The method of claim 4, wherein, In the step S33, when the adjacent temperature mean values are equal, no value is assigned.

Citation Information

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