Internal penetration type weak magnetic detection probe and its operating method
The internal penetration type weak magnetic detection probe addresses the limitations of existing methods by providing high-precision, operator-independent detection and quantitative analysis of titanium heat exchange tube defects through passive magnetic anomaly scanning.
Patent Information
- Application Number
- JP2024534047
- Authority / Receiving Office
- JP · JP
- Patent Type
- Patents
- Current Assignee / Owner
- Priority Date
- 2022-06-29
- Filing Date
- 2022-11-03
- Publication Date
- 2025-07-02
- Estimated Expiration
- 2042-11-03
AI Technical Summary
Existing non-destructive detection methods for titanium heat exchange tubes in condensers, such as eddy current and ultrasonic detection, are limited by surface sensitivity, subjective interpretation, and require operator expertise, making them inadequate for accurately identifying and quantifying defects in titanium tubes used in harsh environments.
An internal penetration type weak magnetic detection probe with evenly distributed weak magnetic sensor groups and a roller mechanism, allowing for passive detection and automatic scanning, which provides high-precision magnetic anomaly detection and quantitative analysis without surface preparation or operator dependency.
The probe effectively identifies and quantifies defects in titanium heat exchange tubes by analyzing magnetic induction changes, offering accurate, efficient, and operator-independent detection suitable for complex geometries and environments.
Smart Images

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Abstract
Description
Technical Field
[0001] This application belongs to the technical field of weak magnetic detection, and specifically relates to an internal penetration type weak magnetic detection probe and its operating method.
[0002] This application claims the priority of a Chinese patent application filed with the State Intellectual Property Office of China on June 29, 2022, with an application number of 202210753040.8 and an invention title of "Internal Penetration Type Weak Magnetic Detection Probe and Its Operating Method", the entire content of which is incorporated herein by reference.
Background Art
[0003] A condenser is an important component of a steam power system. It mainly cools and condenses steam during the steam discharge process of a steam turbine, and plays a role in forming a steam-water energy cycle together with a steam generator. Most condensers in the steam power systems of nuclear (thermal) power plants use a surface-type heat exchange structure where cooling water and steam exchange heat through a solid surface. Currently, shell-and-tube condensers are the most commonly used. However, in actual applications, the welded joint between the heat exchange tubes and the tube sheet of the condenser is a part that is prone to corrosion. The corrosion suffered by the heat exchange tubes generally includes electrochemical corrosion, stress corrosion, and erosion corrosion. Electrochemical corrosion is a common corrosion. In a humid environment, positive and negative electrode potentials are formed, and electrochemical corrosion occurs. Stress sources that cause stress corrosion include operating pressure due to the temperature difference between the inlet and outlet, residual stress generated during processing, and structural stress generated during manufacturing due to structural design. Erosion corrosion mainly occurs at the steam inlet. The erosion of the fluid causes vibration of the tube bundle, which may lead to damage to the heat exchange tubes in severe cases.
[0004] During production, it is common for manufacturers to use metal materials such as stainless steel, copper, and titanium as raw materials for processing heat exchange tubes. In some special corrosive environments, stainless steel is prone to intergranular corrosion, and copper pipes are prone to electrochemical corrosion by circulating water. Currently, in major power plants, in order to ensure the reliable use of supercritical units, it is common to inject ammonia or hydrazine into the circulating water to ensure a high pH value. This, however, increases the requirements for the corrosion resistance of heat exchange tubes. Titanium is a high-quality corrosion-resistant material with high plasticity and toughness, and is easy to weld and process into shape. Therefore, the adoption of titanium heat exchange tubes in major power plants is increasing. Titanium heat exchange tubes, as materials with excellent corrosion resistance, are widely used in devices such as condensers used under harsh conditions. Especially in coastal nuclear power plants, almost all of the materials for the tube bundles, which are crucial heat exchange components of condensers using seawater as the circulating cooling medium, adopt titanium tubes. Heat exchange titanium tubes are used for a long time under harsh operating conditions such as the corrosion of mineral salts and the impact of seawater, so they are prone to corrosion and damage. As a result, the titanium tubes are damaged or malfunction, which has a significant impact on the safe operation of the condenser.
[0005] The non-destructive detection methods for titanium heat exchange tubes usually include eddy current detection and ultrasonic detection. Eddy current detection utilizes the principle of electromagnetic induction to detect defects on the surface or near the surface of the component to be detected. It has high detection sensitivity and a fast detection speed. However, eddy current is an induced current generated by an alternating magnetic field and is affected by the "skin effect", so it is difficult to determine the type of defect from its signal. Ultrasonic detection is also widely used for the detection of pipeline materials. It can locate and quantify the position of defects, but the defect indication by ultrasonic flaw detection is not intuitive, is easily affected by subjective and objective factors, and highly depends on the on-site experience of the detector.
Summary of the Invention
Problems to be Solved by the Invention
[0006] To solve the above-mentioned conventional problems, the present application aims to provide an internal penetration type weak magnetic detection probe and its operating method, which have a simple structure, reasonable design, are easy to operate, can accurately identify and quantitatively analyze defects, have a wide application range, and do not depend on the experience and skill level of the operator.
Means for Solving the Problems
[0007] The present application is achieved by the following technical means.
[0008] The internal penetration type weak magnetic detection probe disclosed in the present application includes a main body. Inside the front part of the main body, a signal line storage tube and a plurality of weak magnetic sensor groups are provided, which are peripherally arranged on the inner wall of the main body and evenly distributed. Each weak magnetic sensor group includes two weak magnetic sensors arranged along the axial direction of the main body. The magnetic sensing surface of the weak magnetic sensor is perpendicular to the wall surface of the main body and faces outward. At the rear part of the main body, a roller for driving the main body to move linearly is provided, a motor is connected to the roller, a connection port is provided at the rear end of the rear part of the main body, and the signal lines of the weak magnetic sensors pass through the signal line storage tube and gather at the connection port together with the connection cord of the motor, providing an internal penetration type weak magnetic detection probe.
[0009] Optionally, the main body includes a first main body, an intermediate connector, and a second main body that are removably and sequentially connected. The signal line storage tube and the plurality of weak magnetic sensor groups are provided inside the first main body. The intermediate connector, the signal line storage tube, and the second main body have a through interior. The roller is provided on the second main body, the motor is provided inside the second main body, and the connection port is provided at the rear end of the second main body.
[0010] Optionally, the number of weak magnetic sensor groups is 6 to 12.
[0011] Optionally, a distance measuring sensor is provided at the front end of the main body, and the distance measuring sensor is connected to the connection port via a connection cord.
[0012] Optionally, ranging sensors are provided on both sides of the main body, and the ranging sensors are connected to the connection port via connection cords.
[0013] Optionally, a collision prevention contact is provided at the front end of the main body.
[0014] Optionally, the outer surface of the signal line storage tube is coated with a magnetic shielding material.
[0015] Optionally, a counterweight is provided inside the rear part of the main body.
[0016] The operating method of the above-mentioned internally penetrating type weak magnetic detection probe disclosed in the present application is as follows: Connecting to a weak magnetic flaw detector and a host computer respectively via the connection port, and inputting the parameters of the probe into the host computer; placing the main body at the inlet of the condenser tube, driving the roller to rotate by the motor, and advancing the entire main body; During detection, sequentially performing scans by two weak magnetic sensors of each weak magnetic sensor group, and displaying in real time on the host computer two magnetic induction intensity-time curves obtained by detection by each weak magnetic sensor group, and determining the presence or absence of defects and the type of the defects.
[0017] Optionally, performing differential processing on the magnetic induction intensity-time curve to obtain a corresponding differential curve, setting a threshold line, and intuitively reflecting the sudden change characteristics of the curve exceeding the threshold line range.
Advantages of the Invention
[0018] Compared with the prior art, the present application has the following beneficial technical effects. In the internal penetration type weak magnetic detection probe disclosed in the present application, the weak magnetic non-destructive detection technology is applied to the defect detection of titanium heat exchange tubes. The weak magnetic detection technology is a passive detection technology that does not require an additional excitation source. Thereby, while simplifying the design of the probe process, it is possible to avoid the influence on the detection process of the interference source field caused by the non-directional stress of the excitation source. In addition, the weak magnetic detection method is easy to acquire and use. Weak magnetic detection does not require special treatment of the surface of the workpiece to be detected, and there are no special requirements for the shape of the workpiece to be detected. Therefore, the detection effect is not affected whether there is a coating or non-contact detection. In the geomagnetic environment, a high-precision weak magnetic sensor is used to scan the surface or near the surface of the test piece, and by collecting the changes in the magnetic induction intensity in various directions, it is determined whether there is a magnetic anomaly in the detection area, and then the collected magnetic signal is processed. The weak magnetic detection method is a comparative measurement method that determines and quantifies the type of defect by comparing the difference values of the signals in the normal area and the magnetic anomaly area. In the present application, according to the characteristics of the small diameter and thin wall of the heat exchange tube of the condenser, the structure of the internal penetration type probe is designed. Several groups of weak magnetic sensor groups are evenly arranged in the circumferential direction inside the front part of the probe, and each weak magnetic sensor group is composed of two weak magnetic sensors. In addition, in order to facilitate the forward and backward movement of the probe in the heat exchange tube, a roller device is provided at the rear part of the probe. The weak magnetic sensor group based on the weak magnetic detection principle realizes the automatic scanning of the titanium tube, intelligently identifies common defects of the heat exchange tube such as thinning and pitting corrosion on the inner wall of the pipeline, and quantitatively analyzes the defects.
[0019] Furthermore, by making the probe body into a separate structure, it is easy to carry, store, repair and maintain.
[0020] Furthermore, by providing a distance measuring sensor at the front end of the main body, it is possible to prevent collisions and damages caused by blockage of the heat exchange tube.
[0021] Furthermore, by providing ranging sensors on both sides of the main body, a decrease in the inner diameter of the heat exchange tube can be quickly detected.
[0022] Furthermore, by providing anti-collision contacts at the front end of the main body, damage to the probe caused by collisions can be prevented.
[0023] Furthermore, by coating the outer surface of the signal line storage tube with a magnetic shielding material, it is possible to avoid the leakage magnetic flux generated from the weak magnetic sensor coil from affecting the stability of the probe.
[0024] Furthermore, by providing a counterweight inside the rear part of the main body, the center of the probe can be placed at the rear part, thereby preventing the front part from sinking, keeping the distance between all the weak magnetic sensor groups and the inner wall of the heat exchange tube constant, and improving the detection accuracy.
[0025] The operation method of the above-mentioned internally penetrating type weak magnetic detection probe disclosed in this application is easy to operate, has high detection efficiency, accurate results, and does not depend on the experience and skill level of the operator.
Brief Description of the Drawings
[0026]
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6a
Figure 6b
Figure 7
Figure 8
Figure 9
Embodiments for Carrying Out the Invention
[0027] Hereinafter, with reference to the drawings and specific embodiments, the present application will be described in more detail. However, the content is not intended to limit the present application and is for explanatory purposes only.
[0028] As shown in FIG. 1, the internal penetration type weak magnetic detection probe of the present application includes a main body. Inside the front part of the main body, a signal line storage tube 3 and a plurality of weak magnetic sensor groups that are peripherally provided on the inner wall of the main body and evenly distributed are provided. Each weak magnetic sensor group includes two weak magnetic sensors 4 arranged along the axial direction of the main body. The magnetic sensing surface of the weak magnetic sensor 4 is perpendicular to the wall surface of the main body and faces outward. At the rear part of the main body, a roller 5 for driving the main body to move linearly is provided. A motor is connected to the roller 5. A connection port is provided at the rear end of the rear part of the main body. The signal lines of the weak magnetic sensors 4 pass through the signal line storage tube 3 and gather at the connection port together with the connection cord of the motor.
[0029] In one preferred embodiment of the present application, ABS plastic is used as the off-tool material of the main body, thereby giving the off-tool excellent impact resistance and predetermined heat insulation properties.
[0030] In one preferred embodiment of the present application, the main body includes a first main body 1, an intermediate connector 6, and a second main body 2 that are removably connected in sequence. The signal line storage tube 3 and the plurality of weak magnetic sensor groups are provided in the first main body 1. The intermediate connector 6, the signal line storage tube 3, and the second main body 2 have a through interior. The roller 5 is provided on the second main body 2. The motor is provided in the second main body 2. The connection port is provided at the rear end of the second main body 2.
[0031] In one preferred embodiment of the present application, the number of the weak magnetic sensor groups may be 6 to 12.
[0032] In one preferred embodiment of the present application, a distance measuring sensor is provided at the front end of the main body, and the distance measuring sensor is connected to the connection port through a connection cord.
[0033] In one preferred embodiment of the present application, distance measuring sensors are provided on both sides of the main body, and the distance measuring sensors are connected to the connection port through connection cords.
[0034] In one preferred embodiment of the present application, a collision prevention contact 7 is provided at the front end of the main body.
[0035] In one preferred embodiment of the present application, the outer surface of the signal line storage tube 3 is coated with a magnetic shielding material. The magnetic shielding material may be a film material processed from permalloy.
[0036] In one preferred embodiment of the present application, a counterweight is provided inside the rear part of the main body.
[0037] The operating method of the above internal penetration type weak magnetic detection probe is as follows: As shown in FIGS. 2, 3, and 4, connecting to a weak magnetic flaw detector 10 and a host computer respectively through the connection port, and inputting the parameters of the probe into the host computer; placing the main body at the inlet of the condensation tube 8, driving the roller 5 to rotate by the motor, and advancing the whole main body; sequentially performing scanning by two weak magnetic sensors 4 of each weak magnetic sensor group during detection, and displaying in real time on the host computer two magnetic induction intensity-time curves obtained by detection by each weak magnetic sensor group, and determining the presence or absence of a defect and the type of the defect.
[0038] In one preferred embodiment of the present application, the magnetic induction intensity-time curve is subjected to difference processing to obtain a corresponding difference curve, a threshold line is set, and the sudden change characteristics of the curve exceeding the threshold line range are intuitively reflected. The Theoretical Basis and Operating Principle of the Present Application Explanation of the Weak Magnetic Principle
[0039] In the detection using a weak magnetic flaw detector, when a defect occurs in the workpiece to be detected, a stress change occurs in the material itself. As a result, the atomic structure within the material crystal changes, and thereby, an abnormal magnetic field is spontaneously generated. When the relative magnetic permeability of the material itself is greater than that of the discontinuous defect of the material, based on the reason that the magnetic resistance is inversely proportional to the relative magnetic permeability, the corresponding magnetic resistance increases in the local region near the defect. As a result, the magnetic flux lines passing through the material bend, bypass the defect, and pass through the surrounding material. A schematic diagram of the weak magnetic detection principle is shown in Fig. 5.
[0040] Assuming that the magnetic permeability of the main body of the material to be detected is μ and the magnetic permeability of the discontinuous region inside the workpiece is μ', when the relative magnetic permeability of the discontinuous region is greater than that of the material to be detected, that is, when μ'>μ, when the weak magnetic sensor passes through this region, the magnetic induction intensity curve becomes concave. When the relative magnetic permeability of the discontinuous region is smaller than that of the material to be detected, that is, when μ'<μ, when the weak magnetic sensor passes through this region, the magnetic induction intensity curve becomes convex. The weak magnetic detection technology uses a high-precision magnetic sensor to detect abnormal signals caused by sudden changes in magnetic induction intensity and characterizes the defects of the material. Calculation of Detection Signal Feature Values
[0041] Titanium metal is a paramagnetic material. According to the weak magnetic detection principle, as a result of uniformly scanning a titanium tube using a weak magnetic probe, it was found that at locations without defects, the weak magnetic signal remained flat, near the defect, the weak magnetic signal began to rise, and near directly above the defect, a peak was observed in the weak magnetic signal. In the quantitative study of defects, the present application extracts the characteristic values related to the weak magnetic signal of the defect, and then achieves the quantitative estimation of the defect through the calculation and inversion of a large amount of data.
[0042] The form of magnetic anomalies is closely related to the magnetic induction intensity curve caused by defects. In particular, when a weak magnetic probe scans above a defect, as shown in Fig. 6a, the host computer software shows a nearly axisymmetric figure in real time. By extracting characteristic values such as the amplitude and width of the signal and performing formula calculations on them, size data regarding the magnetic induction intensity value can be obtained. Let the difference between the maximum peak value and the minimum value at the left end of the defect signal be ΔB1, and the half-wave width on the left side of the defect signal be ΔL1. Let the difference between the maximum peak value and the minimum value at the right end of the defect signal be ΔB2, and the half-wave width on the right side of the defect signal be ΔL2. The following formula can be easily obtained.
[0043] JPEG0007702045000001.jpg7161
[0044] JPEG0007702045000002.jpg7161
[0045] JPEG0007702045000003.jpg7161
[0046] In the formula, ΔB is the average amplitude difference between the peak and valley of the defect signal, ΔL is the average half-wave width of the defect signal, JPEG0007702045000004.jpg6161 is the average magnetic induction intensity at the defect location.
[0047] As shown in Fig. 6b, the dotted line on the left and the solid line on the right are weak magnetic signals from two adjacent weak magnetic sensors that sequentially scan the same defect location. ΔBm is the difference between the maximum peak value of the first weak magnetic sensor and the magnetic induction intensity at the corresponding position of the second weak magnetic sensor. Furthermore, let the amplitude difference obtained by the first weak magnetic sensor be ΔBu, the average value of the magnetic induction intensity obtained by the first weak magnetic sensor be JPEG0007702045000005.jpg6161, the average value of the magnetic induction intensity obtained by the second weak magnetic sensor be JPEG0007702045000006.jpg6161, and let the distance between the two weak magnetic sensors be ΔS, taking a fixed value of 1 mm. Therefore, the following empirical formula can be obtained.
[0048] JPEG0007702045000007.jpg18161
[0049] Here, K is the proportional control coefficient, A1 and A2 are empirical coefficients related to the magnetic permeability of the material, and D is the depth of the defect.
[0050] In a specific embodiment, a total of six pairs of weak magnetic sensor groups are evenly distributed along the circumferential direction of the inner wall of the probe. Two weak magnetic sensors are arranged side by side to form a pair of weak magnetic sensors. The probe is connected to the weak magnetic flaw detector through a connection port. One end of the weak magnetic flaw detector is connected to the probe, and the other end is connected to a host computer (laptop computer) via an Ethernet cable. The host computer (notebook) functions as the control terminal of the entire detection system, can analyze the weak magnetic signal in real time through the host computer software, and can also receive the signals transmitted from the probe contacts and roller devices in real time and perform feedback processing. In the detection process, two weak magnetic sensors arranged in parallel sequentially scan the detection target area. After data processing by the host computer, two magnetic induction intensity-time curves are displayed in real time. Then, characteristic values such as amplitude and half-wave width are accurately obtained by an algorithm, and finally, based on the empirical formula obtained in multiple past tests, it is determined whether there is a (corrosion) defect in the detection target area, and the degree of damage of the defect is estimated.
[0051] The specific operation process is as follows. 1. Connect the detection probe of this application to the weak magnetic flaw detector to ensure that the collected weak magnetic signal is displayed in real time on the software interface of the host computer. 2. Place the detection probe at the inlet of the pipeline, issue an instruction from the host computer (control terminal) to start the servo motor, and enable the detection probe to move forward and backward normally within the pipeline. 3. Place the distance measuring sensor immediately before the probe contact point. If the (measured) feedback distance data is shorter than the length of the heat exchange tube, it indicates that there is a blockage in this pipeline and human intervention is required. Distance measuring sensors are also arranged on the left and right of the probe contact point. If the measured data is larger than the diameter of the heat exchange tube or directly diverges, it indicates that there is a perforation defect in the inner wall of the pipeline at this position or the detection probe has exited from the opening of the pipeline. At this time, the servo motor will automatically stop. 4. Input the K value, A1 value, and A2 value suitable for this titanium tube into the host computer software. 5. When starting the detection, the host computer software displays 6 sets of interfaces in real time, and each set of interfaces displays 2 magnetic induction intensity - time curves in real time. Then, accurately obtain characteristic values such as amplitude and half - wave width with an algorithm, and based on the empirical formula obtained from multiple past tests, determine whether there is a (corrosion) defect at this position and estimate the degree of damage of the defect.
[0052] In one specific test example, it includes the following steps. 1. As shown in Figure 7, manually fabricate 4 inner - wall thinning rings on a titanium tube with a size of φ25×0.5mm, and the specific sizes are shown in Table 1. 2. Connect the probe to the weak magnetic flaw detector to ensure that the collected weak magnetic signal is displayed in real time on the host computer software interface. 3. Input the K value, A1 value, and A2 value suitable for the titanium tube into the host computer software. 4. Fix the titanium tube, move the probe from left to right, and scan four pre - arranged artificial defects at a constant speed. The scanning curve is shown in Figure 8. When differential processing is performed on the original curve, a more intuitive differential curve as shown in Figure 9 can be obtained. 5. After the scanning is completed, save the test data, perform data analysis as shown in Table 2, and calculate the corresponding defect information.
[0053]
Table 1
[0054]
Table 2
[0055] It can be seen from Table 2 that when the probe of the present application is used, it has high accuracy and can meet the actual detection needs.
[0056] The above are merely examples of the present application, and the protection scope of the present application is not limited thereto. Changes or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed by the present application, or equivalent structural or equivalent flow conversions made using the content of the description and drawings of the present application, or direct or indirect applications to other related technical fields are all included within the protection scope of the present application.
Explanation of Reference Signs
[0057] 1... First main body, 2... Second main body, 3... Signal line storage tube, 4... Weak magnetic sensor, 5... Roller, 6... Intermediate connector, 7... Collision prevention contact, 8... Condensation tube, 9... Wire harness, 10... Weak magnetic flaw detector
Claims
1. An internally penetrating weak magnetic detection probe, comprising: a main body, within the front portion of which are provided a signal line storage tube (3) and a plurality of weak magnetic sensor groups circumferentially provided on the inner wall of the main body and evenly distributed. Each weak magnetic sensor group includes two weak magnetic sensors (4) arranged along the axial direction of the main body. The magnetic sensitive surface of the weak magnetic sensor (4) is perpendicular to the wall surface of the main body and faces outward. At the rear portion of the main body, a roller (5) for driving the main body to linearly move is provided. A motor is connected to the roller (5). A connection port is provided at the rear end of the rear portion of the main body. The signal lines of the weak magnetic sensors (4) pass through the signal line storage tube (3) and converge at the connection port together with the connection cord of the motor. An internally penetrating weak magnetic detection probe, characterized by the above.
2. The main body includes a first main body (1), an intermediate connector (6), and a second main body (2) that are removably and sequentially connected. The signal line storage tube (3) and the plurality of weak magnetic sensor groups are provided within the first main body (1). The interior of the intermediate connector (6), the signal line storage tube (3), and the second main body (2) is penetrated. The roller (5) is provided on the second main body (2). The motor is provided within the second main body (2). The connection port is provided at the rear end of the second main body (2). The internally penetrating weak magnetic detection probe according to Claim 1, characterized by the above.
3. The number of weak magnetic sensor groups is 6 to 12. The internally penetrating weak magnetic detection probe according to Claim 1, characterized by the above.
4. A distance measuring sensor is provided at the front end of the main body, and the distance measuring sensor is connected to the connection port via a connection cord. The internally penetrating weak magnetic detection probe according to Claim 1, characterized by the above.
5. Distance measuring sensors are provided on both sides of the main body, and the distance measuring sensors are connected to the connection port via a connection cord. The internally penetrating weak magnetic detection probe according to Claim 1, characterized by the above.
6. A collision prevention contact (7) is provided at the front end of the main body. The internally penetrating weak magnetic detection probe according to Claim 1, characterized by the above.
7. The outer surface of the signal line storage tube (3) is coated with a magnetic shielding material. The internally penetrating weak magnetic detection probe according to Claim 1, characterized by the above.
8. A counterweight is provided within the rear portion of the main body. The internally penetrating weak magnetic detection probe according to Claim 1, characterized by the above.
9. A method for operating an internal penetration type weak magnetic detection probe according to claims 1 to 8, comprising: Connecting to a weak magnetic flaw detector (10) and a host computer via the connection port respectively, and inputting probe parameters into the host computer; Placing the main body at the inlet of the condenser tube (8), driving the roller (5) to rotate by the motor, and advancing the whole main body; During detection, sequentially performing scanning by two weak magnetic sensors (4) of each weak magnetic sensor group, and displaying in real time two magnetic induction intensity-time curves obtained by detection by each weak magnetic sensor group on the host computer, and determining the presence or absence of a defect and the type of the defect. The method is characterized by the above steps.
10. The method for operating an internal penetration type weak magnetic detection probe according to claim 9, wherein the magnetic induction intensity-time curve is subjected to differential processing to obtain a corresponding differential curve, a threshold line is set, and the sudden change characteristics of the curve exceeding the threshold line range are intuitively displayed.
Citation Information
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