A Method and System for Identifying Post-Disaster Cracks in Arch Dams Based on Curvature Anomaly Measurement

Abstract

This invention discloses a method and system for identifying post-disaster cracks in arch dams based on curvature anomaly measurement. The method includes selecting multiple virtual arches and cantilever arms within the arch dam body and performing virtual structural reparameterization of the arch dam based on deformation monitoring facilities; extracting horizontal displacement monitoring values ​​at various measuring points of the arch dam before and after the natural disaster; calculating the bidirectional curvature of the horizontal displacement monitoring values ​​for each measuring point controlled by the virtual arches and cantilever arms; calculating the curvature anomaly measurement for each measuring point based on the bidirectional curvature calculated before and after the disaster; calculating the anomaly index for each region based on the dam body's zoning, and calculating the probability of crack occurrence in each region, determining its statistical significance. This invention proposes a method for identifying arch dam cracks using the static displacement curvature of the dam body before and after a natural disaster, effectively overcoming the limitations of current arch dam crack identification methods.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of water conservancy and hydropower engineering safety, and particularly relates to an arch dam post-disaster crack identification method and system based on curvature abnormality measurement. BACKGROUND

[0002] Extreme climate events and frequent hydrological fluctuations in the basin, combined with the effects of earthquakes, temperature gradients, load changes, and material degradation, make arch dams, a key hydraulic structure, face higher operational risks in flood control, water supply, power generation, navigation, and irrigation function protection, and are prone to cracking.

[0003] Engineering practice generally relies on discrete displacement monitoring points to continuously monitor and analyze the operating state of the dam body; however, traditional arch dam displacement monitoring and analysis methods mainly rely on the absolute change of displacement values for judgment, and are difficult to effectively identify structural response differences caused by local stiffness degradation or fine cracks. When the dam body is affected by external loads or environmental conditions, the overall displacement change often masks the local damage characteristics, making it difficult to directly reflect cracks through conventional indicators. Therefore, point-level threshold discrimination of traditional monitoring data also lacks integrated robust aggregation and statistical significance quantification from points to regions; and existing monitoring means cannot diagnose the area where cracks occur at the first time after a natural disaster. Based on this, there is an urgent need for an arch dam crack positioning method that can fully integrate monitoring information, adapt to uneven distance scattered monitoring points, and implement robust aggregation and statistical testing on regional results. SUMMARY

[0004] The technical problem to be solved by the present application is to provide an arch dam post-disaster crack identification method based on curvature abnormality measurement, which directly uses pre-disaster and post-disaster displacement monitoring data for comparative analysis to accurately determine whether the arch dam has local cracking after encountering a natural disaster, realizes rapid identification and positioning of arch dam cracks, and improves the engineering applicability and decision reliability of abnormal identification.

[0005] To solve the above technical problems, the present application provides the following technical solutions:

[0006] Firstly, the present application provides an arch dam body damage identification method, comprising the following steps:

[0007] (1) According to the actual deformation measuring point arrangement of the arch dam engineering, a plurality of virtual arch rings and cantilevers are selected from the inside of the dam body, and the arch dam is re-parameterized virtually;

[0008] (2) Extract the horizontal displacement monitoring values of the arch dam before and after the natural disaster, and for each virtual arch ring and cantilever controlled measuring point, calculate the bidirectional curvature of the horizontal displacement monitoring values;

[0009] (3) Calculate the curvature anomaly measurement at each measuring point based on the bidirectional curvature obtained before and after the disaster.

[0010] (4) Based on the dam body zoning, calculate the anomaly index of each region and the probability of cracks appearing in each region, and determine its statistical significance.

[0011] Furthermore, the virtual structure reparameterization described in step (1) has the following characteristics:

[0012] a) Based on the layout of displacement monitoring points measured in engineering practice, the arch dam is reparameterized in two categories: horizontal and vertical, according to the spatial coordinates of each monitoring point.

[0013] b) In the horizontal dimension, monitoring points with the same elevation are grouped together and connected in spatial order along the arch axis to form several virtual arches;

[0014] c) In the vertical dimension, monitoring points on the same vertical line are grouped together and connected in spatial order from the dam foundation to the dam crest to form several virtual cantilever lines;

[0015] Furthermore, the horizontal displacement monitoring value described in step (2) has the following characteristics regarding its bidirectional curvature along the arch axis and elevation direction:

[0016] According to the Euler-Bernoulli beam equations, there is a mathematical relationship between the displacement and bending moment at any point on the beam:

[0017]

[0018] in, For structural bending stiffness, For the beam bending moment, Let be the second derivative of the structural displacement; then, define the displacement curvature. This is equivalent to the second derivative:

[0019]

[0020] For any node on the beam Define its adjacent nodes as follows: and ;at this time, and , and The spacing is expressed as follows: and ; , , The displacements of the three points are respectively expressed as: , , ; respectively , At the node Perform Taylor expansion at this point:

[0021]

[0022]

[0023] Multiply the two equations above by . and After adding them together and ignoring higher-order infinitesimals, we can simplify to obtain:

[0024]

[0025] At this point, according to the definition of curvature, the displacement curvature of any node on the beam is expressed as:

[0026]

[0027] For any virtual cantilever formed by vertical measuring points, the curvature of any displacement measuring point on the cantilever can be calculated using this formula. For any virtual arch formed by equal elevation measuring points, based on known structural mechanics methods, it can be simplified into an equivalent beam fixed to the left and right banks, and the curvature of any displacement measuring point on the arch can be calculated using this formula. At this point, the formula can be converted into a general expression for arches and beams:

[0028] , ,

[0029] In particular, when = When, it represents solving for the horizontal displacement curvature in the arch direction. At this time, according to the simplifying assumptions, and Representing the measuring points respectively and , and The spacing between the three points along the equivalent beam direction, and the horizontal displacements of the three points are respectively , , ;when = When, it represents solving for the horizontal displacement curvature in the cantilever direction. and Representing the measuring points respectively and , and The distance between the three points in the elevation direction, and the horizontal displacements of the three points are respectively , , For measuring points at the intersection of any virtual arch and cantilever Its bidirectional curvature is , ;

[0030] Preferably, given that the bending moment at the free end of the virtual cantilever is zero, and that the adjacency requirement of the curvature calculation method is not met at the boundaries of the virtual arch and the cantilever, the treatment of the boundary measuring points is specified as follows:

[0031] a) Virtual cantilever free end (dam crest) measuring point: Because it lacks an upper neighboring point in the cantilever direction, curvature is calculated only in the arch direction; its curvature anomaly metric is defined as... ;

[0032] b) Measurement points at the fixed ends of the virtual cantilever (inside the dam heel or dam foundation) and the fixed ends of the virtual arch (at the connection between the left and right banks or inside the dam abutment): Since the internal point conditions that satisfy the three-point difference are not met, the curvature and its anomaly measurement of the measurement point are not calculated; its horizontal displacement value is only used as the boundary input for the curvature estimation of adjacent internal points in the calculation.

[0033] Furthermore, the curvature anomaly measurement described in step (3) has the following characteristics:

[0034] ,

[0035]

[0036] in, , These represent the calculated displacement curvature of the measuring point in the arch or cantilever direction before and after the disaster, respectively. It is a very small positive number; This refers to the unidirectional curvature anomaly calculated using the SMAPE index. That is, the measurement points after fusion using the L1 norm. Curvature anomaly measurement;

[0037] Furthermore, the regional anomaly index described in step (4) has the following characteristics:

[0038] Based on the actual engineering conditions, the arch dam body is divided into , ... Equal discrete regions, arbitrary regions It can be represented as:

[0039] , ...

[0040] If for any region to be evaluated within, share Let there be a set of displacement measurement points, and denote the curvature anomaly measures of each measurement point within this region as:

[0041]

[0042] And sorted in descending order as follows:

[0043]

[0044] Let the upper quantile ratio parameter be... ,definition:

[0045]

[0046] At this time, the area to be evaluated The abnormality index is expressed as:

[0047]

[0048] Among them, when When the median is even, the median is taken as the th. With the The arithmetic mean of the number; for all discrete regions, the region with the highest anomaly index is marked, and it is considered that a crack has appeared there:

[0049] .

[0050] Furthermore, the probability of cracks appearing in the area described in step (4) and its statistical significance have the following characteristics:

[0051] Let the set of regional anomaly scores be . Take temperature parameters The standard deviation of the set Based on this, the Softmax function is used to map the regional anomaly index to the probability of cracks appearing:

[0052]

[0053] The probability is used to characterize the relative likelihood that each region is the most anomalous region; further, for the region with the highest anomalous index... , leaving the rest The arithmetic mean and sample standard deviation of the scores for each region are respectively and Construct a single tail Statistic:

[0054]

[0055] In calculating a single tail After obtaining the statistics, based on known probability theory methods, using a set of degrees of freedom... of The cumulative distribution function is used to obtain the corresponding one-tailed distribution. Value, used for quantification Is it significantly higher than the scores in other regions?

[0056] Preferably, the statistical significance test results Configurations can be tailored to the specific needs of the project, including:

[0057] a) General criterion (marginal significance): When the test yields... The value satisfies When the marginal significance is determined, it is considered significant.

[0058] b) Strict criterion (significance): when The value satisfies When the condition is met, it is considered significant, and the reliability of identifying cracks in the corresponding area is high only when this strict criterion is met.

[0059] c) The threshold range can be adjusted according to the engineering scenario and does not constitute a limitation on the applicability of the method.

[0060] Secondly, the present invention also proposes an electronic system comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the method steps of the present invention.

[0061] Furthermore, the present invention also proposes a computer-readable storage medium storing computer instructions for causing the computer to execute the method steps of the present invention.

[0062] Finally, the present invention provides a computer program product comprising a computer program / instruction which, when executed by a processor, implements the steps of the aforementioned method of the present invention.

[0063] The present invention adopts the above technical solution and has the following technical effects compared with the prior art:

[0064] This invention reparameterizes the spatial structure of an arch dam into a virtual arch ring and virtual cantilever system. Based on existing displacement monitoring points, it enables bidirectional curvature calculation and anomalous strength analysis of dam displacement, effectively capturing local stiffness degradation and deformation anomalies caused by cracks. At the computational level, this method employs techniques such as unequal curvature solving, robust aggregation, and significance testing, making the identification results insensitive to the distribution of monitoring points, noise, and environmental disturbances. This significantly improves the accuracy, robustness, and interpretability of crack location.

[0065] Therefore, this invention can achieve rapid and reliable determination and identification of crack areas after a disaster, and can be directly embedded into existing dam safety monitoring systems to provide quantitative support for arch dam operation safety assessment and post-disaster emergency decision-making. Attached Figure Description

[0066] Figure 1 This is a schematic diagram of the reparameterization of the virtual structure of the model in an embodiment of the present invention.

[0067] Figure 2 This is a schematic diagram of the arch dam zoning and cracking areas according to an embodiment of the present invention.

[0068] Figure 3 This is a bidirectional curvature comparison diagram of an embodiment of the present invention.

[0069] Figure 4 This is a line graph showing the curvature anomaly measurement according to an embodiment of the present invention.

[0070] Figure 5 This is a diagram showing the predicted cracked area according to an embodiment of the present invention.

[0071] Figure 6 This is a flowchart of a method for identifying post-disaster cracks in arch dams based on curvature anomaly measurement. Detailed Implementation

[0072] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only for explaining this invention and are not intended to limit this invention.

[0073] Reference Figure 1 This invention uses a three-dimensional finite element model of a hyperbolic arch dam as the research object. The project employs a forward and backward plumb monitoring system to monitor the horizontal displacement of the arch dam. Based on the steps of virtual structure reparameterization, and using the dam's monitoring system as a foundation, seven virtual cantilever arms and five virtual arch rings are separated. Furthermore, according to calculation rules, edge measuring points and internal measuring points are selected, as follows:

[0074] a) Virtual cantilever free end (dam crest) measuring point: Because it lacks an upper neighboring point in the cantilever direction, curvature is calculated only in the arch direction; its curvature anomaly metric is defined as... ;

[0075] b) Measurement points at the fixed ends of the virtual cantilever (inside the dam heel or dam foundation) and the fixed ends of the virtual arch (at the connection between the left and right banks or inside the dam shoulder): Since the internal point conditions that satisfy the three-point difference are not met, the curvature and its anomaly measurement of the measurement point are not calculated; its horizontal displacement value is only used as the boundary input for the curvature estimation of adjacent internal points in the calculation.

[0076] Finally, all vertical measuring points that need to be calculated for horizontal displacement curvature are determined. Since the vertical measuring points contained in the outermost virtual cantilever on the left and right banks do not have their curvature calculated, these two virtual cantilevers can be removed. Finally, 5 virtual cantilevers (C1, C2, C3, C4, C5) and 5 virtual arches (A1, A2, A3, A4, A5) are reparameterized.

[0077] Reference Figure 2 This is a schematic diagram of the arch dam partitioning and cracking area according to an embodiment of the present invention. The arch dam is divided into 4 discrete regions (RL, RC, RR, RT). To simulate the post-disaster dam state, a parallel crack penetrating 1 / 2 the thickness of the foundation surface of the dam body is set in the RT region (no cracks are set in the pre-disaster state of the dam). The vertical measuring points of each region are classified into partitions according to their spatial location.

[0078] Reference Figure 3 To simulate the actual displacement values ​​of each vertical measuring point under pre-disaster and post-disaster conditions, finite element static calculations were performed on models with and without cracks under the same water level load to obtain the horizontal displacement values ​​at each vertical measuring point. The bidirectional curvature of all measuring points was calculated, and the comparison of the bidirectional curvature of the corresponding measuring points of the virtual cantilever C5 and the virtual arch A5 yielded the results. Figure 3 As shown; Figure 3 The left side shows the curvature comparison results along the cantilever direction. Figure 3 The right side shows the curvature comparison results along the direction of the arch.

[0079] The specific calculation process for bidirectional curvature is as follows:

[0080] According to the Euler-Bernoulli beam equations, there is a mathematical relationship between the displacement and bending moment at any point on the beam:

[0081]

[0082] in, For structural bending stiffness, For the beam bending moment, Let be the second derivative of the structural displacement; then, define the displacement curvature. This is equivalent to the second derivative:

[0083]

[0084] For any node on the beam Define its adjacent nodes as follows: and ;at this time, and , and The spacing is expressed as follows: and ; , , The displacements of the three points are respectively expressed as: , , ; respectively , At the node Perform Taylor expansion at this point:

[0085]

[0086]

[0087] Multiply the two equations above by . and After adding them together and ignoring higher-order infinitesimals, we can simplify to obtain:

[0088]

[0089] At this point, according to the definition of curvature, the displacement curvature of any node on the beam is expressed as:

[0090]

[0091] For any virtual cantilever formed by vertical measuring points, the curvature of any displacement measuring point on the cantilever can be calculated using this formula. For any virtual arch formed by equal elevation measuring points, based on known structural mechanics methods, it can be simplified into an equivalent beam fixed to the left and right banks, and the curvature of any displacement measuring point on the arch can be calculated using this formula. At this point, the formula can be converted into a general expression for arches and beams:

[0092] , ,

[0093] In particular, when = When, it represents solving for the horizontal displacement curvature in the arch direction. At this time, according to the simplifying assumptions, and Representing the measuring points respectively and , and The spacing between the three points along the equivalent beam direction, and the horizontal displacements of the three points are respectively , , ;when = When, it represents solving for the horizontal displacement curvature in the cantilever direction. and Representing the measuring points respectively and , and The distance between the three points in the elevation direction, and the horizontal displacements of the three points are respectively , , For measuring points at the intersection of any virtual arch and cantilever Its bidirectional curvature is , .

[0094] Reference Figure 4 Based on the bidirectional curvature calculation results, the curvature anomaly measurement at all measuring points after the disaster was calculated, and a line graph of the curvature anomaly measurement at all measuring points was plotted. The curvature anomaly measurement at measuring points adjacent to the crack (C4A4, C5A4, C4A5) was significantly higher than that at measuring points far from the crack, indicating that this indicator can reflect the cracking situation. Specifically, it was calculated using the following formula:

[0095] ,

[0096]

[0097] in, , These represent the calculated displacement curvature of the measuring point in the arch or cantilever direction before and after the disaster, respectively. It is a very small positive number; This refers to the unidirectional curvature anomaly calculated using the SMAPE index. That is, the measurement points after fusion using the L1 norm. Curvature anomaly measurement.

[0098] Furthermore, in this embodiment, the specific calculation process of the regional anomaly index is as follows:

[0099] Based on the actual engineering conditions, the arch dam body is divided into , ... Equal discrete regions, arbitrary regions It can be represented as:

[0100] , ...

[0101] If for any region to be evaluated within, share Let there be a set of displacement measurement points, and denote the curvature anomaly measures of each measurement point within this region as:

[0102]

[0103] And sorted in descending order as follows:

[0104]

[0105] Let the upper quantile ratio parameter be... ,definition:

[0106]

[0107] At this time, the area to be evaluated The abnormality index is expressed as:

[0108]

[0109] Among them, when When the median is even, the median is taken as the th. With the The arithmetic mean of the number; for all discrete regions, the region with the highest anomaly index is marked, and it is considered that a crack has appeared there:

[0110] .

[0111] The calculation process for the probability of cracks appearing in a region and its statistical significance is as follows:

[0112] Let the set of regional anomaly scores be . Take temperature parameters The standard deviation of the set Based on this, the Softmax function is used to map the regional anomaly index to the probability of cracks appearing:

[0113]

[0114] The probability is used to characterize the relative likelihood that each region is the most anomalous region; further, for the region with the highest anomalous index... , leaving the rest The arithmetic mean and sample standard deviation of the scores for each region are respectively and Construct a single tail Statistic:

[0115]

[0116] and with degrees of freedom of Distribution calculation of one tail Value, used for quantification Is it significantly higher than the scores in other regions?

[0117] Reference Figure 5 The image shows the predicted cracking region of this invention. The calculated curvature measures of each measuring point are sorted by region, and the anomaly indices of the four regions RL, RC, RR, and RT are calculated.Figure 5 The bar chart corresponds to the anomaly index of the four regions, with the region containing cracks having the highest RT score (2.58); the line chart corresponds to the probability of cracks appearing in the four regions, with the region containing cracks having the highest RT probability (71.1%); the statistical significance test results of the anomaly index of the RT region are as follows. This indicates that the reliability of the crack appearing here is extremely high.

[0118] Reference Figure 6 The diagram shows a flowchart of a method for identifying post-disaster cracks in arch dams based on curvature anomaly measurement. The specific process is as follows:

[0119] S1: Based on the actual deformation measuring point layout of the arch dam project, multiple virtual arches and cantilever arms are selected from the inside of the dam body to perform virtual structural reparameterization of the arch dam.

[0120] S2: Extract the horizontal displacement monitoring values ​​of each measuring point of the arch dam before and after the sudden occurrence of natural disasters, and solve the bidirectional curvature of the horizontal displacement monitoring values ​​for each measuring point controlled by the virtual arch ring and cantilever.

[0121] S3: Calculate the curvature anomaly measurement at each measuring point based on the bidirectional curvature obtained before and after the disaster.

[0122] S4: Based on the dam body zoning, calculate the anomaly index for each region and the probability of crack occurrence in each region, and determine its statistical significance.

[0123] Example 2: This example proposes an electronic system, including: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the steps of the method described in Example 1 of the present invention.

[0124] Example 3: This example proposes a computer-readable storage medium storing computer instructions, which are used to cause the computer to perform the steps of the method described in Example 1 of the present invention.

[0125] Example 4: This example provides a computer program product, including a computer program / instructions, characterized in that the computer program / instructions, when executed by a processor, implement the steps of the method described in Example 1 of this invention.

[0126] It should be noted that the processing flows of Embodiments 2 to 4 correspond to the specific steps of the method provided in the embodiments of the present invention, and have the corresponding functional modules and beneficial effects of the method. Technical details not described in detail in this embodiment can be found in the method provided in the embodiments of the present invention.

[0127] The program code used to implement the methods of this application may be written in any combination of one or more programming languages. This program code may be provided to a processor or controller of a general-purpose computer, special-purpose computer, or other programmable data processing device, such that when executed by the processor or controller, the functions / operations specified in the flowcharts and / or block diagrams are implemented. The program code may be executed entirely on a machine, partially on a machine, as a standalone software package partially on a machine and partially on a remote machine, or entirely on a remote machine or server.

[0128] In the context of this application, a machine-readable medium can be a tangible medium that may contain or store a program for use by or in conjunction with an instruction execution system, apparatus, or device. A machine-readable medium can be a machine-readable signal medium or a machine-readable storage medium. Machine-readable media can be, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. More specific examples of machine-readable storage media include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0129] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0130] The above embodiments are merely illustrative of the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solutions based on the technical concept proposed in this invention shall fall within the scope of protection of this invention.

Claims

1. A method for identifying post-disaster cracks of an arch dam based on a curvature anomaly metric, characterized in that, Comprising the following steps: According to the actual deformation measuring point arrangement of the arch dam project, a plurality of virtual arch rings and cantilevers are selected from the inside of the dam body to re-parameterize the virtual structure of the arch dam; Extract the horizontal displacement monitoring values of the arch dam before and after the natural disaster, and solve the bidirectional curvature of the horizontal displacement monitoring values of each virtual arch ring and cantilever along the arch axis and the elevation direction; Based on the bidirectional curvature calculated before and after the disaster, the curvature anomaly measure of each measuring point is calculated; Based on the dam body partition, the anomaly index of each region is calculated, and the crack occurrence probability of each region is calculated to judge its statistical significance; Wherein, the bidirectional curvature along the arch axis and the elevation direction is calculated by the following formula: According to the Euler-Bernoulli beam equation, there is a mathematical relationship between the displacement of any point on the beam and the bending moment: ， wherein, is the structural bending stiffness, is the beam bending moment, is the second derivative of the structural displacement; at this point, the displacement curvature is defined as the second derivative of the structural displacement: ， For any node on the beam Define its adjacent nodes as follows: and ; and , and The spacing is expressed as follows: and ; , , The displacements of the three points are respectively expressed as: , , ; respectively , At the node Perform Taylor expansion at this point: ， ， Multiplying the above two equations by and and adding them, neglecting the higher order infinitesimals, we obtain ， At this time, according to the definition of curvature, the displacement curvature of any node on the beam is: ， For any virtual cantilever, the curvature of any displacement measuring point on the cantilever is calculated by the formula; For any virtual arch ring formed by isopotential measuring points, according to the known structural mechanics method, it is simplified as an equal beam fixed on the left and right banks, and the curvature of any displacement measuring point on the arch ring is calculated by the formula; The formula is converted into a general expression for arches and beams: , , ， When = 0, the curvature of the horizontal displacement of the arch direction is solved, ;​​​​​​​​​ When = , the curvature of the horizontal displacement of the cantilever in the direction of suspension is solved, and respectively represent the distance in the elevation direction between the measuring points and , and , and the horizontal displacement of the three points is , , ; The measuring point is located at the intersection of any virtual arch ring and cantilever The bidirectional curvature is , .

2. The method of claim 1, wherein: The virtual structure re-parameterization is as follows: a) Based on the displacement monitoring point layout of the project, the arch dam is re-parameterized in horizontal and vertical dimensions according to the spatial coordinates of each monitoring point; b) In the horizontal dimension, the monitoring points with the same elevation are connected to form several virtual arch rings in the spatial order along the arch axis; c) In the vertical dimension, the monitoring points of the same vertical line are connected to form several virtual cantilevers in the spatial order from the dam foundation to the dam top.

3. The method of claim 1, wherein, The curvature anomaly measure is calculated by the following formula: ， ， ， wherein, , respectively represent the calculated displacement curvature of the measuring point before and after the disaster, is a very small positive number; is the one-way curvature anomaly calculated by the SMAPE index, is the measuring point after fusion by the L1 norm curvature anomaly measure.

4. The method of claim 1, wherein, The anomaly index of each region is calculated by the following formula: According to the engineering actual situation, the arch dam body is divided into , … discrete regions, and any region is represented as: ， …… ， If for any region to be evaluated there are in total displacement measurement points, let the curvature anomaly measure of each measurement point in the region be denoted as a set: ， And arranged in descending order as: ， Let the upper quantile proportion parameter be defined as: ， At this time, the area to be evaluated The abnormality index is expressed as: ， wherein, when the median is taken as the arithmetic mean of the number; for all discrete regions, the region with the highest anomaly index is marked as where a crack occurs: ， wherein represents the highest abnormality index region.

5. The method of claim 1, wherein, The crack occurrence probability of each region is calculated to judge its statistical significance, which is calculated by the following method: Let the set of regional anomaly scores be , take the temperature parameter to be the standard deviation of this set , and map the regional anomaly index to the probability of a crack being present using the Softmax function: ， the probability for characterizing the relative likelihood of each region being the most abnormal region; For the region with the highest anomaly index , let the arithmetic mean of the remaining region scores be and the sample standard deviation be . Construct a one-tailed statistic: ， After calculating the one-tailed statistic, the corresponding one-tailed value is obtained from the cumulative distribution function of the distribution with degrees of freedom ν = n - 1 using known methods of probability theory, for quantifying whether the score is significantly higher than the rest of the region scores.

6. The method of claim 1, wherein, The curvature calculation method of the boundary measuring point is as follows: a) Virtual cantilever free end measurement point: Only for arches, the curvature anomaly measure is defined as ; b) Virtual cantilever fixed end and virtual arch ring outer fixed end measuring point: the curvature and its anomaly measure of the measuring point are not calculated, and the horizontal displacement value is only used as the boundary input of adjacent inner point curvature estimation to participate in the calculation.

7. A computer apparatus / device / system comprising a memory, a processor, and a computer program stored on the memory, wherein the computer program comprises instructions that when executed by the processor cause the processor to perform the method of any one of claims 1-6. The processor executes the computer program to realize the steps of the method of any one of claims 1-6.

8. A computer readable storage medium having stored thereon computer programs / instructions, characterized in that, The computer program / instructions are executed by the processor to realize the steps of the method of any one of claims 1-6.

9. A computer program product comprising computer programs / instructions, characterized in that, The computer program / instructions are executed by the processor to realize the steps of the method of any one of claims 1-6. The computer program / instructions are executed by the processor to realize the steps of the method of any one of claims 1-6.

Images