A multi-point joint monitoring method for dam structural damage

Abstract

This invention discloses a multi-point joint monitoring method for dam structural damage, comprising: firstly, constructing a prediction model for each monitoring point and obtaining the residual value between the measured value and the predicted value; then, fitting the marginal distribution of the residual sequence and determining the Vine Copula model for calculating the multidimensional joint probability distribution; then, substituting the marginal distribution corresponding to the new monitoring data residuals into this model to obtain the joint cumulative distribution function value at each time step; and judging whether there is damage in the structure by comparing it with an anomaly threshold. This invention analyzes the correlation between the residual sequences of multiple monitoring points, uses the Vine Copula model to fit the joint probability distribution of the residual sequences, and compares the obtained cumulative distribution function value with a threshold to monitor possible damage in the dam structure, thereby improving the sensitivity of static monitoring for identifying local structural damage.

Description

Technical Field

[0001] This invention relates to the field of dam structure damage monitoring technology, and in particular to a multi-point joint monitoring method for dam structure damage. Background Technology

[0002] Reservoirs and dams serve multiple functions, including flood control, power generation, irrigation, and water supply. They are vital infrastructure for the national economy. Under the influence of environmental changes, loads, and natural disasters, operating dam projects may experience localized or overall structural damage and a deterioration in their load-bearing capacity. This will continuously reduce the safety, serviceability, and durability of the structure. For dam structures that are often affected by slow and continuous deterioration mechanisms that are not easily detected, monitoring their safety status and identifying anomalies and damage in the structure as early as possible is of great significance for ensuring the long-term stable and safe operation of dams.

[0003] Currently, most reservoir dams use static structural health monitoring to detect structural damage or degradation. Since the project is affected by numerous environmental changes and loads during operation, data-based predictive models can be constructed to understand the response behavior of individual sensor monitoring data to different factors. These models include statistical models using multiple linear regression or stepwise regression, as well as machine learning-based models such as artificial neural networks, extreme learning machines, and support vector machines. Based on this, traditional static monitoring targets a single measuring point and uses the confidence interval method to determine monitoring indicators. The predicted interval for future measurements is defined as the warning limit. Based on this, new data from each sensor is evaluated individually to determine whether to issue an alarm.

[0004] However, although the single-point monitoring method can obtain the abnormal status of the monitoring value of any sensor response variable in the dam structure, and can make a reasonable judgment on whether there is damage to the overall structure after analysis, it cannot reflect the interrelationship between different monitoring points in the dam as a whole, nor can it truly reflect the overall health status of the structure. Especially when the scope and degree of structural damage are small, it usually does not cause significant changes in the sensor monitoring data. In this case, the single-point monitoring method may not be able to effectively monitor the structural anomalies. Therefore, this invention proposes a multi-point joint monitoring method for dam structural damage to solve the problems existing in the prior art. Summary of the Invention

[0005] To address the aforementioned problems, the present invention aims to propose a multi-point joint monitoring method for dam structural damage, which solves the problem that existing static structural health monitoring methods for reservoir dams cannot reflect the interrelationships between different monitoring points in the overall dam and cannot accurately reflect the overall health status of the structure, thus failing to effectively monitor structural anomalies in reservoir dams.

[0006] To achieve the objectives of this invention, the present invention is implemented through the following technical solution: a multi-point joint monitoring method for dam structural damage, comprising the following steps:

[0007] Step 1: First, set up monitoring points at different locations on the dam to monitor its appearance deformation. Then, based on the monitoring data obtained from the monitoring points set up on the dam, fit the corresponding prediction model for each monitoring point. Then, calculate the residual between the measured value of each monitoring point and the predicted value of each prediction model to obtain each residual sequence.

[0008] Step 2: First, Kendall's rank correlation coefficient is selected as a measure of the dependence of residual sequences to analyze the correlation and consistency between residual sequences. Then, the maximum tree generation algorithm is used to select the Vine structure with the largest sum of absolute values ​​of Kendall's rank correlation coefficients. The kernel density estimation method is used to fit the probability density function of the residual sequence distribution to obtain the marginal distribution of each residual sequence.

[0009] Step 3: First, select a binary Copula function for each pair of edge distributions in the Vine structure in Step 2 according to the Akaike Information Criterion. Then, use the maximum likelihood estimation method to estimate the parameters of the selected binary Copula function for each edge in the Vine. Finally, construct the Vine Copula model based on the selected Copula function and the selected binary Copula function.

[0010] Step 4: First, calculate the difference between the currently acquired monitoring data and the predicted value of the prediction model and obtain the current residual sequence. Substitute the current residual sequence into the probability density function in Step 2 to obtain the marginal distribution. After judgment, substitute the marginal distribution into the Vine Copula model in Step 3 to obtain the joint cumulative distribution function value corresponding to each time step.

[0011] Step 5: First, determine the anomaly threshold, then compare the joint cumulative distribution function value obtained in Step 4 with the anomaly threshold, and determine whether there is damage in the dam structure based on the comparison results.

[0012] A further improvement lies in: In step two, when analyzing the correlation and consistency among the residual sequences, let X{x1, x2, ..., x...} n} and Y{y1, y2, L, y n Let} be the residual sequence of two measurement points, (x i y i ) and (x j y j ) are the residual data pairs of points on both sides at times i and j, respectively. If x i <x j And y i <y j, or x i >x j And y i >y j Then it is called (x) i y i ) and (x j y j If x is consistent, i <x j And y i >y j , or x i >x j And y i <y j Then it is called (x) i y i ) and (x j y j (Not consistent, when points on both sides of X and Y share a common point) For each distinct pair of residual data, the Kendall rank correlation coefficient is defined as:

[0013]

[0014] In the formula, c represents a consistent pair of residual functions, and d represents a non-consistent pair of residual data.

[0015] A further improvement lies in the following: In step two, the formula for the maximum tree generation algorithm is:

[0016]

[0017] In the formula, T i Let t be the set of all possible tree structures in the i-th tree. i Let e ​​represent the structure of a specific i-th tree, where e is the tree t. i For any edge in δ i.j Let represent the Kendall rank correlation coefficient of a pair of residual sequences corresponding to edge e.

[0018] A further improvement lies in the following: In step two, the expression for the probability density function is:

[0019]

[0020] In the formula, To fit the probability density function, x i The data consists of residual sequences, K is the Gaussian kernel function, and h is the bandwidth, which is selected based on the optimization of the integral mean square error.

[0021] A further improvement lies in the following: In step three, the calculation formula for the Akaike Information Criterion is as follows:

[0022] AIC = 2K - 2ln(L)

[0023] In the formula, K is the number of parameters. For the five Copula functions, Frank Copula, Clayton Copula, Gumbel Copula, Gaussian Copula, and t-Copula, K is 1 for the t-Copula function, except for the t-Copula function which has K of 2. L is the maximum value of the likelihood function.

[0024] A further improvement is made in step three, where the formula for calculating the likelihood function is as follows:

[0025]

[0026] In the formula, n represents the sample size, and θ = (θ1, θ2, ... θ) k ) represents the parameter vector of the Vine Copula model, c(·) is the density function of the Copula function C(·), and F(·) is the marginal distribution.

[0027] A further improvement is made in step four, where the formula for determining the edge cumulative distribution function value is:

[0028]

[0029] In the formula, CDF is the marginal cumulative distribution function value.

[0030] A further improvement is made in step five, where, when comparing the joint cumulative distribution function value with the anomaly threshold, if the joint cumulative distribution function value is lower than the anomaly threshold, the dam's structural behavior is abnormal; if the joint cumulative distribution function value is higher than the anomaly threshold, the dam's structural behavior is normal.

[0031] The beneficial effects of this invention are as follows: After constructing the prediction model for each measuring point, this invention does not directly use the confidence interval method to determine the monitoring interval of a single measuring point. Instead, it considers the correlation between the residual sequences of multiple measuring points, fits their joint probability distribution based on the Vine Copula model, and uses the cumulative distribution function (CDF) value as an indicator for judging anomalies. It compares the CDF value of the calculated joint probability distribution to monitor possible damage in the dam structure. This monitoring method considers the correlation of the spatial location of the measuring points in the dam and the overall safety status of the structure, proposes a unified anomaly judgment index for multiple measuring points, and improves the sensitivity of static monitoring to local damage monitoring of the structure. Attached Figure Description

[0032] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0033] Figure 1 This is a schematic diagram of the monitoring method flow according to Embodiment 1 of the present invention;

[0034] Figure 2 This is a schematic diagram of the distribution of cracks on the dam crest and the arrangement of measuring points according to Embodiment 2 of the present invention;

[0035] Figure 3 This is a schematic diagram of the dam axis crack in Embodiment 2 of the present invention;

[0036] Figure 4 This is a schematic diagram of the pit inspection situation in Embodiment 2 of the present invention;

[0037] Figure 5 This is a schematic diagram comparing the measured and predicted values ​​of the dam crest displacement along the river in Embodiment 2 of the present invention;

[0038] Figure 6 This is a D-Vine structure diagram of the residual sequence of the monitoring points for the displacement along the river crest of the dam in Embodiment 2 of the present invention;

[0039] Figure 7 This is a schematic diagram of the frequency distribution and fitting probability density function of the measurement point residual sequence in Embodiment 2 of the present invention;

[0040] Figure 8 This is a schematic diagram of the damage monitoring results of the multi-point joint structural health monitoring method according to Embodiment 2 of the present invention;

[0041] Figure 9 This is a schematic diagram of the river-direction displacement monitoring section of the dam crest at measuring point TP16 in Embodiment 2 of the present invention. Detailed Implementation

[0042] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0043] Example 1

[0044] See Figure 1 This embodiment provides a multi-point joint monitoring method for dam structural damage, including the following steps:

[0045] Step 1: First, set up monitoring points at different locations on the dam to monitor its appearance deformation. Then, based on the monitoring data obtained from the monitoring points set up on the dam, fit the corresponding prediction model for each monitoring point. Then, calculate the residual between the measured value of each monitoring point and the predicted value of each prediction model to obtain each residual sequence.

[0046] Step 2: Since the residual sequence is a time series variable and has a certain order, this embodiment uses the Kendall rank correlation coefficient as a measure of the dependence of the residual sequences to analyze the correlation and consistency among the residual sequences. Let X{x1, x2, ..., x... n} and Y{y1, y2, L, y n Let} be the residual sequence of two measurement points, (x i y i ) and (x j y j ) are the residual data pairs of points on both sides at times i and j, respectively. If x i <x j And y i <y j , or x i >x j And y i >y j Then it is called (x) i y i ) and (x j y j If x is consistent, i <x j And y i >y j , or x i >x j And y i <y j Then it is called (x) i y i ) and (x j y j (Not consistent, when points on both sides of X and Y share a common point) Let c represent a consistent pair of residual data and d represent a non-consistent pair of residual data. Then the Kendall rank correlation coefficient is defined as:

[0047]

[0048] Then, using the maximum tree generation algorithm, the Vine structure with the largest sum of the absolute values ​​of Kendall's rank correlation coefficients is selected, expressed by the formula:

[0049]

[0050] In the formula, T i Let t be the set of all possible tree structures in the i-th tree. i Let e ​​represent the structure of a specific i-th tree, where e is the tree t. i For any edge in δ i.j Let e ​​represent the Kendall rank correlation coefficient of a pair of residual sequences corresponding to edge e;

[0051] The probability density function of the residual sequence distribution is fitted using the kernel density estimation method. The expression is:

[0052]

[0053] In the formula, To fit the probability density function, x i Given residual sequence data, K is the Gaussian kernel function, and h is the bandwidth, which is selected based on the optimization of the integral mean square error, to obtain the marginal distribution of each residual sequence used to construct the Vine Copula model;

[0054] Step 3: First, select a binary Copula function C(·) for each pair of marginal distributions in the Vine structure from Step 2, based on the Akaike Information Criterion (AIC). Then, select the Copula function type that minimizes the AIC value. The formula is:

[0055] AIC = 2K - 2ln(L)

[0056] In the formula, K is the number of parameters. For the five Copula functions, Frank Copula, Clayton Copula, Gumbel Copula, Gaussian Copula, and t-Copula, K is 1 for the t-Copula function, except for the t-Copula function which has K of 2. L is the maximum value of the likelihood function.

[0057] Next, the parameters of the selected bivariate Copula function for each edge in Vine are estimated using the maximum likelihood estimation method (MLE). The formula for calculating the likelihood function is as follows:

[0058]

[0059] In the formula, n represents the sample size, and θ = (θ1, θ2, ... θ) k Let ) represent the parameter vector of the Vine Copula model, c(·) be the density function of the Copula function C(·), and F(·) be the marginal distribution. Let θ be the maximum likelihood estimate, then we have According to the following system of likelihood equations:

[0060]

[0061] The model parameters can then be solved.

[0062] Then, a VineCopula model is constructed based on the selected Copula function and the chosen binary Copula function;

[0063] Step 4: First, calculate the difference between the currently acquired monitoring data and the predicted value of the prediction model to obtain the current residual sequence. Substitute the current residual sequence into the probability density function in Step 2 to obtain the marginal distribution. After judgment, substitute the marginal distribution into the VineCopula model in Step 3 to obtain the joint cumulative distribution function (CDF) value corresponding to each time step. The formula for judging the marginal cumulative distribution function value is:

[0064]

[0065] In the formula, CDF is the marginal cumulative distribution function value;

[0066] Step 5: First, determine the anomaly threshold as α / 2 (α is the significance level, taken as 1%). Then, compare the joint cumulative distribution function value obtained in Step 4 with the anomaly threshold. If the joint cumulative distribution function value is lower than the anomaly threshold, the dam structure is abnormal. If the joint cumulative distribution function value is higher than the anomaly threshold, the dam structure is normal, thus realizing the monitoring of whether the dam structure is damaged.

[0067] Example 2

[0068] See Figure 2 , Figure 3 , Figure 4 , Figure 5 , Figure 6 , Figure 7 , Figure 8 , Figure 9 This embodiment uses a gravel-soil core rockfill dam in Southwest China as the monitoring object. The dam has a maximum height of 186m, a crest elevation of 856.00m, a crest width of 14m, a normal reservoir water level of 850.00m, a flood season operating limit water level of 841.00m, and a dead water level of 790.00m. On November 2, 2020, during a routine inspection of the rockfill dam, an open crack approximately 2mm wide was found near the dam crest axis. Figure 2 and Figure 3 As shown. To determine the depth of the crack, an excavation inspection was conducted on-site from November 3rd to 5th, 2020. Figure 4As shown in the diagram. Pit inspection revealed that the maximum depth of the crack did not exceed 1.5m and did not extend to the core wall. To prevent rainwater from seeping into the crack and affecting the seepage stability of the dam body, and to prevent potential structural integrity damage due to the continued development of the crack, on November 9, 2020, the management unit used fine sand, asphalt, and other materials to seal the longitudinal cracks along the dam crest axis. From the time of repair until December 31, 2020, no new opening cracks were found.

[0069] The project employed an intelligent measurement robot to monitor the external deformation of the rockfill dam. To verify the effectiveness of the proposed method for monitoring structural damage, five monitoring points (TP12, TP13, TP14, TP15, and TP16) located near the cracks on the dam crest were selected as the analysis objects. Figure 2 As shown, the downstream displacement monitoring data from August 10, 2018 to December 31, 2020 are analyzed. The monitoring data are divided into two periods according to time. The fitting period is from August 10, 2018 to August 10, 2020, and the verification period is from August 11, 2020 to December 31, 2020. The corresponding monitoring data are referred to as Dataset 1 and Dataset 2, respectively.

[0070] The structural health monitoring of this earth-rock dam using the method of the present invention is carried out in the following specific steps:

[0071] S1: Based on dataset 1, a prediction model for the displacement of the dam crest along the river direction at each measuring point is obtained. The displacement of the earth-rock dam mainly consists of water pressure, temperature, and time-dependent components. Among them, the time-dependent component is related to the rheological deformation of the rockfill. To reflect the irreversible deformation over time, a time-dependent separation method is used to construct the prediction model. Therefore, the expression of the prediction model is as follows:

[0072]

[0073] In the formula, Here is the expression for the water pressure component in the downstream displacement, where H is the reservoir water level. The expression for the temperature component in the downstream displacement is θ = (t - t0) / 100, where t0 is the monitoring start date and t is the monitoring date. For the expression of the time-dependent component, a i b1, b2, c1, c2, c3, and c4 are model coefficients, and d is a constant term. Based on the monitoring data in dataset 1, the prediction model coefficients are shown in Table 1 below. A comparison of the monitoring data of the dam's displacement along the river and the fitted values ​​of the prediction model is shown below. Figure 5 As shown;

[0074] Table 1. Prediction Model Coefficients

[0075] measuring point <![CDATA[a1]]> <![CDATA[a2]]> <![CDATA[b1]]> <![CDATA[b2]]> <![CDATA[c1]]> <![CDATA[c2]]> <![CDATA[c3]]> <![CDATA[c4]]> d TP12 -16.83 0.01 -3.04 -6.63 -11.58 -2.36E-28 17.96 -49.19 6557.58 TP13 -19.97 0.01 -5.99 -8.27 7132.65 -2.52E+01 -2.29 -6976.4 7794.23 TP14 -21.61 0.01 -5.82 -8.40 65.63 -2.38E+09 -6.15 85.90 8463.77 TP15 -21.65 0.01 -4.87 -7.99 68.66 -3.79E+07 -5.04 33.53 8519.68 TP16 -18.31 0.01 -3.02 -6.16 27.98 -1.42E+09 -6.03 124.82 7253.51

[0076] S2: The difference between the monitoring data along the river crest of the dam and the fitted values ​​of the prediction model is taken as the residual sequence corresponding to each measuring point. The Kendall rank correlation coefficient, a measure of the dependence between the residual sequences corresponding to each measuring point, is calculated as shown in Table 2. The rank correlation coefficients in bold italics are relatively large. As can be seen from Table 2, the Kendall rank correlation coefficients between the residual sequences of each measuring point are all above 0.55, indicating a certain degree of correlation. The rank correlation coefficient between each pair of adjacent measuring point residual sequences is the largest, that is, the residual sequences of measuring points TP12 and TP13, TP13 and TP14, TP14 and TP15, and TP15 and TP16 have the strongest correlation, showing an overall "serial" characteristic. Therefore, the following method is adopted: Figure 6 The D-Vine structure shown;

[0077] Table 2 Prediction Model Coefficients

[0078] TP12 TP13 TP14 TP15 TP16 TP12 1.0000 0.7230 0.7122 0.6566 0.5578 TP13 0.7230 1.0000 0.8182 0.7976 0.6588 TP14 0.7122 0.8182 1.0000 0.8472 0.6987 TP15 0.6566 0.7976 0.8472 1.0000 0.7230 TP16 0.5578 0.6588 0.6987 0.7230 1.0000

[0079] S3: The kernel density estimation method was used to fit the residual sequence distribution as the marginal distribution required to construct the Vine Copula model. The kernel density estimation bandwidths of the residual sequences corresponding to measurement points TP12 to TP16 were 0.5182, 0.6290, 0.7354, 0.7677, and 0.7243, respectively. The fitted probability density curves and the frequency distribution of the residual sequences are shown below. Figure 7 As shown;

[0080] S4: The optimal Copula connection function type for each connection edge in D-Vine is selected using the Akaike information criterion. The parameters of each binary Copula function in the Vine Copula model are determined by the maximum likelihood estimation method, as shown in Table 3.

[0081] Table 3. Copula function type selection and parameter list in the Vine-Copula model.

[0082]

[0083] S5: Based on dataset 1 and the prediction model constructed in step S1, a new residual sequence is obtained. A new marginal distribution is obtained according to the kernel density function in step S3, and then substituted into the constructed Vine-Copula model to calculate the corresponding joint CDF value. Finally, the multi-point joint structural health monitoring method yields the structural damage monitoring results as follows: Figure 8 As shown, the horizontal dashed line represents the anomaly threshold of CDF being 0.005 (α = 1%), the left vertical dashed line represents the time point when the crack was discovered, and the right vertical dashed line represents the time point when sealing treatment was carried out. Figure 8It can be seen that the joint monitoring method issued 19 alarms in three periods: September 12 to September 21, October 9 to October 28, and November 3 to November 7, 2020.

[0084] S6: To compare the effectiveness and accuracy of the proposed method and the method based on a single-point monitoring model in anomaly monitoring, the residual sequences of each measuring point obtained in step S2 were used to determine the left and right quantiles of the residuals at a significance level of 1%, as shown in Table 4. Then, based on the prediction model constructed in step S1, the operational warning value for each measuring point was determined. Monitoring results show that from August 11 to December 31, 2020, when using the traditional single-point monitoring method, only the monitoring data of TP16 out of the five measuring points exceeded the monitoring interval, and the number of alarms within three months was extremely low, only five. Figure 9 As shown.

[0085] Table 4. Left and right quantiles of the residual sequences at monitoring points (α = 99%)

[0086] TP12 TP13 TP14 TP15 TP16 Right quantile 4.414 5.198 7.035 5.546 4.496 Left quantile -4.089 -5.539 -5.882 -5.720 -4.372

[0087] This example utilizes monitoring data from an earth-rock dam from August 10, 2018 to August 10, 2020 to construct a predictive model for the river-direction displacement of the dam crest at each monitoring point, fit the probability distribution of the corresponding residual sequences at each monitoring point, and construct a vine copula model for calculating the multidimensional joint probability distribution. Monitoring data from August 11, 2020 to December 31, 2020 is defined as "newly acquired river-direction displacement monitoring data" for structural damage monitoring. Simultaneously, traditional single-point monitoring methods are used to monitor for anomalies in the monitoring data, thereby verifying the effectiveness and accuracy of the proposed method.

[0088] according to Figure 8 and Figure 9The results show that the joint monitoring method generates far more alarms than the single-point monitoring model, and the alarms are also more densely distributed over time. In dam safety management, this situation cannot be simply regarded as a data anomaly, but should be considered as an anomaly caused by structural damage. Damage monitoring results indicate that since September 12, monitoring data from the monitoring points at the dam crest have shown abnormalities, triggering alarms. Therefore, it can be inferred that the dam crest cracks may have been gradually developing before being discovered during the inspection on November 2. Furthermore, after the cracks were sealed on November 9, no new cracks appeared on the dam crest until December 31, presumably because the reservoir water level changed from rising to gradually declining during this period. Correspondingly, no cases of the joint CDF value exceeding the anomaly threshold occurred during this period. This demonstrates that, compared to the monitoring method based on the single-point monitoring model, the method proposed in this paper can effectively and accurately monitor dam structural damage.

[0089] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A multi-point joint monitoring method for dam structural damage, characterized in that, Includes the following steps: Step 1: First, set up monitoring points at different locations on the dam to monitor its appearance deformation. Then, based on the monitoring data obtained from the monitoring points set up on the dam, fit the corresponding prediction model for each monitoring point. Then, calculate the residual between the measured value of each monitoring point and the predicted value of each prediction model to obtain each residual sequence. Step 2: First, Kendall's rank correlation coefficient is selected as a measure of the dependence of residual sequences to analyze the correlation and consistency between residual sequences. Then, the maximum tree generation algorithm is used to select the Vine structure with the largest sum of absolute values ​​of Kendall's rank correlation coefficients. The kernel density estimation method is used to fit the probability density function of the residual sequence distribution to obtain the marginal distribution of each residual sequence. Step 3: First, select a binary Copula function for each pair of edge distributions in the Vine structure in Step 2 according to the Akaike Information Criterion. Then, use the maximum likelihood estimation method to estimate the parameters of the selected binary Copula function for each edge in the Vine. Finally, construct the VineCopula model based on the selected Copula function and the selected binary Copula function. Step 4: First, calculate the difference between the currently acquired monitoring data and the predicted value of the prediction model and obtain the current residual sequence. Substitute the current residual sequence into the probability density function in Step 2 to obtain the marginal distribution. After judgment, substitute the marginal distribution into the Vine Copula model in Step 3 to obtain the joint cumulative distribution function value corresponding to each time step. Step 5: First, determine the anomaly threshold, then compare the joint cumulative distribution function value obtained in Step 4 with the anomaly threshold, and determine whether there is damage in the dam structure based on the comparison results.

2. The multi-point joint monitoring method for dam structural damage according to claim 1, characterized in that: In step two, when analyzing the correlation and consistency among the residual sequences, let X{x1, x2, ..., x...} n } and Y{y1, y2, L, y n Let} be the residual sequence of two measurement points, (x i y i ) and (x j y j ) are the residual data pairs of points on both sides at times i and j, respectively. If x i <x j And y i <y j , or x i >x j And y i >y j Then it is called (x) i y i ) and (x j y j If x is consistent, i <x j And y i >y j , or x i >x j And y i <y j Then it is called (x) i y i ) and (x j y j (Not consistent, when points on both sides of X and Y share a common point) For each distinct pair of residual data, the Kendall rank correlation coefficient is defined as: In the formula, c represents a consistent pair of residual functions, and d represents a non-consistent pair of residual data.

3. The multi-point joint monitoring method for dam structural damage according to claim 1, characterized in that: In step two, the formula for the maximum tree generation algorithm is: In the formula, T i Let t be the set of all possible tree structures in the i-th tree. i Let e ​​represent the structure of a specific i-th tree, where e is the tree t. i For any edge in δ i.j Let represent the Kendall rank correlation coefficient of a pair of residual sequences corresponding to edge e.

4. The multi-point joint monitoring method for dam structural damage according to claim 1, characterized in that: In step two, the expression for the probability density function is: In the formula, To fit the probability density function, x i The data consists of residual sequences, K is the Gaussian kernel function, and h is the bandwidth, which is selected based on the optimization of the integral mean square error.

5. The multi-point joint monitoring method for dam structural damage according to claim 1, characterized in that: In step three, the formula for calculating the Akaike Information Criterion is as follows: AIC = 2K - 2ln(L) In the formula, K is the number of parameters. For the five Copula functions, FrankCopula, ClaytonCopula, GumbelCopula, GaussianCopula, and t-Copula, K is 1 for the t-Copula function, except that K is 2. L is the maximum value of the likelihood function.

6. The multi-point joint monitoring method for dam structural damage according to claim 5, characterized in that: In step three, the formula for calculating the likelihood function is as follows: In the formula, n represents the sample size, and θ = (θ1, θ2, ... θ) k ) represents the parameter vector of the Vine Copula model, c(·) is the density function of the Copula function C(·), and F(·) is the marginal distribution.

7. The multi-point joint monitoring method for dam structural damage according to claim 1, characterized in that: In step four, the formula for determining the edge cumulative distribution function value is as follows: In the formula, CDF is the marginal cumulative distribution function value.

8. The multi-point joint monitoring method for dam structural damage according to claim 1, characterized in that: In step five, when comparing the joint cumulative distribution function value with the anomaly threshold, if the joint cumulative distribution function value is lower than the anomaly threshold, the dam's structural behavior is abnormal; if the joint cumulative distribution function value is higher than the anomaly threshold, the dam's structural behavior is normal.

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