Interpolation algorithm for feature analysis of deformation field of high arch dam

Abstract

The invention relates to the technical field of high arch dam deformation field feature analysis, in particular to an interpolation algorithm for high arch dam deformation field feature analysis. According to the technical scheme, the method comprises the steps of data collection and classification, variation function initial parameter setting, variation function fitting through a local weighted least square method, variation function parameter global optimization, Kriging interpolation calculation and consistency checking and parameter adjustment, in the data collection and classification process, monitoring data of the high arch dam under different load working conditions are collected, and the monitoring data of the high arch dam under different load working conditions are obtained. The load working conditions comprise a high water level in a flood period and a low temperature period in winter, and the deformation data of different parts and different time from the total station, the level gauge, the inclinometer and the strain gauge are associated with the corresponding load working conditions and monitoring point coordinate information. Through comprehensive data association, reasonable parameter setting and optimization, accurate interpolation calculation and a reliable result adjustment mechanism, more accurate deformation field analysis of the high arch dam under different load conditions is realized, and safe operation of the dam is guaranteed.

Description

Technical Field

[0001] The present invention relates to the technical field of high arch dam deformation field characteristic analysis, and particularly to an interpolation algorithm for high arch dam deformation field characteristic analysis. Background Art

[0002] As a key structure of large-scale water conservancy and hydropower projects, high arch dams play a crucial role in the comprehensive utilization of water resources and energy development. During its long-term operation, due to the action of various complex loads, including self-weight, water pressure, temperature change, earthquake, etc., the dam body will produce varying degrees of deformation. Accurately monitoring and analyzing the deformation field of high arch dams is crucial for ensuring the safe operation of the dams.

[0003] Currently, by arranging a large number of monitoring instruments inside and on the surface of high arch dams, such as total stations, levels, inclinometers, strain gauges, etc., deformation data of different parts of the dam at different times can be obtained. These data form the basis for the analysis of the high arch dam deformation field. However, many challenges are faced in the actual analysis process.

[0004] In the analysis of high arch dam deformation field characteristics, a relatively prominent problem is the uneven spatial distribution of monitoring data. Due to factors such as monitoring costs and the complexity of the dam body structure, monitoring points cannot be arranged at every position of the dam body, which results in the deformation data we obtain being discrete in space and unable to fully describe the continuous change of the entire high arch dam deformation field.

[0005] For example, in some key parts of the dam body (such as near the crown cantilever), the monitoring points may be relatively dense, but in areas such as the dam abutment, the monitoring points are relatively sparse. This spatial discreteness of the data will have a serious impact on the accurate analysis of the overall deformation field characteristics of the dam, making it difficult in tasks such as evaluating the deformation trend of the dam body and identifying potential deformation abnormal areas.

[0006] Interpolation algorithms can effectively solve this problem. Taking Kriging interpolation as an example, based on the principle of geostatistics, it considers the spatial correlation of monitoring data and can reasonably estimate the deformation values of unknown points according to the distance between monitoring points and the variogram of the data. In this way, the discrete monitoring data can be transformed into a continuous deformation field, providing a basis for a more comprehensive and accurate analysis of high arch dam deformation field characteristics. For example, it can more accurately draw the deformation isogram of the dam body and analyze the change of deformation gradient, which helps to timely discover potential safety hazards of the dam body.

[0007] When using the Kriging interpolation algorithm to solve the problem of uneven spatial distribution of high arch dam deformation field monitoring data, how to determine the optimal parameters of the variogram so that the interpolation results in sparse monitoring point areas such as the dam shoulders can accurately reflect the local deformation trend, and at the same time be physically consistent with the deformation data in dense monitoring point areas such as the crown cantilever. Also, consider the influence of different load conditions, such as high water levels during flood periods and low temperatures during winter periods, on the variogram parameters.

[0008] In summary, this application proposes an interpolation algorithm for high arch dam deformation field feature analysis. Summary of the Invention

[0009] The purpose of the present invention is to address the problem in the background technology that the optimal parameters of the variogram cannot be determined, so that the interpolation results in sparse monitoring point areas such as the dam shoulders can accurately reflect the local deformation trend, and to propose an interpolation algorithm for high arch dam deformation field feature analysis.

[0010] The technical solution of the present invention: An interpolation algorithm for high arch dam deformation field feature analysis includes the following steps:

[0011] Step 1: Data collection and classification. Collect the monitoring data of the high arch dam under different load conditions, where the load conditions include high water levels during flood periods and low temperatures during winter periods. Associate the deformation data from different parts and different times of total stations, level gauges, inclinometers, and strain gauges with the corresponding load conditions and monitoring point coordinate information.

[0012] Step 2: Initial parameter setting of the variogram. For each load condition, set the initial parameters of the variogram, including sill (base value), range (range), and nugget (nugget value). The initial parameters are estimated using the finite element analysis method.

[0013] Step 3: Fitting the variogram using the locally weighted least squares method. For each monitoring point, according to the distance from it to other monitoring points and the corresponding deformation data difference, use the locally weighted least squares method to fit the variogram and calculate the local variogram parameters around each monitoring point under the current load condition. The formula is as follows:

[0014]

[0015] where, z(x i ) is the deformation data of the monitoring point x i , c is a constant term, b j are the coefficients to be determined, f j (x i ) is a function related to the monitoring point coordinates, w i is the weighting coefficient, n is the number of monitoring points participating in the calculation, and k is the function f jThe number;

[0016] Step 4: Globally optimize the variogram parameters. Through the global optimization algorithm, combined with the local variogram parameters of all monitoring points under the current load condition, optimize and adjust the sill, range, and nugget of the overall variogram to minimize the sum of squared errors in the sparse area of the abutment monitoring points and the dense area of the crown beam monitoring points. The optimization objective function is as follows:

[0017]

[0018] where L is the number of monitoring areas, n l is the number of monitoring points in the l-th monitoring area, and z l (x i ) is the actual deformation data of the monitoring point x i in the l-th monitoring area, is the estimated deformation data calculated using the current variogram parameters;

[0019] Step 5: Kriging interpolation calculation. According to the optimized variogram parameters, use the Kriging interpolation formula to calculate the deformation values of unknown points in the deformation field of the high arch dam. The formula is as follows:

[0020]

[0021] where, is the estimated deformation value of the unknown point x0, and λ i is the weight coefficient calculated through the variogram and the monitoring point data. Z(x i ) is the deformation value of the known monitoring point x i , and n is the number of monitoring points participating in the interpolation calculation. The weight coefficient λ i is solved through the following system of equations:

[0022]

[0023] where C(x i , x j ) is the covariance function between the monitoring points x i and x j , which is derived from the variogram, and μ is the Lagrange multiplier;

[0024] Step 6: Consistency check and parameter adjustment. Compare the interpolation results with the actual monitoring data to check the deformation trend and numerical consistency in different areas of the abutment and crown beam. If the error exceeds the preset threshold, adjust the variogram parameters according to the error distribution, and re-execute Steps 3 to 5 until the consistency requirement is met.

[0025] Optionally, in the data collection and classification, the coefficient of thermal expansion data of the dam body material is also collected and associated with the deformation data.

[0026] Optionally, the finite element analysis method is as follows:

[0027] Establish a three-dimensional numerical model of the high arch dam, simulate the deformation of the dam body under different load conditions, calculate the spatial autocorrelation function of the deformation data according to the finite element simulation results, obtain the theoretical variogram curve by fitting the autocorrelation function, and extract the values of sill, range, and nugget from the curve as the initial parameters.

[0028] Optionally, in the local weighted least squares method for fitting the variogram, the calculation method of the weighting coefficient is

[0029]

[0030] where d i is the distance between the current monitoring point and the monitoring point x i participating in the calculation, and the p value is taken as 2 under the high water level condition during the flood period and 3 under the low temperature condition in winter.

[0031] Optionally, in the local weighted least squares method for fitting the variogram, the function f j (x i ) includes the first-order and second-order terms of the Cartesian coordinates of the monitoring point and the polar coordinate functions ρsinθ and ρcosθ, where ρ is the polar radius and θ is the polar angle.

[0032] Optionally, in the global optimization of variogram parameters, the global optimization algorithm uses the simulated annealing algorithm, the initial temperature is set to 10 times the sum of squared errors, the temperature decrease rate is 10% reduction per 100 iterations, and the termination condition is that the change in the sum of squared errors is less than 0.01 for 20 consecutive iterations and reaches the maximum number of iterations of 1000 times.

[0033] Optionally, in the Kriging interpolation calculation, the covariance function formula between the monitoring points x i and x j is as follows:

[0034]

[0035] where C0 is the nugget value, C max is the sill value, h is the distance between two points, a is the range, and C0, C max and a are adjusted accordingly according to different load conditions during the calculation.

[0036] Optionally, in the consistency check and parameter adjustment, the error of the deformation value of the preset threshold in the abutment area does not exceed ±5 mm, and the error of the deformation value in the crown beam area does not exceed ±3 mm. The consistency of the deformation trend is calculated by the slope deviation, and the slope deviation threshold is set to 0.1.

[0037] Optionally, in the consistency check and parameter adjustment, if the error in the abutment area exceeds the preset threshold and is mainly concentrated in the part near the dam edge, increase the number of monitoring points in this area and re - execute steps 1 to 5; if the error in the crown beam area exceeds the preset threshold and shows a local concentration trend, increase the monitoring frequency in this local area and re - execute steps 1 to 5.

[0038] Optionally, in the consistency check and parameter adjustment, when adjusting the variogram parameters according to the error distribution, if the deformation value error in the abutment area exceeds ±5 mm, increase the range parameter by 5%; if the deformation value error in the crown beam area exceeds ±3 mm, adjust the sill parameter by 3% and adjust the nugget parameter by 2%.

[0039] Compared with the prior art, the present application includes at least one of the following beneficial technical effects:

[0040] By integrating data from multiple monitoring instruments and correlating with different load conditions, monitoring point coordinate information, and the thermal expansion coefficient of the dam material, all key factors affecting the deformation of the high - arch dam are comprehensively covered, making the analysis of the dam deformation more accurate and avoiding errors caused by one - sided data. Special treatment for typical load conditions can better capture the unique deformation mechanisms of the dam under different environments, thus accurately reflecting the actual deformation of the dam under complex conditions and helping to deeply understand the deformation law of the dam under various conditions;

[0041] Using finite - element analysis to establish a three - dimensional numerical model to estimate the initial parameters of the variogram. Based on physical mechanics principles and precise model construction, a solid theoretical basis is provided for setting the variogram parameters, ensuring that subsequent interpolation calculations can better fit the spatial correlation of the actual deformation of the dam. The simulated annealing algorithm is used to globally optimize the variogram parameters. By reasonably setting the initial temperature, temperature - decreasing rate, and termination conditions, it effectively avoids falling into local optimal solutions and can search for the optimal parameter combination in the complex parameter space, significantly improving the adaptability of the interpolation algorithm to the deformation of different areas of the dam, especially the sparse area of the abutment and the dense area of the crown beam.

[0042] By using the locally weighted least squares method to determine the weighting coefficients based on the distances between monitoring points and load conditions, and combining various functions related to the coordinates of monitoring points, the influence of local data can be highlighted, the local changes of data under different working conditions can be adapted, and the parameters of the local variogram can be more accurately fitted, so as to better capture the local deformation law of the dam body. Adjust the covariance function according to different load conditions, so that the interpolation calculation can more accurately reflect the change of the correlation of deformation data between monitoring points under different working conditions, improve the accuracy of the interpolation calculation of the deformation field of the entire high arch dam, and ensure that the deformation values of unknown points can truly reflect the actual deformation state of the dam body.

[0043] The present invention formulates corresponding parameter adjustment strategies for the error conditions in different regions of the dam shoulder and crown beam, and reasonably adjusts the variogram parameters. This mechanism ensures the reliability and accuracy of the interpolation results in long-term use, helps to timely discover potential safety hazards of the dam body, and guarantees the safe operation of the dam.

[0044] Through comprehensive data association, reasonable parameter setting and optimization, accurate interpolation calculation and reliable result adjustment mechanism, the present invention realizes more accurate deformation field analysis of high arch dams under different load conditions, and guarantees the safe operation of the dam. Brief Description of the Drawings

[0045] Figure 1 It is a flowchart of an interpolation algorithm for analyzing the characteristics of the deformation field of a high arch dam. Detailed Embodiment

[0046] The technical solutions of the present invention will be further described below in conjunction with the drawings and specific embodiments.

[0047] Embodiment

[0048] As Figure 1 shown, an interpolation algorithm for analyzing the characteristics of the deformation field of a high arch dam proposed by the present invention includes data collection and classification, initial parameter setting of the variogram, locally weighted least squares method for fitting the variogram, global optimization of variogram parameters, Kriging interpolation calculation, and consistency test and parameter adjustment. Each step will be described in detail below.

[0049] I. Data Collection and Classification

[0050] Collect monitoring data, use various monitoring instruments such as total stations, levels, inclinometers, and strain gauges to measure the high arch dam, and obtain the deformation data of the dam shoulder and crown beam at different time points. These data include deformation information such as horizontal displacement, vertical displacement, and angle change.

[0051] Special data collection is carried out for different load conditions, with a focus on two typical conditions: high water level during the flood period and low temperature during the winter. During the high water level in the flood period, the deformation data of the dam body during the water level change process is closely recorded; during the low temperature in winter, the shrinkage deformation data of the dam body caused by temperature reduction is mainly obtained. At the same time, the coordinate information (three-dimensional coordinates) of the monitoring points during each measurement is recorded to ensure that each deformation data has corresponding spatial position information.

[0052] Collect data on the thermal expansion coefficient of the dam body materials. The thermal expansion coefficient data of the dam body materials is obtained by referring to the technical data and laboratory test reports of the dam body construction materials. These data reflect the expansion or contraction characteristics of the dam body materials when the temperature changes. The thermal expansion coefficient data and the deformation data are stored in association according to the same monitoring points and time dimensions for subsequent analysis of the influence of temperature changes on the dam body deformation. Establish the database table structure, where each row of data includes the monitoring point number, time, deformation data, load condition, coordinate information, and the field of thermal expansion coefficient.

[0053] Not only collect the deformation data of various monitoring instruments (total station, level, inclinometer, strain gauge) at different times and positions, but also associate them with different load conditions (high water level during the flood period, low temperature during the winter) and the coordinate information of the monitoring points, and incorporate the thermal expansion coefficient data of the dam body materials. This comprehensive data collection and association method fully considers various factors affecting the dam body deformation, enabling subsequent analysis to more accurately reflect the deformation of the dam body under actual working conditions and avoiding analysis errors caused by data missing or incomplete consideration of factors. Special data collection and processing are carried out for the two typical load conditions of high water level during the flood period and low temperature during the winter, which have a significant impact on the dam body deformation. This helps to more accurately capture the deformation characteristics of the dam body in a complex environment because the stress and deformation mechanisms of the dam body are different under different load conditions. For example, the water pressure during the flood period mainly affects the radial deformation of the dam body, while the low temperature in winter more causes the deformation due to material shrinkage. By separately processing the data under these conditions, the deformation law of the dam body under various conditions can be better understood and analyzed.

[0054] II. Initial parameter setting of the variogram

[0055] Establish a three-dimensional numerical model of the high arch dam

[0056] According to the actual design drawings and geological exploration data of the high arch dam, a three-dimensional numerical model is established using the finite element modeling software ANSYS. During the modeling process, the geometric shape, material properties, and boundary conditions of the dam body are accurately simulated. For the geometric shape of the dam body, the curved surface and thickness change details of the dam body are precisely constructed according to the design requirements. According to the geological report, the shape and material parameters of the foundation are set, considering the distribution and characteristics of different rock layers. In terms of material properties, the elastic modulus, Poisson's ratio, and density parameters of the dam body concrete are input, which are obtained from the material test report.

[0057] Boundary condition setting: For the contact surface between the dam body and the foundation, appropriate contact elements are set according to the actual connection method and mechanical properties. For the boundaries of the foundation, the constraint conditions are determined according to the geological conditions. The bottom boundary is set as a fixed constraint, and the surrounding boundaries are set as normal constraints according to the actual situation.

[0058] Simulate the deformation of the dam body under different load conditions. Different load conditions are applied to the established finite element model. For the high water level condition during the flood period, according to the historical flood water level data and hydraulics principles, the corresponding water pressure load is calculated and applied. The distribution of the water pressure is determined according to the geometric shape of the dam body surface and the water level height. The hydrostatic pressure formula is used to calculate the pressure values at different depths, and they are applied as surface loads on the upstream face of the dam body. Under the low temperature condition in winter, the temperature change range is determined according to the local meteorological data, and the temperature load is applied as a body load on the dam body. Considering the heat conduction characteristics and thermal expansion coefficient of the dam body material, the deformation of the dam body caused by temperature change is calculated through thermo-structural coupling analysis.

[0059] Calculate the spatial autocorrelation function of the deformation data and fit the variogram curve. Run the finite element analysis to obtain the deformation results of each node (simulated monitoring points) of the dam body under different load conditions. Conduct spatial autocorrelation analysis on these deformation data to calculate the change of the correlation of deformation data between different nodes with distance. Use the least squares method to fit the spatial autocorrelation function to obtain the theoretical variogram curve. During the fitting process, a spherical model is selected to describe the variogram curve, and the best fitting curve is determined according to the mean square error of the fitting accuracy index.

[0060] Extract variogram parameters

[0061] Extract sill (base value), range (range), and nugget (nugget value) from the fitted variogram curve as initial parameters. These parameters will be used as the starting values for subsequent local weighted least squares fitting and global optimization.

[0062] The initial parameters of the variogram are determined by establishing a three-dimensional numerical model of the high arch dam to simulate the dam body deformation under different load conditions. This method is based on physical mechanics principles and numerical simulation techniques, and can more accurately reflect the spatial correlation of deformation data of the dam body under complex loads and geometric conditions compared to simply relying on experience or simple calculations. The finite element model can precisely consider factors such as the geometric shape, material properties, and boundary conditions of the dam body, thereby providing a reliable theoretical basis for the estimation of variogram parameters and making subsequent interpolation calculations more in line with the actual situation.

[0063] III. Fitting the variogram by the locally weighted least squares method

[0064] The calculation method of the weighting coefficient is as follows:

[0065]

[0066] where d i is the distance between the current monitoring point and the monitoring point x i participating in the calculation. The p value is taken as 2 under the high water level condition during the flood period and 3 under the low temperature condition in winter; this enables better adaptation to the local change characteristics of data under different load conditions when fitting the local variogram parameters, highlighting the importance of local data and improving the accuracy of capturing local deformation laws.

[0067] In the locally weighted least squares method for fitting the variogram, the function f j (x i ) related to the monitoring point coordinates includes the first-order and second-order terms of the Cartesian coordinates of the monitoring point and the polar coordinate functions ρsinθ and ρcosθ, where ρ is the polar radius and θ is the polar angle; the first-order and second-order terms of the Cartesian coordinates of the monitoring point and the polar coordinate functions are selected as the functions related to the monitoring point coordinates. This rich function form can more comprehensively describe the influence of the position relationship of the monitoring point in space on the deformation data, and can better fit both linear and complex non-linear relationships, thus more accurately reflecting the spatial variation law of the dam body deformation data.

[0068] For the locally weighted least squares method of fitting the variogram, for each monitoring point, according to the distance from it to other monitoring points and the corresponding deformation data difference, the variogram is fitted using the locally weighted least squares method to calculate the local variogram parameters around each monitoring point under the current load condition. The formula is as follows:

[0069]

[0070] where z(x i ) is the deformation data of the monitoring point x i , c is a constant term, b j is the coefficient to be determined, fj (x i ) is a function related to the coordinates of the monitoring points, w i is the weighting coefficient, n is the number of monitoring points participating in the calculation, and k is the number of functions f j ;

[0071] IV. Global Optimization of Variogram Parameters

[0072] Through the global optimization algorithm, combined with the local variogram parameters of all monitoring points under the current load condition, the sill, range, and nugget of the overall variogram are optimized and adjusted to minimize the sum of squared errors in the sparse area of the abutment monitoring points and the dense area of the crown beam monitoring points. The optimization objective function is as follows:

[0073]

[0074] where L is the number of monitoring areas, n l is the number of monitoring points in the l-th monitoring area, z l (x i ) is the actual deformation data of the monitoring point x i in the l-th monitoring area, is the estimated deformation data calculated using the current variogram parameters; the global optimization algorithm uses the simulated annealing algorithm. The initial temperature is set to 10 times the sum of squared errors, the temperature decrease rate is 10% per 100 iterations, and the termination condition is that the change in the sum of squared errors is less than 0.01 for 20 consecutive iterations and the maximum number of iterations reaches 1000 times. This effectively avoids the algorithm falling into a local optimal solution. The randomness and annealing process of the simulated annealing algorithm simulate the thermal equilibrium process of the physical system, enabling the algorithm to have better ergodicity when searching for the global optimal parameters, and being able to find the variogram parameters that minimize the sum of squared errors in the sparse area of the abutment monitoring points and the dense area of the crown beam monitoring points in the complex parameter space, improving the adaptability of the interpolation algorithm to the entire dam deformation field.

[0075] V. Kriging Interpolation Calculation

[0076] The calculation formula for the covariance function between the monitoring points x i and x j is as follows:

[0077]

[0078] where C0 is the nugget effect, C max is the sill, h is the distance between two points, a is the range, and C0, C max and a are adjusted accordingly according to different load conditions during the calculation;

[0079] According to the optimized variogram parameters, the deformation values of unknown points in the deformation field of the high arch dam are calculated using the Kriging interpolation formula, as follows:

[0080]

[0081] Among them, is the estimated deformation value of the unknown point x0, λ i is the weight coefficient calculated through the variogram and the data of monitoring points, Z(x i ) is the deformation value of the known monitoring point x i , n is the number of monitoring points participating in the interpolation calculation, and the weight coefficient λ i is solved through the following system of equations:

[0082]

[0083] Among them, C(x i , x j ) is the covariance function between the monitoring points x i and x j , which is derived from the variogram, and μ is the Lagrange multiplier. The nugget value, sill value, and range in the covariance function are adjusted accordingly according to different load conditions. This consideration of load conditions enables the covariance function to more accurately reflect the change in the correlation of deformation data between monitoring points under different conditions, thereby improving the accuracy of the interpolation calculation and making the calculated deformation values of unknown points more consistent with the actual deformation of the dam body under various load conditions.

[0084] VI. Consistency check and parameter adjustment

[0085] Compare the interpolation results with the actual monitoring data

[0086] Compare the deformation values of each point of the dam calculated by Kriging interpolation with the actual monitoring data. For key areas of concern such as the dam shoulder and the crown beam, check the consistency of their deformation trends and values respectively.

[0087] Calculate the deformation value error of each monitoring point. In the dam shoulder area, check whether the deformation value error exceeds the preset threshold of ±5 mm; in the crown beam area, check whether the deformation value error exceeds ±3 mm. At the same time, calculate the slope deviation of the deformation trend. If the slope deviation exceeds the threshold of 0.1, it is considered that the deformation trend is inconsistent.

[0088] Adjust the parameters according to the error situation

[0089] If the error in the dam shoulder area exceeds the preset threshold and is mainly concentrated in the part near the edge of the dam body, increase the number of monitoring points in this area. Re-execute steps 1 to 5, collect new monitoring data, re-fit the variogram, optimize the parameters, and perform interpolation calculations.

[0090] If the error in the crown beam area exceeds the preset threshold and shows a local concentration trend, increase the monitoring frequency for this local area to obtain more deformation data. Then re-execute Steps 1 to 5 to update the interpolation result.

[0091] When adjusting the variogram parameters according to the error distribution, if the deformation value error in the abutment area exceeds ±5 mm, increase the range parameter by 5%; if the deformation value error in the crown beam area exceeds ±3 mm, adjust the sill parameter by 3% and adjust the nugget parameter by 2%. After adjusting the parameters, perform interpolation calculation and consistency check again until the consistency requirement is met. Preset reasonable error thresholds, the deformation value error in the abutment area does not exceed, the crown beam area does not exceed, the slope deviation threshold, and a targeted parameter adjustment strategy is formulated according to the error distribution in different areas of the abutment and crown beam. When the error exceeds the threshold, by increasing the number of monitoring points (when the error at the abutment edge is large) or increasing the monitoring frequency (when the local error in the crown beam is concentrated), and the corresponding adjustment of the variogram parameters (increasing the range parameter amplitude in the abutment, adjusting the sill and nugget parameter amplitudes in the crown beam), the interpolation algorithm can be corrected in time to continuously adapt to the changes in the actual dam body deformation, ensuring the long-term reliability and accuracy of the interpolation result, which is beneficial to timely discovering potential safety hazards of the dam body.

[0092] The above specific embodiments are merely several alternative embodiments of the present invention. Based on the technical solution of the present invention and the relevant inspirations of the above embodiments, those skilled in the art can make various alternative improvements and combinations to the above specific embodiments.

Claims

1. An interpolation algorithm for the analysis of the deformation field characteristics of high arch dams, characterized in that It includes the following steps: Step 1: Data collection and classification. Collect the monitoring data of the high arch dam under different load conditions, where the load conditions include high water levels during the flood season and low temperatures during the winter. Associate the deformation data from different parts and at different times of total stations, level gauges, inclinometers, and strain gauges with the corresponding load conditions and monitoring point coordinate information. Step 2: Initial parameter setting of the variogram. For each load condition, set the initial parameters of the variogram, including sill, range, and nugget. The initial parameters are estimated using the finite element analysis method. Step 3: Fitting the variogram using the locally weighted least squares method. For each monitoring point, based on the distance to other monitoring points and the corresponding deformation data differences, use the locally weighted least squares method to fit the variogram and calculate the local variogram parameters around each monitoring point under the current load condition. The formula is as follows: Among them, z(x i ) is the deformation data of the monitoring point x i , c is the constant term, b j is the coefficient to be determined, f j (x i ) is a function related to the coordinates of the monitoring point, w i is the weighting coefficient, n is the number of monitoring points participating in the calculation, and k is the number of functions f j ; Step 4: Global optimization of the variogram parameters. Through the global optimization algorithm, combine the local variogram parameters of all monitoring points under the current load condition to optimize and adjust the sill, range, and nugget of the overall variogram, minimizing the sum of squared errors in the sparse area of the abutment monitoring points and the dense area of the crown beam monitoring points. The optimization objective function is as follows: where L is the number of monitoring areas, and n l is the number of monitoring points in the l-th monitoring area, and z l (x i ) is the actual deformation data of the monitoring point x i in the l-th monitoring area, and is the estimated deformation data calculated using the current variogram parameters; Step 5: Kriging interpolation calculation. According to the optimized variogram parameters, use the Kriging interpolation formula to calculate the deformation values of unknown points in the deformation field of the high arch dam. The formula is as follows: Among them, is the estimated deformation value of the unknown point x0, and λ i is the weight coefficient calculated through the variogram and the monitoring point data, Z(x i ) is the deformation value of the known monitoring point x i , n is the number of monitoring points participating in the interpolation calculation, and the weight coefficient λ i is solved by the following system of equations: Among them, C(x i , x j ) is the covariance function between monitoring points x i and x j , which is derived from the variogram, and μ is the Lagrange multiplier; Step 6: Consistency test and parameter adjustment. Compare the interpolation results with the actual monitoring data to check the deformation trend and numerical consistency in different areas of the abutment and crown beam. If the error exceeds the preset threshold, adjust the variogram parameters according to the error distribution and re - execute Steps 3 to 5 until the consistency requirement is met.

2. The interpolation algorithm for analyzing the characteristics of the deformation field of a high arch dam according to claim 1, wherein In the data collection and classification, the thermal expansion coefficient data of the dam body material is also collected and associated with the deformation data.

3. The interpolation algorithm for analyzing the characteristics of the deformation field of a high arch dam according to claim 1, wherein The specific finite element analysis method is as follows: Establish a three - dimensional numerical model of the high arch dam to simulate the deformation of the dam under different load conditions. According to the finite element simulation results, calculate the spatial autocorrelation function of the deformation data, obtain the theoretical variogram curve through fitting the autocorrelation function, and extract the values of sill, range, and nugget from this curve as the initial parameters.

4. An interpolation algorithm for analyzing the characteristics of the deformation field of a high arch dam according to claim 1, wherein, In the fitting of the variogram using the locally weighted least squares method, the calculation method of the weighting coefficient is Among them, d i is the distance between the current monitoring point and the monitoring point x participating in the calculation i The p value is taken as 2 under the high water level condition during the flood period and 3 under the low temperature condition in winter.

5. The interpolation algorithm for analyzing the characteristics of the deformation field of a high arch dam according to claim 1, wherein In the locally weighted least squares method for fitting the variogram, the function f j (x i ) includes the linear term, quadratic term of the Cartesian coordinates of the monitoring points, and the polar coordinate functions ρsinθ and ρcosθ, where ρ is the polar radius and θ is the polar angle.

6. The interpolation algorithm for analyzing the characteristics of the deformation field of a high arch dam according to claim 1, wherein, In the global optimization of the variogram parameters, the global optimization algorithm uses the simulated annealing algorithm. The initial temperature is set to 10 times the sum of squared errors, the temperature reduction rate is 10% per 100 iterations, and the termination condition is that the change in the sum of squared errors for 20 consecutive iterations is less than 0.01 and the maximum number of iterations reaches 1000 times.

7. An interpolation algorithm for analyzing the characteristics of the deformation field of a high arch dam according to claim 1, characterized in that, In Kriging interpolation calculation, for the monitoring points x i and x j The calculation formula for the covariance function between them is as follows: Among them, C0 is the nugget effect, C max is the sill value, h is the distance between two points, a is the range, and C0, C max and a are adjusted accordingly according to different load conditions during calculation.

8. An interpolation algorithm for analyzing the characteristics of the deformation field of a high arch dam according to claim 1, characterized in that, In the consistency test and parameter adjustment, the preset threshold is that the deformation value error in the abutment area does not exceed ±5 mm, and the deformation value error in the crown beam area does not exceed ±3 mm. The consistency of the deformation trend is checked by calculating the slope deviation, and the slope deviation threshold is set to 0.

1.

9. The interpolation algorithm for analyzing the characteristics of the deformation field of a high arch dam according to claim 8, wherein In the consistency test and parameter adjustment, if the error in the abutment area exceeds the preset threshold and is mainly concentrated in the part close to the dam edge, increase the number of monitoring points in this area and re - execute Steps 1 to 5; if the error in the crown - beam area exceeds the preset threshold and shows a local concentration trend, increase the monitoring frequency in this local area and re - execute Steps 1 to 5.

10. An interpolation algorithm for analyzing the characteristics of the deformation field of a high arch dam according to claim 8, characterized in that, In the consistency test and parameter adjustment, when adjusting the variogram parameters according to the error distribution, if the deformation value error in the abutment area exceeds ±5 mm, increase the range parameter by 5%; if the deformation value error in the crown - beam area exceeds ±3 mm, adjust the sill parameter by 3% and adjust the nugget parameter by 2%.

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