A four-dimensional spatiotemporal distribution model of temperature in concrete arch dams based on multi-point measured temperature.

Abstract

This invention discloses a method for constructing a four-dimensional spatiotemporal distribution model of concrete arch dam body temperature based on multi-point measured temperature, belonging to the field of concrete arch dam safety monitoring technology. This invention is achieved through the following steps: S1, anomaly identification, removal, substitution, and five-day moving average preprocessing of the measured temperature data; S2, establishing a normalized spatial coordinate system for the dam body (…). x , or , g S3. Representative points are set up on the cross-section of the arched beam. The temperatures of these representative points are used as the first set of undetermined parameters in the inversion model. A two-dimensional temperature field is constructed using cubic B-spline fitting. S4. Temperature adjustment parameters for the left and right banks are set as the second set of undetermined parameters in the inversion model. Bank-direction correction is performed through quadratic interpolation and a |η|³ weighting function to obtain a three-dimensional temperature field. S5. Spatiotemporal correlation constraints are established to limit the temperature difference between adjacent points and the parameter variation range between adjacent time periods. S6. With the goal of minimizing the measured-fit residual, the undetermined parameters are inverted using the least squares method to obtain a four-dimensional continuous temperature field. S7. Abnormal measurement points are identified and eliminated based on the fitting residual iteratively until convergence. This invention realizes the reconstruction of a continuous, stable, and reliable four-dimensional spatiotemporal temperature field from discrete data containing outliers. It has the ability to automatically identify and iteratively purify anomalies, and the reconstruction accuracy is high with good spatiotemporal continuity. It can provide reliable basic data for stress deformation analysis and full-time safety evaluation of arch dams.

Description

Technical Field

[0001] This invention relates to the field of temperature analysis technology for concrete arch dams, and more specifically, to a four-dimensional spatiotemporal distribution model of temperature in a concrete arch dam body based on multi-point measured temperature. Background Technology

[0002] Concrete arch dams are hydraulic structures significantly affected by temperature; the spatiotemporal variations of their internal temperature field directly determine the dam's stress, deformation, and structural safety. The dam's temperature field constantly evolves with seasonal air temperature, solar radiation conditions, reservoir water level changes, and the dam's own material properties, exhibiting significant time-varying, spatially inhomogeneous, and nonlinear characteristics. Therefore, accurately obtaining the dam's temperature distribution is fundamental for conducting dam safety monitoring, stress-strain analysis, deformation inversion, and operational status assessment.

[0003] Currently, large arch dams typically employ multi-point temperature measurement systems within the dam body, using embedded thermometers to collect temperature data over extended periods. However, the following technical challenges exist in practical engineering applications:

[0004] (1) Abnormalities and failures of measuring points: Some temperature measuring points may have long-term unchanged, sudden changes or deviations from reasonable range due to sensor aging, water ingress, voiding or construction disturbances, which directly affect the reliable reconstruction of the temperature field.

[0005] (2) The spatial distribution of measuring points is uneven: Although a large number of temperature measuring points are arranged, there are still problems such as sparseness, concentration, and blind spots in the dam body elevation direction, dam thickness direction and left and right bank directions, making it impossible to directly obtain the whole dam temperature field that meets the requirements of numerical analysis.

[0006] (3) Temperature changes have multi-scale characteristics. Temperature changes on the dam surface and in the shallow area are significantly affected by diurnal temperature range and sunshine, while the temperature changes slowly in the deep concrete. This results in significant differences in the measured values ​​of different areas on the time scale, and direct modeling can easily lead to unstable fitting results.

[0007] (4) Traditional temperature field models are difficult to construct high-dimensional, continuous, and smooth temperature distributions. Existing methods mostly rely on simple interpolation, empirical formulas, or low-dimensional regression models, which cannot effectively describe the continuous field characteristics of dam body temperature in the four-dimensional time-space domain. They are also difficult to make full use of multi-point monitoring data for mutual calibration and elimination of bad data to improve model accuracy.

[0008] Therefore, there is an urgent need for a new four-dimensional spatiotemporal temperature distribution model that can make full use of measured temperature data, automatically identify abnormal measuring points, construct a continuous temperature field in space, and maintain a smooth transition in the time dimension, in order to solve the problems of insufficient representativeness of measuring points, unstable temperature field fitting, and difficulty in meeting the needs of full-time safety analysis of arch dams in existing technologies. Summary of the Invention

[0009] To address the problems existing in the prior art, this invention proposes a four-dimensional spatiotemporal distribution model of temperature in concrete arch dams based on multi-point measured temperature.

[0010] A four-dimensional spatiotemporal temperature distribution model for a concrete arch dam based on multi-point measured temperature is proposed. This model involves cleaning and constructing a coordinate system from the measured temperature data of the arch dam, then establishing and optimizing the four-dimensional temperature field of the entire dam through modeling, correction, and parameter inversion. Finally, reliable results are obtained by iteratively eliminating outlier measurement points. The model includes the following steps:

[0011] S1: Preprocess the measured temperature data inside the arch dam, including abnormal measuring point identification, abnormal data removal, measuring point temperature replacement, and smoothing of the five-day temperature average.

[0012] S2: Establish a normalized spatial coordinate system for the dam body, and map the physical coordinates of the dam body to a dimensionless coordinate system through normalization transformation. )middle, The relative elevation of that point is represented by the lowest elevation of the dam body as 0 and the crest elevation of the dam as 1. The relative positions of the left and right banks of the point are represented by the cross-sectional position of the arch crown beam as 0, the radial cross-sectional position of the left arch end as -1, and the radial cross-sectional position of the right arch end as 1. The upstream and downstream relative positions of the point are represented by the mid-surface of the dam body as 0, the upstream dam face as -1, and the downstream dam face as 1.

[0013] S3: Along different elevation directions of the arched beam section Select several points in the upstream and downstream directions. Several points are selected to construct a two-dimensional discrete representative point set. The temperatures of these representative points are used as the first set of undetermined parameters in the inversion model. A B-spline function is then used to fit the temperatures of the representative points to obtain the continuous temperature field function of the arched beam profile. ;

[0014] S4: Set the average temperature adjustment value for both left and right banks With linear temperature difference adjustment value As the second set of undetermined parameters in the inversion model, a three-dimensional spatial temperature adjustment function is obtained by interpolation along the elevation direction. The resulting temperature field is then corrected along the bank direction to obtain the three-dimensional temperature field function of the entire dam. ;

[0015] S5: Establish spatiotemporal correlation constraints for the temperature field and apply continuity constraints to the temperature field parameters in adjacent time periods;

[0016] S6: Perform parameter inversion with the objective of minimizing the difference between the measured temperature and the fitted temperature to obtain the four-dimensional temperature field function of the entire dam.

[0017] S7: Determine whether the measuring point is abnormal based on the difference between the measured temperature at the measuring point and the fitted temperature at that location derived from the four-dimensional temperature field function of the whole dam. Abnormal measuring points with differences exceeding the allowable threshold are removed and refitted to obtain the final temperature field result.

[0018] More specifically, in step S1, the anomaly identification in the preprocessing includes determining whether the temperature measurement point is unchanged for a long time, changes abruptly, crosses the boundary, or deviates significantly from the neighboring temperature field, and then eliminating such cases.

[0019] More specifically, in step S1, the temperature measurement point is replaced by data from measurement points on the dam surface in other areas with similar water depth or sunshine conditions when there are insufficient effective measurement points on the dam crest or dam surface.

[0020] More specifically, in step S1, the five-day temperature average processing is to take the average of the current time and the values ​​of the previous four days to reduce the impact of short-term diurnal temperature fluctuations.

[0021] More specifically, in step S3, along different elevation directions of the arched beam cross-section Take 6 points ( =0, 0.2, 0.4, 0.6, 0.8, 1.0), upstream and downstream directions Take 6 points for direction ( The undetermined temperature values ​​are found at 36 points: -1, -0.6, -0.2, 0.2, 0.6, 1.0. The undetermined temperature values ​​at these 36 points are used to construct a two-dimensional discrete representative point set, which serves as the undetermined parameters of the temperature field.

[0022] More specifically, in step S3, the B-spline fitting function is:

[0023] ;

[0024] In the formula, for spline functions for The independent variable of a spline function; for spline function in the th The function value at each node. ;

[0025] Depend on Determine the entire cross-section ( =0~1, Temperature field =-1~1) By fitting the B-spline function, the same (Upstream and downstream directions), different (Elevation direction) 6 value:

[0026] ;

[0027] In the formula, For fixed = At that time, along the elevation Temperature distribution function in the direction; For the (th) section Temperature values ​​of ) representative points;

[0028] Then in any In the above formula, take respectively Six temperature values ​​along the upstream and downstream directions are obtained. These six temperature values ​​are then used to obtain a specific temperature value through a cubic B-spline function. Fitted temperature field values ​​at:

[0029] ;

[0030] In the formula, For any point on the cross-section of the arched beam ( The temperature field function.

[0031] More specifically, in step S4, on the left and right banks ( =-1,1) dam bottom, middle and dam crest ( Set the average temperature adjustment values ​​at points (=0, 0.5, 1) respectively. and linear temperature difference adjustment value There are a total of 12 pending adjustment values, and these adjustment values ​​are along... Directional quadratic interpolation to determine Adjustment value at:

[0032] ;

[0033] In the formula, Elevation of the left and right banks of the dam The average temperature adjustment function; This is the adjusted value for the average temperature at the bottom of the dam; This is the adjusted value for the average temperature in the central region; This is the adjusted value for the average temperature at the dam crest;

[0034] ;

[0035] In the formula, Elevation of the left and right banks of the dam The linear temperature difference adjustment function; This is the baseline temperature difference adjustment value for the dam. This is the adjustment value for the linear temperature difference in the middle section; This is the adjustment value for the linear temperature difference at the dam crest;

[0036] The final temperature field function for the left bank portion of the dam is:

[0037] ;

[0038] The final temperature field function for the right bank portion of the dam is:

[0039] ;

[0040] In the formula, Let be the three-dimensional temperature field function at any point on the dam body; The weighting function makes the temperature adjustment along the left and right banks more inclined to adjust the temperature of the dam body closer to the banks; For the left bank along the elevation The average temperature adjustment function; The right bank along the elevation The average temperature adjustment function; For the left bank along the elevation The linear temperature difference adjustment function; The right bank along the elevation The linear temperature difference adjustment function.

[0041] More specifically, in step S5, the spatial association constraint is:

[0042] ;

[0043] ;

[0044] In the formula, The ( ) section Temperature at ) coordinate points; The ( ) section Temperature at ) coordinate points; ; This is the average temperature adjustment value; The upper limit of the average temperature adjustment value is set between 2 and 4. ; This is the linear temperature difference adjustment value; The upper limit of the linear temperature difference adjustment value is set to 2~4. ;

[0045] Temporal correlation constraints can be applied to undetermined variables in adjacent time periods of 5 days, as follows:

[0046] ;

[0047] ;

[0048] In the formula, For the ( ) coordinate points in Temperature at any moment; For the ( ) coordinate points in Temperature at any moment; This represents the threshold for temperature parameter changes between adjacent time periods. ; For the first Average temperature adjustment parameters for the time period; For the first Average temperature adjustment parameters for the time period; The threshold for the average adjustment value change over adjacent time periods. ; For the first Linear temperature difference adjustment parameters for different time periods; For the first Linear temperature difference adjustment parameters for different time periods; This is the threshold for adjusting the temperature difference between adjacent time periods. .

[0049] More specifically, in step S6, parameter inversion is performed by... , and A total of 48 parameters were identified as undetermined variables in the inversion analysis. The least squares method, based on the difference between the fitted and measured values, was used to obtain the parameters from the measured temperature values ​​through inversion. , and Thus, the four-dimensional temperature field function of the entire dam is obtained.

[0050] More specifically, in step S7, the temperature fluctuation range is distinguished from the temperature fluctuation range by fitting the temperature difference, wherein the threshold for the large fluctuation range is 2~3℃ and the threshold for the small fluctuation range is 1~2℃.

[0051] The technical effects of this invention include:

[0052] (1) To address the issues of abnormal and failed measurement points, a three-level data cleaning system and a five-day moving average smoothing mechanism were constructed. An iterative identification and elimination mechanism for abnormal measurement points based on the fitting residuals was established. Differentiated residual thresholds of 1~2℃ and 2~3℃ were set for the stable fluctuation area and the significant area, respectively. Through repeated optimization until the entire field converged, the interference of abnormal measurements on the temperature field fitting was effectively eliminated, and the reliability and representativeness of the input data were significantly improved. Through iterative optimization, the dataset was automatically purified, making the model robust and able to output a physically reasonable temperature field even under the condition of measurement point failure.

[0053] (2) To address the problem of uneven spatial distribution of measuring points, a dimensionless normalized spatial coordinate system is established. This method maps any physical location of the dam body to a regular computational domain; it uses a cubic B-spline function to fit the two-dimensional temperature field, and extends the two-dimensional field into a three-dimensional temperature field of the entire dam by adjusting the shoreline parameters, thus standardizing the expression of the complex geometric dam body and breaking through the limitations of the physical distribution of measuring points; it achieves continuous reconstruction of the temperature field of the entire dam through parametric modeling, which greatly reduces the dependence on the density of measuring points and effectively solves the problems of spatial sparsity, partial aggregation and blind spots.

[0054] (3) To address the multi-scale characteristics of temperature changes, the interference of short-term diurnal fluctuations is weakened by smoothing the five-day moving average. Spatiotemporal correlation constraints are set, and spatial temperature difference thresholds are applied to adjacent representative points, upper limit constraints are applied to the average temperature and linear temperature difference adjustment values, and temporal change thresholds are applied to parameter changes in adjacent time periods. This effectively separates and suppresses high-frequency noise in multi-scale temperature changes, ensuring that the inverted temperature field is spatially continuous and smooth in time, and avoiding the fitting instability caused by the difference in the rate of temperature change between deep and shallow parts in traditional methods.

[0055] 4. Addressing the difficulty in constructing high-dimensional continuous fields,

[0056] Technical approach: The undetermined variables are used as the inversion object, with the goal of minimizing the measured-fit residual, and the constrained least squares method is used to solve the problem; by using spatiotemporal continuity constraints, the multi-point monitoring data are transformed into overall constraints, driving parameter optimization and realizing continuous and smooth reconstruction of the temperature field in the four-dimensional time-space domain. The global constraint capability of all monitoring data is fully utilized, and the inversion accuracy is significantly better than that of traditional interpolation or low-dimensional regression models; the model output can support temperature queries at any location and at any time, meeting the requirements of arch dam stress deformation analysis for high time-frequency and high spatial resolution temperature data.

[0057] Overall, this model provides solid and reliable technical support for achieving high-precision, full-time temperature field simulation and safety assessment of arch dams. Attached Figure Description

[0058] Figure 1 A schematic diagram of 36 representative temperature points on the cross-section after spatial normalization transformation.

[0059] Figure 2 Temperature distribution diagram of the cross section of the arched beam on day 1870.

[0060] Figure 3 This is a temperature distribution map of the dam body and dam surface on day 1870.

[0061] Figure 4 Time history diagram of dam body temperature at 3 / 5 of the dam height on the upstream face of the arched dam beam.

[0062] Figure 5 A schematic diagram of a four-dimensional spatiotemporal temperature distribution model for a concrete arch dam body based on multi-point measured temperatures. Detailed Implementation

[0063] The present invention will be further described below with reference to embodiments. These embodiments are implemented based on the technical solution of the present invention, providing detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0064] Example: Over 200 temperature monitoring points were deployed along different elevations, dam thicknesses, and on both the left and right banks inside a high concrete arch dam, forming a relatively complete dam temperature monitoring system. Each monitoring point continuously records the temperature changes within the dam body, providing fundamental data for temperature field inversion.

[0065] Temperature data preprocessing: Temperature monitoring data of the arch dam since its construction was collected. The raw measured temperature data was first preprocessed, including anomaly identification, anomaly removal, data substitution, and time series smoothing. Temperature monitoring points with consistently high temperatures, sudden changes exceeding 5°C, or significant deviations from the trends of surrounding monitoring points were considered anomalies and removed. For areas with insufficient effective monitoring points, such as the dam crest and face, monitoring points above the water surface with similar sunlight conditions were selected as substitute data to enhance the spatial representativeness of the temperature field. Considering the significant slow evolution of temperature changes within the dam body, to mitigate the impact of short-term diurnal temperature fluctuations, a five-day moving average was applied to the temperature series of each monitoring point; that is, the average of the current time and the values ​​of the previous four days was used as the representative temperature for that moment.

[0066] Construction of Normalized Spatial Coordinates for the Dam Body: A normalized three-dimensional spatial coordinate system is established for the dam body to uniformly describe the position of any measuring and calculation points within the dam body. Relative Elevation Coordinates With the lowest elevation of the dam body as 0 and the crest elevation of the dam as 1; the relative coordinates of the left and right banks With the cross-section of the arch crown beam as 0, the radial cross-section of the left arch end as −1, and the radial cross-section of the right arch end as 1; the upstream and downstream relative coordinates The mid-surface of the dam is defined as 0, the upstream dam face as −1, and the downstream dam face as 1. This normalized coordinate system maps the complex geometry of the dam into a regular dimensionless space, providing a unified foundation for subsequent temperature field modeling and interpolation calculations.

[0067] Construction of the two-dimensional temperature field of the arched beam profile: Ignoring the temperature difference between the left and right banks, the arched beam profile is selected as the base profile. Two-dimensional discrete representative point sets are then established on this profile along the elevation direction and the upstream and downstream directions. (See attached...) Figure 1 As shown, six relative position points are selected along the elevation direction. =0, 0.2, 0.4, 0.6, 0.8, 1.0, select 6 relative position points along the upstream and downstream directions. =−1, −0.6, −0.2, 0.2, 0.6, 1.0, forming 36 two-dimensional representative points, whose temperature values ​​serve as undetermined parameters for the profile temperature field. A cubic B-spline function is used to fit the undetermined temperatures of these 36 representative points, first along the same upstream and downstream... Different elevations in different directions temperature Perform spline interpolation to obtain the elevation Temperature distribution function in the direction Then along the same elevation Different upstream and downstream By performing B-spline fitting, a continuous two-dimensional temperature distribution function at any location on the cross-section of the arched beam is finally obtained. Appendix Figure 2 The temperature distribution results of the arch crown beam profile obtained after inversion analysis are shown. It can be seen that the fitted temperature field is continuous and smooth in space and can reasonably reflect the temperature change law inside the dam body.

[0068] Temperature Correction and 3D Temperature Field Construction in the Left and Right Bank Directions: Based on the 2D temperature field, a bank-direction temperature adjustment mechanism is introduced to account for the temperature differences between the left and right banks of the dam. At the left and right bank locations ( =−1 and =1) and the dam base, middle and crest ( Set the average temperature adjustment values ​​at points (=0, 0.5, 1) respectively. and linear temperature difference adjustment value As parameters to be determined, temperature adjustment functions at arbitrary elevations on the left and right banks are obtained through quadratic interpolation along the elevation direction. and The above adjustment function is superimposed on the two-dimensional temperature field of the arched beam profile, and combined with the weighting function. By controlling the influence range on the shore, a three-dimensional temperature distribution covering the entire dam body was ultimately obtained. Appendix Figure 3 The temperature distribution on the upstream face of the dam body on day 1870, obtained after inversion analysis, is shown. It can be seen that the temperature gradients formed on the left and right banks and at different elevations are affected by water temperature, ground temperature and other factors.

[0069] Spatiotemporal correlation constraints and parameter inversion: To ensure the smoothness and physical rationality of the temperature field in space and time, spatial continuity constraints and temporal continuity constraints are applied to the representative point temperature parameters and shoreline adjustment parameters. The spatial continuity constraint condition is as follows: Upper limit of average temperature adjustment value and Take 4 The time continuity constraint is a threshold for the change in temperature parameters between adjacent time periods. Threshold for changes in average adjusted value between adjacent time periods Threshold for temperature difference adjustment value between adjacent time periods Using 48 parameters—36 representative points on the cross-section with undetermined temperatures, 6 adjusted average temperatures, and 6 adjusted linear temperature differences—as variables to be inverted, and aiming to minimize the residuals between the measured and fitted temperatures, the least squares method and the constrained variable scaling method were employed for inversion to obtain parameters for each time period, thereby constructing a four-dimensional temperature field for the entire dam. .

[0070] Anomaly point identification and iterative optimization: Calculate the fitting residuals for each measuring point, setting a residual threshold of 1.5℃ for the stable temperature fluctuation zone and 2.5℃ for the significant temperature fluctuation zone. Measuring points exceeding the thresholds are removed, and the iteration continues until the residuals of all measuring points meet the requirements. Figure 3 The time-history curve of dam body temperature at 3 / 5 of the dam height on the upstream dam face of the arched beam is shown. It can be seen that the temperature calculated by the model changes periodically with the seasons and is smooth and continuous, which is consistent with the actual evolution law of dam body temperature.

Claims

1. A four-dimensional space-time distribution model of concrete arch dam body temperature based on multi-point measured temperature, characterized in that Includes the following steps: S1: Preprocess the measured temperature data inside the arch dam, including abnormal measuring point identification, abnormal data removal, measuring point temperature replacement, and smoothing of the five-day temperature average. S2: Establish dam body normalized space coordinate system, map the physical coordinates of the dam body to the dimensionless coordinate system (0, 1) through normalization transformation, ) in which, The relative elevation of the point, with the lowest elevation of the dam body as 0 and the elevation of the dam crest as 1; The relative position of the point on the left and right banks, with the crown beam profile position as 0, the left arch end radial profile position as -1, and the right arch end radial profile position as 1; The relative position of the point on the upstream and downstream, with the mid-plane of the dam body as 0, the upstream dam surface as -1, and the downstream dam surface as 1; S3: different elevation directions along the arch crown beam profile Select several points in the upstream and downstream directions Select several points, construct a two-dimensional discrete representative point set, use the temperatures of these representative points as the first group of undetermined parameters in the inversion model, and use B-spline functions to fit the representative point temperatures to obtain a continuous temperature field function of the arch crown beam profile ; S4: Set left and right bank average temperature adjustment value With linear temperature difference adjustment value As the second group of undetermined parameters in the inversion model, the three-dimensional temperature adjustment function is obtained by interpolation along the elevation direction, and the obtained temperature field is corrected towards the bank to obtain the three-dimensional temperature field function of the whole dam ; S5: Establish spatiotemporal correlation constraints for the temperature field and apply continuity constraints to the temperature field parameters in adjacent time periods; S6: Perform parameter inversion with the objective of minimizing the difference between the measured temperature and the fitted temperature to obtain the four-dimensional temperature field function of the entire dam. S7: Determine whether the measuring point is abnormal based on the difference between the measured temperature at the measuring point and the fitted temperature at that location derived from the four-dimensional temperature field function of the whole dam. Abnormal measuring points with differences exceeding the allowable threshold are removed and refitted to obtain the final temperature field result.

2. The multi-point measured temperature based four-dimensional spatio-temporal distribution model of concrete arch dam body temperature according to claim 1, characterized in that In step S1, the anomaly identification in the preprocessing includes determining whether the temperature measurement point is unchanged for a long time, abruptly changes, goes out of bounds, or deviates significantly from the temperature field of the neighborhood, and then removing it.

3. The multi-point measured temperature based four-dimensional spatio-temporal distribution model of concrete arch dam body temperature according to claim 1, characterized in that In step S1, the temperature measurement point is replaced by data from measurement points on the dam face in other areas with similar water depth or sunshine conditions when there are insufficient effective measurement points on the dam crest or dam face.

4. The multi-point measured temperature based four-dimensional spatio-temporal distribution model of concrete arch dam body temperature according to claim 1, characterized in that In step S1, the five-day average temperature is processed by averaging the current temperature and the values ​​measured over the previous four days to reduce the impact of short-term diurnal temperature fluctuations.

5. The four-dimensional spatiotemporal distribution model of concrete arch dam body temperature based on multi-point measured temperature as described in claim 1, characterized in that... In step S3, the different elevation directions along the arch crown beam section Take 6 points (x, y) = (0, 0), (0.2, 0), (0.4, 0), (0.6, 0), (0.8, 0), (1.0, 0) in the upstream and downstream directions Take 6 points (x, y) = (-1, 0), (-0.6, 0), (-0.2, 0), (0.2, 0), (0.6, 0), (1.0, 0) in the transverse direction Take 6 points (x, y) = (-1, 0), (-0.6, 0), (-0.2, 0), (0.2, 0), (0.6, 0), (1.0, 0) in the transverse direction Take 6 points (x, y) = (-1, 0), (-0.6, 0), (-0.2, 0), (0.2, 0), (0.6, 0), (1.0, 0) in the transverse direction Construct a two-dimensional discrete representative point set of the 36 points with 6. The four-dimensional spatiotemporal distribution model of concrete arch dam body temperature based on multi-point measured temperature as described in claim 1, characterized in that... In step S3, the B-spline fitting function is: ； In the formula, for spline functions for The independent variable of a spline function; for spline function in the th The function value at each node. ; Depend on Determine the entire cross-section ( =0~1, Temperature field =-1~1) By fitting the B-spline function, the same (Upstream and downstream directions), different (Elevation direction) 6 value: ； In the formula, For fixed = At that time, along the elevation Temperature distribution function in the direction; For the (th) section Temperature values ​​of ) representative points; Then in any In the above formula, take respectively Six temperature values ​​along the upstream and downstream directions are obtained. These six temperature values ​​are then used to obtain a specific temperature value through a cubic B-spline function. Fitted temperature field values ​​at: ； In the formula, For any point on the cross-section of the arched beam ( The temperature field function.

7. The four-dimensional spatiotemporal distribution model of concrete arch dam body temperature based on multi-point measured temperature as described in claim 1, characterized in that... In step S4, on the left and right banks ( =-1,1) dam bottom, middle and dam crest ( Set the average temperature adjustment values ​​at points (=0, 0.5, 1) respectively. and linear temperature difference adjustment value There are a total of 12 pending adjustment values, and these adjustment values ​​are along... Directional quadratic interpolation to determine Adjustment value at: ； In the formula, Elevation of the left and right banks of the dam The average temperature adjustment function; This is the adjusted value for the average temperature at the bottom of the dam; This is the adjusted value for the average temperature in the central region; This is the adjusted value for the average temperature at the dam crest; ； In the formula, Elevation of the left and right banks of the dam The linear temperature difference adjustment function; This is the baseline temperature difference adjustment value for the dam. This is the adjustment value for the linear temperature difference in the middle section; This is the adjustment value for the linear temperature difference at the dam crest; The final temperature field function for the left bank portion of the dam is: ； The final temperature field function for the right bank portion of the dam is: ； In the formula, Let be the three-dimensional temperature field function at any point on the dam body; As a weighting function, the temperature adjustment along the left and right banks tends to adjust the temperature of the dam body closer to the bank. For the left bank along the elevation The average temperature adjustment function; The right bank along the elevation The average temperature adjustment function; For the left bank along the elevation The linear temperature difference adjustment function; The right bank along the elevation The linear temperature difference adjustment function.

8. The four-dimensional spatiotemporal distribution model of concrete arch dam body temperature based on multi-point measured temperature as described in claim 1, characterized in that... In step S5, the spatial association constraint is: ； ； In the formula, The ( ) section Temperature at ) coordinate points; The ( ) section Temperature at ) coordinate points; ; This is the average temperature adjustment value; The upper limit of the average temperature adjustment value is set between 2 and 4. ; This is the linear temperature difference adjustment value; The upper limit of the linear temperature difference adjustment value is set to 2~4. ; Temporal correlation constraints can be applied to undetermined variables in adjacent time periods of 5 days, as follows: ； ； In the formula, For the ( ) coordinate points in Temperature at any moment; For the ( ) coordinate points in Temperature at any moment; This represents the threshold for temperature parameter changes between adjacent time periods. ; For the first Average temperature adjustment parameters for the time period; For the first Average temperature adjustment parameters for the time period; The threshold for the average adjustment value change over adjacent time periods. ; For the first Linear temperature difference adjustment parameters for different time periods; For the first Linear temperature difference adjustment parameters for different time periods; This is the threshold for adjusting the temperature difference between adjacent time periods. .

9. The four-dimensional spatiotemporal distribution model of concrete arch dam body temperature based on multi-point measured temperature as described in claim 1, characterized in that... In step S6, the parameters are inverted to... , and A total of 48 parameters were identified as undetermined variables in the inversion analysis. The least squares method, based on the difference between the fitted and measured values, was used to obtain the parameters from the measured temperature values ​​through inversion. , and Thus, the four-dimensional temperature field function of the entire dam is obtained.

10. The four-dimensional spatiotemporal distribution model of concrete arch dam body temperature based on multi-point measured temperature as described in claim 1, characterized in that... In step S7, the temperature fluctuation range is distinguished from the temperature fluctuation range by fitting the temperature difference. The threshold for the large fluctuation range is 2~3℃, and the threshold for the small fluctuation range is 1~2℃.

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