Concrete temperature field detection method based on adaptive gradient compensation

Abstract

The invention discloses a concrete temperature field detection method based on adaptive gradient compensation, and relates to the field of concrete temperature field detection.The method comprises the steps that it is assumed that concrete is a homogeneous isotropic medium, and gradient distribution (three-dimensional non-uniform temperature gradient) of a three-dimensional temperature field is extracted from discrete temperature data; interpolation is carried out on discrete temperature data based on the local gradient amplitude, the interpolation weight can be dynamically adjusted according to the local gradient amplitude, and refined reconstruction of the nonlinear temperature field is achieved; the interpolation result and the constraint of the Fourier heat conduction equation are combined to construct the target function residual error so as to obtain the target function, a dual correction mechanism of data driving and physical law can be formed, the extrapolation reliability is remarkably improved, and the accurate concrete temperature field is obtained through solving.

Description

Technical Field

[0001] This invention relates to the field of concrete temperature field detection, and specifically to a concrete temperature field detection method based on adaptive gradient compensation. Background Technology

[0002] In large-scale construction projects, the hydration reaction of concrete releases a large amount of heat. Large-volume concrete structures, such as dams, may experience significant internal and external temperature differences due to the difficulty in dissipating internal heat, generating temperature stress. This causes the concrete to expand internally and shrink externally. If the temperature exceeds the tensile strength of the concrete, it can lead to cracks and threaten structural safety. Therefore, temperature field monitoring of concrete is of great significance in engineering.

[0003] Traditional methods for detecting concrete temperature fields primarily rely on a network of temperature sensors arranged at fixed intervals, combined with linear or polynomial interpolation algorithms to reconstruct the temperature field distribution. For example, patent CN119509737A proposes a method to determine the internal temperature of a battery by solving partial differential equations based on Fourier's law of heat conduction. However, this method neglects the application of actually measurable data, i.e., it ignores the crucial data-driven aspect. However, as... Figure 2 As shown, in most cases, due to the presence of steel pipes and other equipment inside the concrete, sensor nodes cannot be uniformly arranged. Secondly, as a homogeneous material with low thermal conductivity, concrete exhibits significant nonlinear characteristics in its internal temperature gradient due to the release of hydration heat and boundary heat dissipation. This leads to inherent defects in linear interpolation methods based on uniformly spaced sensors: First, the temperature gradient within the sensor spacing is simplified to a linear change, ignoring the hysteresis and nonlinear characteristics of actual heat conduction; second, while physical models such as the finite element method can describe the temperature field through the Fourier heat conduction equation, they rely on dense mesh generation, resulting in a large number of sensors and a heavy computational burden; third, existing data-driven methods lack integration with the physical laws of heat conduction, easily leading to distortion when sensors are sparse or the environment changes abruptly. Furthermore, traditional compensation algorithms often use fixed-weight interpolation, which cannot be dynamically adjusted according to the temperature gradient amplitude, resulting in significant fluctuations in monitoring accuracy during the high-temperature hydration stage and the low-temperature stable stage. Summary of the Invention

[0004] To address the aforementioned shortcomings in existing technologies, this invention provides a concrete temperature field detection method based on adaptive gradient compensation, which solves the problem that existing technologies struggle to accurately detect concrete temperature fields.

[0005] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is: A method for detecting the temperature field of concrete based on adaptive gradient compensation is provided, which includes the following steps: Discrete temperature data is collected by temperature sensors embedded in the concrete structure. Calculate the gradient distribution of the three-dimensional temperature field based on discrete temperature data; Interpolation of discrete temperature data based on gradient distribution yields the interpolation results; Construct constraints for the Fourier heat conduction equation; Based on the interpolation results and the constraints of the Fourier heat conduction equation, the objective function residual is constructed, and the objective function is obtained by minimizing the objective function residual. Solve the objective function to complete the detection of the temperature field of concrete.

[0006] Furthermore, the specific method for calculating the gradient distribution of the three-dimensional temperature field based on discrete temperature data includes the following steps: Select a target point and construct the concrete temperature field by treating the temperature field near the target point as a linear function. The expression for the concrete temperature field is: in express The temperature field of the concrete at that location; The temperature at the target point; , and They are respectively gradient of direction gradient of direction and Gradient of direction; The coordinates of the target point; Indicates time; Construct the temperature residual function and represent it in matrix form: in This refers to the temperature residual. The first temperature sensor is deployed near the target point Temperature values ​​measured at each point; )for The coordinates of the point where the temperature value is located; Based on the temperature residual, a weight is introduced for each point where a temperature sensor is deployed near the target point. The weighted sum of squared residuals is constructed, and its expression is: in This is the weighted sum of squared residuals; The total number of points near the target point where temperature sensors are deployed; where the weights are... Inversely proportional to distance; Minimize the weighted sum of squared residuals using weighted least squares method. The gradient distribution of the three-dimensional temperature field is obtained; the expression for the gradient distribution of the three-dimensional temperature field is: in , indicating the gradient to be determined; , ; The inverse distance weight matrix, ; for Transpose of; , representing the temperature field value difference vector.

[0007] Furthermore, the specific method for interpolating discrete temperature data based on gradient distribution is as follows: Interpolating discrete temperature data using radial basis functions is expressed as follows: in Indicating concrete structures Interpolation result at the location; These are the weighting coefficients; The number of basis functions, i.e., the number of basis functions selected in the concrete structure that are related to... The number of temperature sensors near the location; are basis functions; ) indicates the selected concrete structure that is similar to The location near the first The coordinates of the points where temperature sensors are installed; To support the radius, , and For custom parameters, , and They represent ) Location at The square of the gradient in the direction Sum of squares of gradients in direction The square of the gradient in the direction.

[0008] Furthermore, the constraint expression for the Fourier heat conduction equation is: in The position vector of the target point; For gradient operators; The temperature at the target point; The density of concrete; This refers to the specific heat capacity of concrete. is the thermal diffusivity.

[0009] Furthermore, the expression for the residual of the objective function is: in The residual of the objective function; For the first concrete structure The predicted temperature value at each temperature sensor location, i.e., the temperature value obtained by interpolation; For the first concrete structure The actual temperature value at each temperature sensor location; For regularization parameters; Representation space.

[0010] Furthermore, the expression for the objective function is: in The number of polynomial basis functions; For coefficient vectors; This indicates that the input data is the first... Location of each sensor exist The combined basis functions of temperature measurements at any given time; It is a constant, taking values ​​from 1 to... ; This indicates that the input data is the first... Location of each sensor exist The combined basis functions of the temperature measurements at time points, including the basis functions... and polynomial basis functions; express Time and The time difference between moments.

[0011] Furthermore, when solving the objective function, the temperature of the concrete structure surface is used as the boundary temperature.

[0012] Furthermore, the temperature sensors embedded in the concrete structure are spaced 1 to 3 meters apart.

[0013] Furthermore, the area near the target point is the space covered by a sphere with the target point as the center and a radius of 10 meters.

[0014] Furthermore, basis functions The Wendland tight support function is used.

[0015] The beneficial effects of this invention are as follows: This invention assumes that concrete is a homogeneous and isotropic medium, extracts the gradient distribution of the three-dimensional temperature field (three-dimensional non-uniform temperature gradient) from discrete temperature data, and interpolates the discrete temperature data based on this. The interpolation weight can be dynamically adjusted according to the local gradient amplitude to achieve a refined reconstruction of the nonlinear temperature field. By combining the interpolation results with the constraints of the Fourier heat conduction equation to construct the objective function residual and then obtain the objective function, a dual correction mechanism of "data-driven + physical law" can be formed, which significantly improves the reliability of extrapolation and obtains an accurate concrete temperature field. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating the method. Figure 2 A schematic diagram of a temperature sensor embedded in a concrete structure; Figure 3 This is a temperature field contour map of concrete. Detailed Implementation

[0017] The specific embodiments of the present invention are described below to facilitate understanding of the present invention by those skilled in the art. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations utilizing the concepts of the present invention are protected.

[0018] like Figure 1 As shown, the concrete temperature field detection method based on adaptive gradient compensation includes the following steps: S1. Collect discrete temperature data by temperature sensors embedded in the concrete structure; S2. Calculate the gradient distribution of the three-dimensional temperature field based on discrete temperature data; S3. Interpolate the discrete temperature data based on the gradient distribution to obtain the interpolation result; S4. Constructing constraints for the Fourier heat conduction equation; S5. Based on the interpolation results and the constraints of the Fourier heat conduction equation, construct the objective function residual, and obtain the objective function by minimizing the objective function residual; S6. Solve for the objective function to complete the detection of the concrete temperature field.

[0019] In this embodiment, it is assumed that the concrete is a homogeneous and isotropic medium. Taking a small element within the medium, we can apply the law of conservation of energy as follows: in The heat flowing into the concrete; The heat dissipated by the internal heat source of the concrete; The heat that causes the concrete temperature to rise.

[0020] By introducing the heat flux density vector and combining it with Fourier's law of heat conduction—that heat flows from a high temperature area to a low temperature area, and the amount of heat flowing in a certain direction is proportional to the rate of temperature decrease in that direction—the Fourier equation of heat conduction can be derived: in It refers to the heat flowing out of a heat source per unit volume per unit time.

[0021] The specific method for calculating the gradient distribution of the three-dimensional temperature field based on discrete temperature data in step S2 includes the following steps: S2-1. Select a target point and construct the concrete temperature field by treating the temperature field near the target point as a linear function. The expression for the concrete temperature field is: in express The temperature field of the concrete at that location; The temperature at the target point; , and They are respectively gradient of direction gradient of direction and Gradient of direction; The coordinates of the target point; Indicates time; S2-2. Construct the temperature residual function and express it in matrix form: in This refers to the temperature residual. The first temperature sensor is deployed near the target point Temperature values ​​measured at each point; )for The coordinates of the point where the temperature value is located; S2-3. Based on the temperature residual, introduce weights for each point where a temperature sensor is deployed near the target point. The weighted sum of squared residuals is constructed, and its expression is: in This is the weighted sum of squared residuals; The total number of points near the target point where temperature sensors are deployed; where the weights are... It is inversely proportional to the distance and Gaussian weights can be used; S2-4. Minimize the weighted sum of squared residuals using the weighted least squares method. The gradient distribution of the three-dimensional temperature field is obtained; the expression for the gradient distribution of the three-dimensional temperature field is: in , indicating the gradient to be determined; , ; The inverse distance weight matrix, ; for Transpose of; , representing the temperature field value difference vector.

[0022] The specific method for interpolating discrete temperature data based on gradient distribution in step S3 is as follows: Interpolating discrete temperature data using radial basis functions is expressed as follows: in Indicating concrete structures Interpolation result at the location; These are the weighting coefficients; The number of basis functions, i.e., the number of basis functions selected in the concrete structure that are related to... The number of temperature sensors near the location; The basis functions are Wendland compact support functions. ) indicates the selected concrete structure that is similar to The location near the first The coordinates of the points where temperature sensors are installed; To support the radius, , and For custom parameters, , and They represent ) Location at The square of the gradient in the direction Sum of squares of gradients in direction The square of the gradient in the direction can be used to adaptively adjust the interpolation weights according to the local temperature gradient, and the interpolation weights can be dynamically adjusted by the gradient magnitude.

[0023] The expression for the constraint of the Fourier heat conduction equation in step S4 is: in The position vector of the target point; For gradient operators; The temperature at the target point; The density of concrete; This refers to the specific heat capacity of concrete. is the thermal diffusivity.

[0024] In this embodiment, the objective function residual is defined. The objective function residual is a weighted sum of the data fitting error and the physical residual. Therefore, the expression for the objective function residual in step S5 is: in The residual of the objective function; For the first concrete structure The predicted temperature value at each temperature sensor location, i.e., the temperature value obtained by interpolation; For the first concrete structure The actual temperature value at each temperature sensor location; This is a regularization parameter that controls the strength of physical constraints; Representation space.

[0025] The expression for the objective function in step S5 is: in The number of polynomial basis functions; For coefficient vectors; This indicates that the input data is the first... Location of each sensor exist The combined basis functions of temperature measurements at any given time; It is a constant, taking values ​​from 1 to... ; This indicates that the input data is the first... Location of each sensor exist The combined basis functions of the temperature measurements at time points, including the basis functions... and polynomial basis functions; express Time and The time difference between moments.

[0026] In the specific implementation process, in order to further improve the detection accuracy, the temperature of the concrete structure surface can be used as the boundary temperature when solving the objective function.

[0027] In this embodiment, temperature sensor nodes are arranged along a three-dimensional space inside the concrete structure (such as a dam), with a node spacing of 2-3 meters, and the spacing is reduced to 1 meter in the boundary area. Each node must include: a temperature sensor (accuracy ±0.1℃, sampling frequency 1 / 30 Hz), a three-dimensional coordinate positioning module (error ≤5cm), and a wireless transmission module (synchronization timestamp error ≤5ms). An auxiliary thermometer is placed at the external boundary to measure the ambient temperature and surface heat dissipation rate. Input parameters include concrete density, thermal conductivity, and specific heat capacity; the hydration heat source value must be experimentally determined. The space near the target point is covered by a sphere with a radius of 10 meters centered at the target point. By inputting the collected discrete temperature data into this method, the corresponding concrete temperature field cloud map can be output. Figure 3 As shown, the interpolation result of using multiple basis functions to interpolate the interpolation points in this embodiment highly coincides with the original line, proving the effectiveness of this method.

[0028] In practical implementation, traditional temperature field detection methods rely solely on sensor node data, neglecting the physical laws of heat conduction in concrete. When the sensor spacing is large (>2 meters), due to the nonlinear characteristics of heat conduction, the interpolation results can deviate from the actual temperature field by more than ±2℃, and it cannot capture sub-meter-level local temperature gradients. This invention employs a dual-drive architecture, embedding the Fourier heat conduction equation as a physical constraint term into the data interpolation process, forming a fusion model of "data-driven term + physical constraint term," ensuring that the reconstructed temperature field simultaneously satisfies both sensor measurements and the laws of heat conduction.

[0029] Traditional interpolation algorithms use static parameters, which cannot adapt to the dynamic changes in temperature gradients during concrete hydration. For example, during the peak of hydration heat release, the temperature gradient can reach 5℃ / m, while during the heat dissipation stage, the gradient drops to below 0.5℃ / m. Fixed-weight interpolation leads to undercompensation in the high-temperature stage and overcompensation in the low-temperature stage. This method uses gradient-sensitive weights and designs an adaptive radial basis function, whose weight coefficients can be dynamically adjusted according to the local gradient magnitude. In high-temperature gradient regions (such as areas of concentrated hydration heat), the algorithm automatically enhances the gradient compensation intensity and suppresses the dependence of the interpolation results on far nodes; in low-temperature gradient regions, the compensation range is widened to maintain smoothness.

[0030] Traditional temperature field detection methods rely on high-precision temperature field reconstruction schemes based on the finite element method or machine learning. These methods depend on high-performance computing equipment (such as GPU clusters) or dense sensor networks (spacing <0.3 meters), resulting in high hardware costs and difficulty in real-time application on construction sites. This method employs lightweight physical constraints: the Fourier heat conduction equation is discretized into regularization terms, which are then combined with data interpolation terms to construct an optimization problem for rapid solution. The computation time is reduced by 90% compared to the finite element method, and it can run in real-time on low-power processors. Only conventional sensor density is required for detection, avoiding construction interference and increased costs associated with deploying ultra-dense sensor networks.

Claims

1. A method for detecting the temperature field of concrete based on adaptive gradient compensation, characterized in that, Includes the following steps: Discrete temperature data is collected by temperature sensors embedded in the concrete structure. Calculate the gradient distribution of the three-dimensional temperature field based on discrete temperature data; Interpolation of discrete temperature data based on gradient distribution yields the interpolation results; Construct constraints for the Fourier heat conduction equation; Based on the interpolation results and the constraints of the Fourier heat conduction equation, the objective function residual is constructed, and the objective function is obtained by minimizing the objective function residual. Solve the objective function to complete the detection of the temperature field of concrete.

2. The method for detecting concrete temperature field based on adaptive gradient compensation according to claim 1, characterized in that, The specific method for calculating the gradient distribution of a three-dimensional temperature field based on discrete temperature data includes the following steps: Select a target point and construct the concrete temperature field by treating the temperature field near the target point as a linear function. The expression for the concrete temperature field is: in express The temperature field of the concrete at that location; The temperature at the target point; , and They are respectively gradient of direction gradient of direction and Gradient of direction; The coordinates of the target point; Indicates time; Construct the temperature residual function and represent it in matrix form: in This refers to the temperature residual. The first temperature sensor is deployed near the target point Temperature values ​​measured at each point; )for The coordinates of the point where the temperature value is located; Based on the temperature residual, a weight is introduced for each point where a temperature sensor is deployed near the target point. The weighted sum of squared residuals is constructed, and its expression is: in This is the weighted sum of squared residuals; The total number of points near the target point where temperature sensors are deployed; where the weights are... Inversely proportional to distance; Minimize the weighted sum of squared residuals using weighted least squares method. The gradient distribution of the three-dimensional temperature field is obtained; the expression for the gradient distribution of the three-dimensional temperature field is: in , indicating the gradient to be determined; , ; The inverse distance weight matrix, ; for transpose; , representing the temperature field value difference vector.

3. The method for detecting concrete temperature field based on adaptive gradient compensation according to claim 2, characterized in that, The specific method for interpolating discrete temperature data based on gradient distribution is as follows: Interpolating discrete temperature data using radial basis functions is expressed as follows: in Indicating concrete structures Interpolation result at the location; These are the weighting coefficients; The number of basis functions, i.e., the number of basis functions selected in the concrete structure that are related to... The number of temperature sensors near the location; are basis functions; ) indicates the selected concrete structure that is related to The location near the first The coordinates of the points where temperature sensors are installed; To support the radius, , and For custom parameters, , and They represent ) Location at The square of the gradient in the direction, Sum of squares of the gradient in the direction The square of the gradient in the direction.

4. The method for detecting concrete temperature field based on adaptive gradient compensation according to claim 3, characterized in that, The constraint expression for the Fourier heat conduction equation is: in The position vector of the target point; For gradient operators; The temperature at the target point; The density of concrete; This refers to the specific heat capacity of concrete. is the thermal diffusivity.

5. The method for detecting concrete temperature field based on adaptive gradient compensation according to claim 4, characterized in that, The expression for the residual of the objective function is: in The residual of the objective function; For the first concrete structure The predicted temperature value at each temperature sensor location, i.e., the temperature value obtained by interpolation; For the first concrete structure The actual temperature value at each temperature sensor location; For regularization parameters; Representation space.

6. The method for detecting concrete temperature field based on adaptive gradient compensation according to claim 5, characterized in that, The expression for the objective function is: in The number of polynomial basis functions; For coefficient vectors; This indicates that the input data is the first... Location of each sensor exist The combined basis functions of temperature measurements at any given time; It is a constant, taking values ​​from 1 to... ; This indicates that the input data is the first... Location of each sensor exist The combined basis functions of the temperature measurements at time points, including the basis functions... and polynomial basis functions; express Time and The time difference between moments.

7. The method for detecting concrete temperature field based on adaptive gradient compensation according to claim 1, characterized in that, When solving the objective function, the temperature of the concrete structure surface is used as the boundary temperature.

8. The method for detecting concrete temperature field based on adaptive gradient compensation according to claim 1, characterized in that, The spacing between temperature sensors embedded in concrete structures is 1 to 3 meters.

9. The method for detecting concrete temperature field based on adaptive gradient compensation according to claim 2, characterized in that, The area near the target point is the space covered by a sphere with a radius of 10 meters centered at the target point.

10. The method for detecting the concrete temperature field based on adaptive gradient compensation according to claim 3, characterized in that, basis functions The Wendland tight support function is used.

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