A method and system for reconstructing a three-dimensional temperature field of a container stacking structure based on multi-medium heat transfer topology constraints

Abstract

The application provides a kind of based on the reconstruction method and system of three-dimensional temperature field of stacking box structure of multi-medium heat transfer topological constraint, applied to hydraulic concrete structure monitoring, heat transfer modeling and three-dimensional field reconstruction technical field. Obtain structure temperature measurement data and air temperature, wind speed, solar radiation and box medium temperature, complete time synchronization and abnormal processing;Three-dimensional structure is dispersed and heat transfer topological graph is established according to concrete, liquid and gas area, and the Euclidean distance is replaced by path equivalent thermal resistance, combined with longitudinal attenuation and dynamic boundary node calculation composite weight;Through independent calibration test point calibration parameter and traverse grid, output dynamic three-dimensional temperature field with credibility identification. The application can inhibit non-physical interpolation across cavity, across wall, and is suitable for temperature monitoring and safety analysis of stacking box aqueduct and other structures.

Description

Technical Field

[0001] This invention relates to the fields of monitoring, heat transfer modeling, and three-dimensional field reconstruction of hydraulic concrete structures, and particularly to a method and system for reconstructing the three-dimensional temperature field of a stacked box structure based on multi-medium heat transfer topological constraints. Background Technology

[0002] A stacked box girder structure is a concrete box-shaped structure formed by two or more adjacent chambers. It can be applied to aqueducts, water conveyance culverts, bridge box girders, and other hydraulic or civil engineering structures with multi-cavity structures. Taking a stacked box girder aqueduct as an example, the upper chamber can be used for water conveyance, while the lower chamber can serve as an air circulation chamber or maintenance chamber. The concrete structure, the liquid inside the chamber, the gas inside the chamber, and the external environment together constitute a multi-medium heat transfer system.

[0003] The top slab, bottom slab, web, cell junctions, and rigid frame nodes of a stacked box structure possess different geometric dimensions, boundary exposure conditions, and thermal inertia. Under the combined influence of solar radiation, ambient air temperature, wind speed, liquid temperature, and internal heat sources, the internal temperature of the structure exhibits significant spatiotemporal nonuniformity. Temperature gradients and temperature differences between the inner and outer surfaces further affect temperature stress, deformation, and crack risk; therefore, obtaining a continuous and reliable three-dimensional temperature field under limited measurement points is necessary.

[0004] Existing temperature field reconstruction methods typically employ inverse distance weighting, radial basis functions, Kriging interpolation, or correction of finite element calculation results. Ordinary spatial interpolation primarily assigns weights based on the Euclidean distance between the measurement point and the prediction point. When two points are geometrically close but separated by box walls, cavities, or different media, they may still be assigned a large weight, resulting in non-physical temperature propagation across cavities, walls, or non-connected media.

[0005] Existing technologies correct for different media by setting fixed material weights or fixed boundary temperatures. However, fixed weights are difficult to characterize the combined effects of heat transfer path length, contact area, and interfacial thermal resistance. Fixed water temperature, air temperature, or convection coefficients also cannot reflect the boundary conditions of the actual environment that change over time. Furthermore, directly using a preset temperature difference threshold to forcibly modify the reconstruction results may mask real temperature anomalies and make it difficult to form independent verification of reconstruction accuracy.

[0006] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0007] Other features and advantages of this application will become apparent from the following detailed description, or may be learned in part by practice of the invention.

[0008] According to one aspect of this application, a method for reconstructing the three-dimensional temperature field of a stacked box structure based on multi-medium heat transfer topology constraints is provided, comprising: acquiring a three-dimensional geometric model of the stacked box structure, temperature measurement points of the structure, and boundary environment monitoring data; solidifying multi-medium heat transfer parameters, measurement point layout rules, and boundary equivalent temperature calculation standards; relying on the principles of heat transfer topology constraints, dynamic boundary adaptation, and independent verification and calibration, clarifying the target functional boundaries of data preprocessing, geometric discretization partitioning, heat transfer topology construction, composite weight calculation, and parameter calibration and verification; setting an effective thermal resistance threshold and a dual-constraint threshold for reconstruction root mean square error; determining rigid reconstruction rules that propagate along the actual heat transfer contact path and verify the independent measurement points; constructing a six-layer closed-loop reconstruction system of data preprocessing-geometric partitioning-topology construction-temperature solution-verification and calibration-result output; and formulating minimum thermal resistance path calculation standards and media... The system includes zoning identification rules and dynamic update specifications for boundary nodes to suppress non-physical cross-zone weighted errors. It divides the structural regions into two levels of reconstruction accuracy standards: conventional and refined. For the junctions of enclosures, rigid frame nodes, and media interfaces, it implements refined measurement points and detailed mesh subdivision, establishing a control system with traceable parameters, quantifiable errors, and tiered reliability throughout the entire process. Based on the structural geometric characteristics, measurement point distribution, and target spatial resolution, it matches the mesh discrete scale and uses a unified shortest path algorithm to solve for the minimum thermal resistance path, aggregating multi-source environmental and structural monitoring data for collaborative calculation. For three types of anomalies—cross-zone non-physical interpolation, composite weight deviation, and parameter calibration mismatch—it employs differentiated resolution mechanisms, including tiered configuration of topological path constraints, residual verification of heat dissipation balance, and parameter recalibration in low-reliability areas. It also fully retains the reconstruction parameters, verification errors, and reliability identification fields for full-process traceability.

[0009] Another aspect of this application is a three-dimensional temperature field reconstruction system for a stacked box structure based on multi-medium heat transfer topology constraints, used to execute executable instructions to implement the above-described three-dimensional temperature field reconstruction method for a stacked box structure based on multi-medium heat transfer topology constraints.

[0010] According to another aspect of this application, an electronic device includes: a first processor; and a memory for storing executable instructions of the first processor; wherein the first processor is configured to execute the above-described method for reconstructing the three-dimensional temperature field of a stacked box structure based on multi-medium heat transfer topology constraints by executing the executable instructions.

[0011] According to another aspect of this application, a computer-readable storage medium is provided, on which a computer program is stored, which, when executed by a second processor, implements the above-described method for reconstructing the three-dimensional temperature field of a stacked box structure based on multi-medium heat transfer topology constraints.

[0012] The beneficial technical effects of this application are as follows: Replacing the simple Euclidean distance with the minimum equivalent thermal resistance path in the heat transfer topology diagram allows the influence of source nodes to propagate along the actually permissible heat transfer path in the structure, reducing erroneous weighting across cavities, walls, and non-connected media. Incorporating path length, heat transfer area, medium thermal conductivity, interface thermal resistance, and longitudinal position into a composite influence weighting system adapts to the geometric characteristics of stacked box structures with multiple chambers, multiple media, and longitudinal extension. It transforms ambient air temperature, wind speed, solar radiation, liquid temperature, and internal gas temperature into dynamic boundary nodes, enabling multi-source environmental monitoring data to directly participate in temperature field reconstruction, avoiding the problem of fixed boundary temperatures failing to reflect on-site changes.

[0013] Furthermore, this application utilizes independently verified measuring points to calibrate parameters, and combines the residual from heat dissipation balance with data integrity rate to evaluate reliability. This ensures that the reconstruction accuracy evaluation and engineering threshold judgment are independent of each other, facilitating the identification of areas with insufficient measuring points, boundary anomalies, and decreased model applicability. It is applicable to stacked box culverts, stacked box culverts, bridge box-type components with upper and lower chambers, and other multi-cavity concrete structures. It can dynamically update the three-dimensional temperature field according to the sampling cycle, providing a data foundation for temperature stress analysis, crack risk assessment, temperature-controlled curing, and operational monitoring.

[0014] It should be understood that the above general description and the following detailed description are merely examples, explanatory and not intended to limit this disclosure. Attached Figure Description

[0015] Figure 1 The flowchart illustrates a method for reconstructing the three-dimensional temperature field of a stacked box structure based on multi-medium heat transfer topology constraints, according to an embodiment of this application. Figure 2 This is a schematic diagram of the cross-sectional medium zoning and measuring point arrangement of a stacked box structure. Figure 3 This is a schematic diagram of a heat transfer topology and the path with minimum equivalent thermal resistance. Figure 4 This is a schematic diagram of a parameter calibration process driven by an independent calibration measurement point. Figure 5 This is a schematic diagram of a three-dimensional temperature field mesh for a stacked box structure. Detailed Implementation

[0016] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0017] In one implementation, Figure 1 A schematic flowchart of a three-dimensional temperature field reconstruction method for a stacked box structure based on multi-medium heat transfer topology constraints, according to an embodiment of this application, is shown.

[0018] S101: Acquire the three-dimensional geometric model of the stacked box structure, structural temperature measurement points and boundary environment monitoring data, and solidify the multi-medium heat transfer parameters, measurement point layout rules and boundary equivalent temperature calculation standards.

[0019] In one implementation, a three-dimensional geometric model of the stacked box structure is used to provide the spatial geometric reference for the reconstructed object, clarifying the spatial positions of the structural entities, cavities, and media interfaces. The model must completely include all geometric elements such as concrete walls, box cavities, rigid frame nodes, and media interfaces, and adopt a unified three-dimensional Cartesian coordinate system with the horizontal axis as the x-axis, the vertical axis as the y-axis, and the longitudinal axis as the z-axis, with the unit of length being meters. In practical applications, structural models in industrial design or building information model formats can be directly read to extract core parameters such as geometric contours, wall thickness, and cavity dimensions.

[0020] Taking a segment of a stacked box aqueduct as an example, the corresponding 3D model includes two independent chambers, an upper chamber for water conveyance and a lower chamber for maintenance and ventilation. The model accurately records the thickness of the top plate (0.5 m), bottom plate (0.6 m), and web plate (0.5 m), the chamfer dimensions and reinforcement length of the rigid frame nodes at the chamber junctions, and the spatial coordinate ranges of three interfaces: liquid and concrete, gas and concrete, and external environment and structural surface. The model has a total length of 30 m, a total width of 8 m, and a total height of 6 m. This model will be directly used for subsequent mesh discretization and media partitioning, serving as the spatial carrier for constructing the heat transfer topology. Acquiring structural temperature measurement data provides measured temperature source data within the structure, which is the core constraint for temperature field reconstruction. Each measurement data point must include four core fields: spatial coordinates of the measurement point, acquisition time, temperature value, and the structural region to which the measurement point belongs. All measurement points use a unified network time synchronization benchmark to ensure that the time dimensions of data from different measurement points are aligned.

[0021] Taking the same section of the stacked box aqueduct as an example, a total of 128 structural temperature measuring points are deployed throughout the section. Each measuring point corresponds to a unique three-dimensional spatial coordinate. The sampling period is set to 1 hour, and each acquisition record carries a millisecond-level timestamp, while also indicating the top plate, bottom plate, web plate, box junction, or rigid frame node area to which the measuring point belongs. All measuring points are deployed in three layers along the wall thickness direction, corresponding to positions near the inner surface, the middle of the structure, and near the outer surface, respectively, to capture temperature gradient changes along the wall thickness direction. After the measuring point data is aggregated through the transmission link, it will enter the preprocessing stage to complete time sequence alignment and anomaly cleaning, and finally serve as the source node input for temperature calculation. Boundary environment monitoring data acquisition provides environmental parameters of the surrounding and internal media of the structure for calculating dynamic boundary temperatures. The monitoring items include at least five categories: ambient air temperature, wind speed, solar radiation intensity, internal liquid medium temperature, and internal gas medium temperature. All monitoring equipment and structural temperature measuring points share the same time reference.

[0022] Taking this aqueduct project as an example, an environmental monitoring station is set up in an open area around the structure to collect air temperature, wind speed, and solar radiation intensity every hour; three water temperature measuring points are set at different depths in the upper water conveyance chamber to collect the liquid temperature of different water layers; and one gas temperature measuring point is set at the middle and top of the lower maintenance chamber to collect the gas temperature inside the chamber. All monitoring data are aggregated to the central computing unit via wired or wireless transmission links, providing real-time input for subsequent dynamic boundary equivalent temperature calculations and supporting synchronous updates of boundary node temperatures as the environment changes. Data preprocessing rules solidify the time alignment, anomaly identification, and missing data handling standards for multi-source data, ensuring the consistency and validity of input data. All rules are uniformly executed and reused throughout the process.

[0023] The first is the time alignment rule. Structural temperature measurement data and boundary environment monitoring data are mapped to a pre-defined unified time series according to the acquisition timestamp. For data with time deviations within the time tolerance, the most recent timestamp is used for matching; for data with time deviations exceeding the tolerance, linear interpolation is used to map to a unified time. Taking a 1-hour sampling period as an example, the time tolerance is set to 5 minutes. Measurement data with deviations within 5 minutes are directly matched to the whole time, while data exceeding the range are obtained by linear interpolation of data from two consecutive sampling times to obtain the temperature value at the corresponding time.

[0024] The second is the abnormal data identification rule. For each structural temperature measurement point, the lower quartile, upper quartile, and interquartile range are calculated within a preset sliding time window. Data points below the lower quartile minus 1.5 times the interquartile range, or above the upper quartile plus 1.5 times the interquartile range, are marked as candidate abnormal data. The rate of temperature change of the candidate abnormal data relative to the temperature data at adjacent valid time points is further calculated. When the rate of temperature change exceeds a preset rate of change threshold, the candidate abnormal data is confirmed as abnormal data. Taking a 24-hour sliding window and a rate of change threshold of 5 degrees Celsius per hour as an example, data points exceeding the statistical distribution and with hourly temperature changes exceeding 5 degrees Celsius are judged as abnormal and not included in subsequent reconstruction calculations. This dual discrimination rule can distinguish between sensor noise glitches and real rapid temperature change events, avoiding the accidental deletion of valid data.

[0025] Thirdly, there are rules for handling missing data. For data with a consecutive missing duration not exceeding a preset missing duration threshold, linear interpolation is used to fill in the missing data using valid temperature data from the same measurement point before and after the missing period. For data with a consecutive missing duration exceeding the preset missing duration threshold, the corresponding structural temperature measurement point is removed from the source node set participating in temperature field reconstruction during the corresponding missing period. Taking a missing duration threshold of 4 hours as an example, measurement points missing for 2 hours are filled in using valid data before and after the missing period, while the data quality coefficient of that measurement point is reduced accordingly. Measurement points with a consecutive missing duration of 6 hours are removed from the source node set during this period and do not participate in temperature weight calculation.

[0026] Fourthly, the data quality coefficient determination rules. The source node data quality coefficient ranges from 0 to 1, and is determined comprehensively based on four dimensions: data integrity rate, sensor self-test status, recent noise level, and time alignment error. The lower the data integrity rate, the more abnormal the self-test, the higher the recent noise level, and the greater the time alignment error, the lower the corresponding data quality coefficient. The data quality coefficient is calculated using a weighted average method, and the expression is: ,in, This is the data integrity rate component coefficient, and its value is equal to the data integrity rate within the corresponding statistical period of the measurement point. This is the sensor self-test sub-factor coefficient, which is 1 when the self-test is normal and 0.3 when the self-test is abnormal; This is the noise level factor, calculated based on the ratio of the standard deviation of the data within the statistical period to the normal level. It is set to 1 under the normal level, and the higher the noise, the lower the value. This is the factor for time alignment error. It is set to 1 when the alignment error is less than the time tolerance, and the value decreases as the error increases. , , , The default values ​​for the weighting coefficients of the corresponding sub-items are 0.4, 0.3, 0.2, and 0.1, respectively. All sub-item coefficients range from 0 to 1, and the final data quality coefficient ranges from 0 to 1. This coefficient will directly participate in the calculation of subsequent composite influence weights, realizing the quantitative constraint of data quality on the reconstruction results.

[0027] The standardization of multi-medium heat transfer parameters and thermal resistance calculations is crucial. This step unifies the values ​​of thermal parameters for different media and interfaces, and standardizes the calculation method for the equivalent thermal resistance of topological edges. This forms the physical basis for subsequent heat transfer topology construction, minimum thermal resistance path solving, and thermal balance verification. All parameters and calculation rules must be consistent throughout the process and cannot be arbitrarily changed. The first category of standardized core medium thermal property parameters is the thermal conductivity of the medium itself. Standardized thermal conductivity values ​​are established for the three types of core media involved in the stacked tank structure. The default thermal conductivity for concrete is 2.3 W / m / Kelvin; for water as the medium, it is 0.6 W / m / Kelvin; and for air as the medium, it is 0.026 W / m / Kelvin. If special materials or media are used in the project, the corresponding experimentally measured values ​​can be used. When parameters exhibit temperature dependence, dynamic corrections are performed using parameter curves that change linearly with temperature.

[0028] The second category is volumetric thermal property parameters. Unified solidification density and specific heat capacity parameters are used for subsequent residual verification of heat dissipation equilibrium. The concrete density is taken as 2400 kg / m³, and the specific heat capacity as 920 J / kg / Kelvin. These parameters, combined with the mesh cell volume, can calculate the heat capacity of a single mesh, thereby verifying the physical consistency of the reconstructed temperature field and determining whether there are any non-physical temperature abrupt changes. The topological edge equivalent thermal resistance calculation standard solidifies the equivalent thermal resistance as the core calculation benchmark for heat transfer topology, solidifying calculation rules for two scenarios: within the same medium and across media interfaces.

[0029] The first type consists of adjacent topological nodes within the same dielectric region. The formula for calculating the equivalent thermal resistance is as follows: ,in, This represents the equivalent heat transfer path length between adjacent topology nodes. The thermal conductivity of the corresponding medium. This represents the equivalent heat transfer area of ​​the common contact surface of adjacent grid cells. Taking two adjacent grids inside concrete as an example, the heat transfer path length is 0.2 meters, the thermal conductivity is 2.3 W / m / Kelvin, and the common heat transfer area is 0.04 square meters. Substituting these values ​​into the calculation, the equivalent thermal resistance is approximately 2.17 Kelvin / W.

[0030] The second category consists of adjacent topological nodes on both sides of different medium regions. The formula for calculating the equivalent thermal resistance is as follows: ,in, and These are the equivalent heat transfer path lengths from the two nodes to the medium interface, respectively. and These are the thermal conductivity coefficients of the media on both sides, The contact thermal resistance at the interface of the medium. This represents the equivalent heat transfer area. For interfaces with perfect contact and no gaps, the contact thermal resistance is taken as 0. For interfaces with formwork, insulation layers, construction joints, or air gaps, the contact thermal resistance is calculated based on the thickness and thermal conductivity of the corresponding materials. For well-constructed concrete-liquid interfaces, the typical range of contact thermal resistance is 0 to 0.01 Kelvin per watt (m²); for concrete-gas interfaces, the typical range is 0.02 to 0.05 Kelvin per watt (m²); and for concrete interfaces with construction joints, the typical range is 0.01 to 0.03 Kelvin per watt (m²).

[0031] Taking the interface between concrete and insulation layer as an example, the heat transfer path length on the concrete side is 0.1 meters, with a thermal conductivity of 2.3 W / m / Kelvin. The insulation layer thickness on the insulation side is 0.05 meters, with a thermal conductivity of 0.03 W / m / Kelvin. The heat transfer area is 0.04 square meters, and the interface has good contact with no additional thermal resistance. Substituting these values ​​into the calculation, the equivalent thermal resistance is approximately 52.72 Kelvin / W. For convection boundary scenarios, the formula for calculating solidified convection thermal resistance is: Where h is the convective heat transfer coefficient and A is the equivalent heat transfer area of ​​the corresponding surface. This formula is used to calculate the thermal resistance between the boundary equivalent temperature node and the structural surface mesh, and is the core basis for boundary heat transfer calculation.

[0032] The rules for setting up monitoring points have been standardized. This step unifies the standards for setting up structural temperature monitoring points, guiding the installation of monitoring points on site and providing a rule-based basis for subsequent zoned accuracy control, effective source node selection, and reliability evaluation. The first rule concerns the longitudinal section layout. At least two monitoring sections should be set up along the longitudinal direction of the structure. The spacing between the sections is determined based on the longitudinal temperature correlation length of the structure, ensuring that the temperature correlation between adjacent sections is within a reasonable range.

[0033] Taking a 30-meter-long aqueduct segment as an example, a monitoring section is set up every 10 meters, for a total of 4 monitoring sections. The measurement points on each section are arranged symmetrically, covering all key structural parts, providing data support for the calibration of the longitudinal temperature attenuation coefficient. Secondly, there is a regional hierarchical layout rule. The structural area is divided into two categories: conventional areas and densely populated areas. The junctions of box ducts, rigid frame nodes, media interfaces, structural corners, and areas of thickness variation belong to the densely populated areas, where the spacing between measurement points is significantly smaller than in conventional areas. Taking this aqueduct as an example, the spacing between measurement points in the conventional concrete solid area is controlled at 2 meters, and the spacing between measurement points at the interface between the liquid medium and concrete is controlled at 0.8 meters. Two additional measurement points are added at the rigid frame nodes to cover stress concentration locations, ensuring sufficient measurement point constraints in areas with severe temperature gradients and improving the reconstruction accuracy of key areas. Thirdly, there is a thickness-direction layout rule.

[0034] At least three layers of measuring points are set along the thickness of the concrete wall, one near the inner surface, one in the middle of the structure, and one near the outer surface, respectively, to accurately capture the temperature gradient along the wall thickness. Taking a 0.6-meter-thick web as an example, measuring points are set at distances of 0.05 meters, 0.3 meters, and 0.55 meters from the inner surface. The longitudinal and transverse coordinates of the three layers of measuring points are consistent, with only the vertical coordinates differing, providing multi-layered constraints for reconstructing the temperature distribution along the wall thickness. Finally, there is a measuring point zoning and coverage rule. The structural temperature measuring points of each monitoring section must cover at least the top slab, bottom slab, web, the junction area of ​​the box girder, and the structural corner area, ensuring that all critical stress-bearing parts of the structure are constrained by measuring points and avoiding large-area reconstruction blind spots without measuring points.

[0035] The standard for calculating the equivalent boundary temperature is solidified. This step transforms multi-source environmental monitoring data into boundary node temperatures that can be directly used in heat transfer topology calculations. It is the core calculation logic for achieving dynamic boundary adaptation and consists of three types of boundary node calculation rules and unified topology connection rules. The first type is liquid medium boundary nodes. The boundary temperature directly adopts the measured liquid temperature of the corresponding region. When the liquid flow velocity is high and the cross-sectional temperature is uniform, a unified boundary temperature is used for the same zone; when the liquid flow velocity is slow and there is obvious temperature stratification, multiple boundary nodes are set along the depth direction, each matching the measured water temperature at the corresponding depth. Taking the upper water delivery chamber as an example, when the water flow velocity in the chamber is greater than 0.5 m / s, a unified water temperature boundary value is used within the entire liquid surface height range; when the water flow velocity is less than 0.1 m / s, one boundary temperature node is set every 2 meters along the water depth, each using the measured water temperature at the corresponding depth as the node temperature, adapting to the temperature distribution characteristics under different flow states. The second type is gas medium boundary nodes. The boundary temperature adopts the measured gas temperature inside the chamber, and the convective heat transfer coefficient is determined according to the gas flow state.

[0036] The convective heat transfer coefficient is calculated using a wind speed correlation method, and the formula is as follows: Where v is the real-time wind speed, and a, b, and n are constants calibrated based on surface orientation and site conditions. For natural convection scenarios on the outer surface of concrete structures, the typical values ​​for constant a are 3 to 6 W / m² / Kelvin, b is 2 to 4 W / m² / Kelvin / m / s (power of n), and n is 0.5 to 0.8. Taking an outdoor horizontal windward surface as an example, the recommended initial values ​​are a 4.0, b 3.0, and n 0.6, which can be further calibrated and corrected based on actual field measurements. The convective heat transfer coefficient increases with increasing wind speed, and the corresponding convective thermal resistance decreases accordingly. Taking the lower maintenance cavity as an example, when the cavity is under natural ventilation and the wind speed is 0.2 m / s, the convective heat transfer coefficient is taken as 5 W / m² / Kelvin; when the cavity is under forced ventilation and the wind speed reaches 2 m / s, the convective heat transfer coefficient is updated to 12 W / m² / Kelvin. The convective thermal resistance between the corresponding boundary nodes and the structural surface is adjusted synchronously to ensure that the boundary heat transfer calculation fits the actual ventilation condition.

[0037] The third category is outer surface boundary nodes. The equivalent temperature comprehensively considers the combined effects of ambient air temperature, solar radiation, long-wave radiation, and convective heat transfer. The curing calculation formula is: ,in, For ambient temperature, The intensity of solar radiation. The surface solar radiation absorption coefficient. The net heat flux density for long-wave radiation. The coefficient of thermal transfer is time-varying. The surface solar radiation absorption coefficient is determined based on the material of the outer surface of the structure; when long-wave radiation is neglected, the net heat flux density of long-wave radiation is taken as 0.

[0038] Taking monitoring data at a specific moment as an example, with an ambient temperature of 25 degrees Celsius, a solar radiation intensity of 800 watts per square meter, a surface solar radiation absorption coefficient of 0.65, a long-wave radiation net heat flux density of 50 watts per square meter, and a convective heat transfer coefficient of 15 watts per square meter per Kelvin, the calculated equivalent surface temperature at that moment is 29 degrees Celsius. This calculation method can respond to changes in environmental parameters in real time, avoiding calculation deviations caused by fixed boundary temperatures.

[0039] Finally, the topological connection rules of the boundary nodes are solidified. Liquid medium boundary nodes only establish heat transfer connections with the mesh nodes corresponding to the liquid and concrete interface, gas medium boundary nodes only establish heat transfer connections with the mesh nodes corresponding to the gas and concrete interface, and outer surface boundary nodes only establish heat transfer connections with the mesh nodes corresponding to the outer surface of the structure. This ensures that the boundary temperature is only transferred into the structure along the actual heat transfer interface, thus avoiding non-physical cross-regional temperature propagation from the source.

[0040] S102, based on the principles of heat transfer topology constraints, dynamic boundary adaptation, and independent verification and calibration, clarifies the target functional boundaries of data preprocessing, geometric discretization partitioning, heat transfer topology construction, composite weight calculation, and parameter calibration and verification. It sets effective thermal resistance threshold and reconstruction root mean square error dual constraint threshold, and determines the reconstruction rigid rules that propagate along the actual heat transfer contact path and verify the independent measurement points.

[0041] In one implementation, based on the requirements of suppressing non-physical interpolation across cavities, adapting to time-varying environmental boundaries, and ensuring independently verifiable reconstruction accuracy, the entire process of reconstructing the three-dimensional temperature field of the stacked box structure is subjected to heat transfer topology connectivity constraints, dynamic mapping of boundary equivalent temperatures, and independent isolation of verification measurement points. The global mesh temperature is calculated through minimum equivalent thermal resistance path solving and composite influence weight normalization, generating a set of valid source nodes, mesh reconstruction temperature, verification error statistics, and credibility information. For three typical problems—interpolation distortion across cavities, rigid boundary conditions, and self-looping accuracy verification—three types of processing are performed respectively: heat transfer topology connectivity constraints, dynamic mapping of boundary equivalent temperatures, and independent isolation of verification measurement points. Finally, the global mesh temperature is calculated through minimum equivalent thermal resistance path solving and composite influence weight normalization, outputting four core types of information: a set of valid source nodes, mesh reconstruction temperature, verification error statistics, and credibility information.

[0042] The heat transfer topology connectivity constraint suppresses non-physical temperature interpolation across cavities and walls from the bottom layer of the path. Traditional spatial interpolation methods only assign measurement point weights based on Euclidean linear distance. When two points are geometrically close but separated by box walls, cavities, or non-connected media, they are still assigned higher weights, causing temperature propagation to deviate from actual heat transfer laws. This application constructs the temperature propagation path solely based on actual heat transfer contact relationships, allowing temperature effects to be transmitted between corresponding nodes only when two mesh elements share a common heat transfer contact surface.

[0043] The specific execution logic is as follows: using the center point of the grid cell, the structural temperature measurement point, and the boundary equivalent temperature node as topological nodes, topological edges are established based on the actual heat transfer contact relationship between adjacent nodes, forming a complete heat transfer topology graph. For nodes without direct heat transfer contact, no direct topological edges are established; temperature effects can only be transferred along connected solid heat transfer paths. Based on this, the minimum equivalent thermal resistance path from each source node to the grid point to be reconstructed is solved. The equivalent thermal resistance of all topological edges on the path is accumulated to obtain the thermal resistance topological distance, which is used to replace the traditional Euclidean distance as the core basis for weight allocation. The formula for calculating the thermal resistance topological distance is as follows: ,in, Let be the allowed heat transfer path from source node i to the grid point q to be reconstructed. The thermal resistance topological distance is the minimum of the sum of the equivalent thermal resistances of all topological edges in all feasible paths.

[0044] The calculation can be performed using Dijkstra's algorithm. The algorithm or other non-negative edge-weighted shortest path algorithm is implemented. Taking the upper and lower double-box structure of a stacked box aqueduct as an example, temperature measuring points are arranged on the outer wall of the upper box, and there are grid points to be reconstructed on the inner wall of the lower box. The Euclidean straight-line distance between the two points is only 0.8 meters, but there are three layers of structure in between: the bottom plate of the upper box, the cavity, and the top plate of the lower box, so there is no direct heat transfer path. This application will not establish a direct topological edge between the two points. The temperature influence can only bypass along the solid path of the rigid frame node at the junction of the box, and the total heat transfer path length reaches 3.2 meters. Moreover, it passes through multiple medium interfaces, and the cumulative equivalent thermal resistance increases significantly. The influence weight of the corresponding source node is automatically reduced, thus avoiding non-physical weighting across the cavity at the path level.

[0045] The dynamic mapping of equivalent boundary temperature adapts to time-varying environmental boundaries, avoiding the disconnect between fixed boundary temperatures and actual field conditions. The solution transforms multi-source environmental monitoring data into equivalent boundary temperature nodes that can participate in topology calculations in real time. The boundary node temperatures are updated synchronously with the monitoring data, ensuring that the reconstruction process always conforms to the current actual environmental conditions.

[0046] Boundary nodes are divided into three categories, each corresponding to different calculation and mapping rules. The first category is liquid medium boundary nodes, where the temperature is directly taken from the measured liquid temperature of the corresponding region, connected to the mesh nodes at the liquid-concrete interface through convective thermal resistance. The second category is gas medium boundary nodes, where the temperature is taken from the measured gas temperature inside the chamber, with the convective heat transfer coefficient adjusted in real time according to the gas flow state, and the convective thermal resistance updated synchronously. The third category is outer surface boundary nodes, where the equivalent temperature comprehensively considers the combined effects of ambient air temperature, solar radiation, long-wave radiation, and convective heat transfer; the calculation formula is as follows: ,in, For ambient temperature, The intensity of solar radiation. The surface solar radiation absorption coefficient. The net heat flux density for long-wave radiation. is the time-varying convective heat transfer coefficient. When long-wave radiation is neglected, the net heat flux density of long-wave radiation is taken as 0. All boundary nodes establish heat transfer connections only with the corresponding mesh nodes at the interface, ensuring that boundary heat is transferred into the structure only along the actual heat transfer surface.

[0047] Taking a real-world engineering test scenario as an example, at a certain moment, the ambient temperature is 25 degrees Celsius, the solar radiation intensity is 800 watts per square meter, the solar radiation absorption coefficient of the structural surface is taken as 0.65, the net long-wave radiation heat flux density is 50 watts per square meter, and the convective heat transfer coefficient calculated based on the real-time wind speed is 15 watts per square meter per Kelvin. Substituting these values ​​into the calculation, the equivalent temperature of the outer surface at that moment is 29 degrees Celsius. When night falls and the solar radiation intensity drops to 0, and the wind speed increases, causing the convective heat transfer coefficient to become 20 watts per square meter per Kelvin, the equivalent temperature of the outer surface will be updated synchronously to 22.5 degrees Celsius, achieving real-time dynamic adaptation of boundary conditions.

[0048] By independently isolating the verification measurement points, this mechanism ensures that the reconstruction accuracy can be independently verified, avoiding artificially high accuracy caused by verification data participating in the reconstruction calculation. The scheme designates some structural temperature measurement points as verification measurement points. These verification measurement points do not participate in the source node set of the temperature field reconstruction throughout the entire process and are only used for post-accuracy verification and parameter calibration, ensuring that the accuracy evaluation results are objective and reliable, and that there is no data self-fitting problem.

[0049] The specific execution logic is as follows: Using either a leave-one-point cross-validation or a partitioned validation method, at least one measurement point is selected as a validation point each time. The remaining structural temperature measurement points and boundary equivalent temperature nodes are used as source nodes to complete the reconstruction calculation, obtaining the reconstructed temperature at the validation point location. After traversing all validation measurement points, the deviation between the reconstructed temperature and the measured temperature at all validation points is statistically analyzed, and the overall root mean square error of the reconstruction is calculated, serving as the core indicator for accuracy evaluation. The parameter calibration process also strictly adheres to the measurement point isolation principle, using only the validation error to drive parameter optimization, and does not directly replace the reconstruction results with the measured values ​​of the validation measurement points.

[0050] Taking an aqueduct segment with 128 structural temperature measurement points as an example, when using the method of leaving one measurement point for cross-verification, each measurement point is used as a verification point in turn. The remaining 127 measurement points, along with all boundary nodes, are used as source nodes to participate in temperature reconstruction, thereby obtaining the reconstructed temperature values ​​of the 128 verification measurement points. After all traversals are completed, the overall root mean square error is calculated based on the 128 sets of reconstructed values ​​and measured values. This error index is obtained entirely from independent measurement points and can truly reflect the actual accuracy level of the reconstruction method. After completing the above three types of constraint processing, the thermal resistance topological distance from all source nodes to the grid points to be reconstructed is obtained by solving the minimum equivalent thermal resistance path. The composite influence weight is calculated by combining the thermal resistance topological distance, the longitudinal coordinate difference, and the source node data quality coefficient.

[0051] The formula for calculating the unnormalized composite influence weight is as follows: ,in, This is the source node data quality coefficient, with a value ranging from 0 to 1. The longitudinal attenuation coefficient is... and , where are the longitudinal coordinates of the source node and the grid point to be reconstructed, respectively, and p is the thermal resistance distance decay exponent. The zero-prevention constant is greater than zero. The longitudinal attenuation term is used to characterize the temperature-dependent attenuation characteristics along the longitudinal direction of the structure, the thermal resistance distance attenuation index is used to control the influence of thermal resistance distance on the weight, and the zero-prevention constant is used to avoid calculation anomalies when the thermal resistance distance is zero.

[0052] The formula for weight normalization is: ,in, is the unnormalized composite influence weight, and is the initial weight of the source node j for the grid point q to be reconstructed; This is the set of valid source nodes participating in the calculation of the q-temperature of the grid points to be reconstructed. The formula for calculating the reconstructed temperature of the grid points to be reconstructed is as follows: The reconstructed temperature of each grid point is obtained by weighted summation. Taking a certain grid point to be reconstructed as an example, the thermal resistance topological distance of the corresponding effective source node is 20 Kelvin per watt, the longitudinal coordinate difference is 2 meters, the data quality coefficient is 0.95, the longitudinal attenuation coefficient is 0.05 per meter, the thermal resistance distance attenuation exponent is 2, and the anti-zero constant is 0.01 Kelvin per watt. Substituting these values ​​into the calculation, the unnormalized weight of this source node is approximately 0.0021. There are 5 candidate source nodes. Their respective weights are calculated and normalized, and finally, the reconstructed temperature of the grid point is obtained by weighted summation.

[0053] Based on the architectural requirements of heat transfer topology constraints, dynamic boundary adaptation, and independent verification and calibration, the core process of temperature field reconstruction is modularized and functionally divided. This involves dividing the work into modules for data preprocessing, geometric discretization and partitioning, heat transfer topology construction, composite weight calculation, and parameter calibration and verification. The execution logic and data flow relationships of each module are clearly defined, forming a reconstruction execution system that collaboratively operates time-series alignment and anomaly removal, mesh generation and medium identification, topology mapping and thermal resistance calculation, weight normalization and temperature solution, and error inversion and parameter calibration. Based on the overall architectural requirements of heat transfer topology constraints, dynamic boundary adaptation, and independent verification and calibration, the core process of temperature field reconstruction is functionally divided into six independent modules. The execution logic and data flow relationships of each module are clearly defined, forming a reconstruction execution system that collaboratively operates time-series alignment and anomaly removal, mesh generation and medium identification, topology mapping and thermal resistance calculation, weight normalization and temperature solution, and error inversion and parameter calibration.

[0054] The data preprocessing module provides standardized input data for the entire process. Its core functions are to perform time synchronization, anomaly identification, missing data handling, and quality evaluation of multi-source data. The module takes raw structural temperature measurement data and boundary environment monitoring data as input. The execution logic is as follows: first, it maps data from different acquisition devices to a unified time series to achieve time alignment; then, it uses a method combining interquartile range and temperature change rate to identify abnormal data; next, it performs interpolation to complete the missing data or removes measurement points based on the duration of continuous missing data; finally, it calculates the data quality coefficient for each source node by combining data integrity rate, sensor self-check status, recent noise level, and time alignment error. The module outputs the valid monitoring dataset corresponding to the same reconstruction time and the data quality coefficients for each source node.

[0055] Taking monitoring data with a 1-hour sampling period as an example, the module first matches the collected data with deviations within 5 minutes at each measuring point to the whole time. Data exceeding the deviation range is mapped to the target time through linear interpolation. Then, a 24-hour sliding window is used to calculate the statistical distribution of each measuring point, identify candidate outliers, and finally confirm the final abnormal data by combining the hourly change rate threshold of 5 degrees Celsius. For measuring points with two consecutive hours of missing data, linear interpolation of the preceding and following data is used to fill in the gaps, while the data quality coefficient is reduced from 1.0 to 0.8; for measuring points with six consecutive hours of missing data, they are removed from the set of valid source nodes within the corresponding time period.

[0056] The Geometry and Medium Partitioning module provides the spatial carrier for heat transfer topology construction. Its core function is to complete the mesh discretization of the 3D geometric model and the identification of medium regions. The module input is a 3D geometric model of a stacked box structure. The execution logic is as follows: first, determine the mesh size of each region based on the structural geometric features, measurement point distribution, and target resolution, and perform full 3D meshing of the structure; then, identify the attributes of each mesh cell according to concrete medium region, liquid medium region, and gas medium region; finally, divide the boundary regions of each medium interface and the outer surface of the structure. The module output is a set of mesh cells with medium attributes and boundary labels.

[0057] Taking a 30-meter-long stacked box girder aqueduct segment as an example, the module discretizes the structure into a hexahedral mesh. The mesh size for the conventional concrete solid area is 0.5 meters, while the mesh size for the denser areas such as box-cell boundaries, rigid frame nodes, and medium interfaces is 0.2 meters. Approximately 680 candidate reconstructed mesh nodes are generated for the entire structure. Each mesh cell records its own spatial coordinates, volume, and the medium region it belongs to, providing a complete spatial foundation for subsequent topology construction.

[0058] The heat transfer topology construction module is the core component for implementing topological constraints. Its core function is to build a heat transfer topology graph and calculate the minimum thermal resistance path. The module takes as input a partitioned mesh set and fixed heat transfer parameters. The execution logic is as follows: First, it traverses all adjacent mesh cells to determine if a common heat transfer contact surface exists; if so, it builds the corresponding topological edge. Then, it calculates the equivalent thermal resistance of each topological edge according to two rules: same medium and cross-medium interface. Finally, it uses a shortest path algorithm to calculate the minimum equivalent thermal resistance path from all source nodes to each mesh point to be reconstructed, obtaining the full mesh thermal resistance topological distance set. The module outputs a complete heat transfer topology graph and a global thermal resistance topological distance dataset.

[0059] Taking the boundary region between the upper and lower chambers as an example, when the module traverses adjacent meshes, for adjacent meshes belonging to the same concrete region and sharing a complete contact surface, the equivalent thermal resistance of the topological edge is directly calculated using the single-medium thermal resistance formula; for meshes belonging to the concrete and liquid regions respectively and adjacent at the interface, the equivalent thermal resistance is calculated by superimposing the interface contact thermal resistance using the cross-medium thermal resistance formula; for meshes located in the upper and lower chambers respectively and adjacent only by the cavity, no topological edge is established. After all topological edges are calculated, Dijkstra's algorithm is used to solve for the minimum thermal resistance path from each source node to all connected mesh points, forming a thermal resistance topological distance matrix.

[0060] The boundary node generation module is the core unit for achieving dynamic boundary adaptation. Its core function is to generate time-varying boundary equivalent temperature nodes based on environmental monitoring data. The module takes boundary environmental monitoring data and a fixed boundary calculation standard as input. Its execution logic calculates the equivalent temperature for three types of boundaries: liquid media, gas media, and outer surfaces. It generates corresponding temperature nodes for each type of boundary and establishes heat transfer connections between the boundary nodes and the structural surface mesh according to rules. The module outputs a set of boundary equivalent temperature nodes with temperature values ​​and topological connectivity relationships.

[0061] Taking the outer surface boundary as an example, the module reads real-time monitoring data such as air temperature, wind speed, and solar radiation, calculates the current boundary temperature according to the formula for the equivalent temperature of the outer surface, matches the corresponding boundary node for each outer surface mesh unit, and establishes topological connections through convective thermal resistance. When environmental parameters are updated, the boundary node temperature is updated synchronously, realizing dynamic mapping of boundary conditions.

[0062] The temperature field reconstruction module is the core execution unit for temperature solution. Its core functions are to select effective source nodes, calculate composite influence weights, and solve for the global grid temperature. The module inputs include the thermal resistance topological distance set, synchronous effective monitoring data, source node data quality coefficients, and calibrated reconstruction parameters. The execution logic is as follows: first, select the effective source node set for each point to be reconstructed based on the effective thermal resistance threshold; then, calculate the unnormalized composite influence weight of each effective source node; next, normalize all weights; finally, obtain the reconstructed temperature of each grid point by weighted summation. The module output is the global grid reconstructed temperature field data.

[0063] Taking a grid point in a certain encrypted area as an example, the module first selects six source nodes whose thermal resistance topological distance is less than or equal to the effective thermal resistance threshold and whose data is valid. The composite weight of each source node is then calculated, with source nodes having lower weights for larger vertical distances and greater thermal resistance topological distances. After weight normalization, the measured temperature of each source node is multiplied by its corresponding weight and summed to obtain the reconstructed temperature of that grid point at the current moment.

[0064] The parameter calibration and reliability evaluation module is a closed-loop unit that ensures reconstruction accuracy and physical consistency. Its core functions are parameter calibration, error statistics, and reliability evaluation. The module's inputs are the grid reconstruction temperature, measured data from calibration points, and the heat transfer topology diagram. The execution logic is as follows: first, calculate the overall root mean square error based on the reconstruction errors of independent calibration points; then, calculate the residual distance from heat dissipation equilibrium for each grid based on the heat transfer topology diagram; next, search for the optimal parameter combination that combines the calibration error and the heat balance residual using a parameter optimization algorithm, and return the calibrated parameters to the temperature field reconstruction module for reuse; finally, combine the calibration error, the residual distance from heat dissipation equilibrium, and the data integrity rate of effective source nodes to generate a reliability identifier for each grid point. The module's outputs are the calibrated parameter set, calibration error statistics, and a global reliability identifier.

[0065] The objective function for parameter calibration includes two constraints: root mean square error (RMSE) and residual from heat dissipation equilibrium. The formula for calculating the RMSE is as follows: ,in, For the set of parameters to be calibrated, To verify the number of samples, and These are the reconstructed temperature and the measured temperature, respectively. The formula for calculating the residual from heat dissipation equilibrium is: ,in, , and These are the grid cell density, specific heat capacity, and volume, respectively. The set of adjacent nodes that are directly connected to the grid cell q through heat transfer. The equivalent thermal resistance of adjacent topological edges. The intensity of the volumetric heat source is taken as 0 when there is no internal heat source. Let be the reconstructed temperature of adjacent node j at time t; Let q be the reconstructing temperature of the mesh element q at time t.

[0066] Taking the initial parameter calibration as an example, the initial thermal resistance distance attenuation index is set to 2, the longitudinal attenuation coefficient is 0.05 per meter, and the corresponding root mean square error (RMSE) is 1.2 degrees Celsius. The module adjusts the thermal resistance distance attenuation index within the range of 0.5 to 4 and the longitudinal attenuation coefficient within the range of 0.01 to 0.2 per meter using a grid search method, while also considering the constraint requirements of residual heat dissipation balance. Ultimately, it finds the parameter combination that optimizes the overall objective, reducing the corresponding RMSE to 0.6 degrees Celsius. Simultaneously, the reliability of each grid is graded according to three evaluation indicators, with higher indicators indicating higher reliability. The six modules proceed sequentially according to the data flow order, and the output parameters of the parameter calibration module can be reused for temperature reconstruction at all subsequent times, forming a collaborative operation system of forward calculation and reverse calibration.

[0067] Combining the requirements of physical consistency, computational efficiency, and quantifiable accuracy in reconstruction, and based on the heat transfer topology connectivity characteristics and parameter calibration accuracy control indicators, a dual-dimensional control index of effective thermal resistance threshold and root mean square error in reconstruction is set. This is supplemented by physical constraints related to heat dissipation balance residuals, establishing rigid rules that heat transfer occurs only along the actual heat transfer contact path and that verification measurement points are independent and do not participate in the reconstruction calculation. The effective thermal resistance threshold control index is used to balance reconstruction calculation efficiency and physical rationality, filtering out source nodes with excessive thermal resistance or negligible actual temperature influence, thus avoiding invalid calculations. The effective thermal resistance threshold is one of the core criteria for source nodes to enter the valid set. The initial value of the effective thermal resistance threshold can be determined based on structural dimensions, medium thermal conductivity characteristics, and target accuracy requirements. The principle for setting the value is to ensure that the number of valid source nodes in the normal area meets the preset minimum requirement. For concrete structures such as stacked box aqueducts, the typical range of the initial effective thermal resistance threshold is 40 to 80 Kelvin per watt, the typical range of the upper limit of the threshold is 80 to 120 Kelvin per watt, and the typical range of the threshold widening step is 5 to 15 Kelvin per watt. When the thermal resistance topological distance from the source node to the grid point to be reconstructed exceeds this threshold, its temperature influence is assumed to be negligible and is not included in the weight calculation range.

[0068] A valid set of source nodes must simultaneously meet three conditions: first, it must be located in the same connected component of the heat transfer topology as the grid point to be reconstructed; second, its thermal resistance topological distance must not exceed the effective thermal resistance threshold; and third, it must have valid temperature data at the current reconstruction time. When the number of valid source nodes meeting the conditions for a grid point is less than the preset minimum number, the effective thermal resistance threshold is gradually increased according to a preset step size until the number of source nodes reaches the target or the threshold reaches the preset upper limit. If the number of source nodes is still insufficient after the threshold reaches the upper limit, the grid point is marked as low confidence, and distant non-connected measurement points are not forcibly introduced.

[0069] Taking a typical grid point as an example, the initial effective thermal resistance threshold is set to 50 Kelvin per watt. After screening, only 2 source nodes meet the criteria, which is less than the preset minimum of 3. The module gradually increases the threshold in increments of 10 Kelvin per watt. When the threshold is increased to 60 Kelvin per watt, the number of effective source nodes reaches 3, the threshold expansion stops, and the threshold is used to complete subsequent calculations. If the number of source nodes is still less than 3 when the threshold is increased to the upper limit of 100 Kelvin per watt, the grid point is marked as low confidence.

[0070] The reconstructed root mean square error control indicator is used to quantify the overall reconstruction accuracy, and is one of the core convergence objectives in the parameter calibration process. The root mean square error is calculated based on the reconstructed temperature and measured temperature of all independent verification measurement points, and represents the overall deviation degree between the reconstruction result and the real temperature. During the parameter calibration process, minimizing the root mean square error is always taken as one of the core objectives to search for the optimal parameter combination. When the error drops below the preset accuracy requirement, the parameter calibration is determined to be qualified. Taking the accuracy requirement of a certain project as an example, the qualified threshold of the preset reconstructed root mean square error is 0.8 degrees Celsius. The root mean square error verified under the initial parameters is 1.2 degrees Celsius, which does not meet the accuracy requirement. The parameter optimization process continuously adjusts parameters such as the thermal resistance distance attenuation index, the longitudinal attenuation coefficient, and the interface thermal resistance, until the root mean square error drops to 0.6 degrees Celsius, meeting the control requirement. The corresponding parameter combination at this time is used as the final calibrated parameter for the global reconstruction calculation.

[0071] As a supplement to the dual indicators, the discrete heat balance residual physical constraint ensures the rationality of the reconstruction result from the level of heat transfer physical law, and avoids non-physical temperature mutations caused by pure data fitting. The discrete heat balance residual is calculated based on the principle of conservation of energy. For a single grid cell, the heat storage change per unit time shall be equal to the sum of the net heat transferred through adjacent topological edges and the heat generated by the internal heat source. The larger the absolute value of the residual, the more the reconstruction result deviates from the physical heat transfer law. Taking a concrete grid cell without internal heat sources as an example, the cell volume is 0.125 cubic meters, the density is 2400 kilograms per cubic meter, the specific heat capacity is 920 joules per kilogram per Kelvin, the time step is 1 hour, and the temperature difference between the current moment and the previous moment is 0.5 degrees Celsius. The calculated heat storage change per unit time is about 38.3 watts. At the same time, the net heat transferred by all adjacent grids through the topological edges is calculated to be about 39.8 watts, and the difference between the two, that is, the residual, is about 1.5 watts, with a relative deviation of less than 5%, which meets the physical consistency requirement.

[0072] On the basis of the three types of control indicators, two rigid rules that cannot be broken throughout the whole process are established. The first rule is that temperature propagates only along the actual heat transfer contact paths, that is, the temperature influence of all source nodes can only be transmitted through topological edges with direct heat transfer contact, and any direct weighted calculation across cavities, walls, or non-connected media is prohibited, so as to completely block non-physical interpolation paths at the bottom of the topology. The second rule is that the verification measurement points are independent and do not participate in the reconstruction calculation, that is, all measurement points designated for verification purposes shall not be added to the set of source nodes for temperature reconstruction throughout the whole process, and shall not directly participate in weight calculation and temperature solving, and can only be used for post-event accuracy verification and parameter calibration, so as to ensure that the accuracy evaluation is completely independent and there is no risk of overfitting.

[0073] S103 establishes a six-layer closed-loop reconstruction system consisting of data preprocessing, geometric partitioning, topology construction, temperature calculation, verification and calibration, and result output. It also formulates minimum thermal resistance path calculation standards, medium partitioning identification rules, and boundary node dynamic update specifications to suppress non-physical cross-region weighted errors.

[0074] In one implementation, based on the requirements of suppressing non-physical cross-regional weighting, ensuring the consistency of reconstructed physical properties, and outputting a temperature field with a credibility label, a full-process processing is performed on the multi-source monitoring data and 3D geometric model of the stacked box structure. This process includes time-series alignment and anomaly cleaning, mesh generation and medium identification, heat transfer topology construction and thermal resistance calculation, composite weight solution and temperature reconstruction, calibration of measurement point parameters, result storage, and visualization output. The entire grid temperature is calculated through minimum equivalent thermal resistance path search and composite influence weight normalization, generating four types of output information: heat transfer topology map, mesh reconstruction temperature, calibration parameter set, and credibility label. Around these three core requirements, a six-step full-process processing is sequentially performed on the multi-source monitoring data and 3D geometric model of the stacked box structure. The entire grid temperature is calculated through minimum equivalent thermal resistance path search and composite influence weight normalization, ultimately generating four types of output information: heat transfer topology map, mesh reconstruction temperature, calibration parameter set, and credibility label.

[0075] Time-series alignment and anomaly cleaning provide standardized and effective input data for the entire process. The core is to unify the time base of multi-source data, eliminate outlier data, and fill in short-term missing data. The execution logic maps structural temperature measurement data and boundary environment monitoring data to a preset unified time series according to the acquisition timestamp. For each structural temperature measurement point, the lower quartile, upper quartile, and interquartile range are calculated within a preset sliding time window. Data below the lower quartile minus 1.5 times the interquartile range or above the upper quartile plus 1.5 times the interquartile range are marked as candidate outlier data. The temperature change rate of the candidate outlier data relative to the temperature data at adjacent valid time points is further calculated. When the temperature change rate exceeds a preset change rate threshold, the candidate outlier data is confirmed as outlier data. For data with a continuous missing duration not exceeding a preset missing duration threshold, interpolation is performed using valid temperature data of the same measurement point before and after the missing time period. For data with a continuous missing duration exceeding the preset missing duration threshold, the corresponding structural temperature measurement point is removed from the source node set participating in temperature field reconstruction within the corresponding missing time period.

[0076] Taking the monitoring data of a stacked box trough with a sampling period of 1 hour as an example, a 24-hour sliding window is used to calculate the statistics. The temperature change rate threshold is set to 5 degrees Celsius per hour, and the missing duration threshold is 4 hours. If a certain measuring point is missing 2 consecutive hours, it is filled by linear interpolation of valid data from the preceding and following times, while the data quality coefficient of that measuring point is lowered. If a certain measuring point experiences a temperature change of 8 degrees Celsius in a single hour, exceeding the statistical distribution and rate thresholds, it is judged as abnormal data and removed. All data are uniformly aligned to whole-hour times to form a valid monitoring dataset at the same reconstructed time.

[0077] Mesh generation and medium identification provide a spatially discrete carrier for heat transfer topology construction. The core is to transform the continuous geometric model into computable mesh elements and complete zoning and identification according to medium properties. The execution logic involves discretizing the three-dimensional geometric model into multiple mesh elements. The mesh form can be hexahedral, tetrahedral, or a combination thereof, and the mesh scale is determined based on the degree of structural geometric changes, the density of measuring points, and the target spatial resolution. Each mesh element and boundary surface is identified according to the concrete medium region, liquid medium region, gas medium region, and the corresponding medium interface. The outer surface of the structure is further divided into boundary zones according to orientation, shading status, and overlay layer status.

[0078] For a 30-meter-long stacked box girder aqueduct segment, the mesh size for the conventional concrete solid area was 0.5 meters, while the mesh size for areas with severe temperature gradients, such as box-chamber boundaries, rigid frame nodes, and media interfaces, was 0.2 meters. Approximately 680 candidate reconstructed mesh elements were generated for the entire structure. Each mesh element recorded attributes such as center coordinates, volume, and media type. The upper water conveyance chamber was marked as a liquid media area, the lower maintenance chamber as a gaseous media area, and the structural walls as a concrete media area. The interfaces between the three media types were separately marked.

[0079] Heat transfer topology construction and thermal resistance calculation are the core implementation steps of topology constraints. The core is to construct a topology network based on actual heat transfer contact relationships and calculate the equivalent thermal resistance of each path. The execution logic is as follows: using the center point of the mesh cell, the structural temperature measurement point, and the boundary equivalent temperature node as topology nodes, topology edges are established according to the actual heat transfer contact relationships between adjacent topology nodes, forming the heat transfer topology diagram of the stacked box structure. When two adjacent mesh cells have a common heat transfer contact surface, a topology edge is established between the corresponding topology nodes. When two mesh cells are adjacent in Euclidean space but separated by structural walls, cavities, or non-connected medium regions and do not have a direct heat transfer contact relationship, no direct topology edge is established between the corresponding topology nodes.

[0080] The equivalent thermal resistance of topological edges is calculated in two scenarios. For adjacent topological nodes within the same dielectric region, the formula for calculating the equivalent thermal resistance is as follows: ,in, This is the equivalent heat transfer path length. For the corresponding medium's thermal conductivity, This is the equivalent heat transfer area.

[0081] The formula for calculating the equivalent thermal resistance of adjacent topological nodes on both sides of different medium regions is as follows: ,in and These are the equivalent heat transfer path lengths from the two nodes to the medium interface, respectively. and The thermal conductivity of the two media on both sides are respectively. This represents the contact thermal resistance at the interface between the media.

[0082] After completing the thermal resistance calculations for all topological edges, the minimum equivalent thermal resistance path between each source node and the point to be reconstructed is solved to obtain the thermal resistance topological distance. The formula for calculating the thermal resistance topological distance is as follows: , ,in, Let be the allowed heat transfer path from source node i to the grid point q to be reconstructed. The thermal resistance topological distance is the minimum of the sum of the equivalent thermal resistances of all topological edges in all feasible paths. The calculation is implemented using Dijkstra's algorithm or other non-negative edge weight shortest path algorithms.

[0083] Taking the boundary region between the upper and lower chambers as an example, adjacent grids belonging to the same concrete region have a heat transfer path length of 0.2 meters, a thermal conductivity of 2.3 W / m / Kelvin, and a shared heat transfer area of ​​0.04 square meters, resulting in an equivalent thermal resistance of approximately 2.17 Kelvin / W. Adjacent grids located in the liquid and concrete regions of the upper chamber, respectively, show a significant increase in total equivalent thermal resistance after the interface contact thermal resistance is superimposed. Since the upper and lower chamber grids separated by the cavity do not establish direct topological edges, temperature influences must circumvent along the solid paths of the rigid frame nodes at the chamber boundary, accumulating a substantial increase in thermal resistance. This approach suppresses non-physical weighting across the cavity at the path level.

[0084] The composite weighting and temperature reconstruction are the core steps in temperature field calculation. The core is to calculate the composite weights based on thermal resistance topological distance and multi-dimensional factors to complete the temperature solution of the entire mesh. The execution logic is as follows: based on thermal resistance topological distance, the longitudinal coordinate difference between the source node and the grid point to be reconstructed, and the data quality coefficient of the source node, calculate the composite influence weight of the source node on the grid point to be reconstructed, and then calculate the reconstructed temperature of the grid point to be reconstructed after normalizing the composite influence weights.

[0085] The formula for calculating the unnormalized composite influence weight is as follows: ,in, This is the source node data quality coefficient, with a value ranging from 0 to 1. The longitudinal attenuation coefficient is... and , where are the longitudinal coordinates of the source node and the grid point to be reconstructed, respectively, and p is the thermal resistance distance decay exponent. This is a zero-prevention constant. The weight normalization formula is: ,in, This is the set of valid source nodes that participate in the calculation of the temperature q of the grid points to be reconstructed.

[0086] The formula for calculating the reconstruction temperature of the grid points to be reconstructed is: The effective source node set consists of source nodes that simultaneously meet three conditions: first, they are located in the same connected component of the heat transfer topology graph as the grid point to be reconstructed; second, the thermal resistance topological distance from the source node to the grid point to be reconstructed is not greater than the effective thermal resistance threshold; and third, the source node has effective temperature data at the current reconstruction time. When the number of effective source nodes is less than the preset minimum number, the effective thermal resistance threshold is increased by a preset step size until the number of effective source nodes reaches the preset minimum number or the effective thermal resistance threshold reaches the preset upper limit.

[0087] A given grid point to be reconstructed has 5 valid source nodes. One of these source nodes has a thermal resistance topological distance of 20 Kelvin per watt, a longitudinal coordinate difference of 2 meters, a data quality coefficient of 0.95, a longitudinal attenuation coefficient of 0.05 per meter, a thermal resistance distance attenuation exponent of 2, and a zero-prevention constant of 0.01 Kelvin per watt. The calculated unnormalized weight of this source node is approximately 0.0021. After calculating and normalizing the weights of the 5 source nodes, the weighted sum is used to obtain the reconstructed temperature of the grid point. If only 2 valid source nodes are found under the initial effective thermal resistance threshold, which is less than the preset minimum of 3, the threshold is increased in steps of 10 Kelvin per watt until the requirement is met.

[0088] The calibration of measurement point parameters is a closed-loop process to ensure reconstruction accuracy and physical consistency. Its core is to utilize independent calibration points to complete parameter optimization and physical consistency verification. The execution logic employs a leave-one-point cross-calibration or partitioned leave-out-calibration method, using at least one structural temperature measurement point as a calibration point and the remaining structural temperature measurement points and boundary equivalent temperature nodes as source nodes to calculate the reconstructed temperature of the calibration point. After traversing the calibration points, the root mean square error (RMSE) between the reconstructed temperature and the measured temperature is calculated, and the parameter combination that minimizes the RMS error is searched within a preset parameter range. The objective function for parameter calibration also includes the residual constraint from heat dissipation balance, ensuring that the calibration results balance data accuracy and physical rationality. The objective function is constructed using a weighted summation form, expressed as: J( = RMSE ( + ,in For the set of parameters to be calibrated, RMSE( To verify the root mean square error of the reconstructed temperature at the measurement points, The mean of the absolute values ​​of the residuals from the heat dissipation balance of the entire grid. and Let be the weighting coefficient, and let its value satisfy . + =1, which can be adjusted according to the project's emphasis on data accuracy and physical consistency requirements; the default values ​​are 0.7 and 0.3 respectively. Parameter optimization is based on the objective function J( Minimization is the convergence objective.

[0089] The formula for calculating the root mean square error is: Where θ is the set of parameters to be calibrated. To verify the number of samples, and These are the reconstructed temperature and the measured temperature, respectively. The formula for calculating the residual from heat dissipation equilibrium is: ,in, , and Here, represents the grid cell density, specific heat capacity, and volume, respectively, and N(q) is the set of adjacent nodes directly connected to grid cell q via heat transfer. The equivalent thermal resistance of adjacent topological edges. The volumetric heat source intensity is set to 0 when there is no internal heat source. The parameters to be calibrated include the thermal resistance distance decay index, longitudinal decay coefficient, effective thermal resistance threshold, and interface thermal resistance. Parameter optimization can be achieved using methods such as grid search, Bayesian optimization, or particle swarm optimization. When using the grid search method, the typical search step size for the thermal resistance distance decay index is 0.2, and the typical search step size for the longitudinal decay coefficient is 0.01 per meter. The convergence termination condition is traversing all preset parameter grids. When using Bayesian optimization or particle swarm optimization methods, the convergence termination condition is that the change in the objective function value over 10 consecutive iterations is less than 1e-4, or the preset maximum number of iterations is reached. The typical maximum number of iterations is set to 100.

[0090] For the aqueduct segment with 128 measuring points, a cross-validation method was adopted, leaving one measuring point unchecked. The initial thermal resistance distance attenuation index was set to 2, and the longitudinal attenuation coefficient was set to 0.05 per meter, corresponding to a root mean square error (RMSE) of 1.2 degrees Celsius. The thermal resistance distance attenuation index was adjusted within the range of 0.5 to 4 using a grid search method, and the longitudinal attenuation coefficient was adjusted within the range of 0.01 to 0.2 per meter. Simultaneously, the residual from heat dissipation balance was constrained to remain within a reasonable range. Finally, the optimal parameter combination for the overall objective was found, reducing the RMS error to 0.6 degrees Celsius. The calibrated parameter set was reused for global temperature reconstruction at all subsequent time points.

[0091] Results storage and visualization are the key steps in delivering the reconstruction results. The core is generating a standardized temperature field dataset and providing multi-dimensional visualization capabilities. The execution logic involves storing a dynamic 3D temperature field dataset, containing spatial coordinates, reconstruction time, reconstruction temperature, and confidence level information, into a time-series or relational database. Simultaneously, it provides visualizations such as 3D cloud maps, arbitrary cross-sectional slices, isothermal surfaces, measurement point comparison curves, and confidence level distribution maps. The reconstruction results can be integrated with subsequent business systems such as temperature stress analysis, crack risk assessment, and temperature control equipment control via standard data interfaces.

[0092] The reliability rating is determined based on the verification error, residual from heat dissipation balance, and effective source node data integrity rate, and is divided into three levels: high, medium, and low. Each level is determined according to the following quantitative rules: High reliability requires all three conditions to be met simultaneously: verification error less than 60% of the preset accuracy threshold, the average absolute value of the residual from heat dissipation balance less than 5% of the corresponding grid's heat capacity, and effective source node data integrity rate greater than or equal to 90%. Medium reliability requires all three conditions to be met simultaneously: verification error between 60% and 100% of the preset accuracy threshold, the average absolute value of the residual from heat dissipation balance between 5% and 15% of the corresponding grid's heat capacity, and effective source node data integrity rate between 60% and 90%. Low reliability only requires meeting any one of the following conditions: verification error greater than the preset accuracy threshold, the average absolute value of the residual from heat dissipation balance greater than 15% of the corresponding grid's heat capacity, and effective source node data integrity rate less than 60%.

[0093] The preset accuracy threshold, also known as the control threshold for the root mean square error of reconstruction, can be set according to engineering requirements. A typical value for stacked box trough projects is 0.8 degrees Celsius. The reliability evaluation is only used for result grading, anomaly alerts, and parameter recalibration; it does not directly replace the grid reconstruction temperature with a preset temperature difference or temperature gradient. After the reconstruction of a certain aqueduct is completed, an hourly full-grid temperature dataset is output, with each grid point accompanied by a corresponding reliability level. The system can display cross-sectional temperature cloud maps, longitudinal temperature distribution curves, and internal and external surface temperature difference curves, while highlighting low-reliability areas to prompt maintenance personnel to check sensor status or add measurement points.

[0094] Based on the architectural requirements of topological constraint pre-processing, multi-media hierarchical control, and decoupling of verification and reconstruction, the entire process of 3D temperature field reconstruction is divided into six modular functional divisions. These divisions include data preprocessing, geometric partitioning, topology construction and thermal resistance calculation, temperature solution, verification and calibration, and result output. The execution logic and data flow relationships of each module are clearly defined, forming an operational system where data cleaning, mesh modeling, topology calculation, temperature reconstruction, parameter calibration, and result output are progressively advanced, and calibration parameters are reused throughout the entire reconstruction process.

[0095] For the data preprocessing stage, the input consists of raw structural temperature measurement data and boundary environment monitoring data. The core functions performed are time-series alignment, anomaly identification, missing data completion, and data quality evaluation. The output is the valid monitoring dataset corresponding to the same reconstruction time and the data quality coefficients for each source node. This stage provides standardized input for the entire process, ensuring data quality from the source and preventing outliers from interfering with the accuracy of subsequent reconstructions.

[0096] For the geometric discretization and partitioning stage, the input is a 3D geometric model of a stacked box structure. The core functions performed are geometric feature recognition, partitioned mesh generation, medium region identification, and boundary region division. The output is a set of mesh cells with medium attributes and boundary labels. This stage provides the spatial carrier for heat transfer topology construction, enabling hierarchical control of multiple media and providing a partitioning basis for subsequent topology constraints.

[0097] For the heat transfer topology construction and thermal resistance calculation stages, the input consists of a partitioned mesh set and fixed heat transfer parameters. The core functions performed are adjacency determination, heat transfer topology graph construction, equivalent thermal resistance calculation of topological edges, and minimum thermal resistance path solution. The output is a complete heat transfer topology graph and a global thermal resistance topological distance dataset. This stage is the core carrier for pre-setting topological constraints, blocking non-physical cross-region weighted calculations from the path layer, and is the key step that distinguishes the entire system from ordinary spatial interpolation.

[0098] For the temperature field reconstruction stage, the inputs are the thermal resistance topological distance set, synchronous effective monitoring data, source node data quality coefficients, and calibrated reconstruction parameters. The core functions performed are effective source node selection, composite influence weight calculation, weight normalization, and grid temperature solution. The output is globally grid-reconstructed temperature field data. This stage is the core execution unit for temperature field calculation, integrating multi-source data to complete the final temperature numerical solution.

[0099] For the parameter calibration and verification stage, the inputs are the mesh reconstruction temperature, measured data from the verification points, and the heat transfer topology diagram. The core functions performed include verification error statistics, residual calculation from heat dissipation equilibrium, parameter optimization calibration, and reliability grading evaluation. The outputs are the calibrated parameter set, verification error statistics, and a global reliability indicator. The calibration parameters output from this stage are fed back to the temperature field reconstruction stage for reuse, forming a computational closed loop. This also provides a reliability basis for the results output, achieving complete decoupling between verification and reconstruction.

[0100] For the output stage, the inputs are the global grid reconstruction temperature, calibration parameter set, and confidence identifier. The core functions are standardized data storage, multi-dimensional visualization, and standardized interface integration. The output is temperature field data and visualization results that can be directly used in engineering applications. This stage is the external output port of the entire system, connecting to subsequent engineering business scenarios.

[0101] The six steps proceed sequentially according to the data flow order. The output parameters of the parameter calibration and verification step are reused in reverse to the temperature field reconstruction step, forming a closed-loop operation system of forward calculation and reverse calibration, which not only ensures the clarity of the process, but also achieves continuous optimization of accuracy.

[0102] Combining the requirements of cross-regional interpolation suppression, controllable reconstruction accuracy, and traceable results, and based on the actual heat transfer contact relationships of multiple media and parameter calibration error constraints, this paper formulates a minimum thermal resistance path calculation standard, media zoning identification rules, and boundary node dynamic update specifications. It establishes execution criteria such as no direct topological edge established for no heat transfer contact, real-time updating of boundary equivalent temperature based on monitoring data, and error-driven parameter optimization calibration, thereby achieving the goal of suppressing non-physically weighted errors across cavities and walls. Three core calculation standards and specifications are formulated, and three rigid execution criteria are established, ultimately achieving the goal of suppressing non-physically weighted errors across cavities and walls.

[0103] This standard standard for calculating the minimum thermal resistance path standard unifies the calculation criteria for heat transfer paths and establishes the principle of not establishing direct topological edges without heat transfer contact. The standard clarifies the equivalent thermal resistance calculation methods for both single-medium and cross-medium scenarios, defines the algorithm for solving the minimum thermal resistance path and the definition of thermal resistance topological distance, and requires that all temperature effects propagate along paths with actual heat transfer contact, prohibiting direct topological connections across cavities, walls, and non-connected media. This standard ensures that the reconstruction process conforms to heat transfer laws at the physical path level, fundamentally suppressing non-physical interpolation errors.

[0104] To address the issue of media zoning identification rules, a unified approach to multi-media zoning management is established, defining the implementation criteria for multi-media layered management. The rules clearly define the identification methods for three core media types: concrete, liquid, and gas. They also specify the boundary delineation methods for the interfaces and external surfaces of each media type, requiring separate configuration of heat transfer parameters and topological connection rules for different media regions. Boundary nodes are only connected to the mesh nodes corresponding to the interfaces. Specifically, liquid media boundary nodes are only connected to the mesh nodes corresponding to the liquid and concrete interfaces, gaseous media boundary nodes are only connected to the mesh nodes corresponding to the gas and concrete interfaces, and external environment boundary nodes are only connected to the mesh nodes corresponding to the outer surface of the stacked box structure. This ensures the accurate representation of the heat transfer characteristics of different media and avoids calculation errors caused by media confusion.

[0105] Regarding the specification for dynamic updating of boundary nodes, this specification unifies the treatment of time-varying boundaries and establishes the execution criterion for real-time updating of the equivalent boundary temperature based on monitoring data. The specification clarifies the temperature calculation methods for three types of boundary nodes: liquid, gas, and external surface, and specifies the time-varying adjustment rules for the convective heat transfer coefficient, requiring that the boundary node temperature and corresponding thermal resistance parameters be updated synchronously in each reconstruction cycle.

[0106] The formula for calculating the equivalent temperature of the outer surface boundary is: ,in, For ambient temperature, The intensity of solar radiation. The surface solar radiation absorption coefficient. The net heat flux density for long-wave radiation. This represents the time-varying convective heat transfer coefficient. When long-wave radiation is neglected, the net heat flux density of long-wave radiation is taken as 0. The liquid and gas boundary temperatures are synchronously matched to the measured medium temperatures, and the convective heat transfer coefficient is dynamically adjusted according to the real-time flow conditions. This specification avoids the problem of fixed boundary temperatures being out of sync with the actual field environment, ensuring that the boundary conditions always closely match real-time operating conditions.

[0107] Based on this, execution criteria for error-driven parameter optimization calibration are established. These criteria require that parameter calibration must be conducted based on error data from independent calibration points, with strict separation between training and calibration points. Furthermore, residuals from heat dissipation equilibrium are introduced as physical constraints to ensure that parameter optimization balances data accuracy and physical consistency. The calibrated parameters are fully traceable, and all reconstruction results include corresponding parameter versions and error indices, guaranteeing the reproducibility and traceability of the reconstruction results.

[0108] S104 divides the reconstruction accuracy standards into conventional and refined levels according to structural regions. It performs densified measurement points and fine mesh subdivision in the areas of chamber junction, rigid frame node and medium interface, and establishes a control system with traceable parameters, quantifiable errors and graded reliability throughout the process.

[0109] In one implementation, based on the needs of addressing temperature gradient differences across multiple regions of the stacked box structure, ensuring reconstruction accuracy for key areas, and balancing overall computational efficiency with spatial resolution, hierarchical measurement point deployment and differentiated mesh generation are performed on different regions of the stacked box structure. Reconstruction accuracy is controlled regionally through hierarchical configuration of measurement point spacing and refinement of mesh scale, generating hierarchical measurement point deployment rules and differentiated mesh generation schemes. This hierarchical configuration of measurement point spacing and refinement of mesh scale provides a suitable spatial foundation for subsequent topology construction and temperature calculation.

[0110] The measurement point layout is carried out along four dimensions: longitudinal section, regional classification, thickness direction, and zoned coverage. The spacing between measurement points in the densified areas is significantly smaller than that in the conventional areas. For longitudinal section layout, at least two monitoring sections are set along the longitudinal direction of the structure. The spacing between sections is determined based on the longitudinal temperature correlation length of the structure, ensuring that the temperature correlation between adjacent sections is within a reasonable range. Zoned coverage requires that structural temperature measurement points for each monitoring section be set at least in the top slab, bottom slab, web, box-cell interface area, and structural corner area to avoid reconstruction blind spots in critical areas. In the thickness direction, at least three layers of measurement points are set along the concrete wall thickness direction, respectively near the inner surface, in the middle of the structure, and near the outer surface, to accurately capture temperature gradient changes along the wall thickness direction. Regional classification divides the structure into conventional and densified areas. The interfaces between liquid media and concrete, gaseous media and concrete, rigid frame nodes, structural corners, and areas of thickness variation belong to the densified areas, where the spacing between measurement points is smaller than that in the corresponding conventional areas.

[0111] Taking a 30-meter-long stacked box girder aqueduct segment as an example, a monitoring section is set every 10 meters along the longitudinal direction, for a total of 4 monitoring sections. The measuring points are symmetrically arranged at each section. The spacing between measuring points in the conventional concrete solid area is controlled at 2 meters, and the spacing between measuring points at the interface between the liquid medium and concrete is controlled at 0.8 meters. Two additional measuring points are added at the rigid frame nodes to cover stress concentration locations. For the 0.6-meter-thick web, three layers of measuring points are set at positions of 0.05 meters, 0.3 meters, and 0.55 meters from the inner surface, respectively. The longitudinal and transverse coordinates of the three layers of measuring points are consistent, with only the vertical coordinates differing, providing multi-layer constraints for reconstructing the temperature distribution in the wall thickness direction.

[0112] The mesh generation is tailored to the degree of structural geometric changes, the density of measurement points, and the target spatial resolution, matching the mesh discrete scale accordingly. Different mesh sizes are used for different regions, balancing spatial resolution and computational efficiency. The mesh can be hexahedral, tetrahedral, or a combination thereof, with each mesh cell recording attributes such as center coordinates, volume, and medium type. Larger mesh sizes are used in conventional regions with gentle temperature variations, while finer mesh generation is used in denser regions with dramatic geometric changes and complex medium boundaries.

[0113] For this 30-meter-long stacked box girder aqueduct segment, the mesh size for the conventional concrete solid area is 0.5 meters, while the mesh size for the denser areas such as box girder boundaries, rigid frame nodes, and media interfaces is 0.2 meters, generating approximately 680 candidate reconstructed mesh elements for the entire structure. This configuration ensures spatial resolution in the denser areas, accurately characterizing abrupt temperature gradient changes near the interfaces, while avoiding computational redundancy caused by full-domain fine meshing, effectively balancing reconstruction accuracy and computational efficiency.

[0114] Based on the management architecture requirements of zoned accuracy adaptation, measurement point mesh collaboration, and unified topology rules, the reconstruction accuracy management system is hierarchically divided into two levels: regular areas and key areas. The execution standards and applicable scenarios for measurement point density and mesh scale at each level are clearly defined, forming an accuracy management system with hierarchical measurement point deployment, differentiated mesh subdivision, and unified heat transfer topology constraints operating collaboratively. The regular level accuracy standard corresponds to regular areas and is applicable to concrete solid areas with gradual temperature changes within the structure. These areas have small temperature gradients and uniform heat transfer paths, employing relatively relaxed measurement point spacing and mesh scales to control the overall computational load while ensuring basic reconstruction accuracy. The execution standard is that the measurement point spacing is configured according to a regular scale, the mesh size matches the regular spatial resolution, and all heat transfer topology calculations and weight calculation rules are completely consistent with the global domain.

[0115] Taking the concrete web area in the middle of the aqueduct segment as an example, the temperature change in this area is gradual and falls within the range of conventional accuracy control. Setting the measuring point spacing in this area to 2 meters and the grid size to 0.5 meters can meet the accuracy requirements of the entire foundation reconstruction while effectively controlling the overall calculation scale.

[0116] The encrypted accuracy standard corresponds to the encrypted area and is applicable to chamber boundaries, rigid frame nodes, medium interfaces, structural corners, and areas with thickness variations. These areas have severe temperature gradients, complex medium interfaces, and high structural importance, requiring both encrypted measuring points and fine mesh to ensure reconstruction accuracy. The implementation standard involves significantly reducing the spacing between measuring points and refining the mesh size. Simultaneously, measuring points in these areas are prioritized for inclusion in the verification measuring point extraction range to ensure that the accuracy of key areas can be independently verified.

[0117] Taking the interface region between the bottom plate of the chamber and the liquid as an example, this region has a large temperature gradient, drastic temperature changes, and directly affects the stress distribution of the structure, falling within the scope of the encrypted precision control. The spacing between measuring points in this region is increased to 0.8 meters, and the grid size is refined to 0.2 meters. At the same time, measuring points in this region are preferentially selected as verification samples during parameter calibration to ensure that the reconstruction accuracy near the interface is within a controllable range.

[0118] The two-level accuracy standard only distinguishes between the density of measuring points and the grid scale. The heat transfer topology construction rules, thermal resistance calculation standards, composite weighting algorithms, and parameter calibration logic are consistent throughout the entire process and do not change with the regional accuracy level, ensuring the physical consistency and logical self-consistency of the global reconstruction results.

[0119] To meet the requirements of accurate temperature gradient characterization, effective coverage of key structural components, and quantifiable evaluation of reconstruction results, and based on the severity of temperature changes in structural components, the complexity of media interfaces, and the importance of the structure, two levels of measurement point and mesh accuracy standards are established: standard and refined. The corresponding measurement point spacing thresholds and mesh size ranges for each level are determined. An independent reliability grading evaluation mechanism is established based on verification error, thermal balance residual, and source node data integrity rate. The reliability evaluation is completely independent of the reconstruction calculation process and is only used for result grading, anomaly alerts, and parameter recalibration. It does not directly replace the mesh reconstruction temperature with a preset temperature difference or temperature gradient. Reliability levels are divided into high, medium, and low; the better the performance of the four core indicators, the higher the corresponding reliability level.

[0120] The verification error is calculated by comparing the reconstructed temperature and the measured temperature at independent verification points, using the root mean square error as the quantification index. The calculation formula is as follows: ,in, For the set of parameters to be calibrated, To verify the number of samples, and These are the reconstruction temperature and the measured temperature, respectively. This indicator reflects the degree of agreement between the reconstruction results and the measured data, and is a core accuracy indicator for reliability evaluation.

[0121] The residual from heat dissipation equilibrium is calculated based on the principle of energy conservation and is used to verify the physical consistency of the reconstruction results. The calculation formula is as follows: ,in, , and These are the grid cell density, specific heat capacity, and volume, respectively. The set of adjacent nodes that are directly connected to the grid cell q through heat transfer. The equivalent thermal resistance of adjacent topological edges. The value represents the volumetric heat source intensity; it is set to 0 when there is no internal heat source. The larger the absolute value of the residual, the more significantly the reconstruction result deviates from the physical heat transfer laws, and the lower the reliability accordingly.

[0122] The number of valid source nodes reflects the scale of valid data sources participating in the calculation of the point to be reconstructed. The more sufficient the number, the stronger the constraint of the reconstruction result and the higher the credibility. The data integrity rate of source nodes reflects the quality of the source node data participating in the reconstruction. The lower the data integrity rate, the fewer valid data participates in the calculation, the higher the uncertainty of the reconstruction result, and the lower the credibility accordingly.

[0123] Taking a specific grid point as an example, a grid point with a small verification error, a small residual in heat dissipation balance, a sufficient number of valid source nodes, and a high data integrity rate is marked as high reliability. If a grid point's verification error exceeds the threshold, or the heat balance residual is too large, or the number of valid source nodes is insufficient, or the source node data integrity rate is too low, any failure to meet the standard will result in a lower reliability level, with severe failures marking it as low reliability. Low reliability areas will trigger anomaly alerts, guiding maintenance personnel to check sensor status, supplement measurement points, or recalibrate and reconstruct parameters.

[0124] The entire zoning accuracy control system achieves high-precision and fully controllable reconstruction of encrypted areas under limited measurement points and computing resources by hierarchically configuring monitoring and computing resources. Combined with an independent credibility evaluation mechanism, it not only ensures the accuracy and physical rationality of the reconstruction results, but also intuitively presents the reliability of the results in each area, providing a clear quality reference for subsequent engineering applications such as temperature stress analysis and crack risk assessment.

[0125] S105 uses a unified shortest path algorithm to solve for the minimum thermal resistance path based on the structural geometric characteristics, measurement point distribution, and target spatial resolution matching grid discrete scale, and aggregates multi-source environmental and structural monitoring data for collaborative calculation.

[0126] In one implementation, based on the requirements of ensuring reconstruction spatial resolution, balancing global computational overhead, and adapting to multi-medium heat transfer topology construction, geometric feature identification, partitioned grid scale configuration, and unified solution of minimum thermal resistance path are performed on the geometric model of the stacked box structure, the layout of measuring points, and the results of medium partitioning. Collaborative computation is then completed by temporally matching the preprocessed multi-source monitoring data with the topology calculation results, generating a partitioned grid partitioning scheme, a global thermal resistance topological distance set, and synchronized effective monitoring data. Through four core steps—geometric feature identification, partitioned grid scale configuration, unified solution of minimum thermal resistance path, and temporal matching of multi-source data—collaborative computation is completed, ultimately generating three core outputs: a partitioned grid partitioning scheme, a global thermal resistance topological distance set, and synchronized effective monitoring data, providing a complete spatial and data foundation for subsequent temperature field reconstruction.

[0127] Geometric feature recognition provides a preliminary basis for differentiated mesh generation, with the core being the location of regions with varying geometric complexity and measurement point constraint strength. The execution logic takes the 3D geometric model of the stacked box aqueduct structure, the measurement point layout scheme, and the medium zoning results as input. It identifies regions with drastic geometric changes, medium interfaces, rigid frame nodes, thickness variation sections, and densely distributed measurement points. The refinement requirements for each region are quantified from four dimensions: geometric curvature, wall thickness variation amplitude, number of medium interfaces, and measurement point spacing. Higher index values ​​correspond to stronger mesh densification requirements for that region. For a 30-meter-long stacked box aqueduct segment, the rigid frame nodes at the box junctions, the liquid-concrete interface, the gas-concrete interface, and the structural corner areas are identified as regions with drastic geometric changes, while the solid area in the middle of the web is a region with gentle geometric changes. Simultaneously, it is identified that the measurement point spacing near the interfaces is only 0.8 meters, with a measurement point density significantly higher than in conventional areas. The corresponding mesh needs to be matched with a denser configuration to fully utilize the measurement point constraints.

[0128] The partitioned grid scale configuration achieves a preliminary balance between accuracy and efficiency, with the core being the matching of differentiated grid sizes based on regional characteristics. The execution logic involves matching differentiated grid discrete scales to different regions based on the degree of structural geometric changes, the density of measuring points, and the target spatial resolution. Larger grid sizes are used in conventional regions with gentle temperature gradients and sparse measuring points, while smaller grid sizes are used in key regions with dramatic geometric changes and dense measuring points, controlling the overall number of grids and computational overhead while meeting spatial resolution requirements. The grid form can be hexahedral, tetrahedral, or a combination thereof, with each grid cell recording attributes such as center coordinates, volume, and the type of medium it belongs to. In this aqueduct segment, the grid size for the conventional concrete solid region is 0.5 meters, while the grid size for denser regions such as box-cell boundaries, rigid frame nodes, and medium interfaces is 0.2 meters, generating approximately 680 candidate reconstruction grid cells for the entire structure. This configuration ensures that the denser regions can accurately depict abrupt temperature gradient changes near the interface while avoiding computational redundancy caused by full-domain fine subdivision, effectively balancing reconstruction accuracy and computational efficiency.

[0129] The unified solution for the minimum thermal resistance path is the core computational step in topological constraint calculation. The core is to use a unified algorithm to calculate the global thermal resistance topological distance. The execution logic is as follows: based on the partitioned mesh set and multi-medium heat transfer parameters, a unified shortest path algorithm is used to solve for the minimum equivalent thermal resistance path from each source node to each mesh point to be reconstructed, resulting in a global thermal resistance topological distance set. First, topological edges are established based on the actual heat transfer contact relationships of adjacent meshes. The equivalent thermal resistance of each topological edge is calculated according to two rules: same medium and cross-medium interface. Then, the minimum cumulative thermal resistance path is searched using the equivalent thermal resistance as the path weight. The algorithm is executed uniformly throughout, without changing the computational logic based on the region's precision level, ensuring the consistency of the global topological rules.

[0130] The formula for calculating the equivalent thermal resistance of adjacent topological nodes within the same dielectric region is as follows: ,in, This is the equivalent heat transfer path length. For the corresponding medium's thermal conductivity, This represents the equivalent heat transfer area. The formula for calculating the equivalent thermal resistance of adjacent topological nodes on both sides of different medium regions is as follows: ,in, and These are the equivalent heat transfer path lengths from the two nodes to the medium interface, respectively. and The thermal conductivity of the two media on both sides are respectively. Let be the contact thermal resistance at the interface between the media. The formula for calculating the thermal resistance topological distance from the source node to the mesh point to be reconstructed is: , ,in, Let be the allowed heat transfer path from source node i to the grid point q to be reconstructed. The thermal resistance topological distance is the minimum of the sum of the equivalent thermal resistances of all topological edges in all feasible paths. The calculation can be implemented using Dijkstra's algorithm, A* algorithm, or other non-negative edge weight shortest path algorithms.

[0131] Taking the boundary region between the upper and lower chambers as an example, adjacent grids belonging to the same concrete region have a heat transfer path length of 0.2 meters, a thermal conductivity of 2.3 W / m / Kelvin, and a shared heat transfer area of ​​0.04 square meters. The calculated equivalent thermal resistance is approximately 2.17 Kelvin / W. Since the upper and lower chamber grids separated by the cavity do not establish direct topological edges, temperature influences must travel along the solid paths of the rigid frame nodes at the chamber boundary, significantly increasing the accumulated thermal resistance. After calculating the thermal resistance of all topological edges, Dijkstra's algorithm is used to solve for the minimum thermal resistance path from each source node to all connected grid points, forming a global thermal resistance topological distance matrix.

[0132] Multi-source data time-series matching collaborative computation enables the linkage between static topology and dynamic monitoring data. The core is to improve overall computational efficiency through time-series alignment. The execution logic involves matching pre-processed multi-source monitoring data with topology calculation results according to a unified time benchmark to complete collaborative computation. Structural geometry, medium partitioning, and heat transfer topology relationships are fixed attributes that can be pre-calculated and cached for reuse; structural temperature measurement point data and boundary environment monitoring data are time-varying data, updated synchronously according to the sampling period. At each reconstruction moment, only dynamic data such as measurement point temperature and boundary equivalent temperature need to be refreshed. These are then combined with the pre-stored thermal resistance topology distance set to perform subsequent weight calculations and temperature solutions, eliminating the need for repeated topology construction and path solving. The aqueduct monitoring data sampling period is 1 hour. The heat transfer topology map and thermal resistance topology distance set only need to be recalculated when the structural model changes. During daily reconstruction, structural measurement point temperature, liquid temperature, gas temperature, and external environment parameters are updated synchronously every hour. The synchronized effective monitoring data is matched with the cached thermal resistance topology distance set and directly used for subsequent composite weight calculations, significantly reducing the computation time per moment.

[0133] Based on the architectural requirements of prior geometric modeling, data preprocessing, and topology calculation, the mesh generation and thermal resistance topology calculation tasks are modularized. This involves dividing the tasks into modules for geometric feature analysis, mesh discretization, topology edge thermal resistance calculation, and minimum path solving. The execution logic and data flow relationships of each module are clearly defined, forming a progressive computational execution system of feature recognition, mesh generation, thermal resistance assignment, and path solving. Furthermore, based on the architectural requirements of prior geometric modeling, data preprocessing, and topology calculation, the mesh generation and thermal resistance topology calculation tasks are divided into four functional modules, with clearly defined execution logic and data flow relationships for each module, forming a progressive computational execution system of feature recognition, mesh generation, thermal resistance assignment, and path solving.

[0134] For the geometric feature analysis module, the input includes a 3D geometric model of the stacked box structure, a measurement point layout scheme, and preliminary results of medium zoning. The core functions performed are geometric contour extraction, change region identification, measurement point density statistics, and resolution matching. The output is the geometric feature zoning results and the recommended grid scale range for each region. This module provides the zoning basis for subsequent grid discretization and is a prerequisite for achieving differentiated meshing.

[0135] For the mesh discretization and partitioning module, the input consists of the geometric feature partitioning results and the target accuracy requirements. The core functions are mesh cell generation, medium property identification, and boundary region division. The output is a set of mesh cells with medium properties and boundary labels. This module completes the spatial discretization process and serves as the spatial carrier for heat transfer topology construction.

[0136] For the topology edge thermal resistance calculation module, the input consists of a partitioned mesh set and fixed multi-medium heat transfer parameters. The core functions performed are adjacency determination, topology edge establishment, and equivalent thermal resistance assignment, outputting a complete heat transfer topology map with thermal resistance weights. This module completes the digital mapping of physical heat transfer relationships and is the core component carrying out topology constraints.

[0137] The minimum path solving module takes a heat transfer topology graph with thermal resistance weights and a set of source nodes as input. Its core functions include shortest path search, thermal resistance distance accumulation, and distance matrix generation, outputting a global thermal resistance topology distance dataset. This module completes the unified solution for the minimum thermal resistance path and forms the core foundation for subsequent weight calculations.

[0138] The four modules proceed sequentially according to the data flow order, with the output of the previous module serving as the input of the next module, forming a complete computing chain. The entire process follows unified physical rules and computing standards to ensure global consistency of the topological logic.

[0139] To meet the requirements of controllable reconstruction accuracy, adaptable computational efficiency, and unified topological logic, and based on the degree of structural geometric changes, the density of measurement points, and the target spatial resolution, this paper sets different ranges of mesh size for different regions, rules for calculating equivalent thermal resistance parameters, and effective thermal resistance threshold screening criteria. It also determines differentiated mesh partitioning rules, a unified method for calculating thermal resistance topological distance, and criteria for determining the effective range of source nodes. Furthermore, to meet the requirements of controllable reconstruction accuracy, adaptable computational efficiency, and unified topological logic, and based on the degree of structural geometric changes, the density of measurement points, and the target spatial resolution, three types of core rules are established, clarifying the unified execution standards for differentiated mesh partitioning, unified thermal resistance distance calculation, and determination of the effective range of source nodes.

[0140] The differentiated meshing rules clearly define the mesh size configuration standards for different regions, setting two mesh size ranges: regular regions and densely populated regions. Regular regions correspond to concrete solid areas with gentle geometric changes and sparse measuring points, with mesh sizes in a larger range to control the overall computational load. Densely populated regions correspond to areas with drastic geometric changes, complex media boundaries, and dense measuring points, with mesh sizes in a smaller range to ensure local spatial resolution. The mesh size also matches the measuring point distribution density; the denser the measuring points, the smaller the mesh size, ensuring that the measuring point constraints can be fully utilized. In the aqueduct project, the mesh size range for regular regions is set to 0.4 meters to 0.6 meters, and the mesh size range for densely populated regions is set to 0.15 meters to 0.25 meters. Mesh generation for all regions follows unified media identification and topology connection rules; only the scale differs, without affecting the logical consistency of the overall heat transfer topology.

[0141] The unified rules for calculating thermal resistance topological distance clearly define the standards for thermal resistance calculation and path finding across the entire domain. They establish calculation formulas for equivalent thermal resistance in both the same medium and across different media, clarify the selection principles for the shortest path algorithm, and require that the calculation method for thermal resistance topological distance be completely consistent across all regions. The rules require that thermal resistance parameters be fixed throughout the entire process, and that the path algorithm be consistent throughout. The heat transfer physics rules must not be changed due to regional accuracy levels, ensuring that the weighting benchmark for temperature influence remains consistent across the entire domain. The equivalent thermal resistance of all topological edges in the entire structure is calculated using the two unified formulas, and the minimum thermal resistance path for all source nodes is uniformly solved using the Dijkstra algorithm. The same calculation standards are applied to both regular and refined regions, with only differences in mesh density, ensuring the physical consistency of the reconstruction results.

[0142] The rules for determining the effective range of source nodes clearly define the screening criteria for effective source nodes, setting an effective thermal resistance threshold as the core screening basis, and establishing a mechanism for progressively increasing the threshold. An effective source node must simultaneously meet three conditions: first, it must be located in the same connected component of the heat transfer topology graph as the grid point to be reconstructed; second, the thermal resistance topological distance from the source node to the grid point to be reconstructed is not greater than the effective thermal resistance threshold; and third, the source node must have effective temperature data at the current reconstruction time. When the number of effective source nodes is less than the preset minimum number, the effective thermal resistance threshold is progressively increased according to a preset step size until the number of effective source nodes reaches the target or the threshold reaches the preset upper limit. If the number of source nodes is still insufficient after the threshold reaches the upper limit, the corresponding grid point is marked as low confidence, and distant non-connected measurement points are not forcibly introduced. In a typical region, the initial effective thermal resistance threshold for grid points is set to 50 Kelvin per watt. After screening, only 2 source nodes meet the conditions, less than the preset minimum of 3. The threshold is progressively increased in steps of 10 Kelvin per watt. When the threshold is increased to 60 Kelvin per watt, the number of effective source nodes reaches 3, the threshold expansion stops, and the threshold is used to complete subsequent calculations. If the number of source nodes is still less than 3 even after the threshold is increased to the upper limit of 100 Kelvin per watt-hour, the grid point is marked as low confidence.

[0143] By setting three types of rules in a unified manner, the entire computing system can balance accuracy and efficiency through differentiated grid configuration, ensure the consistency of global reconstruction logic through unified topology and judgment rules, and take into account the differences in data source coverage in different regions through a dynamic threshold adjustment mechanism, thereby achieving a multi-objective balance of accuracy, efficiency and reliability.

[0144] S106 addresses three types of anomalies: cross-regional non-physical interpolation, composite weight deviation, and parameter calibration mismatch. It employs a differentiated resolution mechanism that includes hierarchical configuration of topology path constraints, residual verification of heat dissipation balance, and parameter recalibration in low-confidence areas. It also fully retains traceability fields for reconstruction parameters, verification errors, and confidence identifiers throughout the entire process.

[0145] In one implementation, for three typical reconstruction anomalies—cross-regional non-physical interpolation, composite weight deviation, and parameter calibration mismatch—a differentiated resolution mechanism is configured in stages, including topology path constraints, residual verification of heat dissipation balance, and parameter recalibration in low-confidence areas. At the same time, reconstruction parameters, verification errors, and confidence identifiers are fully retained for traceability throughout the entire process, ensuring that the reconstruction process is reproducible, anomalies are localizable, and results are traceable.

[0146] Cross-regional non-physical interpolation anomalies and topological path constraint resolution stem from the fact that traditional spatial interpolation assigns measurement point weights solely based on Euclidean linear distance. When two points are geometrically close but separated by box walls, cavities, or non-connected media, they are still assigned higher weights, leading to temperature propagation that does not conform to actual heat transfer laws and generating non-physical interpolation errors across cavities and walls. The resolution mechanism blocks non-physical temperature propagation from the bottom layer of the heat transfer path, constructing a heat transfer topology map based solely on actual heat transfer contact relationships. It replaces Euclidean distance with the minimum equivalent thermal resistance path as the core basis for weight allocation, ensuring that temperature effects propagate only along solid paths with direct heat transfer contact. Topological edge establishment follows rigid contact rules. The center point of the grid cell, structural temperature measurement points, and boundary equivalent temperature nodes are used as topological nodes. When two adjacent grid cells have a common heat transfer contact surface, a topological edge is established between the corresponding topological nodes. When two grid cells are adjacent in Euclidean space but separated by structural walls, cavities, or non-connected media regions, and there is no direct heat transfer contact relationship, no direct topological edge is established between the corresponding topological nodes.

[0147] The three types of boundary nodes also follow specific connection rules: liquid medium boundary nodes are only connected to the mesh nodes corresponding to the liquid-concrete interface; gaseous medium boundary nodes are only connected to the mesh nodes corresponding to the gas-concrete interface; and external environment boundary nodes are only connected to the mesh nodes corresponding to the outer surface of the stacked box structure. Equivalent thermal resistance is calculated in two scenarios. For adjacent topological nodes within the same medium region, the formula for calculating the equivalent thermal resistance is... ,in, This is the equivalent heat transfer path length. For the corresponding medium's thermal conductivity, This is the equivalent heat transfer area.

[0148] The formula for calculating the equivalent thermal resistance of adjacent topological nodes on both sides of different medium regions is as follows: ,in, and These are the equivalent heat transfer path lengths from the two nodes to the medium interface, respectively. and The thermal conductivity of the two media on both sides are respectively. Let be the contact thermal resistance at the interface between the media. The minimum thermal resistance path is solved using a unified algorithm. The thermal resistance topological distance from the source node to the grid point to be reconstructed is the minimum sum of the equivalent thermal resistances of all topological edges among all feasible heat transfer paths, calculated using the following formula: , ,in Let i be the allowed heat transfer path from the source node i to the grid point q to be reconstructed. The calculation is implemented using Dijkstra's algorithm or other non-negative edge weight shortest path algorithms, with a consistent execution standard throughout and no adjustment of the calculation logic based on changes in the region.

[0149] Taking a double-box aqueduct as an example, temperature measuring points are arranged on the outer wall of the upper box, and grid points to be reconstructed exist on the inner wall of the lower box. The Euclidean distance between the two points is only 0.8 meters, but there are three layers of structure in between: the bottom plate of the upper box, the cavity, and the top plate of the lower box. There is no direct heat transfer path. During the topology construction stage, no direct topological edge is established between the two points. The temperature influence can only bypass along the solid path of the rigid node at the junction of the boxes. The total heat transfer path length reaches 3.2 meters, and it passes through multiple medium interfaces, significantly increasing the cumulative equivalent thermal resistance. The influence weight of the corresponding source node is automatically reduced, thus completely suppressing the non-physical interpolation anomaly across the cavity at the path level.

[0150] The mechanism addresses the anomalies caused by composite weight deviations and residual verification from heat dissipation equilibrium. These anomalies manifest as deviations in composite weight allocation from actual heat transfer patterns, leading to non-physical abrupt changes in local reconstructed temperatures and an overall temperature field that violates the principle of energy conservation. The resolution mechanism introduces residuals from heat dissipation equilibrium as a physical constraint, verifying the physical consistency of the reconstructed results from an energy conservation perspective and identifying anomalous distributions caused by weight deviations. The residual verification results are directly incorporated into the reliability evaluation system, serving only as a basis for accuracy evaluation and anomaly detection, without directly forcibly replacing the reconstructed temperature to avoid masking true temperature anomalies.

[0151] The residual for heat dissipation equilibrium is calculated based on the principle of energy conservation. For a single grid cell, the change in heat storage per unit time equals the sum of the net heat transferred through adjacent topological edges and the heat generated by internal heat sources. The residual calculation formula is as follows: ,in, , and These are the grid cell density, specific heat capacity, and volume, respectively. The set of adjacent nodes that are directly connected to the grid cell q through heat transfer. The equivalent thermal resistance of adjacent topological edges. The value represents the volumetric heat source intensity; it is set to 0 when there is no internal heat source. The larger the absolute value of the residual, the more significantly the reconstruction result deviates from the physical heat transfer laws, and the higher the probability of composite weight deviation. The residual verification result, verification error, number of valid source nodes, and source node data integrity rate together constitute the basis for credibility evaluation. The residual verification result, verification error, and valid source node data integrity rate together constitute the three direct bases for credibility evaluation. The number of valid source nodes indirectly affects credibility evaluation by influencing the selection of valid source nodes and the calculation of data integrity rate; it is not used as an independent dimension for credibility judgment. Grid points with excessive residuals correspond to a lower credibility level and trigger an anomaly alert, guiding the investigation of the status of surrounding measuring points and boundary conditions.

[0152] Taking a concrete mesh element without an internal heat source as an example, the element volume is 0.125 cubic meters, the density is 2400 kg / m³, the specific heat capacity is 920 J / kg / Kelvin, the time step is 1 hour, and the temperature difference between the current and previous times is 0.5 degrees Celsius. The calculated heat storage change per unit time is approximately 38.3 watts. Simultaneously, the net heat transferred through topological edges from all adjacent meshes is calculated to be approximately 39.8 watts. The difference between these two values, i.e., the residual, is approximately 1.5 watts, with a relative deviation of less than 5%, meeting the physical consistency requirements and the engineering accuracy requirements for this example. The aforementioned 5% is only a specific result for this example and does not constitute a general judgment threshold. A general judgment threshold needs to be determined based on the accuracy requirements and parameter calibration results of a specific project. Based on the results of this example, it can be determined that the composite weights at the corresponding locations have no significant deviation. If the absolute value of the residual of a certain grid cell exceeds the reasonable range, it is marked as an abnormality in physical consistency, and the corresponding confidence level is downgraded, indicating that there may be a deviation in the weight allocation, and further investigation is needed in conjunction with the status of surrounding measurement points.

[0153] Parameter calibration mismatch anomalies and low-confidence area parameter recalibration resolution: These anomalies often occur in scenarios involving changes in the distribution of local measuring points, significant fluctuations in environmental boundary conditions, or changes in the structural heat transfer properties. A mismatch between the globally uniform calibration parameters and actual operating conditions leads to a continuous decline in the reconstruction accuracy of the corresponding area, resulting in widespread low-confidence results. The resolution mechanism establishes a parameter recalibration mechanism triggered by low-confidence conditions. This mechanism focuses on independently verifying the reconstruction error of measuring points and, combined with the constraint of residual distance from heat dissipation balance, re-performs parameter optimization calibration.

[0154] The resolution mechanism establishes a parameter recalibration mechanism triggered by low confidence levels. It focuses on the reconstruction error of independently verified measurement points and, combined with the residual constraint of heat dissipation balance, recalibrates the parameters. The recalibration execution scope covers the low confidence region and its adjacent connected heat transfer regions. Verification measurement points are preferentially extracted from those within the low confidence region, with the remaining measurement points participating in the reconstruction calculation as source nodes. After recalibration, the updated parameter set is uniformly reused for global temperature reconstruction, without setting independent parameter sets for individual regions, ensuring consistency between the global heat transfer topology rules and weight calculation logic.

[0155] The parameter recalibration process strictly adheres to the principle of measurement point isolation, completely separating training and calibration measurement points to avoid artificially high accuracy caused by data self-fitting. The calibrated parameter set is reused for global temperature reconstruction. Parameter calibration uses root mean square error (RMSE) as the core accuracy indicator, while also incorporating residuals from heat dissipation balance as physical constraints to construct a comprehensive objective function. The formula for calculating RMSE is as follows: ,in, This is the set of parameters to be calibrated, covering thermal resistance distance attenuation index, longitudinal attenuation coefficient, effective thermal resistance threshold, and interfacial thermal resistance. To verify the number of samples, and These are the reconstructed temperature and the measured temperature, respectively. When a persistently low-confidence region occurs, the parameter recalibration process is triggered.

[0156] A method of leaving one measurement point for cross-validation or partitioned validation is adopted. At least one measurement point is selected as the validation point each time, and the remaining structural temperature measurement points and boundary equivalent temperature nodes are used as source nodes to complete the reconstruction calculation. After traversing all validation measurement points, the overall root mean square error is calculated. Combined with the residual constraint from heat dissipation balance, the optimal parameter combination for the comprehensive objective is searched within the preset parameter range using methods such as grid search, Bayesian optimization, or particle swarm optimization. For an aqueduct segment containing 128 measurement points, the initial thermal resistance distance attenuation index is set to 2, and the longitudinal attenuation coefficient is set to 0.05 per meter, corresponding to a validation root mean square error of 1.2 degrees Celsius. When a local area consistently exhibits a low confidence level, parameter recalibration is initiated. The thermal resistance distance attenuation index is adjusted within the range of 0.5 to 4 using a grid search method, and the longitudinal attenuation coefficient is adjusted within the range of 0.01 to 0.2 per meter. Simultaneously, the residual from heat dissipation balance is constrained to remain within a reasonable range. Finally, the optimal parameter combination for the comprehensive objective is found, and the corresponding root mean square error is reduced to 0.6 degrees Celsius. The calibrated parameter set is reused for global temperature reconstruction at all subsequent time points, thus eliminating calibration mismatch anomalies at the parameter level.

[0157] To ensure the reproducibility and traceability of the reconstruction results, a full-process traceability field retention mechanism is implemented, retaining three categories of full-process traceability fields. All fields are bound to the temperature field results at the corresponding time point, supporting full-link backtracking and anomaly location. The first category is reconstruction parameter fields, including all calibration parameters such as thermal resistance distance attenuation index, longitudinal attenuation coefficient, effective thermal resistance threshold, and interface thermal resistance, as well as the corresponding parameter versions and calibration times, ensuring that the reconstruction results at any time can be reproduced using the corresponding parameters. The second category is verification error fields, including the root mean square error of the global verification, reconstruction deviation data for each verification measurement point, and statistical results of the residual from heat dissipation balance, fully recording all quantitative basis for accuracy verification. The third category is credibility identifier fields, including the credibility level of each grid point, and four sub-indicators: verification error, residual from heat dissipation balance, number of effective source nodes, and source node data integrity rate, clearly defining the basis for generating the credibility level. By fully retaining the three types of traceability fields, all reconstruction results can be traced back to the corresponding parameters, error data, and credibility judgment criteria, which not only ensures the reproducibility of the results, but also provides complete data support for anomaly investigation, parameter optimization, and solution iteration.

[0158] like Figure 2 As shown, Figure 2 This diagram illustrates the cross-sectional media zoning and measurement point layout of the stacked box structure. A planar coordinate system is established with the horizontal direction as the x-axis and the vertical direction as the y-axis. This visually presents the multi-media zoning morphology and graded temperature measurement point layout scheme of the stacked box structure, along with the core rules for multi-media zoning identification and graded measurement point layout in the scheme.

[0159] The overall structure is a double-chamber configuration with upper and lower chambers stacked on top of each other. The outer solid portion is the concrete medium region 11, which includes the top slab, bottom slab, side webs, and the rigid frame nodes at the junction of the upper and lower chambers. This is the core solid object for the three-dimensional temperature field reconstruction. The upper chamber is the liquid medium region 12, with a cross-section that is flat at the top and curved at the bottom, corresponding to the water conveyance function chamber of the stacked aqueduct, and contains the liquid medium. The lower chamber is the gas medium region 13, with a rectangular cross-section with chamfered corners, corresponding to the maintenance ventilation chamber, and is filled with the gas medium.

[0160] Temperature monitoring points are deployed according to a tiered system. A single row of structural temperature monitoring points (101) is evenly arranged transversely at the top of the structural slab; these are standard surface monitoring points. Multiple sets of structural temperature monitoring points are distributed in a grid pattern inside the concrete walls, covering the top slab, bottom slab, web, and the junction of the box slab and the concrete structure. This creates a multi-layered monitoring point layout along the concrete thickness direction, with points near the outer surface, the interior of the structure, and near the inner surface. At the interfaces between the liquid medium and concrete, and between the gaseous medium and concrete, additional interface-density monitoring points are specifically deployed. The spacing between these points is significantly smaller than that in conventional concrete areas, allowing for precise capture of the dramatic temperature gradients at the medium-to-concrete interfaces and ensuring accurate reconstruction of key areas.

[0161] like Figure 3 As shown, Figure 3 This is a schematic diagram of heat transfer topology and minimum equivalent thermal resistance path. It is used to intuitively present the heat transfer topology connection rules from the source node to the target node and the solution logic of the minimum equivalent thermal resistance path in different medium regions separated by concrete solid. It corresponds to the core technical links of heat transfer topology construction and minimum thermal resistance path calculation in the corresponding scheme, and is used to explain the implementation principle of suppressing non-physical interpolation across walls.

[0162] The vertical rectangle with diagonal fill in the middle of the diagram represents the concrete wall, dividing the space into a left-side medium region and a right-side medium region. This represents the concrete solid wall separating different medium cavities in the stacked box structure. All circular nodes in the diagram are heat transfer topology nodes, corresponding to the center point of the mesh element, the structural temperature measuring point, or the boundary equivalent temperature node. V1 in the lower left corner is the source node i, V10 on the right is the target node q, and V2 to V9 are intermediate topology nodes distributed in the two medium regions and the concrete wall. The black lines connecting the nodes are topology edges. Topology edges are established only when there is an actual heat transfer contact surface between the mesh or measuring point represented by the corresponding node, indicating that temperature influence can be transmitted along this path. Nodes without direct connections do not have direct heat transfer paths, and non-physical interpolation calculations across walls and media based on Euclidean linear distances are prohibited.

[0163] The red curve in the figure represents the minimum equivalent thermal resistance path from source node i to target node q. The path passes through five intermediate nodes: V2, Vl, Vc, Vr, and V8, completing the cross-wall heat transfer along the solid heat transfer path of the concrete wall, rather than directly crossing the point along a Euclidean straight line. The equivalent thermal resistance of each topological edge along the path is calculated based on the thermal conductivity of the corresponding medium, the heat transfer path length, and the equivalent heat transfer area. The thermal resistance topological distance of the entire path is the minimum sum of the equivalent thermal resistances of all topological edges among all feasible heat transfer paths, obtained through the shortest path algorithm. This thermal resistance topological distance is the core basis for subsequent calculations of composite influence weights, replacing the traditional Euclidean straight-line distance and suppressing non-physical interpolation errors from the path's underlying structure.

[0164] like Figure 4 As shown, Figure 4 This is a schematic diagram of a parameter calibration process driven by independent verification measurement points. It corresponds to the core process of independent verification calibration, parameter optimization, and reliability evaluation, reflecting the calibration rules of strict isolation between verification and reconstruction measurement points, error-driven parameter iteration, and consideration of both data accuracy and physical consistency. The process begins with the initialization of the parameters to be calibrated, θ, which include the thermal resistance distance attenuation index p, longitudinal attenuation coefficient β, effective thermal resistance threshold, and interface thermal resistance, etc., while simultaneously setting the initial values ​​and search ranges of each parameter.

[0165] After entering the verification point traversal loop, an independent verification point is first selected. This verification point is not included in the source node set of the temperature field reconstruction. The remaining structural temperature points and boundary equivalent temperature nodes are used as source nodes in the temperature reconstruction calculation. Then, the reconstructed temperature value and the residual from heat dissipation equilibrium at the corresponding location of the verification point are calculated. After completing the calculation for a single verification point, it is determined whether all verification points have been traversed. If not, the process returns to select the next independent verification point and repeats the reconstruction and calculation steps.

[0166] After all calibration points have been traversed, the overall reconstruction root mean square error (RMSE), global residuals from heat dissipation balance, and corresponding physical constraint indicators are statistically calculated to form a comprehensive evaluation basis for parameter calibration. Based on the comprehensive evaluation results, the values ​​of calibration parameters such as thermal resistance distance attenuation index p, longitudinal attenuation coefficient β, effective thermal resistance threshold, and interface thermal resistance are updated.

[0167] The system then determines whether the current parameter combination meets the preset convergence condition. If the convergence condition is not met, it returns to the calibration point selection stage and starts a new round of iterative calculation. If the convergence condition is met, the optimization process terminates, and the optimal calibration parameters are finally output. The confidence evaluation model is used to generate a corresponding confidence label for each grid point to be reconstructed. The parameter set obtained from the calibration is reused in the subsequent global temperature field reconstruction.

[0168] like Figure 5 As shown, Figure 5 This is a schematic diagram of a three-dimensional temperature field mesh visualization for a stacked box structure. It corresponds to the temperature field visualization display function in the output stage, used to intuitively present the spatial distribution characteristics of the reconstructed temperature across the entire domain. A three-dimensional Cartesian coordinate system is established in the diagram, with the X-axis representing the horizontal direction, the Y-axis the vertical direction, and the Z-axis the vertical direction, all in millimeters. The legend in the upper right corner explains that the black solid line represents the outer contour of the block, the blue solid line represents the boundary of the water-filled area in the upper box, and the red dashed line represents the boundary of the air circulation area in the lower box. A temperature color scale is set on the right, in degrees Celsius, with the color transitioning from blue to red, corresponding to a gradual increase in temperature from 3.5 degrees Celsius to 5.5 degrees Celsius.

[0169] The figure presents all the grid points to be reconstructed within the concrete solid area as discrete points, with each point's color corresponding to the reconstructed temperature value at that location. The temperature distribution shows a clear vertical temperature gradient: the upper region is cooler, dominated by blue and green hues; the lower region is warmer, dominated by yellow, orange, and red hues. The concrete around the water-filled area in the upper box is relatively uniform in temperature due to the influence of the liquid medium; however, the concrete around the air-circulation area in the lower box exhibits significantly different temperature characteristics compared to the upper part. The overall three-dimensional scatter plot completely covers the concrete solid area of ​​the stacked box structure, allowing for direct observation of the overall structural temperature distribution, the temperature gradient at the medium interface, and the longitudinal temperature variation characteristics, providing visualized data support for temperature stress analysis and crack risk assessment.

[0170] In one embodiment, this application also provides a method for reconstructing the three-dimensional temperature field of a stacked box structure based on multi-medium heat transfer topological constraints, comprising: The multi-source monitoring data collection module is used to collect various types of raw data, including stacked box 3D geometry, structural temperature measurement, and meteorological medium boundary monitoring; it also unifies the calculation and execution standards for solidified medium thermal conductivity, interface thermal resistance, measuring point spacing, and dynamic boundary equivalent temperature. The hierarchical process function division module is used to define the division of labor in six major stages, including data preprocessing and geometric discrete partitioning, based on heat transfer topology constraints, dynamic boundary adaptation, and independent verification calibration as core criteria. It configures dual control thresholds for effective thermal resistance and reconstructed root mean square, and limits the rigid rule that heat transfer is only conducted along the physical heat transfer path and that verification measurement points do not participate in the reconstruction. The six-layer closed-loop topology reconstruction module is used to build a complete computing link from data processing to result output, unify the execution specifications of medium partitioning, minimum thermal resistance path, and time-varying boundary update, and block non-physical temperature interpolation across cavities and walls. The zoning accuracy control module is used to divide the grid into two levels, regular and densified, and to set measurement point standards. It densifies the grid measurement points at the medium interface and chamber nodes, and establishes a full-process control mechanism with traceable parameters, quantifiable errors, and graded reliability. The thermal resistance path solving module is used to combine structural morphology, measurement point density, target resolution and mesh size to solve the minimum equivalent thermal resistance using a unified shortest path algorithm, and integrate time-series synchronous monitoring data to carry out joint temperature calculation. The anomaly verification and traceability module is used to configure topology blocking, thermal balance residual verification, and model recalibration hierarchical handling schemes for three types of problems: interpolation distortion, weight offset, and parameter inaccuracy. It also fully stores the reconstruction parameters, error data, and credibility identifiers for full-link traceability.

[0171] The computer-readable storage medium provided in the above embodiments of this application and the three-dimensional temperature field reconstruction method of stacked box structure based on multi-medium heat transfer topology constraints provided in the embodiments of this application are based on the same inventive concept and have the same beneficial effects as the methods adopted, run or implemented by the application programs stored therein.

[0172] The various embodiments in this application are described in a related manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the embodiments for evaluating the three-dimensional temperature field reconstruction method, system, electronic device, and readable storage medium for stacked box structures based on multi-medium heat transfer topology constraints are basically similar to the embodiments of the three-dimensional temperature field reconstruction method for stacked box structures based on multi-medium heat transfer topology constraints described above, and are therefore described simply. Relevant parts can be referred to in the descriptions of the embodiments of the three-dimensional temperature field reconstruction method for stacked box structures based on multi-medium heat transfer topology constraints described above.

Claims

1. A method for reconstructing the three-dimensional temperature field of a stacked box structure based on multi-medium heat transfer topological constraints, characterized in that, include: Acquire the three-dimensional geometric model of the stacked box structure, structural temperature measurement points and boundary environment monitoring data, and solidify the multi-medium heat transfer parameters, measurement point layout rules and boundary equivalent temperature calculation standards; Based on the principles of heat transfer topology constraints, dynamic boundary adaptation, and independent calibration, the target functional boundaries of data preprocessing, geometric discretization partitioning, heat transfer topology construction, composite weight calculation, and parameter calibration are clarified. The effective thermal resistance threshold and the reconstruction root mean square error dual constraint threshold are set, and the reconstruction rigid rules that propagate along the actual heat transfer contact path and verify the independent measurement points are determined. A six-layer closed-loop reconstruction system was established, consisting of data preprocessing, geometric partitioning, topology construction, temperature calculation, verification and calibration, and result output. Standards for minimum thermal resistance path calculation, medium partitioning identification rules, and dynamic update specifications for boundary nodes were formulated to suppress non-physical cross-regional weighted errors. Based on the structural regions, two levels of reconstruction accuracy standards are defined: conventional and refined. For the junction of the chambers, rigid frame nodes, and medium interface areas, refined measurement points and fine mesh subdivision are implemented to establish a control system with traceable parameters, quantifiable errors, and graded reliability throughout the entire process. Based on the structural geometric characteristics, the distribution of measuring points and the target spatial resolution, the grid discrete scale is matched, and a unified shortest path algorithm is used to solve the minimum thermal resistance path. Multi-source environmental and structural monitoring data are aggregated for collaborative calculation. For three types of anomalies—cross-regional non-physical interpolation, composite weight deviation, and parameter calibration mismatch—a differentiated resolution mechanism is configured with hierarchical topology path constraints, residual verification of heat dissipation balance, and parameter recalibration in low-confidence areas. The entire process of reconstructing parameters, verification errors, and confidence identifiers is fully retained for traceability.

2. The method as described in claim 1, characterized in that, Based on the principles of heat transfer topology constraints, dynamic boundary adaptation, and independent calibration, the target functional boundaries of data preprocessing, geometric discretization and partitioning, heat transfer topology construction, composite weight calculation, and parameter calibration and verification are clearly defined. Effective thermal resistance thresholds and reconstruction root mean square error dual-constraint thresholds are set, and rigid reconstruction rules that propagate along the actual heat transfer contact path and verify independent measurement points are determined, including: Based on the requirements of suppressing non-physical interpolation across cavities, adapting to time-varying environmental boundaries, and ensuring that reconstruction accuracy can be independently verified, the entire process of reconstructing the three-dimensional temperature field of the stacked box structure is subjected to heat transfer topology connectivity constraints, dynamic mapping of boundary equivalent temperatures, and independent isolation of verification measurement points. The full-domain mesh temperature calculation is completed by solving the minimum equivalent thermal resistance path and normalizing the composite influence weight, generating a set of effective source nodes, mesh reconstruction temperature, verification error statistics, and credibility identification information. Based on the architectural requirements of heat transfer topology constraints, dynamic boundary adaptation, and independent verification and calibration, the core process of temperature field reconstruction is modularized and functionally divided. The division of labor is divided into modules for data preprocessing, geometric discretization and partitioning, heat transfer topology construction, composite weight calculation, and parameter calibration and verification. The execution logic and data flow relationship of each module are clarified, forming a reconstruction execution system that coordinates time alignment and anomaly cleaning, mesh generation and medium identification, topology mapping and thermal resistance calculation, weight normalization and temperature solution, error inversion and parameter calibration. Combining the requirements of physical consistency, computational efficiency, and quantifiable accuracy in reconstruction, and based on the heat transfer topology connectivity characteristics and parameter calibration accuracy control indicators, effective thermal resistance threshold and reconstruction root mean square error dual-dimensional control indicators are set. Supplemented by physical constraints of heat dissipation balance residuals, a rigid rule is established that heat transfer only propagates along the actual heat transfer contact path and that verification measurement points are independent and do not participate in reconstruction calculations.

3. The method as described in claim 1, characterized in that, A six-layer closed-loop reconstruction system was established, encompassing data preprocessing, geometric partitioning, topology construction, temperature calculation, calibration, and result output. Standards for minimum thermal resistance path calculation, dielectric partitioning identification rules, and dynamic update specifications for boundary nodes were formulated to suppress non-physical cross-region weighted errors, including: Based on the requirements of suppressing non-physical cross-regional weighting, ensuring the physical consistency of reconstruction, and outputting temperature fields with credibility labels, the entire process of time-series alignment and anomaly cleaning, mesh generation and medium identification, heat transfer topology construction and thermal resistance calculation, composite weight solution and temperature reconstruction, calibration of measurement point parameters, result storage and visualization output of multi-source monitoring data and three-dimensional geometric models of stacked box structures is performed. The whole-domain mesh temperature calculation is completed through minimum equivalent thermal resistance path search and composite influence weight normalization operation, generating four types of output information: heat transfer topology map, mesh reconstruction temperature, calibration parameter set, and credibility label. Based on the architectural requirements of topological constraint pre-processing, multi-media hierarchical control, and decoupling of verification and reconstruction, the entire process of 3D temperature field reconstruction is divided into six modular functions. The modules are divided into data preprocessing, geometric partitioning, topology construction and thermal resistance calculation, temperature solution, verification and calibration, and result output. The execution logic and data flow relationship of each module are clarified, forming an operation system in which data cleaning, mesh modeling, topology calculation, temperature reconstruction, parameter calibration, and result output are progressively advanced and the calibration parameters are reused for the whole domain reconstruction. Combining the requirements of cross-regional interpolation suppression, controllable reconstruction accuracy, and traceable results, and based on the actual heat transfer contact relationship of multiple media and parameter calibration error constraints, we formulate the minimum thermal resistance path calculation standard, media zoning identification rules, and boundary node dynamic update specifications. We establish the execution criteria of not establishing direct topological edges without heat transfer contact, updating the boundary equivalent temperature in real time with monitoring data, and using verification error to drive parameter optimization calibration, thereby achieving the goal of suppressing non-physical weighted errors across cavities and walls.

4. The method as described in claim 1, characterized in that, Based on the structural regions, two levels of reconstruction accuracy standards are established: conventional and refined. For the junctions of chambers, rigid frame nodes, and media interfaces, refined measurement points and fine mesh generation are implemented. A control system is established that ensures traceability of parameters throughout the entire process, quantifiable errors, and tiered reliability, including: Based on the need to address the temperature gradient differences in multiple regions of the stacked box structure, ensure the reconstruction accuracy of key parts, and balance the overall computational efficiency and spatial resolution, hierarchical measurement point layout and differentiated meshing are performed on different regions of the stacked box structure. The reconstruction accuracy is controlled by hierarchical configuration of measurement point spacing and mesh scale partitioning, generating hierarchical measurement point layout rules and differentiated meshing scheme information. Based on the control architecture requirements of partitioned accuracy adaptation, measurement point grid collaboration, and unified topology rules, the reconstructed accuracy control system is hierarchically divided into two levels: regular area and key area. The execution standards and applicable scenarios of measurement point density and grid scale at each level are clarified, forming an accuracy control system with hierarchical measurement point layout, differentiated grid subdivision, and unified heat transfer topology constraints. Combining the requirements of accurate temperature gradient characterization, effective coverage of key structural parts, and quantifiable evaluation of reconstruction results, based on the severity of temperature changes in structural parts, the complexity of medium interfaces, and the importance of the structure, we set two levels of measurement point and grid accuracy standards: regular and densified. We determined the corresponding measurement point spacing thresholds and grid size ranges for each level, and established an independent credibility grading evaluation mechanism based on verification error, thermal balance residual, and source node data integrity rate.

5. The method as described in claim 4, characterized in that, Based on the structural geometric characteristics, measurement point distribution, and target spatial resolution, a grid discretization scale is matched. A unified shortest path algorithm is used to solve for the minimum thermal resistance path. Multi-source environmental and structural monitoring data are aggregated for collaborative calculation, including: Based on the requirements of ensuring reconstruction spatial resolution, balancing global computational overhead, and adapting to the construction of multi-medium heat transfer topology, geometric feature identification, partition grid scale configuration, and unified solution processing of minimum thermal resistance path are performed on the geometric model of stacked box structure, measurement point layout, and medium partitioning results. Collaborative calculation is completed by temporal matching of preprocessed multi-source monitoring data and topology calculation results to generate partition grid partitioning scheme, global thermal resistance topology distance set, and synchronized effective monitoring data information. Based on the architectural requirements of prior geometric modeling, data preprocessing, and topology calculation, the mesh generation and thermal resistance topology calculation tasks are modularized. The modules are divided into geometric feature analysis, mesh discretization, topology edge thermal resistance calculation, and minimum path solution. The execution logic and data flow relationship of each module are clarified, forming a progressive calculation execution system of feature recognition, mesh generation, thermal resistance assignment, and path solution. Combining the requirements of controllable reconstruction accuracy, adaptable computational efficiency, and unified topological logic, based on the degree of structural geometric change, the density of measurement point distribution, and the target spatial resolution, we set different regional grid size ranges, equivalent thermal resistance calculation parameter rules, and effective thermal resistance threshold screening standards, and determined differentiated grid partitioning rules, unified thermal resistance topological distance calculation methods, and source node effective range determination standards.

6. A three-dimensional temperature field reconstruction system for a stacked box structure based on multi-medium heat transfer topological constraints, characterized in that, The system is used to execute executable instructions to perform the three-dimensional temperature field reconstruction method for stacked box structures based on multi-medium heat transfer topology constraints as described in any one of claims 1 to 5.

7. An electronic device, characterized in that, include: First processor; The processor also includes a memory for storing executable instructions of the first processor; wherein the first processor is configured to execute the three-dimensional temperature field reconstruction method for a stacked box structure based on multi-medium heat transfer topology constraints as described in any one of claims 1 to 5 by executing the executable instructions.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the second processor, it implements the three-dimensional temperature field reconstruction method for stacked box structures based on multi-medium heat transfer topology constraints as described in any one of claims 1 to 5.

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