A cross-scale machine learning simulation method for the thermal flow field of an air-cooled heat exchanger

Abstract

The application discloses a kind of wind-cooled heat exchanger hot flow field's cross-scale machine learning simulation method, belongs to energy thermal system intelligent operation and maintenance technical field.The method includes: using the historical multi-source data of wind-cooled heat exchanger to carry out directional training to open source basic model, introduce physical constraint in latent space, generate virtual sample library covering multiple structures, multiple working conditions and multiple scales;Special neural network is constructed, and discrete topological characteristics and continuous physical field characteristics are aligned by cross-modal fusion mechanism, and the target hot flow field is decoded and output;Data-physical joint loss function is used, and physical constraint is applied by weak form integral, and network parameters are optimized by stage unfreezing and gradual weighting strategy;The trained network is deployed on cloud platform, and generates hot flow field by hybrid inference mode, and uses multilevel correction mechanism to suppress or correct model drift.The application solves the problems of time-consuming CFD calculation and sample scarcity under the premise of ensuring physical consistency, and has long-term online correction capability.

Description

Technical Field

[0001] This invention belongs to the field of intelligent operation and maintenance technology of energy and thermal systems, and specifically relates to a cross-scale machine learning simulation method for the heat flow field of an air-cooled heat exchanger. Background Technology

[0002] As a key component in energy and power systems, the accurate acquisition of the heat flow field distribution of air-cooled heat exchangers is crucial for ensuring the efficient and safe operation of the system. While traditional computational fluid dynamics (CFD) numerical simulation methods can depict the details of the flow field, the computation time is too long, which cannot meet the needs of real-time analysis and online optimization in engineering projects.

[0003] In recent years, data-driven machine learning methods have been increasingly applied to thermal flow field prediction, but the following bottlenecks still hinder their engineering implementation: Weak cross-scale modeling capability: Existing models mostly predict only single indicators such as outlet temperature or heat exchange, lacking the ability to reconstruct complete high-dimensional physical fields including temperature field and velocity field, and it is difficult to take into account cross-scale characteristics from tube bundle level to fin level.

[0004] Physical consistency is difficult to guarantee: Pure data-driven models often ignore fluid dynamics control equations (such as mass, momentum, and energy conservation), which can lead to non-physical distortions in prediction results and poor extrapolation ability when faced with unseen working conditions.

[0005] Insufficient multimodal information fusion: There is a strong coupling relationship between the structural topology of the air-cooled heat exchanger (as shown in the figure, structure and geometric parameters) and the real-time operating conditions (such as wind speed and temperature). Existing methods are difficult to effectively fuse discrete structural features and continuous physical field features.

[0006] Lack of online calibration: In actual operation, equipment aging, dust accumulation and environmental disturbances can cause model drift. Existing digital twin systems lack an effective multi-level online calibration mechanism and cannot maintain long-term prediction accuracy.

[0007] Therefore, there is an urgent need for a cross-scale machine learning simulation method for the thermal flow field of air-cooled heat exchangers in intelligent operation and maintenance scenarios of energy and thermal systems, in order to solve the problems of insufficient samples, weak cross-scale modeling ability, insufficient physical consistency, poor training stability, and difficulty in achieving real-time extrapolation and online correction in existing technologies. Summary of the Invention

[0008] To address the aforementioned problems in the existing technology, the purpose of this invention is to provide a cross-scale machine learning simulation method for the heat flow field of an air-cooled heat exchanger.

[0009] This invention provides the following technical solution: a cross-scale machine learning simulation method for the heat flow field of an air-cooled heat exchanger, comprising the following steps: Step S1: Construct a heat flow field generation model for air-cooled heat exchangers based on a fine-tuned large model, and generate a cross-scale virtual sample library.

[0010] First, multi-source heterogeneous data on air-cooled heat exchangers under different mechanical structures, operating conditions, and spatial resolutions are collected to construct a training sample set suitable for fine-tuning a large-scale model. Then, structural and topological data, operating parameter data from the training samples are used as input, and multi-physical quantity thermal flow field visualization data are used as labels to perform domain-adaptive fine-tuning of the open-source basic large-scale model, enabling it to learn the mapping relationship between the air-cooled heat exchanger's structural topology, operating parameters, and thermal flow field representation. Finally, corresponding thermal flow field samples are generated under given structural constraints, operating constraints, and scale conditions, thus forming a cross-scale virtual sample library covering macro-scale, meso-scale, and micro-scale. The formula for representing the thermal flow field generation process is as follows: (1); in, This represents the target thermal flux field generated at the corresponding scale. Represents structural connections and coupling topology inputs. Represents the working condition vector, Indicates the target output type, Indicates scale label, This represents the finely tuned thermal flow field generation model.

[0011] The specific process is as follows: S11: Collect multi-source data related to the air-cooled heat exchanger and construct a training dataset.

[0012] Multi-source data related to the air-cooled heat exchanger are collected and a training dataset is constructed. This training dataset includes at least structural and topological data, operating parameter data, and multi-physical quantity thermal flow field visualization data. Samples are hierarchically labeled based on the spatial scale characteristics corresponding to the thermal flow field, forming a cross-scale training dataset for fine-tuning large models. The multi-physical quantity thermal flow field visualization data refers to data organized as multi-channel images, tensors, or corresponding fields of one or more physical fields, such as temperature, velocity, and pressure. Preferably, it includes temperature, velocity, and pressure fields simultaneously. In the subsequent construction of latent space physical prior constraints and end-to-end weak-form physical constraints, mass conservation, momentum conservation, and energy conservation residuals are preferentially calculated based on samples that simultaneously include temperature, velocity, and pressure fields. For samples containing only some physical quantities, physical constraint terms corresponding to the included physical quantities are enabled according to the target output type label. To facilitate the expression of the connection and coupling relationships between equipment structural units, the structural and topological data can be abstracted as a graph structure. By using graph structure representation, the structural composition, connection relationship and flow heat transfer coupling relationship of the air-cooled heat exchanger can be uniformly encoded, forming the prior expression of the structure and topology input in the subsequent heat flow field generation model and dedicated neural network.

[0013] S12: Sample standardization and conditional expression.

[0014] The training dataset obtained in step S11 is subjected to unified standardization and conditional encoding to construct normalized input samples suitable for fine-tuning of open-source large models, and to enable the large model to generate thermal flow fields on demand under given structural constraints, operating condition constraints, scale constraints and target output constraints.

[0015] S13: Strategy for directional fine-tuning of large models and introduction of weak formal physical prior constraints in latent space.

[0016] An open-source foundational model with multimodal understanding and conditional generation capabilities is selected as the initial model. Targeted fine-tuning is performed using the conditional training sample set constructed in steps S11 and S12, and a weak-form physical prior constraint oriented towards sample generation is introduced into the latent space of the fine-tuning and denoising process. This prior constraint, by penalizing latent variable generation trajectories that do not conform to basic physical laws, guides the model to learn the true physical manifold distribution in the latent variable space, thereby improving the physical plausibility boundary when generating cross-scale virtual samples and eliminating common non-physical illusions in large-scale model generation. The total training loss function in the large-scale model fine-tuning stage is no longer limited to the conventional image generation domain, but instead establishes the physical plausibility boundary of the spatial distribution of the thermal flow field virtual samples by introducing a weak-form physical prior constraint oriented towards sample generation.

[0017] S14: Virtual sample generation and sample library construction.

[0018] Using the heat flow field generation model obtained in step S13, virtual samples of heat flow fields across scales are generated under different structural conditions, different operating conditions, and different target output conditions. The generated samples are then organized, filtered, labeled, and stored to construct a virtual sample library covering multiple structural forms, multiple operating condition combinations, and multiple scale levels.

[0019] In addition, the imaged thermal flow field generated in step S13 can be used not only to construct a cross-scale virtual sample library, but also as a priori source, initialization input or alternative input for the visual input of the thermal flow field in step S2 when the visual input of the real thermal flow field of the air-cooled heat exchanger is missing, incomplete or of insufficient quality, so as to enhance the ability of the dedicated neural network to represent the spatial field distribution.

[0020] Step S2: Construct a dedicated neural network for cross-scale modeling of air-cooled heat exchangers, achieving cross-modal fusion of topological, visual, and physical information. This step overcomes the communication barrier between discrete topology and continuous physical domains, achieving strict alignment of multimodal features through a graph-mesh mapping mechanism, laying the physical foundation for subsequent cross-scale solutions. The specific process is as follows: S21: Definition of Special Neural Network and Input Layer Definition

[0021] The dedicated neural network is a multimodal fusion prediction network for cross-scale modeling of the thermal flux field of air-cooled heat exchangers. It learns the nonlinear mapping relationship between structural and topological inputs, visual and physical inputs of the thermal flux field, and the target thermal flux field output, thereby achieving cross-scale representation, field distribution prediction, and temporal evolution modeling of the thermal flux field of the air-cooled heat exchanger. The dedicated neural network includes at least an input layer, an encoding layer, a cross-modal fusion layer, and a decoding output layer. The input layer receives structural and topological inputs, visual and physical inputs of the thermal flux field, and scale labels. The encoding layer extracts topological, visual, and physical features respectively. The cross-modal fusion layer aligns, models the correlations, and fuses the topological, visual, and physical features to obtain a unified feature representation. The decoding output layer maps the unified feature representation to the target thermal flux field output.

[0022] The input format of the dedicated neural network is uniformly defined, and the input includes at least structural and topological input, thermal flow field visual input, and physical input, used to characterize the structural connection relationship, spatial distribution of the thermal flow field, and operating conditions and spatiotemporal state information of the air-cooled heat exchanger, respectively. The structural and topological input originates from the structural and topological data of the air-cooled heat exchanger in step S11, and is expressed as structural connection and coupling topological information through graph structuring. The thermal flow field visual input can originate from real observations, discrete measurement point reconstruction results, historical extrapolation results, or prior images constructed offline and cached based on a generative model. The prior images constructed offline and cached based on the generative model can serve as a visual prior source, initialization input, or substitute input when real visual input is insufficient. The physical input originates from operating condition parameter data, physical coordinate information, time information, frequency information, and operating condition vectors. The scale label is used to indicate the spatial analytical scale of the current thermal flow field.

[0023] S22: Graph structure encoding module, visual encoding module and time-space-frequency fusion embedding module.

[0024] The structural connection and coupling topology information, thermal flow field visual information, and physical input information are encoded separately to extract topological features, visual features, and physical features. Scale labels are incorporated as conditional information into the physical feature encoding or subsequent decoding process. First, a topology graph is established based on the component hierarchy of the air-cooled heat exchanger, and graph structure encoding is used to encode the structure and topology input, outputting topological features characterizing cross-component coupling relationships and distribution patterns. Second, using the thermal flow field visual input as the object, thermal flow field images or image-based spatial representations at macro and mesoscales are encoded to extract visual features characterizing the spatial distribution pattern, local gradient changes, and hotspot region features of the thermal flow field. The image-based spatial representation can include at least one or more of the following: real observation images, discrete measurement point interpolation reconstruction images, historical projection result images, prior thermal flow field images generated by the thermal flow field generation model, and recursive image-based representations formed by converting the predicted thermal flow field results from the previous moment. Finally, physical coordinate information, time information, frequency information, and operating condition vectors are jointly embedded and encoded to output physical features.

[0025] S23: Physical Embedding Enhancement and End-to-End Conservation Constraint Module.

[0026] In step S22, the spatiotemporal-frequency fusion embedding module is used to jointly embed and encode physical coordinate information, time information, frequency information, and operating condition vectors to form physical features. Unlike step S13, which uses latent spatial physical priors to guide the large model's data generation, the constraints in this step directly affect the real physical field output by the network after decoding. The physical laws corresponding to mass conservation, momentum conservation, energy conservation, and boundary consistency are embedded into the training process of the dedicated neural network in an end-to-end weakly formal physical conservation constraint manner oriented towards cross-scale derivation. This allows the model to maintain consistency with the basic conservation laws and boundary conditions in predicting the thermal flow field while learning the cross-modal mapping relationship between structural topological features, visual features, and physical features.

[0027] The physical embedding enhancement module does not re-encode the input physical information. Instead, based on the unified feature representation obtained in step S24 and the target thermal flow field result output in step S25, it constructs the conservation equation residuals and boundary residuals, and forms weak-form physical constraint terms through weighted integration of the test function. These weak-form physical constraint terms are then used as part of the physical loss in network parameter optimization. Furthermore, for locally compactly supported test functions or Gaussian test functions used for local weak constraints, they satisfy the requirement of square integrability of the first-order weak derivative within the corresponding local subdomain. For piecewise constant functions used for regional average weak constraints, they are used as weight functions or indicator functions on the integral control subdomain.

[0028] The weak physical constraints include at least mass conservation constraints, momentum conservation constraints, energy conservation constraints, and boundary consistency constraints; the mass conservation residual is used to characterize fluid continuity deviations; the momentum conservation residual is used to characterize the balance deviations between flow drive, viscous diffusion, and pressure distribution; the energy conservation residual is used to characterize the balance deviations between convective heat transfer, conductive diffusion, and heat source terms; and the boundary consistency constraint term is used to characterize the consistency of conditions such as inlet flow rate, outlet pressure, wall slip-free, wall heat transfer flux, or temperature boundary.

[0029] The end-to-end weak-form conservation constraint in this step refers to not requiring the predicted heat flow field from the model to strictly satisfy the point-state residuals of the conservation equations at every discrete point to be zero. Instead, it involves weighted integration of the residuals of the conservation equations with a selected test function within the computational domain, ensuring that the residuals satisfy approximate conservation in the integral sense within the global domain, local subdomains, or boundary neighborhoods. This reduces the impact of local measurement noise, discrete errors, and high-gradient abrupt changes on training stability. For different scale levels, different spatial regions, and different boundary types, different test functions can be called to calculate the weak-form residuals, forming hierarchical physical loss terms.

[0030] To facilitate the selection of appropriate weak-form test functions for different spatial regions, this application defines the relevant regions in the air-side computational domain of the air-cooled heat exchanger as follows: The high-gradient region, micro-scale detail region, boundary disturbance region, mainstream region, overall channel region, and macro-scale region are all functional regions delineated based on the geometric location, structural feature dimensions, boundary distances, and spatial variation intensity of the temperature field, velocity field, or pressure field within the computational domain.

[0031] Specifically, the computational domain on the air side of the air-cooled heat exchanger is divided into several integral control subdomains, and the normalized spatial gradient index of the temperature field, velocity field, or pressure field is calculated for each integral control subdomain. The normalized spatial gradient index is the subdomain average value, maximum value, or weighted combination value obtained by dimensionlessly normalizing the spatial gradient of the corresponding physical quantity according to a characteristic scale; wherein, the characteristic scale includes one or more of the following: temperature characteristic difference, velocity characteristic value, pressure characteristic difference, equivalent length of integral control subdomain, hydraulic diameter of local flow channel, fin spacing, or outer diameter of heat exchange tube.

[0032] The preset gradient threshold is determined statistically based on the normalized spatial gradient indices of each integral control subdomain in a preset operating condition sample library or training sample set. This can be achieved by using the gradient index mean plus a multiple of the standard deviation, or by using the gradient index quantile. The preset high quantile range refers to the range of normalized spatial gradient indices of all integral control subdomains within the same computational domain, the same scale label, or the same training batch, sorted by numerical value, and ranking high within a preset proportion. The preset proportion is determined based on the coverage of local weak physical constraints, computational resources, and the recognition performance of the temperature boundary layer near the fin surface, the windward and leeward sides of the heat exchanger tubes, local hot spots, wake regions, flow separation regions, and reattachment regions in the validation samples.

[0033] When the normalized spatial gradient index is greater than the preset gradient threshold, or falls within the preset high quantile range, the corresponding integral control subdomain is defined as a high gradient region. The high gradient region includes, but is not limited to, the temperature boundary layer near the fin surface, the area near the windward and leeward sides of the heat exchange tube, the area near local hot spots, the wake region, the flow separation region, and the reattachment region.

[0034] The microscale detail area refers to a local area formed by small feature size structures of the air-cooled heat exchanger that needs to be described with a spatial resolution higher than the overall channel scale. This includes, but is not limited to, fin gaps, adjacent layers of the outer wall of the heat exchange tube, the connection area between the fin and the heat exchange tube, the slit or bent edge of the louvered fin, the cut of the serrated fin, and local narrow flow channel areas.

[0035] The boundary disturbance region refers to the local neighborhood located near the inlet boundary, outlet boundary, solid wall boundary, fan outlet boundary, wind chamber boundary, fin leading and trailing edges, heat exchange tube outer wall, and locations where boundary conditions abruptly change. The preset boundary thickness is determined jointly based on the target output resolution, normal grid spacing, local structural feature dimensions, and the estimated thickness of the thermal or momentum boundary layer; for example, a thickness of no less than several normal grid spacings can be used, and corrected in conjunction with fin spacing, tube outer diameter, local flow channel hydraulic diameter, or estimated boundary layer thickness.

[0036] The determination of the local neighborhood includes geometric distance determination and residual mutation determination. For geometric distance determination, the geometric boundary line, boundary surface, or discrete boundary node of the corresponding boundary is extracted, and the shortest distance from the center of the integral control subdomain to the boundary is calculated. When this distance is less than or equal to the preset boundary thickness, the integral control subdomain is included in the boundary disturbance zone. For residual mutation determination, subdomains with velocity, temperature, or pressure residuals exceeding a preset residual threshold are used as seed subdomains. One or more adjacent subdomains are then expanded outward according to mesh adjacency relationships, shared boundary relationships, or a preset support radius. The seed subdomain and its adjacent subdomains together form the local neighborhood.

[0037] The mainstream region refers to the flow region in the air-side computational domain that is far from the solid wall, inlet and outlet boundaries, fan disturbance area, fin gap detail area and local wake recirculation area, and whose velocity direction is basically along the main ventilation direction of the heat exchanger and whose temperature and velocity fields change relatively gently.

[0038] The overall channel area refers to the overall air flow channel on the air side from the fan or air inlet side through the air chamber and finned tube bundle flow channel to the air outlet side, or an equivalent air flow control area composed of multiple tube rows and multiple inter-fin flow channels.

[0039] The macro-scale region refers to the engineering-scale control domain consisting of an entire air-cooled heat exchanger, a single tube bundle, a fan-air chamber-tube bundle combination module, or multiple tube rows, used to describe the overall flow distribution, average temperature change, overall pressure drop, and heat exchange performance.

[0040] Furthermore, based on the aforementioned region division, for high-gradient regions, micro-scale detail regions, or boundary perturbation regions, local tight support test functions or Gaussian test functions are preferentially used to construct local weak constraints; for mainstream regions, overall channel regions, or macro-scale regions, piecewise constant weight functions, control subdomain indicator functions, or piecewise linear functions are preferentially used to construct regional average weak constraints. When the same integral control subdomain simultaneously satisfies multiple region determination conditions, it is preferentially processed as a high-gradient region, micro-scale detail region, or boundary perturbation region to ensure the accuracy of physical constraints in locally drastically changing regions. Through the above methods, physical laws can be stably applied to the training process of the dedicated neural network, improving the physical rationality of prediction results while ensuring sample fitting ability and reducing the risk of training divergence.

[0041] S24: Cross-modal fusion module.

[0042] In step S24, the topological features, visual features, and physical features obtained in step S22 are aligned, their correlation is modeled, and they are fused and encoded to construct a cross-modal fusion function. A unified feature representation is obtained. By using a cross-attention mechanism, discrete graph topological features are projected onto a continuous visual feature space coordinate system, thereby achieving cross-modal alignment and unified representation of structural connectivity and physical field spatial distribution.

[0043] S25: Decoding and output definition.

[0044] The unified features obtained in step S24 The input is fed to the decoder, which maps the latent space features obtained from multimodal fusion to the target heat flow field output. The output includes at least one or more of the following: temperature field, velocity field, pressure field, and heat transfer performance indicators. The output relationship can be expressed as follows: ,in As a decoder, it achieves resolution-independent thermal flow field reconstruction output by performing cross-scale analysis on continuous feature manifolds. Moreover, for time-evolution modeling scenarios, it can also visualize the thermal flow field results output at the previous time step and feed them back as at least part of the visual input of the thermal flow field at the next time step, which together with the structural, topological, and physical inputs at the next time step constitutes the recursive temporal inference input.

[0045] Step S3: Construct a data-physical co-training network training strategy to alleviate training difficulties and enhance physical consistency.

[0046] To address the issues of gradient conflict, training divergence, and convergence difficulties that arise during joint training of hybrid networks composed of graph structure coding modules, visual coding modules, spatiotemporal-frequency fusion embedding modules, and physical embedding reinforcement modules, a data-physical collaborative training strategy is constructed to improve network training stability, physical consistency, and cross-scale prediction accuracy.

[0047] S31: Hierarchical construction of data-physical joint loss and training participation methods.

[0048] A data-physical joint loss function is constructed for training the dedicated neural network. The total loss includes at least a data supervision term, a weakly formal physical constraint term, a boundary consistency constraint term, and a regularization term. The data supervision term is used to characterize the fitting error between the model prediction result and the target thermal flow field sample. The weakly formal physical constraint term is formed using the construction method described in step S23 based on the weighted integral of the conservation equation residual and the test function. The boundary consistency constraint term is used to constrain the consistency of boundary conditions such as the inlet, outlet, and wall. The regularization term is used to suppress overfitting and training oscillations.

[0049] The weak physical constraint terms are not a single, overall physical loss, but rather constructed hierarchically based on scale level, spatial region, boundary type, and gradient change intensity. This results in one or more of the following: macro-scale region physical loss, meso-scale region physical loss, micro-scale region physical loss, and boundary region physical loss. Weights are assigned to physical loss terms at different levels to achieve coordinated constraints on overall conservation, local conservation trends, and boundary consistency. For high-gradient regions, micro-scale detail regions, and boundary perturbation regions, the weight of local weak constraint terms is increased; for mainstream regions, overall channel regions, and macro-scale flat regions, the weight of regional average weak constraint terms is increased; for entrance boundaries, exit boundaries, and wall boundaries, the weights of corresponding boundary consistency constraint terms are configured according to the boundary physical conditions. Through this method, a hierarchical physical loss system oriented towards different scale levels and different spatial regions can be formed.

[0050] During training, the total loss function serves as the unified optimization objective for updating network parameters and participates in backpropagation. In the early stages of training, data supervision is prioritized, allowing the graph structure encoding module, visual encoding module, and spatiotemporal-frequency fusion embedding module to learn stable cross-modal representations first. As training progresses, the weights of weakly form physical constraints and boundary consistency constraints in the total loss are gradually increased, transitioning the training process from data-driven to data-physical co-driven. During the staggered freezing and alternating training phases, the weakly form physical constraints preferentially apply to the parameters of the currently participating modules to alleviate gradient conflicts, training divergence, and convergence difficulties in the multi-module joint optimization process. The weight scheduling of the weakly form physical constraints can be further implemented by combining the staggered freezing strategy of step S32 and the progressive weight scheduling strategy of step S33.

[0051] Furthermore, during cross-scale sampling and hard example mining, the physical loss weights for corresponding regions can be dynamically adjusted based on the regional prediction error, the magnitude of the conserved residual, or the degree of boundary mismatch. Resampling or enhanced training can be implemented for regions with larger errors, thereby improving the model's learning ability and prediction accuracy for local high-gradient details, boundary perturbation regions, and complex working conditions. Through the above-mentioned data-physical joint loss construction and training participation methods, the physical rationality, boundary consistency, and cross-working-condition generalization ability of the model's prediction results can be improved while ensuring sample fitting accuracy.

[0052] S32: Staggered Freeze and Rotation Training.

[0053] The network is divided into a graph structure encoding module, a visual encoding module, a spatiotemporal-frequency fusion embedding module, and a physical embedding reinforcement module. A staggered freezing and alternating training strategy is adopted to alleviate gradient conflicts, training divergence, and convergence difficulties in the overall end-to-end training process. Specifically, the graph structure encoding module, visual encoding module, and spatiotemporal-frequency fusion embedding module can be stabilized first, and then the weak physical constraints corresponding to the physical embedding reinforcement module can be gradually introduced to achieve a smooth transition from feature learning to data-physical co-optimization.

[0054] S33: Physical weight progressive scheduling and cross-scale sampling, hard example mining.

[0055] A phased physical loss weight adjustment strategy is adopted to gradually transition the training process from data-driven to data-physical co-driven. This is based on the training phase... Perform progressive reinforcement without fixing the weights of weak-form physical constraints.

[0056] Step S4: Build a cloud platform to realize real-time simulation and online correction of the thermal flow field.

[0057] The cross-scale heat flow field prediction models obtained in steps S2 and S3 are deployed to a cloud platform. Through mechanisms such as real-time data access, online inference, result caching, visualization, and online correction, real-time simulation and online correction of the heat flow field of the air-cooled heat exchanger are achieved. This step addresses the problem that existing digital twin systems are difficult to deeply couple with high-precision heat flow field models and lack dynamic correction capabilities.

[0058] S41: Cloud deployment and data access, unified data model.

[0059] The multi-scale thermal flow field prediction model is encapsulated as a cloud-based inference service, forming a service-oriented system architecture that includes model inference services, data access services, task scheduling services, and visualization services. The cloud platform connects to edge gateways and data collectors to access operational data in real time and maps this real-time data to a unified data model to ensure consistency between data from different sources and the model input interface.

[0060] S42: Online simulation and rapid generation of thermal flow field.

[0061] The platform invokes the model inference service at fixed time steps or through event triggering. When real visual input is missing, it matches prior thermal flow field images in the vector database through prior degradation and high-speed retrieval routing. It inputs the operating condition vector and structural topology diagram, and quickly outputs the temperature field, velocity field, pressure field, and key performance indicators, realizing real-time online simulation of the thermal flow field of the air-cooled heat exchanger. In the case of time evolution modeling, the platform can also convert the predicted thermal flow field results of the previous moment into a recursive image representation, which is used as at least part of the visual input of the thermal flow field at the current moment, and inputs it into the online inference model together with the operating condition vector and structural topology diagram.

[0062] S43: Online correction and drift adaptation.

[0063] To suppress model drift caused by changes in on-site operating conditions, the platform provides an online correction mechanism, which includes at least one or more of residual correction, weakly supervised fine-tuning, and topology version management.

[0064] S44: Platform visualization and interface openness.

[0065] The platform provides a two-dimensional or three-dimensional thermal flow field visualization interface and provides real-time results, historical playback and other data to the upper-level system through the application programming interface to support monitoring, early warning, performance evaluation and optimization control.

[0066] By employing the above-described technology, the beneficial effects of the present invention compared to the prior art are as follows: 1) This invention constructs a thermal flow field generation model based on a directional fine-tuning large model, and generates cross-scale virtual samples by combining structural conditions, operating conditions and scale labels. This can reduce the direct dependence on high-cost CFD labeled samples, while expanding the coverage of training samples under different structural forms, different operating conditions and different scale levels, thereby providing a data foundation for subsequent thermal flow field modeling.

[0067] 2) This invention constructs the structural units of the air-cooled heat exchanger and their flow coupling and heat transfer coupling relationships as a graph structure input, and performs cross-modal fusion with the visual information of the heat flow field and the physical input information. This can simultaneously characterize the complex structural connection relationship of the equipment, the spatial distribution characteristics of the heat flow field, and the operating conditions and spatiotemporal state information, which is beneficial to improving the unified modeling capability of the complete heat flow field distribution.

[0068] 3) This invention introduces a continuous neural operator mapping mechanism, which simultaneously represents the continuous physical evolution from the macroscopic global flow field to the microscopic boundary layer details through the same set of operator parameters, thereby enhancing the prediction rigor and generalization ability of the model in complex multi-scale thermal flow field scenarios.

[0069] 4) This invention embeds the constraints related to mass conservation, momentum conservation, and energy conservation into the training process in a weak form based on the weighted integral of the test function, and performs synergistic optimization in conjunction with weak boundary condition constraints. This allows the model output to better balance the overall conservation law, local conservation trend, and boundary consistency while meeting the sample fitting requirements. In particular, in high gradient regions, micro-scale detail regions, and boundary perturbation regions, the use of local test functions to construct weak constraints helps reduce the sensitivity of training to single-point residual anomalies, improves the physical rationality of prediction results, and alleviates local non-physical interpretations and boundary distortion problems.

[0070] 5) This invention, by employing training strategies such as data-physical joint loss, priority of weak form physical constraints, staggered freezing and alternating training, progressive scheduling of physical weights, and cross-scale sampling and hard example mining, can alleviate the problems of gradient conflict, training divergence and convergence difficulties in the training process of large-scale hybrid networks, thereby improving the model training stability and cross-condition generalization ability. Attached Figure Description

[0071] Figure 1 This is the overall logic flowchart of the method of the present invention; Figure 2 This is a schematic diagram of the structure of the Graph-ViT-Physics network of the present invention; Figure 3 This is a logical diagram of the training strategy of the present invention; Figure 4 This is a schematic diagram of the cloud platform architecture of the present invention. Detailed Implementation

[0072] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0073] like Figure 1 As shown, a cross-scale machine learning simulation method for the thermal flow field of an air-cooled heat exchanger includes the following steps: Step S1: This embodiment addresses the issues of high computational overhead and scarcity of multi-scale thermal flow field observation data in high-precision computational fluid dynamics simulation of air-cooled heat exchangers. By introducing a physical constraint-oriented fine-tuning of a basic large model with multi-modal understanding capabilities, a dedicated thermal flow field generation model is constructed, thereby rapidly generating high-quality virtual samples in batches.

[0074] S11: Multi-source heterogeneous data acquisition and graph-structured abstraction

[0075] First, initial high-fidelity flow field data of the air-cooled heat exchanger was collected through CFD simulation and reconstruction of historical sensor measurement points in the field, establishing an initial training set containing 5000 operating conditions. The data was divided into three scales based on spatial resolution. The system-level macroscale covered the entire tube bundle area and fan section (e.g., 12m × 12m, mesh resolution 0.1m); the tube-row level mesoscale covered local multi-row heat exchange tubes and finned channels (e.g., 0.5m × 0.5m, mesh resolution 5mm); and the near-wall level microscale was used to analyze fin gaps and the tube wall boundary layer (e.g., 20mm × 20mm, mesh resolution 0.1mm).

[0076] The mechanical structure of the air-cooled heat exchanger is abstracted as a topological graph with node and edge attributes. ,in This is a set of component nodes, where different nodes represent different finned tubes. The set of edges connected by fluid and heat conduction, and the node attribute matrix. Includes geometric parameters and physical property parameters such as pipe diameter and fin spacing, and an edge attribute matrix. This includes the spatial distance between nodes and the heat exchange area.

[0077] S12: Conditional Coding and Multimodal Feature Alignment

[0078] To enable subsequent open-source foundational models to generate thermal flow fields on demand under given structural constraints, operating condition constraints, and target output constraints, this step performs unified standardization on multi-source heterogeneous datasets and constructs normalized condition vectors through a multi-modal feature alignment mechanism. The specific construction process consists of the following three steps: The first step is to independently encode the physical conditions, target category, and scale label. Continuous physical conditions such as inlet wind speed and ambient temperature are extracted using a multilayer perceptron to obtain the condition features. Simultaneously, multiple predicted target types are transformed into dense vectors through an embedding layer. And the scale label of the corresponding sample Transformed into scale feature vectors through the embedding layer .

[0079] The second step is to perform graph topology feature encoding based on spatial message passing. A spatial message passing neural network (MPNN) with edge conditions is used to extract topology features, which can accurately characterize the aerodynamic shading and thermal wake interference effects between the tube bundles of the air-cooled heat exchanger. Attribute graph mapping is used to transform the discrete, irregularly arranged heat exchanger tube bundles in reality into a mathematical matrix that the neural network can process. Within the topology graph with node and edge attributes in S11, the initial node features... Characterizing the geometric properties of the i-th heat exchange tube, where each term represents the tube's horizontal and vertical coordinates in space, outer diameter, fin height and spacing, respectively; edge characteristics The explicit formula includes the relative spatial distance between nodes and the deflection angle of the connecting line, used to characterize the directionality and resistance path of fluid flow. The terms in the formula represent, respectively, the relative distance between pipe j and pipe i on the X and Y axes, the Euclidean distance between the two pipes, and the cosine of the angle between the connecting line of the two pipes and the incoming wind direction. The MPNN network performs message passing at layer L. In layer l, node i receives messages from its neighbor j. Depend on Edge feature modulation is generated, and then local influences are aggregated and hidden layer states are updated. The process and node state update are as follows: Equation (2) and Equation (3): (2); (3); Where l is the current number of neural network layers (i.e., the depth of fluid transmission). The wake effect is transmitted from pipe j in the l-th layer to pipe i. This is a vector concatenation operation, which combines three short vectors into a longer vector. MLP is a multilayer perceptron. It is the set of neighbors of node i (i.e., all pipes that are upstream and around it and that will affect it).

[0080] Finally, global topology aggregation is performed, and the variable-length bundle node feature set is compressed into a fixed-length global topology feature vector using a readout function. This process combines global average pooling and max pooling to capture the overall structural mean and extreme throttling bottlenecks, as well as the topological feature dimension. You can set it yourself, and the process is as follows (4): (4).

[0081] The third step is to concatenate the feature vectors of the four independent modalities along the channel dimension and then pass them through a linear projection layer. Mapping to a unified latent feature space generates the final conditional vector. As shown in equation (5): (5).

[0082] S13: Large Model Oriented Fine-Tuning and Weak Form Physics Prior Guidance

[0083] An open-source foundational model with multimodal understanding and conditional generation capabilities (such as a conditional latent diffusion model based on Diffusion) is selected as the initial model. This model includes a variational autoencoder (VAE) and a conditional denoising U-Net network. Targeted fine-tuning is performed using the conditional training sample set constructed in steps S11 and S12. The specific implementation process consists of the following three steps.

[0084] The first step is the high-dimensional compression and conditional injection of the physical field. To reduce the computational complexity of generating high-resolution flow fields, the encoder in a pre-trained variational autoencoder is first utilized. High-fidelity real samples of thermal flow fields Compressing to a low-dimensional latent space yields latent variables. In the denoising process of U-Net, the unified conditional vector generated in step S12 is... As the key and value of the cross-attention mechanism, they are injected into each layer of the U-Net network, thereby guiding the model to be generated on demand.

[0085] The second step is the fine-tuning of the data-physical joint loss function in large-scale model fine-tuning. The total training loss function in the large-scale model fine-tuning process consists of four terms: generation and reconstruction loss. Conditional consistency loss Weakly Form Physical Prior Loss for Generation Boundary consistency loss The weights of each term are assigned using a progressive scheduling strategy. The total training loss function is as follows (6): (6).

[0086] The generation and reconstruction loss measures the accuracy of the model's denoising predictions in the latent space. In the diffusion model, it is represented by the mean squared error between the predicted noise and the actual added noise; the conditional consistency loss uses a contrastive loss to ensure that the generated latent variable distribution matches the conditional vector. Strong correlation; to ensure that the generated flow field conforms to the laws of fluid dynamics, the latent variables predicted by the network must first be... via decoder Restored to the generated heat flow field It was then analyzed as a velocity field in space. and pressure field ,in This represents a two-dimensional spatial coordinate vector. Taking the continuity equation (mass conservation) of incompressible fluids as an example, a local control volume is constructed. Weak form residuals within As a physical prior guide for the generation side, this process does not directly constrain the final physical field, but rather backpropagates the weak-form residuals to the latent space, ensuring that the characteristic distribution generated by the large model does not deviate from the hydrodynamic baseline. In the equation... To define a Gaussian test function that varies with spatial coordinates over a local subdomain, and At least one of the weak-form physical prior losses of the latent space; the boundary consistency loss is for the heat exchanger tube wall (let's say...). Apply a no-slip condition (u=0, v=0) penalty term. .

[0087] The third step involves progressive fine-tuning and setting weight scheduling parameters. In this example, there is often a conflict in magnitude between the data and physical gradients. Therefore, a progressive weight scheduling strategy is adopted, divided into two stages: warm-up (Epochs 1-20) and physical coupling (Epochs 21-100). In the warm-up stage, the model is driven solely by data and conditions, prioritizing the generation of flow field images with tube geometry characteristics. Then, the physical and boundary constraints are gradually unfrozen. A cosine annealing strategy is used to force the model to find a set of solutions in the latent space that satisfy both the visual features of the image and the manifold of the partial differential equations in fluid dynamics.

[0088] S14: Large-scale sample generation based on Latin hypercube sampling and physical residual posterior filtering

[0089] The fine-tuned heat flow field generation model obtained in step S13 The process of generating virtual samples of multi-scale thermal flow fields under different structural conditions, different operating conditions, and different target output conditions is divided into the following four steps.

[0090] The first step is to define the boundaries of the parameter space and orthogonal sampling. First, define the boundaries of the operating parameters of the air-cooled heat exchanger (such as the maximum / minimum range of inlet air velocity and ambient temperature) and the boundaries of the structural topology parameters (such as the tolerance range of fin spacing and heat exchanger tube blockage rate). Then, use the Latin hypercube sampling algorithm to sample from this joint space. A set of unbiased parameter combinations, transforming these parameters into a corresponding set of conditional combinations. .

[0091] The second step is directional, controlled generation based on fine-tuning of the large model. For each combination of conditions, it is input into the heat flow field generation model fine-tuned in step S13. The model, based on given structural constraints, operating condition constraints, and scale conditions, performs denoising deduction in the latent space, and then reconstructs it using a decoder to generate the corresponding [number of elements]. Target heat flow field The generation process strictly follows the mapping relationship. .

[0092] The third step is sample screening based on weakly form conserved residuals. To eliminate non-physically distorted samples caused by model illusions during the generation process, each generated sample... Perform a physical feasibility test. Calculate. The sum of the mass and momentum conservation residuals within the control domain The weak-form mass-conserving residuals defined in step S13. Set a rejection threshold based on this. .like If the generated sample does not conform to the laws of fluid mechanics, it will be rejected.

[0093] The fourth step is the construction of the virtual sample library and the exposure of prior interfaces. This involves the data retained after residual screening. We organize, label, and store high-quality samples to construct a virtual sample library covering multiple structural forms, multiple operating conditions, and multiple scale levels. The virtual sample library is represented as... Furthermore, the image-based results in this sample library... When the visual input of the real thermal flow field is missing, incomplete, or of insufficient quality, it is directly used as the prior source, initialization input, or alternative input for the cross-modal neural network visual input in step S2.

[0094] Step S2: Construct a dedicated neural network for cross-scale modeling of air-cooled heat exchangers to achieve cross-modal fusion of topological, visual, and physical information. This step overcomes the communication barrier between discrete topology and continuous physical domain, achieving strict alignment of multimodal features. By introducing a graph-mesh spatial mapping mechanism, discrete structural topological features are smoothly projected onto a continuous physical space coordinate system, thereby eliminating the spatial mismatch problem between different modal data.

[0095] like Figure 2 As shown, the dedicated neural network is the Graph-ViT-Physics multimodal fusion prediction network, which includes at least an input layer, a graph structure encoding module, a visual encoding module, a time-space-frequency fusion embedding module, a cross-modal fusion module, and a decoding output layer.

[0096] S21: Definition of Special Neural Networks and Input Layer

[0097] The input format of the multimodal fusion prediction network is uniformly defined. The input layer receives structural connection and coupling topology information, thermal flow field visual information, physical input information, and scale labels. Among them, structural connections and coupling topology information Derived from the attribute diagram of the air-cooled heat exchanger expressed in the graph structure in step S1; visual information of the heat flow field. The data is derived from discrete measurement point interpolation maps or retrieved from an offline, multi-scale virtual sample library to obtain matching high-confidence prior images. In real-time simulation scenarios, to avoid the latency caused by calling large models for denoising and generation, when the real visual input is missing, the model does not perform real-time latent space generation. Instead, based on the current physical condition vector, it performs nearest neighbor (K-NN) retrieval in a pre-built prior feature library to obtain matching prior images, such as RGB tensors with dimensions of 512×512×3; physical input information... Includes physical coordinates, time, and operating condition vectors; scale labels. Used to indicate the spatial analytical scale of the current computational domain, i.e., macroscale, mesoscale, or microscale.

[0098] S22: Graph Structure Coding, Visual Coding, and Spatiotemporal-Frequency Fusion Embedding

[0099] The above inputs are encoded independently to extract single-modal features.

[0100] For the graph structure encoding module, a spatial message-passing neural network (MPNN) with edge conditions is used as the graph structure encoding module. The input topology graph undergoes multi-hop information transfer and global aggregation to output fixed-length topology features. .

[0101] For the visual encoding module, a hierarchical visual encoding module based on a moving window self-attention mechanism is adopted. Visual input Multi-stage downsampling was performed to extract and preserve visual features of the two-dimensional physical structure of the space. .

[0102] For the time-space-frequency fusion embedding module, an encoder that incorporates Fourier feature mapping is used. Extracting frequency information enhances the model's perception of high-gradient regions. From physical input... Extracting continuous spatiotemporal coordinate vectors from the middle Construct Fourier feature maps As shown in equation (7): (7); in Represents the frequency mapping function. This is a frequency sampling matrix used to project low-dimensional spatiotemporal coordinates to a high-frequency space; its elements follow a Gaussian distribution. Sampling was performed on the sample.

[0103] Then high frequency characteristics The working condition vector and the scale label embedding vector are concatenated in the channel dimension, and the final physical features are output by the multilayer perceptron as shown in Equation (8): (8).

[0104] S23: Physical Embedding Enhancement Module

[0105] This module does not add computational burden during the forward inference stage. Instead, during the end-to-end joint training phase of the network, based on the target thermal flow field results with real physical dimensions output by the decoder, it calculates the end-to-end weakly form-conserved residuals based on the weighted integral of the test function, and backpropagates the conservation laws of mass, momentum, and energy as part of the final correction loss. This step aims to improve the degree to which the physical field prediction results satisfy the fluid dynamics conservation equations after feature cross-modal fusion, thereby enhancing the physical consistency and prediction accuracy of online inference. The specific implementation process consists of the following four steps.

[0106] The first step is to prepare the flow field prediction results by analysis and differentiation. From the decoder output in step S25, the velocity field at the corresponding spatial location is analyzed. Pressure field and temperature field Using the automatic differentiation mechanism of a deep learning framework, the above physical quantities are calculated with respect to spatial coordinates. The first and second partial derivatives are used to prepare for constructing the residuals of the partial differential equation.

[0107] The second step is to construct the point-state conservation equation residuals. Based on the fluid physics characteristics inside the air-cooled heat exchanger, a point-state physical conservation residual matrix is ​​constructed. The mass conservation residual is... The residual due to the conservation of momentum is The air density and kinematic viscosity can be provided by the operating condition vector; the energy conservation residual is... ,in Where is the thermal diffusivity, This is the equivalent heat source term for the finned tube wall surface.

[0108] The third step is based on spatial partitioning and test functions. The weak form integral. To avoid directly penalizing the high-frequency gradient noise generated by the point-state residuals, the computational domain is... Divided into A partially overlapping or non-overlapping integral control subdomain Based on the physical gradient characteristics of the flow field region, different test functions are adaptively invoked. For the mainstream region, the overall channel region, or the macro-scale flat region, a piecewise constant function is selected; for the high gradient region, as well as the micro-scale detail region or boundary disturbance region such as the fin gap, a locally tightly supported Gaussian test function is selected. An example of the piecewise constant function is shown in Equation (9), and an example of the locally tightly supported Gaussian test function is shown in Equation (10).

[0109] (9); (10); in For subdomain The center coordinates, The Gaussian variance of the control function's support range. The indicator function is used. Finally, the weighted integral residual term is calculated using the Monte Carlo integration method, and the mass scalar, momentum vector and energy scalar residuals are unified into the same scalar metric space by calculating the square of the second norm of each term, as shown in the following equation (11): (11).

[0110] It should be noted that, due to the different physical dimensions and numerical levels of the residuals of mass, momentum, and energy conservation, in actual network training, the residuals of each physical field are either dimensionless or configured with independent adaptive balancing weights before calculating the L2 norm, in order to prevent a single high-order physical loss from dominating the gradient update direction of the network.

[0111] The fourth step is to apply boundary consistency constraints. To ensure consistency of conditions such as inlet flow rate, outlet pressure, wall slip-free conditions, and temperature boundaries, a mean square error penalty is applied to the corresponding geometric boundaries, as shown in equation (12): (12); in and These represent the entrance and the wall boundary region, respectively, and the wall boundary... The continuous spatial geometric position has been obtained by the cross-modal fusion module and linked with the discrete graph nodes in step S12. The physical coordinates achieve precise spatial mapping alignment. Specify the wind speed at the inlet. The wall temperature, These are a series of boundary weight coefficients.

[0112] Finally, the calculation results of the above steps are combined to output the final loss term of the physical embedding enhancement module, as shown in the following equation (13): (13).

[0113] This item will then be passed to step S3 and participate in the network training as part of the total loss function.

[0114] S24: Cross-modal fusion module

[0115] Visual features It possesses a two-dimensional spatial topological structure, and its topological features With physical characteristics All are one-dimensional global vectors. In order to achieve accurate injection of physical conditions without destroying spatial information, this embodiment adopts a multi-head cross-attention mechanism to unify structural connections and coupling relationships, spatial field distribution and physical conditions into the same representation space.

[0116] Two-dimensional visual features derived from the coding layer Flattening the sequence spatially, it transforms it into a one-dimensional long sequence, which serves as the query baseline sequence Q for the attention mechanism. Simultaneously, the one-dimensional graph structure topological features are... With physical characteristics The sequence is concatenated along the channel dimension and mapped to a global condition sequence containing multiple potential physical modes through a fully connected network. This sequence is used as the key sequence K and value sequence V of the attention mechanism. The flattened visual spatial features are used to query the global physical and structural conditions and calculate the attention distribution of cross-modal features. This cross-attention mechanism not only completes the alignment of feature dimensions but also substantially acts as a graph-mesh spatial mapper. It uses the continuous spatial coordinates of visual features as an index to smoothly project discrete topological features containing tube geometry information and assign them to a continuous two-dimensional physical mesh, thereby effectively overcoming the communication gap between the discrete topological graph and the subsequent continuous physical boundary integral. The core fusion formula retained in this step is as follows (14): (14); in, Intermediate fusion features output by the attention mechanism; This is a dimension scaling factor used to prevent the gradient from vanishing due to excessively large matrix dot product results.

[0117] The fusion feature sequence obtained above After residual connection and layer normalization, a spatial reshaping operation is performed to restore it to its original state. The original two-dimensional spatial topological resolution.

[0118] Finally, a cross-modal fusion function is constructed and a unified feature representation is output as follows: Through this step, the multi-source heterogeneous inputs are scientifically mapped into high-dimensional latent space feature tensors that can be directly computed by the decoder.

[0119] S25: Decoding and Output Definition

[0120] This step maps the latent space features obtained through cross-modal fusion into a high-resolution target thermal flux field readable by humans and downstream systems. The decoder in this embodiment employs a scale-adaptive operator solution architecture and includes a temporal feedback mechanism. The unified feature representation obtained in step S24 is then... Input to decoder The decoder does not use a fixed network depth, but dynamically controls the number of upsampling layers based on the scale label passed in step S21. For computational scenarios with high target output resolution, strong local detail changes, or requiring resolution of near-wall boundary layers, the decoder activates more upsampling and local reconstruction modules; for computational scenarios with low target output resolution or relatively gentle field distribution changes, the decoder uses fewer reconstruction layers. This mechanism ensures that a single network can adaptively output flow field results at different physical scales. After spatial resolution, the decoder uses neural operators to perform cross-scale resolution of continuous feature manifolds. For a given scale label... The output heat flow field In essence, it is the continuous sampling of the operator at the target spatial resolution, and its mapping process is shown in the following equation (15): (15); In the formula, For network parameters The given continuous integral kernel function, as defined in the formula, characterizes the model's ability to reconstruct physical fields across scales in a resolution-independent manner.

[0121] When handling non-steady-state time-series scenarios such as wind turbine start-up and shutdown, and sudden changes in environmental wind, the model introduces a recursive closed-loop mechanism. This mechanism is used to handle the current time... Output thermal flow field results The image representation is re-constructed and used as a feedback signal to input to the next time step. In the visual encoding module, the prediction results from the previous moment, together with the operating parameters and topology graph of the next moment, constitute new inference conditions. This mechanism enables the network to capture transient fluid evolution processes.

[0122] Step S3: Construct a data-physical collaborative network training strategy to alleviate training difficulties and enhance physical consistency. Addressing the issues of gradient conflicts, training divergence, and convergence difficulties that easily arise during joint training of hybrid networks composed of graph structure encoding modules, visual encoding modules, spatiotemporal-frequency fusion embedding modules, and physical embedding reinforcement modules, this invention adopts a strategy combining staged training and dynamic weight scheduling, specifically including the following:

[0123] like Figure 3 As shown, the training process is divided into a feature preheating stage, a physical injection stage, and a full network joint fine-tuning stage. Combined with the progressive scheduling of physical weights and the cross-scale hard example mining mechanism, a smooth transition from data-driven to data-physical collaborative driving is achieved.

[0124] S31: Hierarchical Construction of Data-Physical Joint Loss

[0125] Based on the weak-form physical constraint terms obtained in step S23, a joint loss function for end-to-end network optimization is constructed. For the weak form physical constraint terms The hierarchical construction is performed according to the scale label. The three terms correspond to the weakly weighted integral residuals calculated in step S23 for the mainstream flat area, the overall channel area, and the near-wall high gradient area, respectively. The three coefficients are the spatial hierarchy weights dynamically activated according to the scale label of the current training sample, as shown in the following equation (16): (16).

[0126] S32: Staggered Freeze and Alternating Training

[0127] In multimodal and physical constraint joint training, the directions of data-driven gradients and physically driven gradients are often inconsistent, which can easily lead to network oscillations. This embodiment adopts a staggered freezing and alternating training strategy. Training is divided into three stages. The first stage is feature warm-up, in which only data-driven training of the graph structure encoding module, visual encoding module, and decoder is used, and the physical loss weights are frozen to 0. The second stage is physical injection, in which the parameters of the visual and graph encoders are frozen, the physical loss weights are activated, and physical partial derivatives are calculated only for the cross-modal fusion layer, the spatiotemporal frequency embedding module, and the decoder to optimize these parameters to satisfy the conservation equations. The third stage is joint fine-tuning, in which the entire network is unfrozen and global collaborative optimization is performed with a small learning rate.

[0128] S33: Physical Weight Progressive Scheduling and Cross-Scale Hard Example Mining

[0129] The purpose of this step is to dynamically adjust the strength of physical constraints during training rounds and dynamically focus on high gradient regions that are difficult to fit in the spatial data dimension, thereby achieving a smooth transition from pure data fitting to obedience to physical laws, and ultimately improving the prediction accuracy for complex working conditions and local physical details.

[0130] The incremental scheduling mechanism of physical weights refers to abandoning the fixed hyperparameter settings for the physical constraint weights defined in S31 and adopting a polynomial warm-up scheduling strategy that dynamically increases with the training epoch, as specifically expressed in the following formula (17): (17); in, This is the current training round; The total number of training rounds set; This represents the threshold number of rounds in the preheating phase. The upper limit of the maximum physical loss weights expected to be reached at the end of training; This is a non-linear growth factor, corresponding to the power term requirement in the invention. In the initial training phase... Approaching 0. At this point, the network is entirely driven by data supervision, prioritizing the rapid learning of cross-modal feature alignment mappings to avoid introducing strong second-order partial derivative calculations at the outset, which could lead to gradient explosion. In the later stages of training, physical weights are adjusted according to... The network further applies physical partial differential equation manifold constraints to the already formed flow field profile, enabling the flow field prediction results to better satisfy the laws of mass and momentum conservation.

[0131] The cross-scale sampling strategy targets samples with three different spatial resolutions (macro, meso, and micro) contained in the virtual sample library. When constructing training batches, instead of using purely random sampling, it introduces scale-label-based sampling. Stratified sampling is employed. Microscale samples contain numerous dramatic gradient changes, contributing significantly more to the residuals of the physical equations than macroscale, gentler airflow regions. Increasing the sampling ratio between mesoscale and microscale helps the network learn cross-scale features more evenly, preventing model parameters from collapsing to only respond to macroscopic, low-frequency features. For example, setting the total number of samples in a batch to... The mandatory scale allocation sampling ratio is macroscale: mesoscale: microscale = 1 : 2 : 2.

[0132] During training, a dynamic resampling mechanism is implemented for regions with large prediction errors (such as fluid separation regions). After one training round, for the i-th sample region in the training set, the scalar sum of its local weakly form-conserved residuals is calculated. As shown in equation (18): (18); in, This represents the physical residual assessment value for this region in round e. This represents the probability that the sample will be selected into the batch in the next round of training. To control the degree of tilt towards difficult cases, the temperature over-parameter of resampling is adjusted. Let this be the total number of samples in the pool. Define the dynamic sampling probability. This makes it positively correlated with the physical residual of the previous round, as shown in equation (19): (19).

[0133] Traditional hard case mining typically relies on the data fit error (MSE) to find hard cases. This approach, however, uses physical residuals. As a criterion for judging difficult cases, if the physical residual in a certain local region is extremely large, it indicates that the deep learning model violates the common sense of fluid dynamics in that region. By dynamically increasing its sampling probability, the network is guided to perform targeted optimization on these high-gradient complex regions in the next round of training.

[0134] Step S4: Construct a cloud platform to realize real-time simulation and online correction of the thermal flow field of the air-cooled heat exchanger. This platform is used to solve the problem that existing digital twin systems are difficult to deeply couple with high-precision thermal flow field models and lack dynamic correction capabilities.

[0135] like Figure 4 As shown, the cloud platform adopts a service-oriented architecture, including model inference services, data access services, task scheduling services, and visualization services, and achieves standardized access to on-site operational data through a unified data model.

[0136] S41: Cloud deployment and data access, unified data model

[0137] The dedicated neural network for cross-scale modeling of air-cooled heat exchangers trained in steps S2 and S3 is serialized and packaged into a cloud-based inference service (such as a high-performance computing graph based on ONNX or TensorRT). Simultaneously, the cross-scale virtual sample library generated in step S14 is deployed as a high-performance vector database in the cloud. The operating condition vectors and topological features of each virtual sample in the sample library are extracted as retrieval keys, and their corresponding generated heat flow fields are used as retrieval values, forming an "offline prior knowledge cache layer" independent of the online inference service.

[0138] Construct a real-time data link between the edge gateway and the cloud platform. To eliminate differences in underlying sensor protocols, the accessed continuous time series are cleaned and aligned, and mapped to a unified data model, as shown in equation (20): (20).

[0139] S42: Online simulation and rapid generation of heat flow field

[0140] This step utilizes cloud-based inference services to achieve dynamic and rapid reconstruction of the thermal flow field of the air-cooled heat exchanger. To balance computational efficiency under steady-state conditions with rapid response to transient disturbances, this implementation scheme adopts a hybrid inference mode combining asynchronous event-driven and synchronous frequency keep-alive approaches.

[0141] The platform integrates a real-time unified data model. Then, the following logic triggers the inference calculation.

[0142] Operating condition drift event triggering (asynchronous mode): The system monitors the real-time operating condition vectors received in real time. Calculate the deviation (e.g., Euclidean distance) between the current operating condition and the previous simulated operating condition. If the deviation exceeds the preset drift threshold, or if a step command such as a fan frequency converter or valve adjustment is received, the system immediately triggers the model to perform real-time simulation. This mode ensures that the twin model can detect and update within seconds when there are environmental wind disturbances or operating load adjustments.

[0143] To ensure millisecond-level latency for online simulations and address the issue of missing on-site visual input, the system introduces a "prior degradation and high-speed retrieval routing" mechanism. When an instant simulation is triggered and the digital twin platform determines that a valid physical visual observation map is currently lacking, the system bypasses and calls the retrieval service. Using the currently received real-time operating condition vector and topology version number as query vectors, the system performs a high-speed cosine similarity retrieval in the cloud vector database constructed in step S41, extracting the most similar offline pre-calculated prior thermal flow field image as a visual substitute input within milliseconds. This image is then fed into a cross-scale dedicated neural network for a single forward propagation calculation. This decoupling mechanism reduces the minute-level computational bottleneck caused by calling large models for online diffusion denoising, which is beneficial for meeting the real-time requirements of the digital twin system.

[0144] Fixed-frequency synchronous simulation (synchronization mode): When the operating conditions are relatively stable and the deviation does not reach the threshold, the platform maintains a fixed, low-frequency time step (e.g., = 10s) Periodically call the inference service. This mode is designed to capture the slow physical evolution inside the heat exchange system, ensuring the continuous stability of the digital twin platform's operational status monitoring and data push.

[0145] After the above triggering conditions are met, the platform invokes the neural network model trained and deployed in step S2 for calculation. After receiving the feature tensor output by the model, the decoder layer maps it into temperature, velocity, and pressure field distributions with physical dimensions. Through this hybrid mode, the cloud platform can significantly reduce GPU computing power redundancy while ensuring the physical continuity of the thermal flow field simulation in the time dimension and the immediacy of the operating condition response.

[0146] S43: Online Correction and Drift Adaptation

[0147] During long-term operation, digital twin models inevitably experience deviations between predicted values ​​and actual physical conditions due to unmodeled gradual physical factors such as ash and scale buildup on heat exchange tubes and mechanical aging of fans (i.e., model drift). To ensure the long-term high fidelity of the twin system, this embodiment constructs a multi-level online correction and drift adaptation mechanism.

[0148] To address slight drift, a lightweight residual correction based on data assimilation is employed. During the system's simulation cycle, the platform synchronously receives low-dimensional real-time observation data collected by physical sensors deployed on-site (such as outlet thermocouples and differential pressure transmitters). To align the high-resolution prediction field with sparse discrete measurement points, the system introduces an observation operator. By comparing the actual observations with the predicted values ​​at the corresponding locations in the model, the dynamic compensation is calculated and superimposed onto the entire field. The core correction formula is as follows (21): (twenty one); in, This represents the high-resolution thermal flow field prediction tensor output in real time from step S42; Represents sparse sensor observation vectors collected in real-world conditions; As an observation operator, it is responsible for mapping or spatially interpolating the high-dimensional prediction field to the physical coordinates of the corresponding sensor so as to perform error subtraction in the same dimension; This is used to correct the gain matrix, dynamically balancing the confidence levels of model predictions and field observations. If sensor noise is high, this gain is decreased; if the model deviates significantly, this gain is increased. This is a high-fidelity corrected heat flow field that is ultimately distributed to the downstream system after residual compensation.

[0149] In this embodiment, the correction gain matrix Instead of fixed empirical values, the system is based on ensemble Kalman filtering or adaptive covariance matrix, and is updated in real time online according to the posterior distribution of historical observation errors and model prediction variance, thereby ensuring the asymptotic convergence of the system under complex operating conditions.

[0150] To address moderate drift, a weakly supervised fine-tuning approach based on a sliding window is employed. This is done when the system detects the observed residuals. If the system continues to exceed the tolerance threshold within the set time sliding window, and the lightweight residual correction is no longer able to effectively eliminate the systematic bias, the platform determines that a moderate model drift has occurred (such as the formation of a steady-state scale layer on the heat exchanger surface).

[0151] To address severe physical abrupt changes, topology version management and model reset are implemented. When significant physical changes occur on-site (such as large-scale shutdown and high-pressure water cleaning of heat exchangers, or large-area abnormal blockage of heat exchange tubes), the structural boundary conditions of the flow field fundamentally change, rendering any residual compensation and fine-tuning ineffective. The system will proactively update the topology version number uniformly defined in S41, load the topology graph input reflecting the latest physical structure, and re-extract topology features. This mechanism reduces the risk of model prediction divergence due to "deriving new physical entities from old structural drawings," ensuring the structural consistency of the digital twin throughout the entire equipment lifecycle.

[0152] S44: Platform Visualization and Interface Openness

[0153] The corrected high-dimensional tensor is mapped to a color map or isosurface through a front-end rendering engine (such as WebGL / Three.js), providing a two-dimensional or three-dimensional thermal flow field visualization interface. At the same time, dimensionality-reduced indicators such as local hotspot extrema and average drag pressure drop are pushed to the upper-level DCS (Distributed Control System) or intelligent operation and maintenance system through RESTful API or WebSockets, forming a physical closed loop for fault early warning and optimized control.

Claims

1. A cross-scale machine learning simulation method for the heat flow field of an air-cooled heat exchanger, characterized in that, Includes the following steps: Step S1: Use historical multi-source data of air-cooled heat exchangers to perform targeted training on the open-source basic model, and introduce latent space physical constraints during the training process to obtain the heat flow field generation model. A cross-scale virtual sample library is constructed by generating virtual samples covering multiple structures, operating conditions, and scales using a thermal flow field generation model. Step S2: Construct a dedicated neural network. The dedicated neural network receives structural topology input, thermal flow field visual input, and physical condition input. It achieves alignment between discrete topological features and continuous physical field features through a cross-modal fusion mechanism and decodes and outputs the target thermal flow field. Step S3: Train the dedicated neural network using a data-physical joint loss function, apply the physical constraints in the loss function in a weak form of integration, and optimize the network parameters by combining a phased unfreezing and progressive weighting training strategy. Step S4: Deploy the trained network on the cloud platform, access real-time running data, generate a heat flow field through a hybrid simulation mode, and eliminate model drift using a multi-level correction mechanism.

2. The cross-scale machine learning simulation method for the heat flow field of an air-cooled heat exchanger according to claim 1, characterized in that, The specific process of step S1 is as follows: S11. Collect multi-source heterogeneous data of the air-cooled heat exchanger and construct a conditional training sample set that includes structural and topological data, operating parameter data, multi-physical quantity heat flow field image data, target output type labels and scale labels. S12. Perform conditional encoding on the conditional training sample set to generate a conditional vector containing structural constraints, working condition constraints, and scale constraints. S13. Select an open-source basic model with multimodal understanding and condition generation capabilities, use a conditional training sample set to adjust the parameters of the open-source basic model in a targeted manner, and introduce latent space weak form physical prior constraints during the parameter adjustment process to guide the model to learn a manifold distribution that conforms to physical laws. S14. Generate cross-scale virtual samples using the thermal flow field generation model after parameter adjustment, and construct the virtual sample library after physical rationality screening.

3. The cross-scale machine learning simulation method for the heat flow field of an air-cooled heat exchanger according to claim 2, characterized in that, The specific process of step S12 is as follows: The structural and topological data, operating condition parameter data, target output type label, and scale label are encoded separately. The generated codes are then concatenated along the feature dimension and mapped through a linear projection layer to generate a condition vector containing structural constraints, operating condition constraints, output type constraints, and scale constraints. The scale labels include macroscale, mesoscale, and microscale.

4. The cross-scale machine learning simulation method for the heat flow field of an air-cooled heat exchanger according to claim 1, characterized in that, The specific process of step S2 is as follows: S21: Define the inputs of the dedicated neural network as including structural topology input, thermal flow field visual input, physical input, and scale label; when real observations are missing, the thermal flow field visual input uses prior images from a virtual sample library or prediction results from the previous time step as alternative inputs. S22: Perform feature extraction and encoding on the structural topology input, thermal flow field visual input and physical input respectively to obtain the corresponding topological features, visual features and physical features, and incorporate the scale label as conditional information into the physical feature encoding or subsequent decoding process; S23: Calculate air density, kinematic viscosity and thermal diffusivity based on the operating parameters of the air-cooled heat exchanger, and construct residuals of the mass conservation, momentum conservation and energy conservation equations for the air-side flow channel; embed the residuals into the training process in a weak form; S24: Spatial alignment of discrete topological features and continuous physical field features is achieved through a cross-modal fusion mechanism to obtain a unified feature representation; S25: Decode the unified feature representation into a target heat flow field that includes temperature field, velocity field, pressure field, and heat transfer performance indicators.

5. The cross-scale machine learning simulation method for the heat flow field of an air-cooled heat exchanger according to claim 4, characterized in that, In step S23, a local tight support test function or a Gaussian test function is used in the high gradient region, micro-scale detail region or boundary disturbance region, and a piecewise constant test function is used in the mainstream region, overall channel region or macro-scale region. The support range of the local tight support test function or Gaussian test function is set based on the structural feature size of the corresponding microscale detail region, and the segment boundary of the piecewise constant test function or piecewise linear test function is set based on the structural feature size of the corresponding macroscale region.

6. The cross-scale machine learning simulation method for the heat flow field of an air-cooled heat exchanger according to claim 4, characterized in that, The specific process of step S3 is as follows: S31: Construct a joint loss function that includes a data supervision term, a weakly formal physical constraint term, a boundary consistency constraint term, and a regularization term; S32: The network parameters are optimized in stages using a staggered freezing and alternating training strategy: the first stage trains the feature encoding module; the second stage introduces physical constraints and optimizes the fusion and decoding modules; the third stage performs joint parameter optimization of the entire network. S33: A physical weight progressive scheduling strategy is adopted to gradually increase the weight of physical constraint terms as the training process progresses; combined with cross-scale sampling and hard example mining strategies, the sampling weight of training samples is dynamically adjusted according to the physical residual.

7. The cross-scale machine learning simulation method for the heat flow field of an air-cooled heat exchanger according to claim 1, characterized in that, Step S4 specifically includes: S41: Encapsulate the trained network into a cloud inference service and build a unified data model containing device identifiers, timestamps, operating condition vectors, and topology version numbers to access field data; S42: Employs a hybrid deduction mode combining asynchronous event triggering and synchronous periodic deduction; retrieves alternative images from a virtual sample library when visual input is missing; S43: Perform corresponding corrections based on the degree of drift; S44: Provides a visualization interface for the thermal flow field and a standard data interface to external users.

8. The cross-scale machine learning simulation method for the heat flow field of an air-cooled heat exchanger according to claim 7, characterized in that, The specific process of S43 is as follows: When the residual between field observations and model predictions does not exceed the preset tolerance threshold, a data assimilation algorithm based on ensemble Kalman filtering is used for residual compensation; when the residual exceeds the tolerance threshold within a set time sliding window and weak supervision adjustment is effective, a weak supervision method based on sliding window is used to adjust network parameters; when the topology version changes, the topology version number is updated and the topology graph corresponding to the latest physical structure is loaded as input to reset the model.

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