Ribbed Concrete Thermal Storage System Based on CFD and Machine Learning Collaboration and Its Optimization Method

Abstract

This invention discloses a ribbed concrete thermal energy storage system and its optimization method based on the synergy of CFD and machine learning, relating to the fields of thermal energy storage and energy engineering. The method first establishes a parametric 3D model of the embedded ribbed concrete thermal energy storage unit and generates samples. Second, it uses computational fluid dynamics (CFD) transient simulation to obtain key thermal performance indicators such as charging time, heat release time, and heat storage capacity for each sample, constructing a deep learning training dataset. Subsequently, it builds and trains a wide-network surrogate model with parallel neuron paths to replace time-consuming CFD calculations. Finally, it employs a multi-objective genetic algorithm to globally optimize the surrogate model, obtaining the Pareto front solution set and selecting the optimal combination of structural parameters that balances rapid charging and releasing heat with high thermal storage capacity. This invention deeply integrates data-driven approaches with physical simulation, significantly reducing computational costs. The optimized 8-ribbed structure, 22mm high and 5mm thick, significantly improves the overall thermal performance of the concrete thermal energy storage system.

Description

Technical Field

[0001] This invention relates to the field of thermal energy storage and energy engineering, specifically to a ribbed concrete thermal storage system based on the synergy of CFD and machine learning, and its optimization method. Background Technology

[0002] Thermal energy storage technology plays a crucial role in fields such as solar thermal power generation, grid peak shaving, industrial waste heat recovery, and building energy conservation. Among them, concrete sensible heat storage systems have broad engineering application prospects due to their simple structure, low cost, and excellent high-temperature resistance.

[0003] To overcome the low thermal conductivity of concrete, existing thermal storage systems often add metal fins to the outside of the heat exchange pipes to enhance heat transfer. However, there are highly complex nonlinear coupling relationships among the geometric parameters such as the number, height, and thickness of the fins. Different combinations of parameters can have contradictory and mutually restrictive effects on the system's charging time, heat release time, and overall thermal storage capacity. Current research and engineering designs mostly rely on single-variable control methods or traditional empirical formulas, making it extremely difficult to find a comprehensive optimal solution in a multi-dimensional parameter space that simultaneously satisfies rapid heat charging and releasing and high thermal storage capacity.

[0004] Furthermore, while CFD-based numerical simulations can provide high-precision thermodynamic analysis, their enormous computational cost and lengthy simulation cycles pose significant bottlenecks for practical application when faced with the selection of large-scale parameter combinations and multi-objective optimization. In recent years, surrogate modeling techniques (such as neural networks) have been introduced to replace time-consuming CFD simulations, but existing methods are mostly based on steady-state or constant boundary condition assumptions, making them difficult to apply to the strong transient and time-varying conditions faced by solar thermal storage systems in actual operation.

[0005] Therefore, there is an urgent need in this field for a multi-objective optimization method for ribbed concrete thermal storage systems that can significantly reduce computational resource consumption while ensuring prediction accuracy and is applicable to real time-varying operating conditions. Summary of the Invention

[0006] To address the aforementioned problems in existing technologies, the present invention aims to provide a ribbed concrete thermal storage system, thermal storage unit, equipment, storage medium, and optimization method based on the synergy of CFD and machine learning. This invention aims to solve the problem that traditional CFD simulations, due to their high computational costs and reliance on steady-state assumptions, cannot accurately reflect the transient operating characteristics of solar thermal storage systems.

[0007] The technical solution of this invention is as follows: The first technical solution provides an optimization method for ribbed concrete thermal storage systems based on the synergy of CFD and machine learning, including the following steps: S1. Parametric Modeling and Sample Generation: Construct a three-dimensional geometric model of the embedded ribbed concrete thermal storage unit, set design variables and their value ranges, the design variables including at least the number of ribs, rib height and rib thickness; use the Latin hypercube sampling method to generate multiple sets of structural parameter samples within the value range.

[0008] S2. CFD Numerical Simulation and Dataset Construction: The inlet boundary conditions of the heat charging stage are defined by a user-defined function (UDF) as a dynamic coupling of a time-varying temperature function and a time-varying flow rate function. Transient heat transfer numerical simulations are performed on the heat storage units corresponding to each set of structural parameter samples using computational fluid dynamics software to obtain performance index samples corresponding to each set of structural parameter samples. The performance indexes include at least the heat charging time, heat release time, and heat storage capacity. The structural parameter samples are used as input features, and the performance index samples corresponding to the structural parameter samples are used as output labels to construct a sample dataset.

[0009] S3. Agent Model Construction and Training: A hybrid deep learning neural network agent model is built using a wide network structure. The agent model is trained and tested using the sample dataset. A non-linear mapping relationship between the structural parameters and the performance indicators is established to replace CFD for fast prediction.

[0010] S4. Multi-objective collaborative optimization: With minimizing the heat charging time, minimizing the heat release time, and maximizing the heat storage as optimization objectives, a multi-objective genetic algorithm is used to perform global optimization on the trained surrogate model to obtain a Pareto front solution set containing a series of non-dominated solutions.

[0011] S5. Optimal Structure Selection and Verification: Select at least one set of non-dominated solutions from the Pareto front solution set, substitute the corresponding structural parameters into the CFD software for back-substitution verification, determine and output the structural parameters of the non-dominated solutions as the optimal rib structure scheme.

[0012] Furthermore, in step S1, setting the design variables and their value range includes at least the following steps: by pre-setting the global extreme value of the design variables as a priori geometric boundary hard constraint, ensuring that all sample parameter combinations meet the physical feasibility conditions; the design variables include at least the number of ribs, the height of the ribs, and the thickness of the ribs; the value range of the design variables is set as follows: the number of ribs is 0 to 8, the height of the ribs is 0.01m to 0.022m, and the thickness of the ribs is 0.001m to 0.005m.

[0013] Furthermore, in step S2, defining the inlet boundary conditions of the heat charging stage by the user-defined function as a dynamic coupling of a time-varying temperature function and a time-varying flow rate function includes at least the following steps: setting the inlet temperature of the heat transfer fluid entering the heat storage module in the first 4 hours of the heat charging stage to a sinusoidal temperature rise by the user-defined function (UDF), and setting the inlet mass flow rate of the heat transfer fluid entering the heat storage module in the first 4 hours of the heat charging stage to increase linearly with time.

[0014] Furthermore, in step S2, performing transient heat transfer numerical simulations on the thermal storage unit corresponding to each set of structural parameter samples using computational fluid dynamics (CFD) software includes at least the following steps: the residual convergence criterion in the transient calculation is that the residual threshold of the energy equation is set to 10. -6 The residual thresholds for the continuity equation and momentum equation are set to 10. -4 .

[0015] Furthermore, in step S3, the construction of the hybrid deep learning neural network proxy model using a wide network structure includes at least the following steps: the wide network architecture contains a total of 4 hidden layers, adopts a layer-by-layer recursive topology structure with no skip connections, and each hidden layer only receives the output of the previous layer as input, without including a cross-layer feature reuse and splicing structure; the neurons in each hidden layer use ReLU as the activation function, and a Dropout mechanism is introduced after the activation function.

[0016] Furthermore, the wide network architecture comprises four hidden layers, employing a layer-by-layer recursive topology with no skip connections. Each hidden layer only receives the output of the previous layer as input, and does not include cross-layer feature reuse and splicing structures. Specifically, the wide network architecture adopts a single-branch unified architecture with the number of neurons successively set to 200, 150, 100, and 50, converging layer by layer in a funnel shape. The wide network architecture contains multiple parallel neuron paths in each hidden layer, and the output of each parallel neuron path is passed to the next hidden layer through a weighted summation.

[0017] Furthermore, in step S3, training and testing the surrogate model using the sample dataset includes at least the following steps: before model training, using the Pearson correlation coefficient to evaluate the linear correlation between the input features and the output target to determine key influencing features; and injecting Gaussian noise and selective linear interpolation into the training dataset to enhance robustness.

[0018] The second technical solution provides a ribbed concrete thermal storage unit, obtained by optimizing any of the methods described above, including: The concrete base is a cylindrical structure with a length of 2m and a diameter of 0.62m. Heat exchange tubes are installed inside the concrete matrix; The longitudinal fins are evenly distributed circumferentially along the outer wall of the heat exchange tube, with a total of 8 fins. Each fin has a height of 0.022m and a thickness of 0.005m.

[0019] The third technical solution provides a ribbed concrete thermal storage system, including: The parametric modeling module is configured to construct a three-dimensional geometric model of the embedded ribbed concrete thermal storage unit, set design variables and their value ranges, and use the Latin hypercube sampling method to generate multiple sets of structural parameter samples within the value range of the design variables. The CFD simulation module is configured to define the inlet boundary conditions of the heat charging stage as a dynamic coupling of a time-varying temperature function and a time-varying flow rate function through a user-defined function. It then uses computational fluid dynamics software to perform transient heat transfer numerical simulations on the heat storage unit corresponding to each set of structural parameter samples, obtaining performance index samples for each set of structural parameter samples. These performance indexes include at least the heat charging time, heat release time, and heat storage capacity. The structural parameter samples are used as input features, and the corresponding performance index samples are used as output labels to construct a sample dataset. The proxy model module is configured to build a hybrid deep learning neural network proxy model using a wide network structure. The proxy model is trained and tested using the sample dataset to establish a non-linear mapping relationship between the structural parameters and the performance indicators, so as to replace CFD for fast prediction. The multi-objective optimization module is configured to minimize the heat release time, minimize the heat charging time, and maximize the heat storage as optimization objectives. It uses a multi-objective genetic algorithm to perform global optimization on the trained surrogate model to obtain a Pareto front solution set containing a series of non-dominated solutions. The verification module is configured to select at least one set of non-dominated solutions from the Pareto front solution set, substitute the corresponding structural parameters into the CFD software for back-substitution verification, determine and output the structural parameters of the non-dominated solutions as the optimal rib structure scheme.

[0020] A fourth technical solution provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor is used to perform the steps of the above-described method.

[0021] Compared with the prior art, the present invention has the following beneficial effects: 1. Enhanced adaptability to operating conditions: By defining the dynamic coupled boundary conditions of sinusoidal temperature rise and linear flow rate increase through UDF, CFD simulation can realistically reflect the transient and time-varying operating conditions of solar thermal systems during actual day and night operation. Compared with the steady-state or constant boundary assumptions commonly used in existing technologies, the surrogate model and optimization results trained by this invention have higher engineering applicability.

[0022] 2. Significantly improved computational efficiency: By constructing a wide network proxy model to replace high-fidelity CFD transient simulation, the single performance evaluation is shortened from hours to milliseconds, making it possible to complete global multi-objective optimization within the design space under limited computing resources.

[0023] 3. Highly targeted network structure: It adopts a funnel-shaped wide network structure with no skip connections and no feature reuse splicing. With only three continuous physical quantity inputs, it effectively avoids the problem of low-dimensional original features being mixed into the high-level output without sufficient decoupling, thus interfering with the prediction accuracy. At the same time, it avoids overfitting on a limited CFD sample set due to the exponential growth of parameter size.

[0024] 4. Optimization results break conventional physical compromises: The optimal fin structure obtained through global optimization can significantly shorten the heat charging time and heat dissipation time while increasing the heat storage capacity, thus meeting the dual engineering requirements of rapid response and high-capacity storage. Attached Figure Description

[0025] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the embodiments are briefly described below: Figure 1 This is a flowchart of an optimization method for a ribbed concrete thermal storage system based on the synergy of CFD and machine learning in one or more embodiments of the present invention. Figure 2 This is a technical roadmap of the optimization method for ribbed concrete thermal storage system based on CFD and machine learning collaboration in one or more embodiments of the present invention. Figure 3 This is a three-dimensional structural diagram of an embedded ribbed concrete thermal storage unit in one or more embodiments of the present invention. Figure 4 This is a front view of an embedded ribbed concrete thermal storage unit according to one or more embodiments of the present invention. Figure 5 A flowchart illustrating the construction process of a machine learning agent model in one or more embodiments of the present invention; Figure 6 This is a schematic diagram of a wide network neural network structure in one or more embodiments of the present invention; Figure 7 This is a three-dimensional Pareto front solution set diagram of the heat charging time, heat releasing time, and heat storage in one or more embodiments of the present invention; Figure 8 This is a fitting verification graph comparing the surrogate model predictions and CFD simulation values ​​corresponding to the Pareto front solution set in one or more embodiments of the present invention. Figure 9This is a comparison diagram of the internal temperature changes of the concrete module before and after optimization in one or more embodiments of the present invention. Figure 10 This is a system block diagram of a ribbed concrete thermal storage system based on CFD and machine learning collaboration in one or more embodiments of the present invention. Detailed Implementation

[0026] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0027] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0028] Example 1: This embodiment proposes an optimization method for ribbed concrete thermal storage systems based on the synergy of CFD and machine learning. The method flow is as follows: Figure 1 As shown, the technical route is as follows Figure 2 As shown, the specific steps are as follows: Step 1: Parametric Modeling and Sample Generation S1. Construct a three-dimensional geometric model of the embedded ribbed concrete thermal storage unit, as shown in the figure. Figure 3 As shown, Figure 4 This is a front view of an embedded ribbed concrete thermal storage unit. Specifically, the thermal storage unit is a cylindrical concrete base, 2m in length and 0.62m in diameter. Heat exchange tubes are arranged inside, with water as the heat transfer fluid (HTF) within the tubes. Longitudinal steel ribs can be installed on the outer wall of the tubes.

[0029] The core design variables are identified as the number of ribs, rib height, and rib thickness. These three variables can be used individually, in combination, or together as optimization variables. By pre-setting global extreme values ​​for the design variables as hard constraints on the prior geometric boundaries, it is ensured that all sample parameter combinations meet the physical feasibility conditions. The value ranges for the design variables are set as follows: 0 to 8 ribs, 0.01m to 0.022m rib height, and 0.001m to 0.005m rib thickness. The above-mentioned value range is strictly controlled by the following three objective constraints: First, the geometric interference condition, which must ensure that any combination of parameters does not physically overlap when arranged circumferentially in the heat exchange tubes, and that the fins do not exceed the boundary of the thermal storage module; second, the thermodynamic critical condition, where the upper and lower limits must cross the two physical extremes of no-fin reference and high thermal conductivity but encroaching on the thermal storage volume, respectively, to fully expose the nonlinear game relationship between heat transfer rate and thermal storage capacity, ensuring that the surrogate model can learn the real physical inflection point; and third, the engineering and numerical conditions, where the lower limit of fin thickness and the gap between adjacent fins must meet the requirements of actual manufacturing processes, and avoid divergence in the solution of fluid-structure interaction equations due to severe distortion of the boundary layer mesh during CFD preprocessing. Through the strict limitation of the above constraints, the high fidelity and engineering effectiveness of subsequent sampling and model training are guaranteed from the source.

[0030] One hundred highly representative structural parameter samples were generated within the design space using the Latin Hypercube Sampling (LHS) method. The LHS method was specifically designed for this multi-objective optimization problem in heat transfer. Since the number, height, and thickness of the fins have strong nonlinear cross-influences at the physical level, traditional full-factor experiments are computationally too costly, while pure random sampling is prone to sample clustering and local blind spots in the multidimensional space. The LHS algorithm divides the probability distribution of each parameter into equally probable intervals for stratified sampling, forcing sample points to be orthogonally and uniformly distributed within the multidimensional continuous design space. This ensures sufficient coverage of the design space with minimal computational scale, thus providing highly representative unbiased training data for the wide network. This is a prerequisite for ensuring that the surrogate model can accurately capture complex thermodynamic response surfaces. For mixed sampling of discrete variables (such as the number of ribs) and continuous variables (such as rib height and rib thickness), the LHS algorithm first generates a uniform sampling point matrix in a normalized multidimensional continuous hypercube space, and then restores it to the physical boundary through inverse mapping: continuous variables are directly linearly mapped to preserve their floating-point geometric precision; while discrete variables are mapped using a step-rounding mapping mechanism, that is, first mapped to the corresponding continuous real number range (such as 0-8), and then forced to be rounded to the nearest integer. This approach not only preserves the orthogonality and uniformity of LHS sampling in multidimensional space distribution, but also ensures that discrete integer features can seamlessly drive the automated parameter construction of downstream modeling software (SpaceClaim).

[0031] Step 2: CFD Numerical Simulation and Dataset Construction S2. Transient heat transfer numerical simulations were performed on the thermal storage unit corresponding to each sample using ANSYS FLUENT software. The SST k-ω model was selected as the turbulence model. This model has a built-in low Reynolds number correction formula, which can accurately analyze the boundary layer convective heat transfer characteristics under laminar, transitional, and low-turbulence conditions. It also has high predictive robustness for local secondary flow and flow separation phenomena induced by geometric abrupt changes in regions such as the heat exchanger tube inlet and fin root.

[0032] The inlet boundary conditions for the charging phase are defined using a user-defined function (UDF). To simulate the actual operating conditions of a solar collector, a temperature curve is set to sinusoidally increase from 300 K to 370 K over the first four hours. In practical engineering applications, from dawn to noon, the solar irradiance naturally exhibits a sinusoidal distribution over time. This periodic change in the external heat source directly drives a corresponding sinusoidal increase in the solar collector outlet temperature (i.e., the inlet temperature of the heat transfer fluid entering the thermal storage module). Therefore, the inlet temperature for the first four hours of the charging phase is set to a sinusoidal increase, and the inlet mass flow rate is set to increase linearly with time.

[0033] The mathematical expression for the time-varying temperature function is:

[0034] Mathematical expression of the time-varying function of flow rate:

[0035] in, The inlet temperature is (K). t represents the inlet mass flow rate (kg / s) and t represents time (s). The inlet temperature is constant at 300K during the exothermic phase.

[0036] This dynamic coupling boundary condition, characterized by sinusoidal heating and linearly increasing flow rate, differs from the unrealistic isothermal and constant-flow idealizations in traditional simulations. It closely approximates the dynamic response of solar thermal collectors under real-world day-night weather conditions. This ensures that the assessed thermal performance indicators and the ultimately optimized fin structure possess high reliability and applicability in real-world solar-coupled thermal storage engineering applications.

[0037] To ensure the absolute high fidelity of the underlying CFD sample dataset, the residual convergence criterion in transient computation is set as follows: the residual threshold of the energy equation is set to 10. -6 The residual thresholds for the continuity equation and momentum equation are set to 10. -4Only when a single iteration simultaneously meets the above residual criteria, and the monitored volume average temperature and inlet / outlet heat flow rate curves tend to stabilize, is the time step considered to have converged.

[0038] The performance indicators for each sample were calculated using CFD simulation. The heating time was defined as the duration required for the average volumetric temperature of the concrete to first reach 370K from an initial 300K. The heat release time is defined as the duration required for the average volume temperature of the concrete to drop back to 300K, i.e. The heat storage is the total heat storage during the 4-hour charging phase.

[0039] Considering the huge computational overhead of transient CFD simulation and the efficiency of the LHS algorithm, this study generated and computed 100 high-fidelity samples. 100 sets of structural parameters were used as input features, and the corresponding charging time, releasing time and heat storage were used as output labels to construct a sample dataset. The dataset was divided into training set and test set in a 9:1 ratio, which is sufficient to support the training of wide networks and avoid overfitting.

[0040] Instead of using error-prone automated meshing scripts when acquiring 100 initial samples, SpaceClaim modeling and ANSYS mesh generation were completed manually one by one, and a baseline mesh of 2.07 million was strictly adopted to ensure high fidelity and absolute consistency in capturing flow field features under different topologies. These 100 high-precision manual simulations in the early stage were used to successfully train the wide network proxy model, which enabled the subsequent MOGA multi-objective optimization to completely get rid of the physical constraints of underlying geometric reconstruction and mesh generation.

[0041] Step 3: Construction and Training of Hybrid Deep Learning Agent Model S3. Build a hybrid deep learning neural network proxy model with a wide network architecture. For example... Figure 6 As shown, this wide network architecture adopts a single-branch unified architecture with four hidden layers. The number of neurons in each layer is 200, 150, 100, and 50 respectively, converging layer by layer in a funnel shape. ReLU is used as the activation function for neurons in each hidden layer, and a Dropout mechanism is introduced after the activation function to enhance the robustness of the model and prevent overfitting.

[0042] This wide network architecture contains multiple parallel neuron paths in the hidden layers. The outputs of each parallel neuron path are passed to the next hidden layer through a weighted summation. The output of the final layer is then mapped to the output layer through a weighted summation to obtain the three target predicted values: heat charging time, heat release time, and heat storage. Here, multiple parallel neuron paths refer to multiple neuron nodes arranged in parallel within the wide hidden layers. For example, the first hidden layer uses 200 neurons to process the input features of the number, height, and thickness of the ribs in parallel.

[0043] Before model training, the Pearson correlation coefficient was used to assess the linear correlation between input features and output targets to identify key influencing features. Gaussian noise injection and selective linear interpolation were applied to the training set to enhance robustness. During training, the Adam optimizer was selected, with an initial learning rate of 0.001. A piecewise decay strategy was adopted, multiplying the learning rate by a decay factor of 0.6 every 400 epochs, with a maximum training epoch count of 1800. Hold-out cross-validation was used until the surrogate model achieved a prediction coefficient of determination (R²) greater than 0.93 for all three core performance indicators (heat charging time, heat release time, and heat storage) on the test set, at which point it was considered the optimal surrogate model.

[0044] This wide network architecture differs fundamentally from the three mainstream network architectures of Wide & Deep, ResNet, and DenseNet in structure, and this difference is irreplaceable in this application scenario, as detailed below:

[0045] Firstly, the difference from the Wide & Deep architecture: Wide & Deep is a typical "two-branch" architecture, consisting of a linear wide branch for memorizing sparse discrete features and a deep branch for extracting dense features, with the two branches concatenated at the output. This model, however, is a unified "single-branch" architecture, where "wide" specifically refers to high-dimensional lateral expansion in the first hidden layer. The input to this scenario consists of three purely continuous physical quantities: the number, height, and thickness of the fins. There are no discrete regular features that need to be independently memorized. If a two-branch structure is used, the linear branch cannot effectively capture the high-dimensional nonlinear coupling effect between geometric parameters and the heat transfer field, instead introducing parameter redundancy and gradient update imbalance. This architecture utilizes a unified high-width hidden layer to directly capture the synergistic effect of convection and conduction within the continuous physical feature space.

[0046] Secondly, the difference from the ResNet architecture: ResNet's core topology is "skip connections," which directly accumulates input features across layers to form an identity mapping, aiming to solve the gradient vanishing problem in ultra-deep networks. This wide network, however, adopts a strict layer-by-layer recursive topology, completely removing the cross-layer short-connection mechanism. In this scenario, there are at most 3 input features mapped to 3 output targets. If skip connections are forcibly introduced or the network depth is blindly increased, low-dimensional original geometric features that are not sufficiently decoupled will be directly mixed into the high-level output, interfering with the accurate prediction of charging and discharging times. This network has only 4 hidden layers, which can ensure the smooth propagation of gradients without skip connections. Its funnel-shaped layer-by-layer convergence structure of 200, 150, 100, and 50 can efficiently purify multi-dimensional coupled features.

[0047] Thirdly, the difference from the DenseNet architecture: DenseNet's topological feature is "feature reuse concatenation," where each layer receives the outputs of all preceding layers as input. This wide network only receives the purified output of the previous layer, without any cross-layer feature reuse concatenation. The first hidden layer of this model has as many as 200 neurons. If the dense concatenation structure of DenseNet were introduced, the parameter matrix size would grow exponentially by the fourth layer, inevitably leading to severe overfitting on sample sets generated from limited CFD simulation data. This architecture, through concatenation-free layer-by-layer dimensionality reduction, strictly constrains the model capacity, ensuring excellent generalization ability while maintaining nonlinear fitting capability.

[0048] Based on the above structural difference analysis, this embodiment selects a funnel-shaped wide network with single branch, no skip connections, and no feature reuse splicing as the basic architecture of the proxy model.

[0049] This wide network architecture is particularly suitable for mapping fin parameters to thermal performance because, at the physical level, the synergistic effect of the number, height, and thickness of fins on convection-conduction is transient and hierarchical. The lateral expansion of the first layer of 200 neurons can directly and fully capture this strongly coupled nonlinear cross-effect. At the mathematical level, this non-shortcut topology of "first extremely high dimensionality decoupling, then smooth dimensionality reduction layer by layer (200-150-100-50)" effectively avoids the "information bottleneck" that low-dimensional inputs are prone to generate in deep networks. It constructs an extremely high-precision and continuously smooth surrogate response surface for the multi-objective genetic algorithm (MOGA), thereby completely avoiding gradient deadlock and ensuring the stability and accuracy of global optimization.

[0050] To verify the superiority of this wide network architecture, five configurations were compared horizontally: deep networks, wide networks, residual networks, densely connected networks, and ultra-deep networks. During the architecture comparison and evaluation phase, only the wide network demonstrated the best fitting and generalization capabilities. Please refer to Table 1 below, which shows the performance metrics of the wide network on the training and test sets. On the training set, the wide network achieved an accuracy of MAE 47.67s, RMSE 77.35s, and R² 0.9742; on the test set, it achieved an accuracy of MAE 88.35s, RMSE 105.43s, and R² 0.9504. Its error metrics were significantly lower than other compared networks, and it had the highest coefficient of determination (R²).

[0051]

[0052] Table 1: Performance metrics of wide networks on training and test sets Step 4: Multi-objective collaborative optimization S4. With the optimization objectives of minimizing the heat charging time, minimizing the heat release time, and maximizing the heat storage, a multi-objective genetic algorithm (MOGA) is used to globally optimize the trained surrogate model. The MOGA parameters are set as follows: population size 100, maximum number of iterations 150, crossover probability 0.8, and Pareto front ratio 0.35. The optimized Pareto front solution set, containing a series of non-dominated solutions, is obtained, such as... Figure 7 As shown.

[0053] Step 5: Optimal Structure Selection and Verification S5. Select the optimal combination of design parameters from the Pareto front solution set, substitute it into CFD software for transient heat transfer numerical simulation, and obtain the verification performance index values. Compare the verification performance index values ​​with the performance index values ​​predicted by the surrogate model, such as... Figure 8 As shown, Figure 8 The fitting verification graph is obtained by global back-substitution comparison of the optimal solution set on the Pareto front. The relative error between the two is no more than ±5%, which meets the accuracy requirements. The high overlap between the predicted scatter points and the actual CFD calculation scatter points fully demonstrates that the wide network model has the ability to completely replace traditional CFD solvers for high-fidelity physical predictions in the multidimensional optimization space. The final optimal rib structure scheme determined and output is: 8 ribs, rib height of 0.022m, and rib thickness of 0.005m.

[0054] Compared with the baseline design before optimization (bare tube model without fins), the optimal structure reduces the heat charging time by 15.56%, the heat release time by 10.18%, and the effective heat storage capacity increases by 5.65% within the specified 4-hour period.

[0055] To further analyze the optimization effect, a Pareto frontier plot was drawn (e.g., Figure 7 As shown in the figure, this diagram visually illustrates the constraints and trade-offs among the three optimization objectives: heat charging time, heat release time, and heat storage capacity. Simultaneously, it presents comparative cloud maps of the internal temperature field of the thermal storage unit before and after optimization at different times (t=6840s, 13,680s, 18,240s) (e.g., Figure 9 As shown, the differences in heat transfer performance between the optimal structure (Case 1: 8 fins, fin height 0.022m, fin thickness 0.005m), the reference structure (Case 2: 0 fins), and the intermediate structure (Case 3: 4 fins, fin height 0.0203m, fin thickness 0.0034m) were compared.

[0056] from Figure 9It is clearly evident that the optimized large-size thick ribs construct a high-thermal-conductivity "thermal bridge" network within the concrete matrix. This not only significantly expands the effective heat exchange area but also fundamentally weakens the radial thermal resistance of deep concrete, enabling rapid and uniform heat penetration within the heat storage medium. The essence of the 8-rib design lies in the fact that its constructed "thermal bridge network" perfectly covers the thermally conductive dead zones of the concrete. Without causing "overlapping interference of the heat-affected zone," it minimizes the circumferential heat conduction path, achieving the optimal balance between heat transfer rate and heat storage capacity.

[0057] Computational efficiency comparison: (1) Time taken for a single CFD simulation. In this study, the average computation time for a single high-fidelity transient convection-conduction coupling simulation (including a complete heat charging and heat dissipation cycle) was 4 hours.

[0058] (2) Total time estimation of the pure CFD one-by-one screening scheme. The optimization parameters of the multi-objective genetic algorithm in this study are set as follows: population size 100, maximum number of iterations 150. This means that fitness evaluation is required for 15,000 combinations of structural parameters during the global optimization process. If the traditional pure CFD one-by-one mesh reconstruction and solution scheme is adopted, the total time will reach: 15,000 times × 4 hours / time = 60,000 hours. Such computational cost is completely unacceptable in actual engineering design and scientific research iteration.

[0059] (3) Actual time consumption of the CFD-ML collaborative optimization framework. This study reduced and transferred the massive computational load by introducing a wide network surrogate model: Training set acquisition (the main time-consuming area of ​​CFD): In the early stage, only 100 highly representative initial samples need to be generated and calculated using the LHS algorithm, with a total time consumption of 100 times × 4 hours = 400 hours (and multi-core parallel computing can be easily achieved on workstations or clusters, and the actual wall clock time will be much shorter than this). Surrogate model training time: After extracting the dataset, the wide network is trained with deep learning for 1800 epochs, and the total time for the model to reach stable convergence is only about 15 minutes. MOGA global optimization time: After the surrogate model with extremely high accuracy (R² > 0.93) is trained, the evaluation of 15,000 unknown samples in the multidimensional space by MOGA is completely transformed into the second-level forward propagation operation of the neural network. The entire process of generating the Pareto front takes less than 1 minute.

[0060] The CFD-ML collaborative framework proposed in this study reduces the total computation time for global multi-objective optimization from 60,000 hours in the traditional pure CFD scheme to only about 400 hours (most of which is the necessary sample preparation time in the early stage), reducing the computation time cost by more than 99.3%.

[0061] Example 2: This embodiment provides a ribbed concrete thermal storage system, such as Figure 10 As shown, it includes the following functional modules: Parametric modeling module 10 is configured to construct a three-dimensional geometric model of the embedded ribbed concrete thermal storage unit; set design variables and their value ranges; and generate multiple sets of structural parameter samples within the value range of the design variables using the Latin hypercube sampling method.

[0062] The CFD simulation module 20 is configured to define the inlet boundary conditions of the heat charging stage as a dynamic coupling of a time-varying temperature function and a time-varying flow rate function through a user-defined function. It uses computational fluid dynamics (CFD) software to perform transient heat transfer numerical simulations on the heat storage unit corresponding to each set of structural parameter samples, and obtains performance index samples for each set of structural parameter samples. The performance indexes include at least one of the following: heat charging time, heat release time, and heat storage. The structural parameter samples are used as input features, and the performance index samples of the corresponding structural parameter samples are used as output labels to construct a sample dataset.

[0063] The proxy model module 30 is configured to build a hybrid deep learning neural network proxy model using a wide network structure. The proxy model is trained and tested using a sample dataset to establish a nonlinear mapping relationship between structural parameters and performance indicators, so as to replace CFD for fast prediction.

[0064] The multi-objective optimization module 40 is configured to minimize the heat release time, minimize the heat charging time, and maximize the heat storage as optimization objectives. It uses a multi-objective genetic algorithm (MOGA) to perform global optimization on the trained surrogate model to obtain a Pareto front solution set containing a series of non-dominated solutions.

[0065] The verification module 50 is configured to select at least one set of non-dominated solutions from the Pareto front solution set, substitute the corresponding structural parameters into the CFD software for back-substitution verification, determine and output the structural parameters of the non-dominated solutions as the optimal rib structure scheme.

[0066] Example 3: This embodiment provides a ribbed concrete thermal storage unit optimized from the method of Embodiment 1 above.

[0067] Its specific structure is as follows: a concrete matrix, which is a cylindrical structure with a length of 2m and a diameter of 0.62m; heat exchange tubes, which are set inside the concrete matrix; and longitudinal ribs, which are evenly distributed around the outer wall of the heat exchange tubes, with a quantity of 8 ribs, each rib having a height of 0.022m and a thickness of 0.005m.

[0068] In the thermal storage unit of this embodiment, the spacing between adjacent fins is automatically determined by the prior geometric boundary hard constraint set in step one of embodiment 1. That is, by precisely setting the global extreme value of the variables (upper limit 8 fins, maximum height 22mm, maximum thickness 5mm), it is ensured that even under the most extreme combination of full-load parameters, adjacent fins in the same tube still have sufficient spacing at the root, and the sum of the limit influence radii of adjacent heat exchange tubes is much smaller than the center distance between tubes. The boundary constraint from the mathematical root ensures that every sample parameter combination generated in the LHS sampling and MOGA optimization space is 100% physically feasible and interference-free, which greatly improves the sampling efficiency and optimization convergence speed of machine learning.

[0069] Example 4: This embodiment provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the method as described in Embodiment 1.

[0070] Example 5: This embodiment provides a computer storage medium storing a computer program. When the computer program is executed, it implements the steps of the method as described in Embodiment 1.

[0071] In the embodiments provided by this invention, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be an indirect coupling or communication connection between devices or units through some interfaces, and may be electrical, mechanical, or other forms.

[0072] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0073] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium.

[0074] Based on this understanding, the technical solution of this application, in essence, or the part that contributes to it, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a mobile terminal, personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as a USB flash drive, a portable hard drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0075] In summary, although the present invention has been disclosed above with reference to preferred embodiments, the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the concept of the technical solution of the present invention, should be covered within the scope of protection of the present invention.

[0076] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

Claims

1. An optimization method for ribbed concrete thermal storage systems based on the synergy of CFD and machine learning, characterized in that, Includes the following steps: S1. Construct a three-dimensional geometric model of the embedded ribbed concrete thermal storage unit, set the design variables and their value ranges, and use the Latin hypercube sampling method to generate multiple sets of structural parameter samples within the value ranges; S2. Define the inlet boundary conditions of the heat charging stage as a dynamic coupling of a time-varying temperature function and a time-varying flow rate function using a user-defined function. Perform transient heat transfer numerical simulation on the heat storage unit corresponding to each set of structural parameter samples using computational fluid dynamics (CFD) software to obtain performance index samples corresponding to each set of structural parameter samples. The performance index includes at least one of heat charging time, heat release time, and heat storage. Use the structural parameter samples as input features and the performance index samples corresponding to the structural parameter samples as output labels to construct a sample dataset. S3. A hybrid deep learning neural network proxy model is built using a wide network structure. The proxy model is trained and tested using the sample dataset. A nonlinear mapping relationship between the structural parameters and the performance indicators is established to replace CFD for fast prediction. S4. With minimizing the heat release time, minimizing the heat charging time, and maximizing the heat storage as optimization objectives, a multi-objective genetic algorithm (MOGA) is used to perform global optimization on the trained surrogate model to obtain a Pareto front solution set containing a series of non-dominated solutions; S5. Select at least one set of non-dominated solutions from the Pareto front solution set, substitute the corresponding structural parameters into CFD software for back-substitution verification, determine and output the structural parameters of the non-dominated solutions as the optimal rib structure scheme.

2. The method according to claim 1, characterized in that, Setting the design variables and their value ranges includes at least the following steps: By pre-setting the global extreme values ​​of design variables as prior geometric boundary hard constraints, it is ensured that all sample parameter combinations meet the physical feasibility conditions. The design variables include at least one of the following: number of ribs, rib height, and rib thickness. The number of ribs ranges from 0 to 8, the rib height ranges from 0.01m to 0.022m, and the rib thickness ranges from 0.001m to 0.005m.

3. The method according to claim 1, characterized in that, The construction of a hybrid deep learning neural network proxy model using a wide network structure includes at least the following steps: The wide network architecture contains four hidden layers, adopts a layer-by-layer recursive topology with no skip connections, and each hidden layer only receives the output of the previous layer as input, without including a cross-layer feature reuse and splicing structure. The neurons in each hidden layer use ReLU as the activation function, and a Dropout mechanism is introduced after the activation function.

4. The method as described in claim 3, characterized in that, The wide network architecture comprises four hidden layers, employing a layer-by-layer recursive topology with no skip connections. Each hidden layer receives only the output of the previous layer as input, and does not include cross-layer feature reuse and concatenation structures. The wide network architecture adopts a single-branch unified architecture, and the number of neurons is 200, 150, 100 and 50 respectively, converging layer by layer in a funnel shape; The wide network architecture contains multiple parallel neuron paths in the hidden layer, and the outputs of each parallel neuron path are passed to the next hidden layer by a weighted summation.

5. The method as described in claim 1, characterized in that, The process of defining the inlet boundary conditions for the heat charging stage using a user-defined function as a dynamic coupling of a time-varying temperature function and a time-varying flow rate function includes at least the following steps: The inlet temperature of the heat transfer fluid entering the heat storage module during the first 4 hours of the charging phase is set to sinusoidal temperature rise, and the inlet mass flow rate of the heat transfer fluid entering the heat storage module during the first 4 hours of the charging phase is set to increase linearly with time.

6. The method according to claim 1, characterized in that, The transient heat transfer numerical simulation of the thermal storage unit corresponding to each set of structural parameter samples using computational fluid dynamics (CFD) software includes at least the following steps: In transient calculations, the residual convergence criterion is set to a residual threshold of 10 for the energy equation. -6 The residual thresholds for the continuity equation and momentum equation are set to 10. -4 .

7. The method according to claim 1, characterized in that, Training and testing the proxy model using the sample dataset includes at least the following steps: Before model training, the Pearson correlation coefficient is used to evaluate the linear correlation between the input features and the output target to determine key influencing features; Gaussian noise injection and selective linear interpolation are applied to the training dataset to enhance robustness.

8. A ribbed concrete thermal storage unit, characterized in that, It is obtained by optimization using the method described in any one of claims 1-7, and includes: The concrete base is a cylindrical structure with a length of 2m and a diameter of 0.62m. Heat exchange tubes are installed inside the concrete matrix; The longitudinal fins are evenly distributed circumferentially along the outer wall of the heat exchange tube, with a total of 8 fins. Each fin has a height of 0.022m and a thickness of 0.005m.

9. A ribbed concrete thermal storage system, characterized in that, include: Parametric modeling module 10 is configured to construct a three-dimensional geometric model of the embedded ribbed concrete thermal storage unit; Define the design variables and their value ranges; Multiple sets of structural parameter samples are generated within the range of the design variables using the Latin hypercube sampling method; The CFD simulation module 20 is configured to define the inlet boundary conditions of the heat charging stage as a dynamic coupling of a time-varying temperature function and a time-varying flow rate function through a user-defined function. It then uses computational fluid dynamics (CFD) software to perform transient heat transfer numerical simulations on the heat storage unit corresponding to each set of structural parameter samples, obtaining performance index samples for each set of structural parameter samples. The performance indexes include at least one of the following: heat charging time, heat release time, and heat storage capacity. The structural parameter samples are used as input features, and the corresponding performance index samples are used as output labels to construct a sample dataset. The proxy model module 30 is configured to build a hybrid deep learning neural network proxy model using a wide network structure, train and test the proxy model using the sample dataset, and establish a non-linear mapping relationship between the structural parameters and the performance indicators to replace CFD for fast prediction. The multi-objective optimization module 40 is configured to minimize the heat release time, minimize the heat charging time, and maximize the heat storage as optimization objectives. It uses a multi-objective genetic algorithm (MOGA) to perform global optimization on the trained surrogate model to obtain a Pareto front solution set containing a series of non-dominated solutions. The verification module 50 is configured to select at least one set of non-dominated solutions from the Pareto front solution set, substitute the corresponding structural parameters into the CFD software for back-substitution verification, and determine and output the rib structure scheme with the most optimal structural parameters of the non-dominated solution.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1-7.

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