ORC heat exchanger optimization design method and system based on deep learning

Abstract

The invention relates to an ORC heat exchanger optimization design method and system based on deep learning. The method comprises the steps that S1, original data samples are expanded based on a data enhancement method; s2, screening key input features of the data samples; s3, synthesizing minority class samples to balance a sample data set; s4, a physical information neural network model is constructed and trained, and heat exchanger performance indexes under different structure parameter combinations are predicted based on the trained model; s5, optimizing the structural parameters of the heat exchanger by adopting a multi-objective coevolution optimization algorithm; and S6, simulation verification is conducted, and the optimal plate heat exchanger design scheme of the target scene is obtained. Through three technical breakthroughs of data enhancement driven by physical constraints, neural network architecture embedded in thermotechnical physics and multi-target collaborative optimization guided by forward distance, systematic technical obstacles in design of the ORC heat exchanger are solved, and an unexpected synergistic effect is generated.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of heat exchanger design, in particular to an ORC heat exchanger optimization design method and system based on deep learning. BACKGROUND

[0002] As a core device for realizing efficient energy transfer, heat exchangers play an important role in the field of low-grade heat recovery. Plate heat exchangers (PHE) have been widely used in organic Rankine cycle (ORC) power generation systems due to their compact structure and convenient disassembly and washing. However, the existing PHEs face the following problems in the actual design process:

[0003] In actual engineering, the design data of plate heat exchangers often depends on field testing or small batch simulation. Due to the high cost of testing and the difficulty of simulating extreme conditions, the sample size available for modeling is generally small, and the sample distribution is uneven. This data gap directly leads to overfitting of traditional deep learning models during training, and the generalization ability decreases sharply when facing unseen conditions, resulting in a sharp increase in prediction errors of key performance indicators such as heat transfer efficiency and fluid pressure drop. It cannot provide reliable support for design in different scenarios. At the same time, ORC systems involve phase change heat transfer of working fluids, and the samples generated by traditional data augmentation methods often violate the basic laws of thermodynamics.

[0004] At the same time, the weak data foundation also makes it difficult for the prediction model to balance accuracy and universality. In actual design, there is often a dilemma: while computational fluid dynamics simulation can accurately simulate the flow field and heat transfer characteristics, the single-condition calculation time usually exceeds 4 hours, making it inefficient when facing multiple working conditions and multiple working conditions. Design requirements; relying on empirical formulas can quickly calculate, but the formulas are mostly based on specific working conditions, and once the working condition parameters deviate from the applicable range, the prediction accuracy will decrease by more than 10%; conventional neural network models can balance speed and accuracy, but they do not incorporate thermal physical laws and are prone to output results that violate basic principles. These unreasonable design schemes will cause energy waste and even equipment failure in actual manufacturing and operation.

[0005] In the multi-objective optimization link, plate heat exchanger design needs to consider cost, performance, and environmental protection as three types of objectives, and also needs to meet the constraint requirements in the industry specifications. Commonly used genetic algorithms, particle swarm optimization, and other algorithms, when dealing with such multi-constrained and multi-objective problems, not only need more than 300 iterations to converge, prolonging the design cycle, but also are prone to local optimization, making it difficult to achieve multi-objective collaborative optimization, and cannot adapt to the design priority in different scenarios.

[0006] In summary, the problems of the prior art are not single-link defects, but systematic short boards in the whole process of data, prediction and optimization, which have become the key to restricting the efficient application of plate heat exchangers in low-grade heat utilization in multiple scenarios. SUMMARY

[0007] The purpose of the present application is to overcome the defects of the prior art, and provide an ORC heat exchanger optimization design method and system based on deep learning. The method has three technical breakthroughs: data augmentation driven by physical constraints, neural network architecture embedded with thermophysical properties, and multi-objective collaborative optimization guided by forward distance. It solves the systematic technical obstacles in the design of ORC heat exchangers and produces unexpected synergistic effects.

[0008] To achieve the above purpose, the present application provides the following scheme:

[0009] An ORC heat exchanger optimization design method based on deep learning, comprising:

[0010] S1. Expand the original data samples based on the data augmentation method, and verify the physical consistency of the expanded data samples based on the preset physical verification requirements using a heat transfer model; wherein the original data samples include: cold working fluid flow, hot side fluid flow, working fluid inlet temperature and hot side inlet temperature;

[0011] S2. Using the Pearson correlation analysis method, filter the key input features of the verified data samples;

[0012] S3. Based on the filtered key input features, use the SMOTE technology to synthesize minority class samples to balance the sample data set;

[0013] S4. Construct a physical information neural network model that integrates energy conservation and heat transfer efficiency definition physical constraints, and train the physical information neural network model using the sample data set. Based on the trained model, predict the performance indicators of the heat exchanger under different structure parameter combinations;

[0014] S5. Using a multi-objective collaborative evolution optimization algorithm, based on the predicted performance indicators of the heat exchanger, optimize the structure parameters of the heat exchanger;

[0015] S6. Based on the optimized structure parameters of the heat exchanger, perform simulation verification to obtain the optimal plate heat exchanger design scheme for the target scenario.

[0016] Optionally, in step S1, expanding the original data samples based on the data augmentation method comprises:

[0017] Noise injection enhancement: adding Gaussian noise to the original data samples;

[0018] Scaling transformation enhancement: linearly scaling the original data samples, covering boundary conditions;

[0019] Linear interpolation enhancement: inserting n new samples in the parameter interval of adjacent original samples, calculating the difference of adjacent sample parameters, and generating interpolation parameters based on the difference of adjacent sample parameters;

[0020] Feature engineering enhancement: adding new derived features, including inlet temperature difference, working medium temperature rise, thermal measurement temperature drop, flow ratio, and heat capacity ratio.

[0021] Optionally, in step S1, the preset physical verification requirement is:

[0022] Working medium outlet temperature > working medium inlet temperature and heat transfer power Q calculated based on energy conservation > 0; fluid pressure drop ΔP calculated based on friction pressure drop formula ≤ 15 kPa and heat transfer efficiency η < 100%; based on the value calculated by the energy conservation formula, the heat transfer power Q calculation error ≤ 5%;

[0023] The physical consistency of the expanded data samples is verified by using the heat transfer model, including:

[0024] (1) Nusselt number calculation based on Raffaele criterion:

[0025]

[0026] Where, Re is the Reynolds number, G is the mass flow rate, d is the hydraulic diameter, μ is the dynamic viscosity of the fluid, Pr is the Prandtl number, k is the thermal conductivity of the fluid, β is the corrugation angle of the plate, is the Nusselt number;

[0027] Convective heat transfer coefficient calculation:

[0028]

[0029] Where, is the convective heat transfer coefficient;

[0030] (2) Total heat transfer coefficient calculation by combining convective thermal resistance, fouling thermal resistance, and avoiding thermal conduction thermal resistance:

[0031]

[0032] Where, h hot , h cold are the convective heat transfer coefficients on the hot side and the cold side, R f, hot , R f, cold are the fouling thermal resistances on the hot side and the cold side, t wall is the plate thickness, k wall is the thermal conductivity of the plate material, is the total heat transfer coefficient;

[0033] (3) Logarithmic mean temperature difference calculation:

[0034]

[0035] wherein, ΔT1 is the temperature difference between the hot side inlet and the cold side outlet, ΔT2 is the temperature difference between the hot side outlet and the cold side inlet, is the average temperature difference;

[0036] (4) Heat transfer power calculation based on energy conservation:

[0037]

[0038] wherein, A is the heat transfer area, ΔT cold is the working medium temperature rise, ΔT hot is the hot side temperature drop;

[0039] (5) Heat transfer efficiency calculation based on NTU-ε method, used for abnormal sample elimination basis:

[0040]

[0041] wherein, C is the heat capacity flow rate, and the heat capacity ratio is defined as:

[0042]

[0043] wherein, C cold is the cold side working medium heat capacity flow rate, C hot is the hot fluid heat capacity flow rate;

[0044] When Cᵣ=1:

[0045]

[0046] When Cᵣ<1:

[0047]

[0048] wherein, NTU is the heat transfer efficiency unit, C r is the heat capacity ratio, and ε needs to satisfy 0<ε≤1, samples exceeding the range are determined as physical abnormalities and are eliminated.

[0049] Optionally, in step S2, the key input features are screened from the verified data samples, including:

[0050] calculating the Pearson correlation coefficient between all candidate features and the target parameter, and retaining the correlation coefficient absolute value |r| higher than a preset threshold;

[0051] In the screened key feature set, the core parameters reflecting the working medium flow characteristics must be included, such as the cold side working medium flow m cold , and the hot side fluid flow mhot temperature parameter working fluid inlet temperature T cold, in hot side inlet temperature T hot, in and key geometric parameters describing the structural characteristics of the heat exchanger, plate wave inclination angle β, plate length L, plate width W;

[0052] The newly derived features derived by the feature engineering method will be selectively included according to their actual contribution to the target parameter.

[0053] Optionally, in step S3, the SMOTE technology is used to synthesize minority class samples to balance the sample data set, and the triggering condition is that the working condition sample proportion in the verified data samples is < 10%, and the difference between the proportions of each class of samples is ≥ 30%.

[0054] The samples synthesized by the SMOTE technology need to meet the following conditions after synthesis: the difference between the proportions of each class of samples is ≤ 15%, ensuring that the data distribution is balanced and not distorted, and the feature distribution is consistent with the original sample. At the same time, the synthesized samples need to be physically verified by the heat transfer model to eliminate physically abnormal samples.

[0055] Optionally, in step S4, the physical information neural network model constructed includes:

[0056] The input layer is closed with built-in normalization function, 3 layers of hidden layers are set, each layer contains 128 neurons; the hidden layer activation function uses tanh; the output layer dimension is 4, corresponding to the core performance indicators to be predicted.

[0057] Optionally, in step S4, the total loss function used for training the physical information neural network model is:

[0058]

[0059] wherein, L data is the data loss, λ Q , λ η is the physical loss weight, L Q , Lη is the physical loss, is the total loss function.

[0060] In the process of gradient back propagation of the total loss function, the physical loss term automatically corrects the model parameters, so that the predicted value is close to the calculation result of the heat transfer model, and finally realizes the dual goals of high data fitting accuracy and high physical law compliance.

[0061] Optionally, in step S5, a multi-objective co-evolution optimization algorithm is adopted to generate a Pareto front solution set within the constraint range of the plate heat exchanger core structure parameters, with the objectives of minimizing the annual total cost, minimizing the environmental impact factor, and maximizing the heat transfer efficiency, and the multi-objective co-evolution optimization algorithm realizes multi-objective co-evolution through a sub-population migration mechanism based on forward distance.

[0062] An ORC heat exchanger optimization design system based on deep learning, comprising:

[0063] A data enhancement module is configured to expand original data samples based on a data enhancement method, and verify the physical consistency of the expanded data samples based on a preset physical verification requirement using a heat transfer model; wherein the original data samples include cold working fluid flow, hot side fluid flow, working fluid inlet temperature, and hot side inlet temperature.

[0064] A feature screening module is configured to screen key input features from the verified data samples using a Pearson correlation analysis method.

[0065] A data balancing and division module is configured to balance the sample data set by synthesizing minority class samples using an SMOTE technique based on the screened key input features, and plan the sample data set.

[0066] A prediction module is configured to construct a physical information neural network model that integrates energy conservation and heat transfer efficiency definition physical constraints, train the physical information neural network model using the sample data set, and predict heat exchanger performance indicators under different structure parameter combinations based on the trained model.

[0067] An optimization module is configured to optimize the structure parameters of the heat exchanger based on the predicted heat exchanger performance indicators using a multi-objective co-evolution optimization algorithm.

[0068] A working condition verification module is configured to perform simulation verification based on the optimized structure parameters of the heat exchanger, and obtain an optimal plate heat exchanger design scheme for the target scenario.

[0069] Optionally, in the data enhancement module, expanding original data samples based on a data enhancement method includes:

[0070] Noise injection enhancement: adding Gaussian noise to the original data samples;

[0071] Scaling transformation enhancement: linearly scaling the original data samples to cover boundary conditions;

[0072] Linear interpolation enhancement: inserting n new samples in the parameter interval between adjacent original samples, calculating the difference between adjacent sample parameters, and generating interpolation parameters based on the difference between adjacent sample parameters.

[0073] Feature engineering enhancement: new derived features are added, including import temperature difference, working fluid temperature rise, thermal measurement temperature drop, flow ratio, and heat capacity ratio.

[0074] The beneficial effects of the present application are:

[0075] 1. The data bottleneck of small sample modeling is fundamentally solved, and the physical authenticity of the enhanced data is strictly guaranteed. As shown in the following examples, by comprehensively using four mathematical enhancement methods of noise injection, scaling transformation, linear interpolation and feature engineering, and combining with strict heat transfer model verification, the original 192 effective original samples are expanded to 1767 high-quality enhanced samples. The proportion of extreme working condition samples is significantly improved from 4.2% to 7.8%, and the sample distribution entropy value reaches 1.92 and meets the uniformity condition ≥1.8, providing sufficient and physically consistent data basis for subsequent high-precision modeling.

[0076] 2. A performance prediction model with high prediction accuracy and strong engineering reliability is constructed. By embedding the energy conservation law and heat transfer efficiency definition as physical constraints into the loss function of the neural network (PINN), the model output is forced to comply with the basic heat working law. As shown in the following example results, the PINN model has a prediction accuracy R² of 0.989 and 0.987 for heat transfer power Q and outlet temperature of heat conducting oil on the test set. Compared with traditional neural network models, the core performance index prediction accuracy is improved by 7.7%-8.7%, and the prediction error in extreme working conditions is controlled within 3%, effectively avoiding physical distortion and providing reliable performance evaluation basis for optimization.

[0077] 3. Multi-objective collaborative optimal design of heat exchanger in economy, performance and environmental protection is realized. The multi-objective collaborative evolution optimization (MPCMO) algorithm is applied to minimize the total annual cost, maximize the heat transfer efficiency and minimize the environmental impact factor. As shown in the following example results, the optimal design scheme selected by TOPSIS decision-making has an annual total cost (TAC) reduction of 16.28%, a heat transfer efficiency (η) increase of 7.7%, and an environmental impact factor (EI) reduction of 18.9% compared with the initial design, successfully realizing the comprehensive balance and significant improvement of multi-objectives.

[0078] 4. The adaptability and robustness of the optimized design scheme in actual dynamic and extreme operating conditions are significantly improved. By integrating the REFPROP10.0 high-precision property database, the Pareto optimal solution set is simulated and verified under dynamic and extreme conditions. As shown in the following example verification results, the efficiency fluctuation rate of the optimized scheme obtained by the present application under extreme conditions does not exceed 5%, showing better stability than traditional design schemes, and can better adapt to complex scenes such as industrial waste heat recovery with frequent fluctuations of heat source parameters, ensuring long-term stable operation of the equipment.

[0079] 5. The scalable intelligent design platform is constructed, and the technical paradigm has wide applicability. The technical framework of "physical constraint data enhancement-PINN performance prediction-MPCMO multi-objective optimization" proposed in the application systematically solves the universality problem of the fusion of data-driven design and physical laws. The framework is not only suitable for ORC systems of industrial waste heat recovery, but also the core method thereof can be widely applied to the design of evaporators and condensers of geothermal power generation systems, the optimization of heat storage heat exchangers of solar thermal power generation systems, waste heat recovery devices of chemical processes, and compact heat exchangers of ship power systems and other low-grade heat utilization scenes, realizes the promotion from a specific problem solution to an industry general technical paradigm, and has important industry popularization value and technical radiation effect. BRIEF DESCRIPTION OF DRAWINGS

[0080] In order to more clearly illustrate the technical solutions in the embodiments of the application or the prior art, the drawings needed to be used in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the application, and other drawings can be obtained by those skilled in the art without creative labor under the premise of not paying creative labor.

[0081] Figure 1 A deep learning-based ORC heat exchanger optimization design method flowchart of an embodiment of the application;

[0082] Figure 2 A heat exchanger optimization design system module structure diagram of an embodiment of the application;

[0083] Figure 3 A distribution comparison diagram of core parameters after data enhancement of an embodiment of the application;

[0084] Figure 4 A design variable correlation matrix heatmap of an embodiment of the application;

[0085] Figure 5 A PINN model prediction value and true value fitting curve of an embodiment of the application;

[0086] Figure 6 A PINN model training loss curve of an embodiment of the application;

[0087] Figure 7 An MPCMO algorithm HV convergence curve of an embodiment of the application;

[0088] Figure 8 A Pareto front solution set distribution diagram of an embodiment of the application;

[0089] Figure 9A comparison chart of the change trend of the traditional neural network model and the PINN model of the embodiment of the present application when the heat source flow changes;

[0090] Figure 10 A comparison chart of the change trend of the traditional neural network model and the PINN model of the embodiment of the present application when the heat source flow changes. DETAILED DESCRIPTION

[0091] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative efforts fall within the scope of the present application.

[0092] In order to make the above-mentioned objects, features and advantages of the present application more obvious and easy to understand, the present application will be further described in detail below with reference to the drawings and specific embodiments.

[0093] The object of the present embodiment is an industrial waste heat recovery ORC system plate evaporator, wherein the hot side is a heat conducting oil composed of biphenyl and biphenyl ether in a ratio of 26.5% and 73.5%, the cold side organic working medium is R245fa, the adaptive heat source temperature is 130-150℃, and the flow fluctuation is ±0.3kg / s in the steel plant waste heat recovery scene. A double-variable dynamic working condition model of mass flow and temperature is constructed to ensure that the parameter fluctuation range in actual operation is covered.

[0094] The structural parameter configuration and material selection of the present embodiment:

[0095] Determine the basic structural parameters and materials of the plate heat exchanger, balance the heat transfer performance, structural strength and cost:

[0096] Plate type: herringbone corrugated plate, corrugation inclination initial value 45°;

[0097] Basic geometric parameters: plate length 0.9-1.2m, width 0.2-0.5m, thickness 0.5-1.2mm, plate spacing 3-6mm;

[0098] Material selection: SUS304 stainless steel, thermal conductivity 15W / (m·K), pressure resistance ≥2.0MPa, density 7900kg / m³, suitable for industrial corrosive environment;

[0099] Auxiliary parameters: unit area manufacturing cost 1500yuan / m², design life 10 years, annual operating time 8000h, electricity price 0.6yuan / kWh.

[0100] Thermodynamic model construction and verification:

[0101] The heat transfer model is used as the physical verification core for data enhancement, physical verification and performance prediction, and the key formula is as follows:

[0102] Logarithmic mean temperature difference:

[0103] (1) ;

[0104] In the formula: T cold, in is the inlet temperature of the working medium, T hot, in is the inlet temperature of the hot fluid, T cold, out is the outlet temperature of the working medium, T hot, out is the outlet temperature of the hot fluid;

[0105] Heat transfer power (Q):

[0106] (2) ;

[0107] In the formula: m cold is the working medium flow, m hot is the hot fluid flow, T cold, in is the inlet temperature of the working medium, T hot, in is the inlet temperature of the hot fluid, T cold, out is the outlet temperature of the working medium ， T hot, out is the outlet temperature of the hot fluid;

[0108] Mass flow rate (G):

[0109] (3) ;

[0110] (4) ;

[0111] In the formula: m cold is the working medium flow, n is the number of flow channels, N is the total number of plates, W is the plate width, and S is the plate spacing;

[0112] Hydraulic diameter (d h ):

[0113] (5) ;

[0114] In the formula: φ is the plate expansion coefficient, and the value is 1.2;

[0115] Reynolds number:

[0116] (6) ;

[0117] In the formula: G is the mass flow rate, d h is the hydraulic diameter, and μ cold is the dynamic viscosity of the working medium;

[0118] Prandtl number:

[0119] (7);

[0120] wherein: μ cold is the dynamic viscosity of R245fa, taken as 2.5 x 10 -4 Pa·s, k cold is the thermal conductivity of R245fa, taken as 0.11 W / (m·K);

[0121] Nusselt number:

[0122] (8);

[0123] wherein: β is the corrugation angle, sinβ is taken to be in the range 0.5 to 0.866;

[0124] Convective heat transfer coefficient:

[0125] (9);

[0126] wherein: h hot is the heat transfer coefficient on the side of the heat transfer oil, taken as 200 (W / (m 2 ·K)) by experience;

[0127] Overall heat transfer coefficient (U):

[0128] (10);

[0129] wherein: h hot is the heat transfer coefficient on the side of the heat transfer oil, h cold is the heat transfer coefficient on the side of the heat transfer oil, t wall is the thickness of the plate, k wall is the thermal conductivity of the material of the plate;

[0130] Frictional pressure drop:

[0131] (11);

[0132] (12);

[0133] wherein: L is the length of the plate, ρ cold is the density of the liquid phase of R245fa, C is a coefficient of angular correction, We m is the homogeneous Weber number, Bd is the Bond number, ρ star is the ratio of the densities of the gas and liquid phases;

[0134] Heat transfer efficiency:

[0135] (13);

[0136] (14);

[0137] wherein: A act is the actual heat transfer area, C ratio is the ratio of the heat capacity of the working fluid to the hot fluid.

[0138] As Figure 1 shown, the embodiment proposes an ORC heat exchanger optimization design method based on deep learning, comprising:

[0139] S1. Based on the data enhancement method, the original data samples are expanded, and based on the preset physical verification requirements, the heat transfer model is used to verify the physical consistency of the expanded data samples; wherein the original data samples include: cold measured working fluid flow, hot side fluid flow, working fluid inlet temperature and hot side inlet temperature;

[0140] S2. Using the Pearson correlation analysis method, the key input features of the verified data samples are screened, and the features with strong correlation with the target parameters are retained;

[0141] S3. Based on the screened key input features, the SMOTE technology is used to synthesize minority class samples to balance the sample data set and divide the training set and the test set;

[0142] S4. A physical information neural network model is constructed by fusing the energy conservation and heat transfer efficiency definition physical constraints, and the sample data set is used to train the physical information neural network model, and based on the trained model, the heat exchanger performance index under different structure parameter combinations is predicted, and the multi-objective optimization is provided. High-precision performance prediction basis;

[0143] S5. Using a multi-objective co-evolutionary optimization algorithm, based on the predicted heat exchanger performance index, the structure parameters of the heat exchanger are optimized;

[0144] S6. Based on the REFPROP10.0 property database, the Pareto front is simulated and verified under dynamic working conditions or extreme working conditions, which includes property accuracy verification, dynamic working condition verification and extreme working condition verification, and outputs the optimal plate heat exchanger design scheme for the designer to refer to.

[0145] Further, the mathematical enhancement method and formula used in S1 are as follows:

[0146] Noise injection enhancement: Gaussian noise is added to the core input parameters m cold (cold measured working fluid flow), m hot (hot side fluid flow), T cold, in (working fluid inlet temperature), T hot, in (hot side inlet temperature), the formula is:

[0147] (15);

[0148] wherein, δ is the noise level (1%~5%), N(0, 1) is a standard normal distribution random number;

[0149] Scaling transformation enhancement: linearly scaling the input parameters, covering the boundary working conditions, the formula is:

[0150] (16);

[0151] wherein, the scaling factor k is 0.95~1.05 and the step length of k is 0.01.

[0152] Linear interpolation enhancement: inserting n new samples in the interval of adjacent original sample parameters, wherein n can be 3~8 according to the user's requirement for the number of samples in the output data set, and first calculating the difference ΔX of adjacent sample parameters;

[0153] (17);

[0154] wherein, X i is any sample parameter, and X i+1 is the sample parameter of the previous sample.

[0155] Then the interpolation parameter X intp is generated according to the formula:

[0156] X intp (18);

[0157] wherein, X i is any sample parameter, k is 1, 2,..., n, n is the sample number, and ΔX is the difference of adjacent sample parameters.

[0158] Feature engineering enhancement: five derived features are added, including inlet temperature difference, working medium temperature rise, thermal measurement temperature drop, flow ratio and heat capacity ratio, which together with the features in the original sample form 9 features in the enhanced sample.

[0159] Further, the requirements of physical verification in S1 are:

[0160] T cold, out >T cold, in and Q calculated based on energy conservation is greater than 0; the fluid pressure drop ΔP calculated based on the friction pressure drop formula is less than or equal to 15 kPa and the heat transfer efficiency η is less than 100%; the calculation error of Q is less than or equal to 5% based on the value calculated by the energy conservation formula.

[0161] Further, the plate heat exchanger heat transfer model used for sample physical verification in step S1 includes the following core calculation modules:

[0162] (1) Nusselt number calculation based on Raffaele criterion, which is suitable for the chevron corrugated plate structure of the plate heat exchanger:

[0163] (19);

[0164] where Re is the Reynolds number, G is the mass flow rate, d is the hydraulic diameter, μ is the dynamic viscosity of the fluid, Pr is the Prandtl number, k is the thermal conductivity of the fluid, β is the plate corrugation angle, is the Nusselt number;

[0165] Convective heat transfer coefficient calculation:

[0166] (20);

[0167] where is the convective heat transfer coefficient;

[0168] (2) Total heat transfer coefficient calculation by combining convective thermal resistance, fouling thermal resistance, and avoiding thermal conduction thermal resistance:

[0169] (21);

[0170] where h hot , h cold are the hot side and cold side convective heat transfer coefficients, R f, hot , R f, cold are the hot side and cold side fouling thermal resistances, t wall is the plate thickness, k wall is the plate material thermal conductivity, is the total heat transfer coefficient;

[0171] (3) Log mean temperature difference calculation:

[0172] (22);

[0173] where ΔT1 is the temperature difference between the hot side inlet and the cold side outlet, ΔT2 is the temperature difference between the hot side outlet and the cold side inlet, is the average temperature difference;

[0174] (4) Heat transfer power calculation based on energy conservation:

[0175] (23);

[0176] where A is the heat transfer area, ΔT cold is the working medium temperature rise, ΔT hot is the hot side temperature drop;

[0177] (5) Heat transfer efficiency calculation based on NTU-ε method, used for abnormal sample elimination basis:

[0178] (23) ;

[0179] Wherein, C is the heat capacity flow rate, and the heat capacity ratio is defined as:

[0180] (24) ;

[0181] Wherein, C cold is the cold side working fluid heat capacity flow rate, and C hot is the hot fluid heat capacity flow rate;

[0182] When Cᵣ=1:

[0183] (25) ;

[0184] When Cᵣ<1:

[0185] (26) ;

[0186] Wherein, NTU is the heat transfer efficiency unit, C r The heat capacity ratio, and ε needs to satisfy 0<ε≤1, and the sample exceeding the range is determined as physical abnormality and eliminated.

[0187] Specifically, in the present embodiment, the original data source and pretreatment:

[0188] a. Original data composition: 200 groups of measured data are calculated by plate evaporator physical model.

[0189] b. Variable mapping: input variables m cold、 m hot、 T cold, in、 T hot, in , and output variables are T cold, out、 T hot, out、 Q 、 η;

[0190] c. Data cleaning: 8 groups of abnormal samples (such as Q<0, η>100%, ΔP>20kPa) are eliminated, 192 groups of effective original samples are reserved, the mean μ and standard deviation σ of input and output variables are calculated, and are used for subsequent standardization.

[0191] Data enhancement specific operation:

[0192] Four enhancement methods were employed to expand the sample size. In noise injection, the noise level δ was set to 3%. In scaling transformation, the scaling factors were set to 0.95, 0.98, 1.02, and 1.05. In linear interpolation, the number of interpolation points n was set to 5 to balance data density and computational cost. In feature engineering, the number of derived features was set to 5. Then, the SMOTE technique was applied to balance the data, and the training and test sets were divided in an 8:2 ratio.

[0193] Enhanced data quality verification:

[0194] a. Standardization: Standardize all samples to ensure that the input variables have consistent dimensions;

[0195] b. Sample size: The final effective augmented sample set was 1767 groups, and 28 abnormal 3σ samples were removed. The samples were divided into 1414 groups for training and 353 groups for testing in an 8:2 ratio.

[0196] c. Distribution verification: Plot the input variable m cold and T hot, in Histograms of output variables Q and η, with m selected for extreme operating conditions. cold <0.3kg / s The sample proportion increased from 4.2% to 7.8%, and the sample distribution entropy value H=1.92, which satisfies the condition of ≥1.8, thus the distribution is judged to be uniform.

[0197] d. Physical consistency: All samples were thermodynamically verified, with Q equilibrium error ≤3%, η∈(0, 100%), ΔP∈(0, 15kPa).

[0198] The final distribution comparison chart of the core parameters after data augmentation is shown below. Figure 3 As shown, the heatmap of the design variable correlation matrix in this embodiment is as follows. Figure 4 As shown in the figure, the enhanced data distribution is more extensive, and the overall data remains evenly distributed. Furthermore, the heatmap of the correlation matrix of design variables provides a clear and intuitive understanding of the relationships between the design variables, offering decision-makers a clear and intuitive reference.

[0199] Furthermore, in step S2, the key input features for screening the validated data samples include:

[0200] Calculate the Pearson correlation coefficient between all candidate features and the target parameter, and retain the correlation coefficients whose absolute values ​​|r| are higher than a preset threshold.

[0201] The selected set of key features must include the core parameter reflecting the flow characteristics of the working fluid, namely, the cold-side working fluid flow rate m. cold Hot side fluid flow rate (m) hot Temperature parameters: working fluid inlet temperature T cold, in, hot side inlet temperature T hot, in , and the key geometric parameters of the heat exchanger structure, including the plate wave inclination angle β, the plate length L, and the plate width W;

[0202] The newly derived features derived by the feature engineering method will be selectively included according to their actual contribution to the target parameter.

[0203] Specifically, in this embodiment, the Pearson correlation coefficient is calculated according to the following formula:

[0204] (27) ;

[0205] Where x is the input feature variable, including the original sample parameters in claim 1 and the derived features in claim 2, namely: cold working fluid flow, hot side fluid flow, working fluid inlet temperature, hot side inlet temperature, inlet temperature difference, working fluid temperature rise, hot measuring temperature drop, flow ratio, and heat capacity ratio; n = 9 is the sample size; y is the target parameter variable, including operating cost, heat transfer efficiency, and environmental impact factor.

[0206] The key feature selection rule in S2 is: first, calculate the Pearson correlation coefficient between all candidate features and the target parameter, and retain the features with an absolute value of the correlation coefficient |r| higher than a preset threshold, which is set to be between 0.5 and 0.7. In the selected key feature set, the core parameters reflecting the working fluid flow characteristics, such as the cold working fluid flow m cold , hot side fluid flow m hot , temperature parameters working fluid inlet temperature T cold, in , hot side inlet temperature T hot, in , and the key geometric parameters of the heat exchanger structure, including the plate wave inclination angle β, the plate length L, and the plate width W, must be included. In addition, the newly derived features derived by the feature engineering method, including but not limited to inlet temperature difference, working fluid temperature rise, hot side temperature drop, flow ratio, and heat capacity ratio, will also be selectively included according to their actual contribution to the target parameter. All retained features have undergone strict engineering verification and correlation analysis to confirm that they have a significant impact on the target parameter and the collinearity between features is within an acceptable range, to ensure the stability and prediction accuracy of the model training. At the same time, the key feature dimension needs to be ≤10 to balance the feature extraction ability and training efficiency of the PINN model in step S4 of claim 1, and to avoid overfitting due to high dimension.

[0207] The key features selected in S2 are directly used as the input layer variables of the PINN model in step S4 of claim 1, and the input layer dimension is consistent with the number of key features.

[0208] The triggering condition of the SMOTE technology in S3 is that the proportion of working condition samples in the sample category in claim 1 is less than 10%, and the difference in the proportion of samples in each category is greater than or equal to 30%.

[0209] The formula for synthesizing samples in S3 using the SMOTE technology is:

[0210] (28);

[0211] wherein x is a randomly selected sample in the minority class; x' is the k1 nearest neighbor sample of x, k1 is the number of neighbors, and k1=5 is taken according to industrial conventions, so as to balance the authenticity and diversity of the synthesized samples; and ξ is a random number in the interval [0, 1], which can simulate the continuous change of samples while avoiding jumping abnormalities.

[0212] The synthesized samples in S3 using the SMOTE technology need to meet the following conditions after synthesis: the difference in the proportion of samples in each category is less than or equal to 15%, ensuring that the data distribution is balanced and not distorted, and the feature distribution is consistent with the original sample; at the same time, the synthesized samples need to be physically verified by the plate heat exchanger heat transfer model in claim 1, and physically abnormal samples are removed.

[0213] After the data set is divided according to 9:1, 8:2 or 7:3 based on stratified sampling in S3, the number of training set samples is ensured to be much larger than the number of test set samples to meet the PINN model convergence requirement, to ensure that the model can fully learn the feature mapping relationship, to reduce the overfitting risk of the PINN model, and to improve the generalization ability of the model to extreme working conditions.

[0214] Further, in step S4, the physical information neural network model constructed includes:

[0215] Model structure: a fully connected neural network is adopted, the input layer is closed with built-in normalization function, 3 layers of hidden layers are set, each layer contains 128 neurons; the number is set based on the nonlinear mapping requirement of the heat transfer process, and it is verified by experiments that it can balance the fitting ability and calculation efficiency, and the hidden layer activation function uses tanh, which can enhance the learning ability of complex relationships of temperature, flow and other parameters; the output layer has a dimension of 4, corresponding to the core performance indicators to be predicted;

[0216] Training configuration: the model training adopts the Adam optimizer with default configuration to ensure the stability of training, the initial learning rate is 10 - ³, the batch size is determined to be 64, 128, 256 and the like based on the balance between memory capacity and gradient convergence, and the total number of iterations is greater than or equal to 2000 rounds to ensure that the model fully learns the feature mapping;

[0217] Convergence criterion: the original loss is smoothed by using a 50-round moving average loss to reduce fluctuation interference, and when the loss change is less than or equal to 1x10⁻6 When the model converges.

[0218] Hyperparameter search: Grid search on the physical loss weight λ Q , λ η with range {0.1, 0.3, 0.5, 1.0}, pretrain for 50 epochs, the best combination is λ Q = 0.1, λ η = 0.1, because it corresponds to the minimum validation loss, 24761.0566;

[0219] Loss function construction (PINN core): the total loss is the sum of data loss and physical loss, the formula is as follows:

[0220] (29);

[0221] Where, L data is the data loss, λ Q , λ η is the physical loss weight, L Q , Lη is the physical loss, is the total loss function;

[0222] Data loss (MSE):

[0223] (30);

[0224] Where, is the normalized predicted output value, Y n is the real label value after standardization processing;

[0225] Heat transfer amount physical loss:

[0226] (31);

[0227] Where, is the normalized predicted heat transfer output value, Q phys is the real heat transfer after standardization processing;

[0228] Efficiency physical loss:

[0229] (32);

[0230] Where, is the normalized predicted efficiency output value, η phys is the real efficiency after standardization processing

[0231] The PINN model parameters are set as follows: the input layer dimension is consistent with the number of key features, taking 10 as the value; the number of hidden layers is 3, each layer has 128 neurons, the activation function is hyperbolic tangent activation function tanh, and the output layer dimension is 4; the optimizer uses Adam, the initial learning rate is 1x10 -3 , the batch size is 64, and the total number of iterations is 2000 rounds.

[0232] Model training and test results:

[0233] a. Training parameters: Adam optimizer, learning rate 10 -3 , batch size 64, total number of iterations 2000 rounds, print loss value every 200 rounds, 50 rounds moving average smoothing loss;

[0234] b. Training convergence: the 1820th round reaches convergence, the final training loss = 19777.0254, the 50-round moving average loss = 24761.0566, and the loss curve has no obvious shock;

[0235] c. Test set accuracy: input the test set into PINN, output destandardization, calculate the RMSE and R² of each output variable: the R² of heat transfer power Q is 0.989, and the R² of heat transfer oil outlet temperature is 0.987, and the model fitting effect is good.

[0236] The fitting curve of the PINN model prediction value and the true value is shown in Figure 5 , and the training loss curve is shown in Figure 6 .

[0237] Model performance comparison:

[0238] The embedding of physical constraints including energy conservation Q constraint and efficiency η constraint is the core of PINN model that distinguishes it from traditional neural networks. Without physical constraints, the model can fit the regular working condition data, but it is easy to output results that violate the heat working rules; while the model with constraints can force the prediction value to fit the heat transfer model rules through the gradient back propagation of the physical term in the loss function, not only the core index R² is improved to more than 0.98, but also the prediction error in extreme working conditions is controlled within 3%, providing a reliable performance evaluation basis for subsequent optimization. Compared with the traditional neural network model, the PINN model improves the convergence speed by 15.3%, the core index accuracy by 7.7%-8.7%, the generalization ability by 64.7%, and the loss stability by 60%, completely avoiding physical distortion. The comparison of η and Q trend when the heat source flow changes between the traditional neural network model and the PINN model is shown in Figure 9 、 10 .

[0239] Further, in step S5, a multi-objective co-evolutionary optimization algorithm is employed to generate a Pareto front within the constraint range of the core structure parameters of the plate heat exchanger, with the objectives of minimizing the total annual cost, minimizing the environmental impact factor, and maximizing the heat transfer efficiency, the multi-objective co-evolutionary optimization algorithm achieving multi-objective co-evolution through a sub-population migration mechanism based on forward distance.

[0240] Optimization objectives and decision variable constraints:

[0241] a. Optimization objectives (three-objective coordination): Minimize total annual cost (TAC): including equipment depreciation and operating electricity cost, formula as follows:

[0242] (33) ;

[0243] In the formula: A act = actual heat transfer area, cost area = 1500 yuan / m 2 , life = 10 years, Q vol = volume flow, η pump = 0.7, t op = 8000 h / year, price elec = 0.6 yuan / kWh;

[0244] Maximize heat transfer efficiency (η): calculated based on formula (14), converted to minimize -η in optimization;

[0245] Minimize environmental impact factor (EI): comprehensive operating carbon emissions, material carbon emissions, and working fluid leakage impact, formula as follows:

[0246] (34) ;

[0247] In the formula: W CF = 0.6, W REF = 0.3, CF1 is the operating carbon emission of the spring, CF2 is the operating carbon emission of the plate heat exchanger, REF is the material carbon emission, related to the metal consumption of the heat exchanger; wherein V channel is the volume of the plate evaporator, R leak = 0.5% / year, GWP cold = 1030.

[0248] b. In the formula: W CF = 0.6, W REF = 0.3, CF1 is the operating carbon emission of the spring, CF2 is the operating carbon emission of the plate heat exchanger, REF is the material carbon emission, related to the metal consumption of the heat exchanger; wherein V channel is the volume of the plate evaporator, R leak = 0.5% / year, GWP coldis 1030.

[0249] MPCMO algorithm parameters and iteration process:

[0250] The MPCMO algorithm used in this embodiment realizes multi-objective collaborative evolution through an adaptive migration mechanism based on forward distance. The core lies in quantifying the evolutionary potential of each sub-population using forward distance, and then guiding the migration of individuals and resource allocation between populations. Specifically, forward distance FD i is calculated by statistically analyzing the improvement trend of the objective function in the historical window R=10 generations, effectively identifying the sub-population with strong evolutionary dynamics. Migration is triggered periodically with a probability p mig =0.1, and individuals with high FD values are preferentially selected as migration sources to ensure efficient flow of good evolutionary information between sub-populations. This mechanism enables the algorithm to adaptively balance the optimization process of different objectives, thereby obtaining a high-quality and uniformly distributed Pareto solution set in fewer generations.

[0251] a. Core parameters: sub-population number M=3 (corresponding to 3 objectives), sub-population size N s =30, external archive size N A =100, maximum number of iterations max Gen =500, crossover probability p CR =1.0, mutation factor F=0.5, migration probability p mig =0.1, historical window R=10, used to calculate forward distance FD; its calculation formula is:

[0252] b. (35) ;

[0253] where FD i is the forward distance of the i-th sub-population at the current t-th generation, which is a relative quantity representing the average evolutionary rate and potential of the sub-population in recent iterations; i is the index of the sub-population, in this embodiment i=1, 2, 3 respectively corresponding to three sub-populations focusing on minimizing total annual cost (TAC), minimizing negative heat transfer efficiency (-η), and minimizing environmental impact factor (EI); t is the current iteration number of the optimization algorithm; r is the summation loop variable; f i (t) is the best objective function value of the i-th sub-population at the t-th generation, f i (t-r+1) is the optimal individual objective function value of the i-th sub-population at the (t - r + 1)-th generation; f i (t-R) is the optimal individual objective function value of the i-th sub-population at the (t - R)-th generation, which is the starting point of the historical window, and f i (t-r+1) are used to calculate the objective function change in an interval of R generations; f i max , f i min are the upper and lower bounds of the objective function of the i-th subpopulation in the whole optimization process, respectively, which are used to normalize the objective function to eliminate the differences in dimension and order of magnitude between different objectives; the final receiving subpopulation allocates evolutionary resources according to the relative evolutionary probability eP i , which ensures that resources are tilted towards the direction of great evolutionary potential.

[0254] Algorithm parameters: forward distance is denoted as FD to measure the evolutionary potential of the subpopulation; relative evolutionary probability is denoted as eP to allocate evolutionary resources; DE mutation is used to select elites from the archive; and hyper volume HV value is used for convergence judgment:

[0255] (36) ;

[0256] num dom is the number of sampling points dominated by the Pareto front, num sample is the total number of sampling points used to calculate HV, which is 10 4 here, ref = [15000, -30, 2000] is the reference point, pf min is the minimum value of the Pareto front objective;

[0257] The convergence process of this embodiment is that when iteration is to the third round, the HV change rate is ≤1%, at this time HV = 3457341572.4596, it is judged to converge, and 100 groups of Pareto optimal solution sets are output;

[0258] c. Optimal scheme screening: TOPSIS method is adopted, the weights are cost 30%, efficiency 40%, and environmental protection 30%, respectively, the weighted Euclidean distance of each Pareto solution is calculated, and the scheme with the highest closeness degree is screened.

[0259] Comparison of results before and after optimization:

[0260] Comparison of indicators between the optimal scheme and the traditional initial design scheme (L = 0.9m, W = 0.32m, t = 0.9mm, β = 45°, S = 4.6mm, N = 115) as follows:

[0261] In terms of structural parameters, the length of the plate is shortened from 0.9 m to 0.63 m, with a change rate of -30%; the width of the plate is increased from 0.32 m to 0.49 m, with a change rate of +53%; the thickness of the plate is thinned from 0.9 mm to 0.73 mm, with a change rate of -19%; the corrugation angle is increased from 45° to 50°, with a change rate of +11%; the plate spacing is reduced from 4.6 mm to 3.16 mm, with a change rate of -31%; and the total number of plates is increased from 115 to 120, with a change rate of +4.3%.

[0262] In terms of performance indicators, the heat transfer efficiency is increased from 57.5% to 61.9%, with a change rate of +7.7%; the friction pressure drop is increased from 4.66 kPa to 4.96 kPa, with a change rate of +6.5%; and the total heat transfer coefficient is increased from 160 W / (m²·K) to 172 W / (m²·K), with a change rate of +7.8%.

[0263] In terms of economic indicators, the initial investment is slightly increased from 59616 yuan to 59854 yuan, with a change rate of +0.4%; and the annual total cost is reduced from 9322 yuan / year to 7804 yuan / year, with a change rate of -16.28%.

[0264] In terms of environmental indicators, the environmental impact factor is reduced from 4242 kgCO2-eq / year to 3439 kgCO2-eq / year, with a change rate of -18.9%.

[0265] The HV convergence curve of the MPCMO algorithm is shown in Figure 7 , and the Pareto front solution set is shown in Figure 8 .

[0266] Performance comparison of algorithms:

[0267] The MPCMO algorithm used in this embodiment realizes an information cooperation mechanism through forward distance quantization evolution potential and population migration, compared with the traditional genetic algorithm , while ensuring the diversity of the solution set, significantly shortening the convergence time. Under the same hardware environment, MPCMO only needs 200 generations to reach a stable HV value (3.46×10 9 ), while needs 320 generations to reach a similar solution set quality (HV=2.81×10 9 ); and the optimal scheme generated by MPCMO is superior to in terms of TAC and EI indicators, verifying its superiority in multi-constrained and multi-objective optimization.

[0268] Further, in step S6, simulation verification is performed on the Pareto front based on the REFPROP 10.0 property database to comprehensively evaluate the robustness of the optimization scheme in actual operation, and five rows of precision verification are sequentially performed to compare the deviation of the heat transfer model used in the application from the REFPROP benchmark value; then dynamic condition verification is carried out, continuous fluctuations of the heat source parameters in the range of ±15% to ±20% are simulated, the efficiency fluctuation rate is observed, and finally extreme condition stress testing is carried out under the extreme condition that the heat source temperature suddenly rises by 20% and the flow suddenly drops by 30%, the stability of the scheme is observed, so that the efficiency fluctuation rate under the extreme condition and the simulation error under the dynamic condition are within the user's preset range, and the optimal plate heat exchanger structure design scheme suitable for the target scene is output for the designer to refer to.

[0269] Results and conclusions of the present embodiment:

[0270] Pareto front multi-scheme comparative analysis:

[0271] In order to fully demonstrate the flexibility of the application in multi-objective optimization, the Pareto optimal solution set generated from the MPCMO algorithm is Figure 8 Among them, three representative design schemes are selected for in-depth analysis. Scheme one is a cost priority type, which reduces the annual total cost to about 7650 yuan / year, which is reduced by 17.9% compared with the initial design, and the heat transfer efficiency is maintained at 59.5%; scheme two is a balanced type, i.e. the main selected scheme of the present embodiment, which reduces the cost by 16.3% (TAC is 7804 yuan / year) while increasing the heat transfer efficiency to 61.9%, and reducing the environmental impact factor to per year; scheme three is a high-efficiency and environmentally friendly type, which further increases the heat transfer efficiency to 63.2% and reduces the environmental impact factor by 24.6%, and the annual total cost is 8100 yuan. The structural parameters of the three schemes also show regular changes: from cost priority to high-efficiency and environmentally friendly, the plate length increases from 0.60 m to 0.65 m, and the plate width increases from 0.45 m to 0.52 m. The comparison results show that the application provides an optimal solution set covering different design preferences, rather than a single solution, which gives the designer sufficient decision space.

[0272] Comparison of optimization algorithm performance:

[0273] In order to verify the advancement of the MPCMO algorithm, the MPCMO algorithm is compared with the traditional NSGA-II algorithm under the same conditions. As shown in the convergence curve, Figure 7 the MPCMO algorithm only needs about 200 iterations to converge stably, while the NSGA-II algorithm needs about 320 iterations, and the convergence speed of the application algorithm is improved by about 37.5%. In terms of optimization quality, the hyper volume (HV) value of the Pareto front obtained by the MPCMO reaches 3.46x10 9, which is significantly higher than 2.81x10 9 , and the optimal scheme screened out by it is better in key indicators such as annual total cost and environmental impact factor, proving the efficiency and superiority of MPCMO in solving such complex multi-objective optimization problems.

[0274] Dynamic and extreme working condition adaptability comparison:

[0275] To comprehensively evaluate the robustness of the optimized scheme in actual operation, the application establishes a four-level verification system based on the high-precision property database of REFPROP10.0. The dynamic and extreme working condition simulation verification of scheme two (balanced type) is carried out using the property database of REFPROP10.0, and the results are shown in Figure 9 and Figure 10 First, the property accuracy verification is carried out, and it is found that the deviation of the heat transfer model used in the application from the REFPROP benchmark value is less than 3%, which lays a reliable foundation for subsequent simulation. Then, dynamic working condition verification is carried out, and the results show that the efficiency fluctuation rate of the scheme is strictly controlled within 5% under the condition of continuous fluctuation of heat source parameters within ±15%~±20%. Finally, extreme working condition stress test is carried out, and the scheme can still maintain stability under the extreme condition of 20% temperature rise of heat source and 30% flow rate drop, and the heat transfer efficiency decreases by no more than 8%, fully proving its strong adaptability in complex industrial scenes.

[0276] Implementation effect summary:

[0277] Through the above multi-aspect comparison and analysis, the significant effect of the application is comprehensively verified: in the data layer, the sample size is expanded by nearly ten times; in the prediction layer, the PINN model realizes accurate prediction with R² higher than 0.98; in the optimization layer, the MPCMO algorithm quickly converges and provides a series of Pareto optimal solutions, and the final scheme realizes comprehensive improvement of 16.28% reduction in annual total cost, 7.7% improvement in heat transfer efficiency and 18.9% reduction in environmental impact factor, and excellent stability under extreme working conditions.

[0278] As shown in Figure 2 , the embodiment also proposes an ORC heat exchanger optimization design system based on deep learning, which includes:

[0279] Data enhancement module: used for expanding original data samples based on data enhancement method, and verifying the physical consistency of the expanded data samples based on the preset physical verification requirements; wherein the original data samples include cold working fluid flow, hot side fluid flow, working fluid inlet temperature and hot side inlet temperature;

[0280] Feature screening module: for screening key input features from the verified data samples using Pearson correlation analysis method;

[0281] Data balancing and division module: for balancing the sample dataset by synthesizing minority class samples using SMOTE technology based on the screened key input features, and planning the sample dataset;

[0282] Prediction module: for constructing a physical information neural network model integrating energy conservation and heat transfer efficiency defined physical constraints, training the physical information neural network model using the sample dataset, and predicting the heat exchanger performance indicators under different structure parameter combinations based on the trained model;

[0283] Optimization module: for optimizing the structure parameters of the heat exchanger based on the predicted heat exchanger performance indicators using a multi-objective co-evolutionary optimization algorithm;

[0284] Working condition verification module: for simulation verification based on the optimized structure parameters of the heat exchanger, and obtaining the optimal plate heat exchanger design scheme for the target scenario.

[0285] Further, in the data enhancement module, expanding the original data samples based on data enhancement methods includes:

[0286] Noise injection enhancement: adding Gaussian noise to the original data samples;

[0287] Scaling transformation enhancement: linearly scaling the original data samples to cover boundary conditions;

[0288] Linear interpolation enhancement: inserting n new samples in the parameter interval of adjacent original samples, calculating the difference value of adjacent sample parameters, and generating interpolation parameters based on the difference value of adjacent sample parameters;

[0289] Feature engineering enhancement: adding derived features, including inlet temperature difference, working fluid temperature rise, thermal measurement temperature drop, flow ratio, and heat capacity ratio.

[0290] Specifically, in this embodiment, the system and method steps are matched one by one, and the "data-prediction-optimization-verification" whole process intelligentization is realized through 7 modules, specifically including:

[0291] Data enhancement module: supports importing original samples in CSV / Excel format, performs data enhancement and sample physical consistency verification as described in S1, and outputs a complete sample set that passes physical verification; also supports sample distribution visualization;

[0292] Feature screening module: automatically performs Pearson correlation analysis as described in S2, and outputs a key feature list and a correlation matrix heat map;

[0293] Data balancing and division module: contains SMOTE function, adopts hierarchical sampling to divide training set / test set in 8:2 proportion, and outputs standardization parameters;

[0294] PINN prediction module: built-in PINN network structure and loss function configuration, outputs prediction results, error reports and training loss curves;

[0295] MPCMO optimization module: supports the configuration of the above-mentioned objective function and constraint condition, can visually display the Pareto frontier and iteration convergence curve; supports the export of solution set in Excel / JSON format, and provides TOPSIS method optimal scheme screening function (weight can be customized);

[0296] Working condition verification module: integrates REFPROP10.0 property database, executes dynamic working condition or extreme working condition simulation, and outputs simulation report;

[0297] Output module: generates the optimal design scheme (including structure parameters, working condition parameters and engineering files) meeting the designer's preset requirements, supports CAD model export, technical parameter table generation and sensitivity analysis chart.

[0298] The system of the embodiment comprises a hardware platform and software function modules running on the hardware platform; wherein the hardware platform comprises:

[0299] A data acquisition unit is configured to acquire operating parameters of a plate heat exchanger in an organic Rankine cycle (ORC) system in real time, which comprises:

[0300] Temperature sensors arranged on the cold-side working fluid pipeline and the hot-side fluid pipeline are configured to monitor the inlet temperature and outlet temperature of the working fluid and the fluid;

[0301] Pressure sensors and flow sensors arranged on the cold-side working fluid pipeline and the hot-side fluid pipeline are configured to monitor the pressure and mass flow of the working fluid and the fluid;

[0302] A computing device is communicatively connected to the data acquisition unit, and comprises at least one processor and a memory, wherein the memory stores a computer program, and when the program is executed by the processor, the function of the software function module is realized;

[0303] The method steps of the software function module correspond one by one.

[0304] In the embodiment, a computing device is also provided, which comprises at least one processor and a memory, wherein the memory stores a computer program, and when the program is executed by the at least one processor, the function of the deep learning-based ORC heat exchanger optimization design method and system is realized

[0305] The technology realizes offline analysis through integrated software. A user prepares original data such as flow and temperature of an ORC system plate heat exchanger, and arranges the data into a CSV / Excel format. After the data are imported into the software offline, the user can query the results generated by each module in the user interface of the software, and finally export a CAD model and a technical parameter table of an optimal scheme in an output module, for production or review.

[0306] The embodiment verifies the feasibility and advancement of the application in the design of an industrial waste heat recovery plate heat exchanger through an integrated method of data enhancement, PINN prediction, and MPCMO optimization. In the data enhancement stage, the consistency of thermodynamics of the enhanced samples is ensured through physical model constraints, and the problem of mathematical enhancement but physical distortion is avoided. The PINN model realizes higher prediction accuracy and generalization ability than traditional neural networks through the fusion of energy conservation and efficiency definition constraints. The MPCMO algorithm efficiently solves the three-objective optimization problem through the framework of decomposition and cooperation and the adaptive evolution strategy, and provides a Pareto optimal solution set that meets the engineering requirements.

[0307] Compared with the traditional design method, the application can shorten the design cycle by more than 30%, while realizing the comprehensive improvement of performance, economy, and environmental protection, and providing a standardized engineering scheme for the design of low-grade heat utilization equipment.

[0308] The above-described embodiments are only descriptions of the preferred modes of the application, and do not limit the scope of the application. Without departing from the design spirit of the application, various modifications and improvements to the technical solutions of the application made by those skilled in the art shall fall within the protection scope determined by the claims of the application.

Claims

1. A deep learning-based ORC heat exchanger optimization design method, characterized in that, include: S1. Expand the original data sample based on data augmentation methods, and verify the physical consistency of the expanded data sample using a heat transfer model based on preset physical verification requirements; wherein, the original data sample includes: cold-side working fluid flow rate, hot-side fluid flow rate, working fluid inlet temperature, and hot-side inlet temperature; S2. Use Pearson correlation analysis to screen key input features from the validated data samples; S3. Based on the key input features selected, SMOTE technology is used to synthesize minority class samples to balance the sample dataset; S4. Construct a physical information neural network model that integrates the physical constraints of energy conservation and heat transfer efficiency, and train the physical information neural network model using a sample dataset. Based on the trained model, predict the heat exchanger performance indicators under different combinations of structural parameters. S5. A multi-objective co-evolutionary optimization algorithm is adopted to optimize the structural parameters of the heat exchanger based on the predicted heat exchanger performance indicators; S6. Based on the optimized structural parameters of the heat exchanger, perform simulation verification to obtain the optimal plate heat exchanger design scheme for the target scenario.

2. The deep learning-based ORC heat exchanger optimization design method according to claim 1, characterized in that, In step S1, augmenting the original data sample using data augmentation methods includes: Noise injection enhancement: Gaussian noise is added to the original data samples; Scaling Enhancement: The original data sample is linearly scaled to cover boundary conditions; Linear interpolation enhancement: Insert n new samples into the parameter range of adjacent original samples, calculate the parameter difference between adjacent samples, and generate interpolation parameters based on the parameter difference between adjacent samples; Enhanced Feature Engineering: New derived features include inlet temperature difference, working fluid temperature rise, heat measurement temperature drop, flow ratio, and heat capacity ratio.

3. The deep learning-based ORC heat exchanger optimization design method according to claim 1, characterized in that, In step S1, the preset physical verification requirements are as follows: The working fluid outlet temperature is greater than the working fluid inlet temperature, and the heat transfer power Q calculated based on energy conservation is greater than 0; the fluid pressure drop ΔP calculated based on the friction pressure drop formula is less than 15 kPa, and the heat transfer efficiency η is less than 100%. Based on the calculation value of the energy conservation formula, the calculation error of heat transfer power Q is ≤5%; The physical consistency of the expanded data samples was verified using a heat transfer model, including: (1) Nusselt number calculation based on Raffaele criterion: Where Re is the Reynolds number, G is the mass flow rate, d is the hydraulic diameter, μ is the fluid dynamic viscosity, Pr is the Prandtl number, k is the fluid thermal conductivity, and β is the plate corrugation angle. For Nusselt numbers; Calculation of convective heat transfer coefficient: in, For flow heat transfer coefficient; (2) Calculate the overall heat transfer coefficient by combining convection thermal resistance, fouling thermal resistance, and thermal resistance to avoid thermal conduction: Among them, h hot h cold These are the convective heat transfer coefficients on the hot and cold sides, R. f, hot R f, cold These represent the fouling thermal resistances on the hot and cold sides, respectively, t wall k represents the plate thickness. wall The thermal conductivity of the plate material is... The overall heat transfer coefficient; (3) Calculation of logarithmic mean temperature difference: Where ΔT1 is the temperature difference between the hot-side inlet and the cold-side outlet, and ΔT2 is the temperature difference between the hot-side outlet and the cold-side inlet. The average temperature difference; (4) Calculation of heat transfer power based on energy conservation: Where A is the heat transfer area, ΔT cold For the working fluid temperature rise, ΔT hot For the temperature drop on the hot side; (5) Heat transfer efficiency is calculated based on the NTU-ε method, which serves as the basis for rejecting abnormal samples: Where C is the heat capacity flow rate, and the heat capacity ratio is defined as: Among them, C cold C is the heat capacity flow rate of the working fluid on the cold side. hot The thermal capacity flow rate of the hot fluid; when =1 when <1 hour Wherein, NTU stands for heat transfer efficiency unit. For the heat capacity ratio, ε must satisfy 0 < ε ≤ 1. Samples exceeding this range are judged as physical anomalies and removed.

4. The ORC heat exchanger optimization design method based on deep learning according to claim 1, characterized in that, In step S2, the key input features for filtering the validated data samples include: Calculate the Pearson correlation coefficient between all candidate features and the target parameter, and retain the correlation coefficients whose absolute values ​​|r| are higher than a preset threshold. The selected set of key features must include the core parameter reflecting the flow characteristics of the working fluid, namely, the cold-side working fluid flow rate m. cold Hot side fluid flow rate (m) hot Temperature parameters: working fluid inlet temperature T cold, in Hot side inlet temperature T hot, in The key geometric parameters describing the structural characteristics of the heat exchanger are plate corrugation angle β, plate length L, and plate width W. New features derived through feature engineering methods will be selectively included based on their actual contribution to the target parameters.

5. The deep learning-based ORC heat exchanger optimization design method according to claim 1, characterized in that, In step S3, the triggering condition for using SMOTE technology to synthesize minority class samples to balance the sample dataset is: the proportion of working condition samples in the validated data samples is <10%, and the difference in the proportion of samples in each class is ≥30%; Samples synthesized using SMOTE technology must meet the following requirements after synthesis: the difference in the proportion of each category of the sample is ≤15%, ensuring that the data distribution is balanced and undistorted, and the feature distribution is consistent with the original sample; at the same time, the synthesized sample must be physically verified through a heat transfer model to remove physically abnormal samples.

6. The deep learning-based ORC heat exchanger optimization design method according to claim 1, characterized in that, In step S4, the constructed physical information neural network model includes: The input layer has its built-in normalization function disabled, and three hidden layers are set, each containing 128 neurons; the activation function of the hidden layers is tanh; the output layer has a dimension of 4, corresponding to the core performance indicators to be predicted.

7. The deep learning-based ORC heat exchanger optimization design method according to claim 1, characterized in that, In step S4, the physical information neural network model is trained, and the total loss function used is: Among them, L data For data loss, λ Q , λ η For physical loss weights, L Q Lη represents physical loss. This is the total loss function; During backpropagation, the gradient of the total loss function is used to automatically correct the model parameters using the physical loss term, making the predicted values ​​closer to the calculation results of the heat transfer model. This ultimately achieves the dual goals of high data fitting accuracy and high conformity to physical laws.

8. The ORC heat exchanger optimization design method based on deep learning according to claim 1, characterized in that, In step S5, a multi-objective co-evolutionary optimization algorithm is adopted to minimize the total annual cost, minimize the environmental impact factor, and maximize the heat transfer efficiency. Within the constraints of the core structural parameters of the plate heat exchanger, a Pareto front solution set is generated. The multi-objective co-evolutionary optimization algorithm realizes multi-objective co-evolution through a subpopulation migration mechanism based on forward distance.

9. A deep learning-based ORC heat exchanger optimization design system, characterized in that, The system for implementing the method as described in any one of claims 1-8 includes: Data augmentation module: used to expand the original data sample based on data augmentation methods, and to verify the physical consistency of the expanded data sample using a heat transfer model based on preset physical verification requirements; wherein, the original data sample includes: cold-side working fluid flow rate, hot-side fluid flow rate, working fluid inlet temperature and hot-side inlet temperature; Feature filtering module: Used to filter key input features from validated data samples using the Pearson correlation analysis method; Data balancing and partitioning module: Based on the selected key input features, it uses SMOTE technology to synthesize minority class samples to balance the sample dataset and plan the sample dataset. Prediction module: used to construct a physical information neural network model that integrates the physical constraints of energy conservation and heat transfer efficiency, and to train the physical information neural network model using a sample dataset, and to predict the heat exchanger performance indicators under different combinations of structural parameters based on the trained model; Optimization module: Used to optimize the structural parameters of the heat exchanger based on the predicted heat exchanger performance indicators using a multi-objective co-evolutionary optimization algorithm; Operating condition verification module: Used for simulation verification based on the optimized structural parameters of the heat exchanger to obtain the optimal plate heat exchanger design scheme for the target scenario.

10. The deep learning-based ORC heat exchanger optimization design system according to claim 9, characterized in that, The data augmentation module, which expands the original data sample based on data augmentation methods, includes: Noise injection enhancement: Gaussian noise is added to the original data samples; Scaling Enhancement: The original data sample is linearly scaled to cover boundary conditions; Linear interpolation enhancement: Insert n new samples into the parameter range of adjacent original samples, calculate the parameter difference between adjacent samples, and generate interpolation parameters based on the parameter difference between adjacent samples; Enhanced Feature Engineering: New derived features include inlet temperature difference, working fluid temperature rise, heat measurement temperature drop, flow ratio, and heat capacity ratio.

Images