Heat pump modeling method based on black box model and white box model coupling

Abstract

The invention belongs to the technical field of heat pump system modeling, and particularly relates to a heat pump modeling method based on black box model and white box model coupling, which comprises the following steps: inputting structure parameters, working condition parameters and setting parameters of a heat pump system; determining an initial population of the evaporation temperature and the condensation temperature based on a meta-heuristic intelligent algorithm; determining state parameters of the working medium at different temperatures and pressures; calculating the heat exchange area of the heat exchanger based on a white box model and black box model coupled hybrid model; whether convergence conditions are met or not is judged, and if the convergence conditions are not met, evaporation temperature and condensation temperature populations are regenerated through an intelligent solver based on a meta-heuristic algorithm; if the convergence condition is met, a calculation result is output, and calculation of the heat pump system performance is completed. By coupling the black box model and the white box model, the prediction precision of the heat pump system is remarkably improved.

Description

Technical Field

[0001] The present invention relates to the technical field of heat pump system modeling, and in particular to a heat pump modeling method based on the coupling of a black box model and a white box model. Background Art

[0002] As the global energy transition continues, heat pumps, as a highly efficient heating technology, utilize high-quality energy to convert low-grade thermal energy into high-grade heat. They are widely used in building heating, industrial waste heat recovery, and other fields. Modeling and optimizing heat pump systems are key to improving their energy efficiency and reliability, but existing modeling methods have significant limitations.

[0003] While traditional white-box models based on thermodynamic mechanisms (such as formulated thermodynamic equations and heat transfer models) are highly interpretable and scalable, they are complex and rely on numerous empirical assumptions (such as compressor efficiency and phase change heat transfer coefficients). This leads to large prediction errors and restricts applicability. For example, in compressor performance modeling, isentropic and volumetric efficiency are affected by multiple factors, including speed, pressure ratio, and working fluid properties. Traditional white-box models struggle to accurately describe these complex nonlinear relationships, often requiring simplified assumptions, which reduces prediction accuracy.

[0004] On the other hand, while black-box models (such as data-driven models based on machine learning) can improve prediction accuracy by fitting complex relationships to experimental data, they suffer from low interpretability, poor extrapolation capabilities, and strong data dependence. In heat pump systems in particular, the distribution of operating data under different operating conditions varies significantly. Black-box models are prone to overfitting and are unable to explain the physical meaning of prediction results, limiting their application in system optimization design. Summary of the Invention

[0005] The purpose of the present invention is to provide a heat pump modeling method based on the coupling of a black box model and a white box model to solve the problems existing in the background technology.

[0006] To achieve the above object, the present invention provides the following technical solution: a heat pump modeling method based on the coupling of a black box model and a white box model, characterized in that the method comprises the following steps:

[0007] S1: Input the structural parameters, operating parameters and setting parameters of the heat pump system;

[0008] S2: Based on the meta-heuristic intelligent algorithm, determine the initial population of evaporation temperature and condensation temperature;

[0009] S3: Determine state parameters of the working fluid at different temperatures and pressures, wherein the parameters include specific enthalpy, specific entropy, specific volume, specific heat capacity, thermal conductivity, viscosity, and density;

[0010] S4: Calculate the heat transfer area of the heat exchanger based on the hybrid model coupled with the white box model and the black box model.

[0011] The white box model includes a working medium flow white box model, a condenser white box model, an evaporator white box model and an expansion valve white box model.

[0012] The black box model includes a data-driven model of the compressor isentropic efficiency and volumetric efficiency obtained through training with experimental data;

[0013] S5: Determine whether the convergence conditions are met. If not, the intelligent solver based on the meta-heuristic algorithm regenerates the evaporation temperature and condensation temperature populations. If the convergence conditions are met, the calculation results are output to complete the calculation of the heat pump system performance.

[0014] Preferably, the white box model includes: a working fluid flow white box model, which calculates the working fluid flow based on the compressor exhaust volume, volumetric efficiency, rotational speed and working fluid specific volume; a condenser white box model, which calculates the heat exchange area of the condenser based on the heat balance equation; an evaporator white box model, which calculates the heat exchange area of the evaporator based on the heat balance equation; and an expansion valve white box model, which regards the throttling process of the working fluid in the expansion valve as an isenthalpic process.

[0015] Preferably, the black box model includes: a compressor isentropic efficiency data-driven model and a compressor volumetric efficiency data-driven model trained based on a machine learning algorithm.

[0016] Preferably, the meta-heuristic intelligent algorithm is selected from a genetic algorithm, a particle swarm algorithm, a tabu search algorithm, an artificial bee colony algorithm or a geyser algorithm.

[0017] Preferably, the convergence condition is that the deviation rate between the calculated evaporator heat exchange area and condenser heat exchange area and the input evaporator heat exchange area and condenser heat exchange area does not exceed a preset threshold.

[0018] Preferably, the calculation formula of the working fluid flow in the working fluid flow white box model is:

[0019]

[0020] Where m r is the working fluid flow rate; η v is the volumetric efficiency; V h is the compressor exhaust volume; r is the compressor speed; v is the specific volume of the working fluid.

[0021] Preferably, both the condenser white box model and the evaporator white box model use a lumped parameter method to divide the heat exchange elements, and calculate the heat exchange area based on the heat balance equation and the convection heat transfer coefficient.

[0022] Preferably, the machine learning algorithm includes at least one of a neural network, a support vector machine or a random forest.

[0023] Preferably, the structural parameters include the evaporator heat exchange area, the condenser heat exchange area and the compressor exhaust volume, and the operating parameters include the flow rate and temperature on the heat source side and the flow rate and temperature on the heat sink side.

[0024] Preferably, the modeling results output by the method include compressor isentropic efficiency, volumetric efficiency, heat pump heating capacity and heat pump performance coefficient.

[0025] The beneficial effects of the present invention are as follows: the present invention significantly improves the prediction accuracy of the heat pump system by coupling the black box model with the white box model. For complex nonlinear parameters such as the isentropic efficiency and volumetric efficiency of the compressor, a data-driven black box model is used to replace the traditional empirical assumptions, and a machine learning algorithm is used to extract implicit rules from the experimental data, effectively solving the prediction deviation problem caused by the simplified assumptions of the white box model; at the same time, the white box model is used for components with clear thermodynamic mechanisms such as the condenser and evaporator, ensuring the physical interpretability and scalability of the model. This hybrid modeling method takes into account both the accuracy and interpretability of the model, and can achieve high-precision predictions under different working conditions. It is particularly suitable for heat pump systems with complex working fluid properties and variable operating conditions.

[0026] The present invention significantly improves the convergence efficiency of the model by introducing an intelligent solver based on a meta-heuristic algorithm. Traditional iterative methods are prone to falling into local optimality and converge slowly when optimizing multiple variables such as evaporation temperature and condensation temperature. Meta-heuristic algorithms such as genetic algorithms and particle swarm algorithms have global search capabilities and can quickly generate and screen optimal parameter populations, significantly shortening the calculation time. In addition, the hybrid model reduces unnecessary iterative steps by dynamically adjusting the calculation logic of the black box and white box modules, further improving the efficiency of system performance prediction. This method provides an efficient tool for real-time control and optimization design of heat pump systems, and is particularly suitable for scenarios in engineering practice that require high computing speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0028] Reference Figure 1 This invention provides a heat pump modeling method based on the coupling of black-box and white-box models. By combining the white-box and black-box models, the prediction accuracy of the heat pump system model under different operating conditions is improved. Furthermore, a solver based on a metaheuristic algorithm is introduced to rapidly achieve model convergence. The invention is further elaborated below based on specific implementations.

[0029] Step 1: Input basic parameters of heat pump system

[0030] Input the basic parameters of the heat pump system, including setting parameters, structural parameters, and operating parameters; the setting parameters include the working fluid name, superheat and compressor speed; the structural parameters include the evaporator heat exchange area A evp , condenser heat exchange area A cd , compressor exhaust volume; the operating parameters include heat source side parameters and heat sink side parameters; the heat source side parameters include any two parameters among heat source flow rate, heat source inlet temperature, and heat source outlet temperature; the heat sink side parameters include any two parameters among heat sink flow rate, heat sink inlet temperature, and heat sink outlet temperature.

[0031] Step 2: Set up a metaheuristic solver

[0032] Setting a solver based on a meta-heuristic algorithm includes setting a definition domain of the heat pump evaporation temperature and the condensation temperature, setting the number of iterations, and setting the number of populations. The meta-heuristic algorithm includes but is not limited to a genetic algorithm, a particle swarm algorithm, a tabu search algorithm, an artificial bee colony algorithm, a geyser algorithm, and the like.

[0033] Step 3: Determine the working fluid state parameters

[0034] Based on steps 1 and 2, the state parameters of the working fluid at different temperatures and pressures are determined, including specific enthalpy, specific entropy, specific volume, specific heat capacity, thermal conductivity, viscosity, density, etc. The state parameters will be used for subsequent model calculations.

[0035] Step 4: Establishment of the hybrid model

[0036] The hybrid model is the core of the present invention, including a white box model and a black box model, which combines the thermodynamic process and mathematical model of the heat pump system to calculate the heat exchange area of the heat exchanger, which includes an evaporator and a condenser.

[0037] The thermodynamic process of the heat pump system is as follows:

[0038] In the evaporator, the working fluid acts as the cold fluid, and the fluid on the heat source side acts as the hot fluid, using a reverse cross-heat exchange method. After throttling, the gas-liquid two-phase working fluid enters the evaporator, absorbs heat from the hot fluid, completes a phase change, and reaches a superheated state. This process involves phase change heat (the phase change of the working fluid from liquid to gas) and non-phase change heat (the superheating process of the working fluid). The superheated gaseous working fluid then enters the compressor, where it is compressed into a high-temperature, high-pressure superheated gaseous working fluid and enters the condenser. In the condenser, the working fluid acts as the hot fluid, and the fluid on the heat sink side acts as the cold fluid. The high-temperature, high-pressure superheated gaseous working fluid releases heat to the cold fluid, eventually becoming a liquid working fluid with a certain degree of subcooling. The liquid working fluid enters the expansion valve, where it is throttled and depressurized to transform into a gas-liquid two-phase working fluid and re-enters the evaporator.

[0039] The hybrid model includes the following sub-models:

[0040] 1. Working fluid flow white box model

[0041] Calculate the working fluid flow rate based on the parameters determined in steps 1, 2, and 3. The calculation formula for the working fluid flow rate is as follows:

[0042]

[0043] Where m r is the working fluid flow rate; η v is the volumetric efficiency; V h is the compressor exhaust volume; r is the compressor speed; v is the specific volume of the working fluid.

[0044] 2. Condenser white box model

[0045] According to the parameters determined in steps 1, 2, and 3, the enthalpy values of the working fluid and the cold fluid at each state point are obtained. The heat transfer in the phase change zone and the heat transfer in the non-phase change zone are calculated according to the heat balance equation. The calculation process is as follows:

[0046] The heat balance equation in the condenser is

[0047] m r ·(e lnjk -e lnck )=c·m w,hsi ·(T out,hsi -T in,hsi ) Formula 2

[0048] Where, e lnjk is the condenser inlet enthalpy; e lnck is the enthalpy value of the condenser outlet; c is the specific heat capacity; m w，hsi is the flow rate of the cold fluid in the condenser; T out，hsi is the outlet temperature of the cold fluid; T in，hsi is the inlet temperature of the cold fluid

[0049] Heat transfer area of non-phase change zone A' fxb The calculation formula is

[0050]

[0051] Where Q fxb is the heat transfer in the non-phase change zone; U is the total heat transfer coefficient; Δt m is the logarithmic mean error.

[0052] The total heat transfer coefficient of the non-phase change zone is calculated as follows:

[0053]

[0054] Where h wfis the convection heat transfer coefficient of the working medium; δ is the thickness of the heat transfer surface; λ is the thermal conductivity; h hsi is the convective heat transfer coefficient of the cold fluid.

[0055] The non-phase change zone fluid convection heat transfer coefficient h includes the working medium convection heat transfer coefficient h wf and cold fluid convection heat transfer coefficient h hsi , the calculation formula is:

[0056]

[0057] Where Nu is the Nusselt number; β is the plate corrugation angle; Re is the Reynolds number; Pr is the Prandtl number; D h is the equivalent diameter; λ is the thermal conductivity of the fluid.

[0058] In the phase change heat transfer area, the lumped parameter method is used to divide it into n infinitesimals according to the principle of equal heat transfer. The phase change heat transfer area A' xb The calculation formula is:

[0059]

[0060] Q i =m r ·(e i+1 -e i )=c·m w,hsi ·(T i+1 -T i ) Formula 8

[0061] Where Q i is the heat exchange amount of the i-th infinitesimal element in the phase change zone.

[0062] Calculation formula for convection heat transfer coefficient of working fluid in phase change zone

[0063]

[0064] Formula 5 and Formula 6 are used to calculate the convective heat transfer coefficient of the cold fluid in the phase change zone.

[0065] Calculate the condenser heat exchange area A' cd for:

[0066] A′ cd =A′ fxb +A′ xb Formula 11

[0067] 3. Expansion valve white box model

[0068] The throttling process of the working fluid in the expansion valve is regarded as an isenthalpic process, that is, the enthalpy value of the working fluid remains unchanged during the throttling process.

[0069] 4. Evaporator white box model

[0070] According to the parameters determined in steps 1, 2, and 3, the enthalpy values of the working medium and the hot fluid at each state point in the evaporator are obtained. The heat transfer in the phase change zone and the heat transfer in the non-phase change zone are calculated according to the heat balance equation. The calculation process is as follows:

[0071] The heat balance equation in the evaporator is

[0072] m r ·(e zfjk -e zfck )=c·m w,hs ·(T in,hs -T out,hs ) Formula 12

[0073] Where, e zfjk is the enthalpy of the working fluid at the evaporator inlet; e zfck is the enthalpy of the working fluid at the evaporator outlet; c is the specific heat capacity; m w,hs is the flow rate of the evaporator hot fluid; T out，hs is the outlet temperature of the hot fluid; T in，hs is the hot fluid inlet temperature.

[0074] The calculation formula for the heat transfer area of the evaporator non-phase change zone is consistent with that of the condenser non-phase change zone. The heat transfer area of the evaporator phase change zone is calculated using the lumped parameter method. According to the principle of equal heat transfer, the evaporator phase change heat transfer zone area is divided into several heat transfer micro-elements. The calculation formula for the convective heat transfer coefficient of the working fluid in the evaporator phase change heat transfer process is:

[0075]

[0076] Where, Bo eq,i is the boiling number; ρ l is the density of the working fluid liquid phase; ρ v is the working fluid gas phase density.

[0077] The heat transfer coefficient of the thermal fluid is calculated using Formula 5 and Formula 6.

[0078] Other calculation methods are consistent with the condenser, and the final calculation is the evaporator heat exchange area A' evp .

[0079] 5. Compressor isentropic efficiency and volumetric efficiency black box model

[0080] The black box model is based on a machine learning algorithm and is trained using experimental data. It is used to predict the isentropic efficiency and volumetric efficiency of the compressor in a heat pump system. Through the learning ability of the machine learning algorithm, inherent laws are extracted from a large amount of experimental data to achieve high-precision prediction of the isentropic efficiency and volumetric efficiency. The prediction results are used to calculate the heat exchange area of the heat exchanger and the performance of the heat pump system.

[0081] Step 5: Determine whether the convergence conditions are met

[0082] The convergence condition is to calculate the evaporator heat exchange area A' evp , calculate the condenser heat exchange area A' cd The evaporator heat exchange area A entered in step 1 evp and input condenser heat exchange area A cd The deviation rate does not exceed a certain value; if the convergence condition is not met, the evaporation temperature and condensation temperature populations are regenerated by the intelligent solver based on the meta-heuristic algorithm in step 2, and steps 3-5 are repeated until the convergence condition is met.

[0083] Step 6: Output modeling results

[0084] When it is determined in step 5 that the convergence condition is met, the modeling results are output, which include performance parameters such as the compressor isentropic efficiency, volumetric efficiency, heat pump heating capacity, and heat pump performance coefficient.

[0085] Through the above steps, the present invention can implement a heat pump modeling method based on the coupling of a black box model and a white box model, providing support for improving the prediction accuracy and convergence efficiency of the heat pump model.

Claims

1. A heat pump modeling method based on the coupling of black box model and white box model, characterized in that: The method comprises the following steps: S1: Input the structural parameters, operating parameters and setting parameters of the heat pump system; S2: Based on the meta-heuristic intelligent algorithm, determine the initial population of evaporation temperature and condensation temperature; S3: Determine state parameters of the working fluid at different temperatures and pressures, wherein the parameters include specific enthalpy, specific entropy, specific volume, specific heat capacity, thermal conductivity, viscosity, and density; S4: Calculate the heat transfer area of the heat exchanger based on the hybrid model coupled with the white box model and the black box model. The white box model includes a working medium flow white box model, a condenser white box model, an evaporator white box model and an expansion valve white box model. The black box model includes a data-driven model of the compressor isentropic efficiency and volumetric efficiency obtained through training with experimental data; S5: Determine whether the convergence conditions are met. If not, the intelligent solver based on the meta-heuristic algorithm regenerates the evaporation temperature and condensation temperature populations. If the convergence conditions are met, the calculation results are output to complete the calculation of the heat pump system performance.

2. The heat pump modeling method based on the coupling of black box model and white box model according to claim 1 is characterized in that: The white box model includes: a working fluid flow white box model, which calculates the working fluid flow based on the compressor exhaust volume, volumetric efficiency, rotational speed and working fluid specific volume; a condenser white box model, which calculates the heat exchange area of the condenser based on the heat balance equation; an evaporator white box model, which calculates the heat exchange area of the evaporator based on the heat balance equation; and an expansion valve white box model, which regards the throttling process of the working fluid in the expansion valve as an isenthalpic process.

3. The heat pump modeling method based on coupling of black box model and white box model according to claim 1 is characterized in that: The black box model includes: a compressor isentropic efficiency data-driven model and a compressor volumetric efficiency data-driven model trained based on a machine learning algorithm.

4. The heat pump modeling method based on coupling of black box model and white box model according to claim 1 is characterized in that: The meta-heuristic intelligent algorithm is selected from a genetic algorithm, a particle swarm algorithm, a tabu search algorithm, an artificial bee colony algorithm or a geyser algorithm.

5. The heat pump modeling method based on coupling of black box model and white box model according to claim 1 is characterized in that: The convergence condition is that the deviation rate between the calculated evaporator heat exchange area and condenser heat exchange area and the input evaporator heat exchange area and condenser heat exchange area does not exceed a preset threshold.

6. The heat pump modeling method based on coupling of black box model and white box model according to claim 1 is characterized in that: The calculation formula of the working fluid flow in the working fluid flow white box model is: Where m r is the working fluid flow rate; η v is the volumetric efficiency; V h is the compressor exhaust volume; r is the compressor speed; v is the working fluid specific volume.

7. The heat pump modeling method based on coupling of black box model and white box model according to claim 1 is characterized in that: The condenser white box model and the evaporator white box model both use the lumped parameter method to divide the heat exchange elements, and calculate the heat exchange area based on the heat balance equation and the convection heat transfer coefficient.

8. The heat pump modeling method based on coupling of black box model and white box model according to claim 1 is characterized in that: The machine learning algorithm includes at least one of a neural network, a support vector machine, or a random forest.

9. The heat pump modeling method based on coupling of black box model and white box model according to claim 1 is characterized in that: The structural parameters include the evaporator heat exchange area, the condenser heat exchange area and the compressor exhaust volume, and the operating parameters include the flow rate and temperature on the heat source side and the flow rate and temperature on the heat sink side.

10. The heat pump modeling method based on coupling of black box model and white box model according to claim 1, characterized in that: The modeling results output by the method include compressor isentropic efficiency, volumetric efficiency, heat pump heating capacity and heat pump performance coefficient.

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