A Method for Predicting the Voltage and Efficiency of Electrochemical Hydrogen Pumps Based on Online Correction using PINN and Kalman Filtering
By combining PINN and Kalman filtering in an online correction method, the problems of insufficient extrapolation capability and insufficient physical constraints of the electrochemical hydrogen pump prediction model across operating conditions are solved, and accurate prediction and online adaptability of the electrochemical hydrogen pump voltage and efficiency are achieved.
Patent Information
- Application Number
- CN202611205203.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-08-10
- Publication Date
- 2026-11-06
AI Technical Summary
In predicting the voltage and efficiency of electrochemical hydrogen pumps, existing technologies suffer from limitations in the ability of empirical fitting methods to extrapolate across operating conditions, the lack of physical constraints in purely data-driven neural networks, and the mechanistic models which are susceptible to parameter identification errors and are difficult to adapt to changes in the operating status of the device.
An online correction method based on PINN and Kalman filtering is adopted, which combines electrochemical mechanism, data residual learning and state correction. The voltage residual is predicted by residual neural network and corrected online by Kalman filter. Thermodynamic constraints are applied to obtain the final predicted voltage and efficiency.
It achieves accurate prediction of the energy consumption and operating efficiency of electrochemical hydrogen pumps based on a small amount of experimental data, with physical interpretability and thermodynamic rationality, and can adapt to changes in the operating conditions of the device.
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Figure CN123053306A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of intelligent monitoring and electrochemical system performance prediction technology for hydrogen energy equipment, and particularly relates to a method for predicting the voltage and efficiency of electrochemical hydrogen pumps based on PINN and Kalman filtering online correction. Background Technology
[0002] Electrochemical hydrogen pumps utilize proton exchange membrane electrode assemblies to achieve the electrochemical separation, purification, and pressurization of hydrogen. Their operating voltage directly affects energy consumption, efficiency, and operational safety. The device voltage is influenced by a combination of factors, including temperature, pressure ratio, current density, membrane resistance, catalytic reaction kinetics, mass transfer state, and hydrogen transmembrane permeation.
[0003] Existing empirical fitting methods typically rely on large amounts of experimental data and lack the ability to extrapolate across different operating conditions. While purely data-driven neural networks can approximate nonlinear relationships, they struggle to guarantee thermodynamic validity and are prone to unstable predictions when samples are limited, operating conditions drift, or sensor noise is present. On the other hand, purely mechanistic models are susceptible to parameter identification errors, structural simplification, and unmodeled losses, making it difficult to maintain high accuracy over the long term.
[0004] Therefore, a method is needed that combines electrochemical mechanisms, data residual learning, and online state correction to ensure that the prediction results meet basic physical constraints and can be dynamically corrected as the device's operating conditions and performance change. Summary of the Invention
[0005] This invention aims to provide a method for predicting the voltage and efficiency of an electrochemical hydrogen pump based on online correction using PINN and Kalman filtering, in order to solve the problems of weak extrapolation ability of traditional empirical models, large errors of pure mechanistic models, lack of physical constraints in black-box neural networks, and inability of static models to adapt to changes in the operating state of the device.
[0006] To achieve the above objectives, this invention provides a method for predicting the voltage and efficiency of an electrochemical hydrogen pump based on online correction using PINN and Kalman filtering, comprising: The operating parameters of the electrochemical hydrogen pump device are collected, including: operating temperature, anode hydrogen pressure, cathode hydrogen pressure, current density, and measured operating voltage. Based on the aforementioned operating parameters, the fundamental mechanism voltage is calculated; The operating parameters and the basic mechanism voltage are used as inputs, and the voltage residual is predicted by a pre-trained residual neural network model. Based on the fundamental mechanism voltage and voltage residual, the uncorrected predicted voltage is determined, and the uncorrected predicted voltage is corrected online using a Kalman filter to obtain the corrected predicted voltage. Thermodynamic constraints are applied to the corrected predicted voltage to obtain the final predicted voltage; Based on the final predicted voltage and the hydrogen transmembrane permeation model, the current efficiency, voltage efficiency, and overall efficiency of the electrochemical hydrogen pump device are calculated.
[0007] Optionally, calculating the underlying mechanism voltage based on the operating parameters includes: ; in, Based on the fundamental mechanism voltage, It is a reversible potential. To activate the overpotential, For Ohm overpotential, This represents the concentration overpotential.
[0008] Optionally, the training process of the residual neural network model includes: Calculate the difference between the measured operating voltage and the basic mechanism voltage, and obtain the residual label; The normalized operating temperature, cathode hydrogen pressure, and current density are used as the input vectors of the residual neural network model, and the residual labels are used as the training targets to train the residual neural network model, so that the residual neural network model outputs the predicted voltage residual.
[0009] Optionally, online correction of the uncorrected predicted voltage using a Kalman filter includes: The voltage measured in real time is obtained, and the difference between the real-time measured voltage and the uncorrected predicted voltage is calculated to obtain the measurement residual. The residual bias is updated using a Kalman filter based on the measured residual and the preset Kalman gain. The uncorrected predicted voltage is corrected using the updated residual bias to obtain the corrected predicted voltage.
[0010] Optionally, applying thermodynamic constraints to the corrected predicted voltage to obtain the final predicted voltage includes: The corrected predicted voltage is compared with the reversible potential; If the corrected predicted voltage is less than the reversible potential, then the final predicted voltage is set to the reversible potential; otherwise, the corrected predicted voltage is used as the final predicted voltage.
[0011] Optionally, the final predicted voltage is: ; in, For the final predicted voltage, The voltage residual is obtained from the neural network prediction. This is the residual bias.
[0012] Optionally, the current efficiency of the electrochemical hydrogen pump device can be calculated. Voltage efficiency Overall efficiency of the device include: ; ; ; in, Indicates the variable Limited to between 0 and 1 The current density is the equivalent loss caused by hydrogen reverse osmosis and system leakage, where j is the current density. This is for the final predicted voltage.
[0013] Compared with the prior art, the present invention has the following advantages and technical effects: This invention can accurately predict the energy consumption and operating efficiency of electrochemical hydrogen pumps based on a limited amount of experimental data, as well as extrapolate across different operating conditions. Moreover, the model is based on a physical mechanism model, which ensures the overall physical interpretability and thermodynamic rationality of the model. Attached Figure Description
[0014] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a flowchart of the electrochemical hydrogen pump voltage and efficiency prediction method based on PINN and Kalman filtering online correction according to an embodiment of the present invention. Figure 2 This is a schematic diagram of residual neural network training and online correction according to an embodiment of the present invention; Figure 3 This is a schematic diagram of hydrogen transmembrane permeation and device efficiency calculation according to an embodiment of the present invention; Figure 4 This is a schematic diagram of voltage-cathode pressure curves under different current densities according to an embodiment of the present invention; Figure 5 This is a schematic diagram of the current efficiency-current density curves under different cathode pressures according to an embodiment of the present invention; Figure 6 This is a schematic diagram of voltage efficiency-current density curves under different cathode pressures according to an embodiment of the present invention; Figure 7 This is a schematic diagram of the device efficiency-current density curves under different cathode pressures according to an embodiment of the present invention; Figure 8 This is 1A / cm in an embodiment of the present invention. 2Voltage distribution cloud map of the device under temperature and pressure conditions. Detailed Implementation
[0015] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.
[0016] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.
[0017] This embodiment proposes a method for predicting the voltage and efficiency of an electrochemical hydrogen pump based on online correction using PINN and Kalman filtering, such as... Figure 1 As shown, the specific steps include: The operating parameters of the electrochemical hydrogen pump device are collected, including: operating temperature, anode hydrogen pressure, cathode hydrogen pressure, current density, and measured operating voltage. Based on the aforementioned operating parameters, the fundamental mechanism voltage is calculated; The operating parameters and the basic mechanism voltage are used as inputs, and the voltage residual is predicted by a pre-trained residual neural network model. Based on the fundamental mechanism voltage and voltage residual, the uncorrected predicted voltage is determined, and the uncorrected predicted voltage is corrected online using a Kalman filter to obtain the corrected predicted voltage. Thermodynamic constraints are applied to the corrected predicted voltage to obtain the final predicted voltage; Based on the final predicted voltage and the hydrogen transmembrane permeation model, the current efficiency, voltage efficiency, and overall efficiency of the electrochemical hydrogen pump device are calculated.
[0018] Specifically, this embodiment collects temperature, cathode pressure, anode pressure, current density, and measured operating voltage to establish a mechanistic voltage model that includes reversible compressibility potential, activation polarization, ohmic polarization, and concentration polarization. The difference between the measured operating voltage and the mechanistic voltage is used as the residual label to train a residual neural network. During online prediction, Kalman filtering is used to dynamically update the residual bias, and a physical constraint is applied to ensure the predicted voltage is not lower than the reversible potential to obtain the device operating voltage. Furthermore, current efficiency and device efficiency are calculated by combining hydrogen transmembrane permeation and system leakage. This embodiment features physical interpretability, adaptability to small sample sizes, and online correction capabilities, and can be used for performance prediction, operational optimization, and status monitoring.
[0019] Specifically, the operating temperature of the electrochemical hydrogen pump device is collected. T Anode hydrogen pressure pa Cathode hydrogen pressure p c Current density j and measured operating voltage V exp， As shown in Table 1.
[0020] Table 1 Furthermore, based on the aforementioned operating parameters, the calculation of the fundamental mechanism voltage includes: ; in, Based on the fundamental mechanism voltage, It is a reversible potential. To activate the overpotential, For Ohm overpotential, This represents the concentration overpotential.
[0021] Specifically, Represented as: ; In the formula, Let be the gas state constant. This is Faraday's constant. Two electrons are involved in the oxidation and reduction reactions of hydrogen molecules; therefore, the denominator of the formula contains the coefficient 2F.
[0022] Represented as: ; ; In the formula, j0 is the exchange current density, j 0,ref Here, k represents the exchange current density at the reference temperature, and k is the temperature correction factor. A higher exchange current density indicates faster electrode reaction kinetics; at the same operating current density, the activation polarization loss is usually smaller.
[0023] Represented as: ; ; in, To install an ohmic resistor, The ohmic resistance of the device at the reference temperature, This is a correction factor for the resistance changing with temperature. As temperature increases, the proton conductivity of the proton exchange membrane usually increases, thus reducing the equivalent area resistance.
[0024] Represented as: ; ; In the formula, For limiting current density, This is the concentration polarization correction factor. The limiting current density under reference conditions. This is a correction factor for the effect of cathode pressure on the limiting current density. When near At that time, concentration polarization loss increases significantly.
[0025] Furthermore, the residual neural network training and online correction process based on PINN and Kalman filtering described in this embodiment, as follows: Figure 2 As shown, the specific steps include: Calculate the difference between the measured operating voltage and the basic mechanism voltage, and obtain the residual label; The normalized operating temperature, cathode hydrogen pressure, and current density are used as the input vectors of the residual neural network model, and the residual labels are used as the training targets to train the residual neural network model, so that the residual neural network model outputs the predicted voltage residual.
[0026] Specifically, calculate the measured operating voltage ( The difference between the base voltage and the base voltage: ; The difference is used as a training label for the residual neural network to characterize additional losses that the mechanistic model fails to accurately describe, including factors such as changes in membrane water content, contact resistance, local mass transfer effects, assembly errors, and device aging.
[0027] Furthermore, the temperature, cathode pressure, and current density are normalized and then input into the neural network, which then outputs the predicted residuals. ; ; In the formula, This is the input vector for the residual neural network; These are the normalized operating temperature, cathode pressure, and current density, respectively. This represents the nonlinear mapping relationship expressed by the physical information residual neural network. This refers to the set of weights and bias parameters that need to be trained in the neural network. The voltage residual predicted by the neural network. The training objective is set as follows: ; In the formula, ∆V exp The difference between the measured operating voltage and the fundamental mechanism voltage, i.e., the experimental residual; This is the total loss function during the neural network training process; The number of training samples. The training sample number; This is the regularization coefficient, used to reduce the risk of abnormal oscillations under extrapolated operating conditions; Let L2 be the squared norm of the neural network weights and bias parameters.
[0028] The neural network in this embodiment does not directly predict the full operating voltage, but only learns the residuals of the mechanistic model, thereby reducing the dependence on the scale of experimental data and improving physical interpretability.
[0029] Furthermore, online correction of the uncorrected predicted voltage using a Kalman filter includes: The voltage measured in real time is obtained, and the difference between the real-time measured voltage and the uncorrected predicted voltage is calculated to obtain the measurement residual. The residual bias is updated using a Kalman filter based on the measured residual and the preset Kalman gain. The uncorrected predicted voltage is corrected using the updated residual bias to obtain the corrected predicted voltage.
[0030] Specifically, during online operation, the residual bias is updated based on real-time measured voltage. The predicted voltage without online correction is: ; The measurement residual is: ; The Kalman filter updates the bias based on the measurement residuals: ; in, The predicted voltage is without online correction using Kalman filtering; The first The measurement residuals at each time point, the measured operating voltage, the online bias, and the Kalman gain are all considered. By updating the bias and Kalman filter online, the neural network can adapt to changes in membrane resistance, catalytic performance, assembly state differences, and overall voltage drift caused by slow device aging, without the need for frequent retraining of the neural network.
[0031] Further, applying thermodynamic constraints to the corrected predicted voltage to obtain the final predicted voltage includes: The corrected predicted voltage is compared with the reversible potential; If the corrected predicted voltage is less than the reversible potential, then the final predicted voltage is set to the reversible potential; otherwise, the corrected predicted voltage is used as the final predicted voltage.
[0032] Furthermore, the final predicted voltage is: ; in, For the final predicted voltage, The voltage residual is obtained from the neural network prediction. For residual bias, this constraint ensures that That is, the predicted working voltage is not lower than the thermodynamic reversible compressibility potential, which is in line with the actual engineering practice.
[0033] Furthermore, the mechanism model and device efficiency calculation process based on the physical process of hydrogen transmembrane permeation described in this embodiment are as follows: Figure 3 As shown, the specific steps include: The current efficiency of the electrochemical hydrogen pump device was calculated. Voltage efficiency Overall efficiency of the device include: ; ; ; in, Indicates the variable Limited to between 0 and 1 The current density is the equivalent loss caused by hydrogen reverse osmosis and system leakage, where j is the current density. This is for the final predicted voltage.
[0034] Specifically, to improve the interpretability of efficiency predictions, a hydrogen transmembrane permeation model was further established for simultaneous evaluation of device efficiency. The hydrogen transmembrane flux and hydrogen transmembrane permeation coefficient are expressed as follows: ; ; In the formula, This represents the molar flux of high-pressure hydrogen gas from the cathode side to the anode side in reverse permeation. and These are the hydrogen permeability coefficients at the operating temperature and the reference temperature, respectively. and These are correction factors for proton exchange membrane thickness and membrane water content, respectively. This represents the apparent activation energy for the hydrogen transmembrane permeation process.
[0035] The equivalent loss current density is: ; In the formula, and These are the equivalent loss current density caused by hydrogen reverse osmosis and system leakage, and the equivalent leakage current density caused by gas lines, joints, and sealing structures, respectively.
[0036] Furthermore, current efficiency ( ) is represented as: ; Voltage efficiency ( ) is represented as: ; Overall efficiency of the device ( ) is represented as: ; In the formula, Indicates the variable The efficiency is limited to the range of 0-1. When expressing efficiency as a percentage, the above dimensionless efficiency should be multiplied by 100%.
[0037] Through the above calculations, the predicted voltage can be obtained synchronously. ,like Figure 4 As shown), current efficiency ( ,like Figure 5 As shown), voltage efficiency ( ,like Figure 6 (as shown) and overall device efficiency ( ,like Figure 7 As shown in the figure, to analyze the combined influence of cathode pressure and temperature on the operating voltage of the electrochemical hydrogen pump, this invention further predicts the pressure-temperature-operating voltage contour plot, as shown in the figure. Figure 8 As shown. In summary, this invention can provide a theoretical basis for the performance analysis of electrochemical hydrogen pumps and the optimization design of materials and devices.
[0038] Specifically, the electrochemical hydrogen pump device operates under reference conditions (operating temperature). T Anode hydrogen pressure p a Cathode hydrogen pressure p c Current density j Measured operating voltage under) and model-predicted voltage Predicted voltage efficiency Predicting current efficiency As shown in Table 2.
[0039] Table 2 The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.
Claims
1. A method for predicting the voltage and efficiency of an electrochemical hydrogen pump based on online correction using PINN and Kalman filtering, characterized in that, include: The operating parameters of the electrochemical hydrogen pump device are collected, including: operating temperature, anode hydrogen pressure, cathode hydrogen pressure, current density, and measured operating voltage. Based on the aforementioned operating parameters, the fundamental mechanism voltage is calculated; The operating parameters and the basic mechanism voltage are used as inputs, and the voltage residual is predicted by a pre-trained residual neural network model. Based on the fundamental mechanism voltage and voltage residual, the uncorrected predicted voltage is determined, and the uncorrected predicted voltage is corrected online using a Kalman filter to obtain the corrected predicted voltage. Thermodynamic constraints are applied to the corrected predicted voltage to obtain the final predicted voltage; Based on the final predicted voltage and the hydrogen transmembrane permeation model, the current efficiency, voltage efficiency, and overall efficiency of the electrochemical hydrogen pump device are calculated.
2. The method for predicting the voltage and efficiency of an electrochemical hydrogen pump based on online correction using PINN and Kalman filtering according to claim 1, characterized in that, Based on the aforementioned operating parameters, the calculation of the fundamental mechanism voltage includes: ； in, Based on the fundamental mechanism voltage, It is a reversible potential. To activate the overpotential, For Ohm overpotential, This represents the concentration overpotential.
3. The method for predicting the voltage and efficiency of an electrochemical hydrogen pump based on online correction using PINN and Kalman filtering according to claim 1, characterized in that, The training process of the residual neural network model includes: Calculate the difference between the measured operating voltage and the basic mechanism voltage, and obtain the residual label; The normalized operating temperature, cathode hydrogen pressure, and current density are used as the input vectors of the residual neural network model, and the residual labels are used as the training targets to train the residual neural network model, so that the residual neural network model outputs the predicted voltage residual.
4. The method for predicting the voltage and efficiency of an electrochemical hydrogen pump based on PINN and Kalman filtering online correction according to claim 1, characterized in that, Online correction of uncorrected predicted voltages using a Kalman filter includes: The voltage measured in real time is obtained, and the difference between the real-time measured voltage and the uncorrected predicted voltage is calculated to obtain the measurement residual. The residual bias is updated using a Kalman filter based on the measured residual and the preset Kalman gain. The uncorrected predicted voltage is corrected using the updated residual bias to obtain the corrected predicted voltage.
5. The method for predicting the voltage and efficiency of an electrochemical hydrogen pump based on PINN and Kalman filtering online correction according to claim 2, characterized in that, Applying thermodynamic constraints to the corrected predicted voltage to obtain the final predicted voltage includes: The corrected predicted voltage is compared with the reversible potential; If the corrected predicted voltage is less than the reversible potential, then the final predicted voltage is set to the reversible potential; otherwise, the corrected predicted voltage is used as the final predicted voltage.
6. The method for predicting the voltage and efficiency of an electrochemical hydrogen pump based on PINN and Kalman filtering online correction according to claim 5, characterized in that, The final predicted voltage is: ； in, For the final predicted voltage, The voltage residual is obtained from the neural network prediction. This is the residual bias.
7. The method for predicting the voltage and efficiency of an electrochemical hydrogen pump based on PINN and Kalman filtering online correction according to claim 2, characterized in that, The current efficiency of the electrochemical hydrogen pump device was calculated. Voltage efficiency Overall efficiency of the device include: ； ； ； in, Indicates the variable Limited to between 0 and 1 The current density is the equivalent loss caused by hydrogen reverse osmosis and system leakage, where j is the current density. This is for the final predicted voltage.