Highly robust state estimation method for on-board proton exchange membrane fuel cells

Abstract

The present invention provides a highly robust state estimation method for an on-vehicle proton exchange membrane fuel cell. The method sequentially establishes a fuel cell air supply system mechanism model, analyzes the sensitivity of the system response to key parameters to implement parameter screening, constructs a multi-innovation volumetric Kalman filter and an augmented state Kalman filter based on key parameters, and performs fusion estimation based on validity testing and fuzzy logic. The method realizes real-time verification of the validity of the standard multi-innovation volumetric Kalman filter and dynamic fusion of the two estimation results, thereby providing a precise observation method for the interior of the proton exchange membrane fuel cell system under various conditions. Compared with other existing technologies, the present invention can effectively improve the estimation performance of unmeasurable variables under model mismatch conditions, and is more conducive to providing support for fuel cell system control.

Description

Technical Field

[0001] The present invention belongs to the technical field of proton exchange membrane fuel cells, and in particular relates to a proton exchange membrane fuel cell. Background Art

[0002] As a complex system integrating reactant supply, water and heat management, and power regulation, the proton exchange membrane fuel cell (PEMFC) requires the design and implementation of a rational air supply control strategy to ensure overall PEMFC efficiency and output performance. Because the oxygen excess ratio (OER) and the associated oxygen and nitrogen partial pressures in the cathode flow channel, which are used to measure the PEMFC air supply, remain difficult to measure directly with sensors, current methods rely on mass air flow sensor measurements and calculations as an alternative. However, these calculations are affected by environmental noise and the sensor's inherent response lag, which can affect the accuracy of the results. Existing fuel cell state estimation strategies based on high-gain observers, sliding mode observers, and Kalman filters have been employed. While these approaches offer improved accuracy and reduced equipment costs compared to sensor-based approaches, they also suffer from shortcomings such as poor model-to-real-world matching and frequent model parameter drift due to vehicle speed, temperature, and external noise. Consequently, significant room for improvement in accuracy and robustness remains. Summary of the Invention

[0003] In view of this, and in response to the technical problems existing in the art, the present invention provides a highly robust state estimation method for a vehicle-mounted proton exchange membrane fuel cell, which specifically includes the following steps:

[0004] Step 1: Based on the physical structure and properties of the PEMFC air supply system, including the air compressor, intake manifold, cathode flow channel, and exhaust manifold, as well as the electrochemical reaction process mechanism, a PEMFC system lumped parameter model is established;

[0005] Step 2: Determine the structural characteristic parameters, environmental parameters, and static characteristic parameters involved in the PEMFC system lumped parameter model, determine the main system parameters to establish system state variables, and construct the corresponding system state equation based on this;

[0006] Step 3: Select parameters other than the main system parameters that may affect the system state variables and screen out key parameters by performing variance-based global sensitivity analysis;

[0007] Step 4: Based on the third-order cubature rule, the state prediction equation and measurement prediction equation of the standard cubature Kalman filter are established to predict the system state. The innovation matrix is ​​introduced into the state update process to achieve the fusion of the predicted value and the sensor measurement value by multi-innovation Kalman filtering to update the system state.

[0008] Step 5: Use the system state variables obtained in step 1 and the key parameters selected in step 3 to establish the system state variables and corresponding system state equations of the augmented state, and predict and update the system state based on the standard Kalman filter;

[0009] Step 6. Calculate the normalized innovation square and its changes based on the results of the multi-innovation Kalman filtering and compare them with the corresponding threshold to perform a validity test. If it exceeds the threshold, it indicates that the test fails. At this time, the standard Kalman filtering result of the augmented state system is used as the final system state estimation result; if it does not exceed the threshold, the weighted fusion of the multi-innovation Kalman filtering and the standard Kalman filtering results of the augmented state system is used to obtain the final system state estimation result.

[0010] Furthermore, in step 2, the air compressor speed ω is obtained by identifying the nonlinear least square method based on the trust region. cp , intake pressure in manifold p sm , exhaust pressure in the manifold p rm , oxygen partial pressure in cathode The main system parameters are the partial pressure of nitrogen in the cathode mN2. These main system parameters are used to establish the system state variables:

[0011] Furthermore, the global sensitivity analysis in step 3 is specifically implemented through Sobol principal index analysis, and the process includes: first, using the Latin hypercube sampling method to select 2×10 4 sampling points, and then calculate the Sobol index S of each parameter i :

[0012]

[0013] In the formula, Var(·) represents variance, E(·) represents expectation, and X i represents the i-th input variable;

[0014] By sorting the Sobol index calculation results corresponding to each parameter, the cathode flow channel inlet flow coefficient k is screened out. sm , the flow coefficient k at the cathode flow channel outlet rm And the stack temperature T fc These three key parameters.

[0015] Furthermore, in step 4, the following state prediction equation and measurement prediction equation are specifically established:

[0016]

[0017] Where, is the predicted value of the system state at time k calculated based on the optimal state estimation result at the previous time, f(·) is the nonlinear system transfer equation, Xi,k|k-1 is the volume point set, is the measurement prediction value calculated based on the system state prediction value, H(·) is the measurement equation, Xi,k|k is the value calculated based on The new volume point set of

[0018] Using the calculated Kalman gain matrix K k，L =[K k , K k-1 ,…,K k-L+1 ] and the introduced new information matrix E k，L =[e k , e k-1 ,...,e k-L+1 ]Get updated system status:

[0019]

[0020] Where λ k,L =diag[λ k ,λ k-1 , ..., λ k-L+1 ] is the weight matrix, and L is the scale of the innovation matrix.

[0021] Furthermore, in step 5, the system state variables obtained in step 1 and the key parameters selected in step 3 are used to establish the system state variables of the augmented state: The specific form of the corresponding system state equation is as follows:

[0022]

[0023] In the formula, the superscript a represents the augmented state, w k is the system noise, u k is the system control variable, ucp,k is the air compressor input voltage at time k, which is set to be equal to u k Equivalent.

[0024] Furthermore, in step 6, the normalized innovation square NIS is calculated specifically by the following formula: k，M :

[0025]

[0026] Where M is the moving window size, P zz，k is the innovation covariance at time k;

[0027] When conducting the validity test, firstly calculate the change ΔNIS k,MCompared with the threshold ΔNIS0, if it exceeds the threshold, it indicates that the model mismatch occurs. k，M No matter how it changes, the state estimation results all use the standard Kalman filtering results of the augmented state system; if ΔNIS k,M If NIS is always lower than ΔNIS0, k，M Compared with the threshold χ0, if it exceeds the threshold, it indicates that the result of the multi-innovation Kalman filter is invalid. At this time, the standard Kalman filter result of the augmented state system is also used as the final state estimation result; if NIS k，M and ΔNIS k,M If both do not exceed the corresponding threshold, the final state estimation result is obtained through the following weighted fusion:

[0028]

[0029] Where α is the weight corresponding to the standard Kalman filtering result of the augmented state system, and These are the results of multi-innovation Kalman filtering and standard Kalman filtering for augmented state systems, respectively.

[0030] The highly robust state estimation method for a vehicle-mounted proton exchange membrane fuel cell provided by the present invention establishes a fuel cell air supply system mechanism model, analyzes the sensitivity of the system response to key parameters to implement parameter screening, constructs a multi-information volumetric Kalman filter and an augmented state Kalman filter based on key parameters, and implements fusion estimation based on validity testing and fuzzy logic. This method realizes real-time verification of the validity of the standard multi-information volumetric Kalman filter and dynamic fusion of the two estimation results, thereby providing accurate observation of the interior of the proton exchange membrane fuel cell system under various conditions. Compared with other existing technologies, the present invention can effectively improve the estimation performance of unmeasurable variables under model mismatch conditions, and is more conducive to providing support for fuel cell system control. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 A flowchart of the method provided by the present invention;

[0032] Figure 2 This is a simulation comparison diagram of the method provided by the present invention and other existing technologies. DETAILED DESCRIPTION

[0033] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0034] The present invention provides a highly robust state estimation method for a vehicle-mounted proton exchange membrane fuel cell, such as Figure 1 As shown, the specific steps include:

[0035] Step 1: Based on the physical structure and properties of the PEMFC air supply system, including the air compressor, intake manifold, cathode flow channel, and exhaust manifold, as well as the electrochemical reaction process mechanism, a PEMFC system lumped parameter model is established;

[0036] Step 2: Determine the structural characteristic parameters, environmental parameters, and static characteristic parameters involved in the PEMFC system lumped parameter model, determine the main system parameters to establish system state variables, and construct the corresponding system state equation based on this;

[0037] Step 3: Select parameters other than the main system parameters that may affect the system state variables and screen out key parameters by performing variance-based global sensitivity analysis;

[0038] Step 4: Based on the third-order cubature rule, the state prediction equation and measurement prediction equation of the standard cubature Kalman filter are established to predict the system state. The innovation matrix is ​​introduced into the state update process to achieve the fusion of the predicted value and the sensor measurement value by multi-innovation Kalman filtering to update the system state.

[0039] Step 5: Use the system state variables obtained in step 1 and the key parameters selected in step 3 to establish the system state variables and corresponding system state equations of the augmented state, and predict and update the system state based on the standard Kalman filter;

[0040] Step 6. Calculate the normalized innovation square and its changes based on the results of the multi-innovation Kalman filtering and compare them with the corresponding threshold to perform a validity test. If it exceeds the threshold, it indicates that the test fails. At this time, the standard Kalman filtering result of the augmented state system is used as the final system state estimation result; if it does not exceed the threshold, the weighted fusion of the multi-innovation Kalman filtering and the standard Kalman filtering results of the augmented state system is used to obtain the final system state estimation result.

[0041] In a preferred embodiment of the present invention, in step 2, the air compressor speed ω is obtained by identifying the air compressor speed ω based on the nonlinear least squares method based on the trust region. cp, intake pressure in manifold p sm , exhaust pressure in the manifold p rm , oxygen partial pressure in cathode Nitrogen partial pressure in cathode These main system parameters are used to establish the system state variables as follows:

[0042] In a preferred embodiment of the present invention, the global sensitivity analysis in step 3 is specifically implemented by Sobol principal index analysis, and the process includes: first, using the Latin hypercube sampling method to select 2×10 4 sampling points, and then calculate the Sobol index S of each parameter i :

[0043]

[0044] In the formula, Var(·) represents variance, E(·) represents expectation, and X i represents the i-th input variable;

[0045] By sorting the Sobol index calculation results corresponding to each parameter, the cathode flow channel inlet flow coefficient k is screened out. sm , the flow coefficient k at the cathode flow channel outlet rm And the stack temperature T fc These three key parameters.

[0046] In a preferred embodiment of the present invention, the following state prediction equation and measurement prediction equation are specifically established in step 4:

[0047]

[0048] Where, is the predicted value of the system state at time k calculated based on the optimal state estimation result at the previous time, f(·) is the nonlinear system transfer equation, Xi,k|k-1 is the volume point set, is the measurement prediction value calculated based on the system state prediction value, H(·) is the measurement equation, Xi,k|k is the value calculated based on The new volume point set of

[0049] Using the calculated Kalman gain matrix K k，L =[K k , K k-1 ,…,K k-L+1 ] and the introduced new information matrix E k，L =[e k , e k-1 ,...,e k-L+1 ]Get updated system status:

[0050]

[0051] Where λ k,L =diag[λ k ,λ k-1 , ..., λ k-L+1 ] is the weight matrix, and L is the scale of the innovation matrix.

[0052] In a preferred embodiment of the present invention, in step 5, the system state variables obtained in step 1 and the key parameters selected in step 3 are used to establish the system state variables of the augmented state: The specific form of the corresponding system state equation is as follows:

[0053]

[0054] In the formula, the superscript a represents the augmented state, w k is the system noise, u k is the system control variable, u cp,k is the air compressor input voltage at time k, which is set to be equal to u k Equivalent.

[0055] In a preferred embodiment of the present invention, in step 6, the normalized innovation square NIS is calculated specifically by the following formula: k，M :

[0056]

[0057] Where M is the moving window size, P zz，k is the innovation covariance at time k;

[0058] When conducting the validity test, firstly calculate the change ΔNIS k,M Compared with the threshold ΔNIS0, if it exceeds the threshold, it indicates that the model mismatch occurs. k，M No matter how it changes, the state estimation results all use the standard Kalman filtering results of the augmented state system; if ΔNIS k,M If NIS is always lower than ΔNIS0, k，M Compared with the threshold χ0, if it exceeds the threshold, it indicates that the result of the multi-innovation Kalman filter is invalid. At this time, the standard Kalman filter result of the augmented state system is also used as the final state estimation result; if NIS k，M and ΔNIS k,M If both do not exceed the corresponding threshold, the final state estimation result is obtained through the following weighted fusion:

[0059]

[0060] Where α is the weight corresponding to the standard Kalman filtering result of the augmented state system, and These are the results of multi-innovation Kalman filtering and standard Kalman filtering for augmented state systems, respectively.

[0061] Figure 2 The comparison of the simulation results of the present invention and other prior arts using the MATLAB / SIMULINK platform is shown. It can be seen that the present invention has obvious advantages in both state estimation accuracy and robustness.

[0062] It should be understood that the size of the serial numbers of the steps in the embodiment of the present invention does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiment of the present invention.

[0063] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A highly robust state estimation method for a vehicle-mounted proton exchange membrane fuel cell, characterized by: The specific steps include: Step 1: Based on the physical structure and properties of the PEMFC air supply system, including the air compressor, intake manifold, cathode flow channel, and exhaust manifold, as well as the electrochemical reaction process mechanism, a PEMFC system lumped parameter model is established; Step 2: Determine the structural characteristic parameters, environmental parameters, and static characteristic parameters involved in the PEMFC system lumped parameter model, determine the main system parameters to establish system state variables, and construct the corresponding system state equation based on this; Step 3: Select parameters other than the main system parameters that may affect the system state variables and screen out key parameters by performing variance-based global sensitivity analysis; Step 4: Based on the third-order cubature rule, a state prediction equation and a measurement prediction equation of the standard cubature Kalman filter are established to predict the system state; In the process of state update, the innovation matrix is ​​introduced to achieve the fusion of predicted values ​​and sensor measurement values ​​by multi-innovation Kalman filtering, so that the system state is updated; Step 5: Use the system state variables obtained in step 2 and the key parameters selected in step 3 to establish the system state variables and corresponding system state equations of the augmented state, and predict and update the system state based on the standard Kalman filter; Step 6: Calculate the normalized square of the innovation and its variation based on the multi-innovation Kalman filtering results and compare them with the corresponding threshold to perform a validity check. If the threshold is exceeded, the test fails. In this case, the standard Kalman filtering result of the augmented state system is used as the final system state estimation result. If it does not exceed the threshold, the results of multi-innovation Kalman filtering and standard Kalman filtering of the augmented state system are weighted and fused to obtain the final system state estimation result.

2. The method according to claim 1, wherein: In step 2, the air compressor speed ω is obtained by using the nonlinear least squares method based on the trust region. cp , intake pressure in manifold p sm , exhaust pressure in manifold p rm , oxygen partial pressure in cathode Nitrogen partial pressure in cathode These main system parameters are used to establish the system state variables as follows:

3. The method according to claim 1, wherein: The global sensitivity analysis in step 3 is specifically implemented through Sobol principal index analysis, and the process includes: first, using the Latin hypercube sampling method to select 2×10 4 sampling points, and then calculate the Sobol index S of each parameter i : In the formula, Var(·) represents variance, E(·) represents expectation, and X i represents the i-th input variable; By sorting the Sobol index calculation results corresponding to each parameter, the cathode flow channel inlet flow coefficient k is screened out. sm , the flow coefficient k at the cathode flow channel outlet rm And the stack temperature T fc These three key parameters.

4. The method according to claim 1, wherein: In step 4, the following state prediction equation and measurement prediction equation are specifically established: Where, is the predicted value of the system state at time k calculated based on the optimal state estimation result at the previous moment, f(·) is the nonlinear system transfer equation, χ i,k|k-1 is the volume point set, is the measurement prediction value calculated based on the system state prediction value, H(·) is the measurement equation, χ i,k|k Based on The new volume point set of Using the calculated Kalman gain matrix K k,L =[K k ,K k-1 ,…,K k-L+1 ] and the introduced new information matrix E k,L =[e k ,e k-1 ,…,e k-L+1 ]Get updated system status: Where λ k,L =diag[λ k ,λ k-1 ,…,λ k-L+1 ] is the weight matrix, and L is the scale of the innovation matrix.

5. The method according to claim 4, wherein: In step 6, the normalized innovation square NIS is calculated using the following formula: k,M : Where M is the moving window size, P zz,k is the innovation covariance at time k; When conducting the validity test, firstly calculate the change ΔNIS k,M Compared with the threshold ΔNIS0, if it exceeds the threshold, it indicates that the model mismatch occurs. k,M No matter how it changes, the state estimation results all use the standard Kalman filtering results of the augmented state system; if ΔNIS k,M If it is always lower than ΔNIS0, then NIS k,M Compared with the threshold χ0, if it exceeds the threshold, it indicates that the result of the multi-innovation Kalman filter is invalid. At this time, the standard Kalman filter result of the augmented state system is also used as the final state estimation result; if NIS k,M and ΔNIS k,M If both do not exceed the corresponding threshold, the final state estimation result is obtained through the following weighted fusion: Where α is the weight corresponding to the standard Kalman filtering result of the augmented state system, and These are the results of multi-innovation Kalman filtering and standard Kalman filtering for augmented state systems, respectively.

Images