CN114509947A - Proton exchange membrane fuel cell fault detection method based on robust Kalman filter - Google Patents

Proton exchange membrane fuel cell fault detection method based on robust Kalman filter Download PDF

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CN114509947A
CN114509947A CN202210153511.1A CN202210153511A CN114509947A CN 114509947 A CN114509947 A CN 114509947A CN 202210153511 A CN202210153511 A CN 202210153511A CN 114509947 A CN114509947 A CN 114509947A
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fault detection
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夏安林
杜董生
盛远杰
刘贝
朱秀芳
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Huaiyin Institute of Technology
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Abstract

The invention relates to the technical field of fault detection, and discloses a proton exchange membrane fuel cell fault detection method based on a robust Kalman filter and an evaluation function threshold, wherein a PEMFC dynamic voltage system model is established, and a system state equation is obtained by considering the uncertainty of the system; giving a general form when a system model contains external interference and actuator faults; providing a robust Kalman filter as a residual signal generator, and giving a system initial value required by the filter to obtain an output value predicted by a system model; comparing the predicted value with the actual value to generate a residual sequence; introducing an evaluation function threshold fault detection method, and constructing a decision function and a decision rule; and carrying out fault detection. The invention combines the robust Kalman filter with the fault detection method, realizes the fault detection of the uncertain discrete time system, is applied to the proton exchange membrane fuel cell, and has accurate fault detection, high speed and robustness.

Description

Proton exchange membrane fuel cell fault detection method based on robust Kalman filter
Technical Field
The invention relates to the technical field of fault detection, in particular to a proton exchange membrane fuel cell fault detection method based on a robust Kalman filter.
Background
The global energy demand of the present human society is huge, the storage capacity of the traditional energy is sharply reduced, and the non-regenerability and a series of negative effects on the ecological environment cause that people have to seek to research and develop the utilization of novel energy with high efficiency, environmental protection and cleanness. The growing environmental and resource concerns have accelerated fuel cell technology development and commercial applications. Proton Exchange Membrane Fuel Cells (PEMFC) have the characteristics of high energy conversion rate, environmental friendliness, low working temperature, high starting speed and the like, so that the PEMFC becomes one of the most promising energy sources. Accordingly, much effort has been devoted to the study of the material degradation mechanism of PEMFCs, as well as the design and assembly of fuel cells. In addition to this, the subject of fault diagnosis for PEMFC systems is currently gaining more and more attention.
In recent years, with the improvement of the requirements for reliability and safety of the chemical production process, the fault detection technology has been widely paid attention to by scholars and has been developed unprecedentedly. To date, a number of fault diagnosis methods have been proposed in a large number of documents. The traditional advanced signal processing algorithm is used for identifying the characteristics of the fault, and a fault diagnosis expert manually identifies the fault afterwards, so that time and labor are wasted. With machine learning, deep learning was introduced into the field of fault diagnosis, and many intelligent methods emerged to automatically identify faults instead of experts. At the present stage, a data-driven fault diagnosis method is generally used for fault diagnosis of proton exchange membrane fuel cells, and because the proton exchange membrane fuel cells are complex systems with high nonlinearity and strong coupling, it is difficult to establish an accurate mathematical model, and influence of factors such as interference and parameter perturbation is overcome. The existing fault detection method based on the model rarely considers the uncertainty of the system, so that the precision of the fault detection method cannot meet the requirement in the aspect of fault detection, and the detection precision is low.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problems in the prior art, the invention provides a fault detection method for a proton exchange membrane fuel cell based on a robust Kalman filter, which can carry out state estimation and fault diagnosis when the proton exchange membrane fuel cell system has uncertainty, combines the robust Kalman filter with a threshold fault detection method, monitors the operation process of a PEMFC system, and has the advantages of accurate fault detection, high speed and robustness.
The technical scheme is as follows: the invention provides a proton exchange membrane fuel cell fault detection method based on a robust Kalman filter, which comprises the following steps:
step 1: constructing a PEMFC dynamic voltage model according to a PEMFC principle, and converting a differential equation into a state equation in a standard form;
step 2: based on the state equation in the step 1, giving a general form that the PEMFC dynamic voltage model contains external interference;
and step 3: a pure certainty viewpoint is adopted, a penalty function method is applied to construct a robust regularization least square estimation problem, and a robust Kalman filter is designed;
and 4, step 4: using a robust Kalman filter as a residual signal generator, and giving a system initial value required by the filter to obtain an output value predicted by a system model;
and 5: adding an actuator fault into the PEMFC dynamic voltage model, and comparing the obtained predicted value with the actual value by using the operation method in the step 4 to generate a residual sequence;
and 6: introducing an evaluation function threshold fault detection method, analyzing the statistical characteristics of residual signals, and constructing a decision function and a decision rule;
and 7: and 6, monitoring the operation process of the system according to the decision function and the decision rule in the step 6, and carrying out fault detection.
Further, the PEMFC dynamic voltage model output voltage is expressed as:
Vcell＝n(Enerst-ηact-ηcons-ηohmic) (1)
wherein n represents the number of cells, VcellIs a cell voltage, EnerstIs a Nernst voltage, ηactTo activate the overpotential,. etaconsIs a concentration overpotential, etaohmicOhmic overpotential;
Figure BDA0003511405610000021
wherein the content of the first and second substances,
Figure BDA0003511405610000022
an RC circuit comprising an equivalent capacitor and an equivalent resistor is used as a battery equivalent circuit, and the RC circuit is expressed as follows:
Figure BDA0003511405610000023
Figure BDA0003511405610000024
wherein the content of the first and second substances,
Figure BDA0003511405610000025
is an equivalent voltage, CdIs an equivalent capacitance, τcIs a time constant, RactTo activate polarization loss, RconConcentration polarization loss; selecting
Figure BDA0003511405610000026
As state variables, IdFor current, as a control variable, the linearized continuous system model of the PEMFC is:
Figure BDA0003511405610000031
wherein the content of the first and second substances,
Figure BDA0003511405610000032
further, the PEMFC dynamic voltage model in step 2 contains external disturbances in the general form of:
Figure BDA0003511405610000033
wherein A isz＝eAT，
Figure BDA0003511405610000034
xkRepresents a state variable, ukRepresents a control input, ykRepresenting the output, ωkAnd upsilonkRespectively, process noise and observation noise, and delta a, delta B and delta C are respectively uncertain parameters.
Further, the specific process of designing a robust kalman filter in step 3 is as follows:
s3.1: the uncertain parameters in the PEMFC dynamic voltage model are expressed as follows:
Figure BDA0003511405610000035
wherein E is1、E2、E3、F1、F2、F3Is a constant matrix of known appropriate dimensions, Δ1、Δ2、Δ3The matrix is any compression matrix, delta A, delta B and delta C are respectively uncertain parameters, and I is a unit matrix;
s3.2: at each step k, an a priori estimate is assumed
Figure BDA0003511405610000036
Measurement output ykAnd a control input ukKnown, a min-max constraint optimization problem can be obtained, when the system is most affected by uncertainty, the quadratic cost function is minimum, and the objective function is as follows:
Figure BDA0003511405610000037
s3.3: the following mapping relationship is defined:
Figure BDA0003511405610000038
then system equation (7) can be rewritten as follows:
Y+δY＝(D+δD)X+W (11)
the uncertainty is written in the form:
Figure BDA0003511405610000039
s3.4: the robust regularized least squares estimate is expressed as:
Figure BDA0003511405610000041
s3.5: introducing a penalty function, and rewriting the objective function (9) as:
Figure BDA0003511405610000042
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003511405610000043
s3.6: assuming a priori estimation errors
Figure BDA0003511405610000044
Has an error covariance of P-W has an error covariance of Q, order
Figure BDA0003511405610000045
A determined solution of the objective function (14)
Figure BDA0003511405610000046
The following were used:
Figure BDA0003511405610000047
wherein the content of the first and second substances,
Figure BDA0003511405610000048
Figure BDA0003511405610000049
is a non-negative scalar parameter obtained as a solution to the optimization problem:
Figure BDA00035114056100000410
the objective function Γ (λ) is given as follows:
Γ(λ)＝||z(λ)||2+||Hz(λ)-K||2+λ||FHz(λ)-FK||2 (18)
wherein the content of the first and second substances,
Figure BDA00035114056100000411
s3.7: using approximate calculations
Figure BDA00035114056100000412
Solving the robust regularized least squares estimation problem, where ξ > 0, then x's robust estimation
Figure BDA00035114056100000413
And estimation error
Figure BDA00035114056100000414
The covariance P of (a) can be given by the following symmetric permutation matrix:
Figure BDA0003511405610000051
wherein the content of the first and second substances,
Figure BDA0003511405610000052
s3.8: from this, the robust kalman filter can be derived as follows:
Figure BDA0003511405610000053
wherein the content of the first and second substances,
Figure BDA0003511405610000054
further, when the actuator fault is added to the PEMFC voltage model, the form of the fault including the external disturbance is as follows:
Figure BDA0003511405610000055
wherein A isz＝eAT，
Figure BDA0003511405610000056
xkRepresents a state variable, ukRepresenting a control input, ωkAnd upsilonkRespectively process noise and observation noise, fkIndicating actuator failure, xkThe state variable is represented by a number of variables,
Figure BDA0003511405610000057
for state estimation, δ a, δ B, δ C are uncertainty parameters, respectively.
Further, the residual sequence generated in step 5 is:
Figure BDA0003511405610000061
wherein r iskAs residual sequence, ekIndicating an error.
Further, the method for detecting the evaluation function threshold fault introduced in step 6 specifically includes:
predefining a suitable threshold JthAnd an evaluation function
Figure BDA0003511405610000062
The residual evaluation function is:
Figure BDA0003511405610000063
the threshold value is:
Figure BDA0003511405610000064
where M is the end time of the entire run and α is a given constant.
Further, the decision logic for determining whether the system fails in step 6 is as follows:
given a constant α, fault detection can be implemented by the following decision logic:
Figure BDA0003511405610000065
has the advantages that:
1. the threshold fault detection method based on the robust Kalman filter uses the robust Kalman filter as a residual signal generator, can realize state estimation on an uncertain discrete system on the basis of the linear Kalman filter, is combined with the threshold fault detection method, and can detect faults of a PEMFC system with uncertainty. Simulation results prove that the method can accurately and quickly detect the fault and is suitable for the PEMFC voltage system.
2. The invention can carry out state estimation and fault diagnosis when the proton exchange membrane fuel cell system has uncertainty, combines the robust Kalman filter with a threshold fault detection method, monitors the operation process of the PEMFC system, and has accurate fault detection, high speed and robustness. The method can accurately realize fault detection on line, can obtain a model prediction output value, collects data and analyzes the data at the same time, needs a small amount of samples, reduces on-line calculation time, meets the requirement of on-line fault detection on a system, is suitable for the condition of uncertainty of the system, and is more timely and wider in application range compared with other detection methods.
3. As known from the current literature, no scholars adopt an evaluation function threshold fault detection method based on a robust Kalman filter to realize fault detection simultaneously containing faults, external interference, uncertainty and a PEMFC system, so that the fault detection method provided by the invention is novel and has reference value.
Drawings
FIG. 1 is a schematic structural diagram of a PEMFC system according to an embodiment of the invention;
FIG. 2 is a schematic diagram of an equivalent RC circuit of the PEMFC according to the embodiment of the present invention;
FIG. 3 shows the actual voltage state (V) of the PEMFC system according to the embodiment of the present inventionstack) And the estimated state (V)upd)；
FIG. 4 is a schematic diagram of a fault signal f (k) according to an embodiment of the present invention;
fig. 5 is a diagram of a fault detection result according to an embodiment of the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
The invention provides a method for detecting faults of a PEMFC system evaluation function threshold based on a robust Kalman filter aiming at faults in the system by taking a PEMFC system as an implementation object.
The invention relates to a method for detecting faults of a PEMFC system evaluation function threshold based on a robust Kalman filter, which comprises the following steps:
step 1: according to the PEMFC principle, a PEMFC dynamic voltage model is constructed and a differential equation is converted into a state equation in a standard form:
the PEMFC dynamic voltage model system is mainly influenced by load current, reaction temperature and gas pressure factors, and the output voltage is expressed as:
Vcell＝n(Enerst-ηact-ηcons-ηohmic) (1)
wherein n represents the number of cells, VcellIs a cell voltage, EnerstIs a nerceSpecific voltage, ηactTo activate the overpotential,. etaconsIs the concentration overpotential, etaohmicIs an ohmic overpotential. Respectively, as follows:
Figure BDA0003511405610000071
wherein the content of the first and second substances,
Figure BDA0003511405610000072
the relevant parameters in the dynamic voltage model are shown in table 1.
TABLE 1 relevant parameters in the dynamic Voltage model
Figure BDA0003511405610000073
Figure BDA0003511405610000081
In order to simulate the effect of the electric double layer phenomenon in the PEMFC on its dynamic output characteristics, an RC circuit including an equivalent capacitance and an equivalent resistance was used as a cell equivalent circuit, which is expressed as:
Figure BDA0003511405610000082
Figure BDA0003511405610000083
wherein the content of the first and second substances,
Figure BDA0003511405610000084
is an equivalent voltage, CdIs an equivalent capacitance, τcIs a time constant, RactTo activate polarization loss, RconConcentration polarization loss. Selecting
Figure BDA0003511405610000085
As state variables, IdIs the current as the control variable. The linearized continuous system model of the PEMFC is then
Figure BDA0003511405610000086
Wherein the content of the first and second substances,
Figure BDA0003511405610000087
and 2, step: based on the equation of state in step 1, the general form of the PEMFC dynamic voltage model with external disturbances is given:
in an actual pem fuel cell system, disturbances and malfunctions such as temperature, pressure variations, equipment aging, etc. may occur. Considering these uncertainty factors, we need to add perturbation and uncertainty to the system and discretize it to get the following discrete system
Figure BDA0003511405610000091
Wherein A isz＝eAT，
Figure BDA0003511405610000092
xkRepresents a state variable, ukRepresents a control input, ykRepresenting the output, ωkAnd upsilonkRespectively, process noise and observation noise, and delta a, delta B and delta C are respectively uncertain parameters.
And step 3: a pure certainty view is adopted, a robust regularization least square estimation problem is constructed by applying a penalty function method, and a robust Kalman filter is designed:
the PEMFC system model uncertainty parameter is expressed in the form:
Figure BDA0003511405610000093
wherein E is1、E2、E3、F1、F2、F3Is a constant matrix of known appropriate dimensions, Δ1、Δ2、Δ3Is an arbitrary compression matrix, and I is an identity matrix.
At each step k, an a priori estimate is assumed
Figure BDA0003511405610000094
Measurement output ykAnd a control input ukAs is known, a min-max constrained optimization problem can be obtained. When the system is influenced most by uncertainty, the quadratic cost function is minimum, and the objective function is as follows:
Figure BDA0003511405610000095
the following mapping relationship is defined:
Figure BDA0003511405610000096
the system (7) can be rewritten as follows:
Y+δY＝(D+δD)X+W (11)
the uncertainty is written in the form:
Figure BDA0003511405610000097
the robust regularized least squares estimate can be expressed as:
Figure BDA0003511405610000101
introducing a penalty function, and rewriting the objective function (9) into:
Figure BDA0003511405610000102
wherein:
Figure BDA0003511405610000103
assuming a priori estimation errors
Figure BDA0003511405610000104
Has an error covariance of P-W has an error covariance of Q, order
Figure BDA0003511405610000105
A determined solution of the objective function (14)
Figure BDA0003511405610000106
The following were used:
Figure BDA0003511405610000107
wherein the content of the first and second substances,
Figure BDA0003511405610000108
Figure BDA0003511405610000109
is a non-negative scalar parameter obtained as a solution to the optimization problem
Figure BDA00035114056100001010
The objective function Γ (λ) is given as follows:
Γ(λ)＝||z(λ)||2+||Hz(λ)-K||2+λ||FHz(λ)-FK||2 (18)
wherein the content of the first and second substances,
Figure BDA00035114056100001011
using approximate calculations
Figure BDA00035114056100001012
Solving the robust regularized least square estimation problem, where ξ > 0, then X's robust estimation
Figure BDA00035114056100001013
And estimate error
Figure BDA00035114056100001014
The covariance P of (a) can be given by the following symmetric permutation matrix:
Figure BDA0003511405610000111
wherein the content of the first and second substances,
Figure BDA0003511405610000112
from this, the robust kalman filter can be derived as follows:
Figure BDA0003511405610000113
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003511405610000114
and 4, step 4: using a robust Kalman filter as a residual signal generator, providing a system initial value required by the filter, and obtaining an output value predicted by a system model:
the optimum working temperature of the PEMFC is influenced by various factors such as ambient temperature, reaction gas humidity, current and the like, and a fitting formula is determined as
Figure BDA0003511405610000115
Wherein the content of the first and second substances,
Figure BDA0003511405610000121
is the air humidity. Since the ambient temperature and the air humidity are not controllable during the experiment, only the influence of the load current on the optimal operating temperature is considered during the simulation. The ambient temperature was fixed at 298K and the air humidity was fixed at 60%. The working current is set by the electronic load, and the battery pack operates under the set current condition. The specific working condition is 100s running time, the load current is set to be 4A, and the test mode is a constant current mode.
After the PEMFC voltage dynamic model is established, the model is simulated based on the MATLAB platform, and the obtained model prediction output value is as shown in fig. 3.
And 5: adding a fault item into the PEMFC voltage model, synchronizing the operation method of the step 4, comparing the obtained predicted value with the actual value, and generating a residual sequence:
the general form when the PEMFC voltage model contains external disturbances and faults is:
Figure BDA0003511405610000122
the generated residual sequence is:
Figure BDA0003511405610000123
wherein r iskAs residual sequence for fault detection of the system, ekAn error is indicated.
Step 6: introducing an evaluation function threshold fault detection method, analyzing the statistical characteristics of residual signals, and constructing a decision function and a decision rule:
in order to sensitively detect a fault, a suitable threshold value J needs to be predefinedthAnd an evaluation function
Figure BDA0003511405610000124
The residual evaluation function is:
Figure BDA0003511405610000125
wherein M is the end time of the whole operation process, and alpha is a given constant;
the threshold values are set as follows:
Figure BDA0003511405610000126
and 7: and 6, carrying out fault detection by utilizing the operation process of the monitoring system according to the decision function and the decision rule in the step 6. The decision logic for judging whether the system fails is as follows:
referring to a specified constant α, fault detection can be implemented by the following decision logic:
Figure BDA0003511405610000127
according to the method, the operation process of the system is monitored, and fault detection can be realized.
In the present embodiment, taking the constant α to be 0.7, the failure sequence f (k) is given as follows:
Figure BDA0003511405610000131
wherein rand (n) is a random sequence, and x is more than or equal to 0 and less than or equal to 1 (n), and n is 1,2,3 and …. After adding this fault to the system, the evaluation function response states are shown in fig. 5 for both fault and no fault conditions. From the simulation results, it is found that when k is 52, a failure is detected.
As can be seen from the simulation result, aiming at the fault detection of the PEMFC, the fault detection method designed by the invention can detect whether the system has a fault on line in time, and has important practical reference value.
The above embodiments are merely illustrative of the technical concepts and features of the present invention, and the purpose of the embodiments is to enable those skilled in the art to understand the contents of the present invention and implement the present invention, and not to limit the protection scope of the present invention. All equivalent changes and modifications made according to the spirit of the present invention should be covered within the protection scope of the present invention.

Claims (8)

1. A proton exchange membrane fuel cell fault detection method based on a robust Kalman filter is characterized by comprising the following steps:
step 1: constructing a PEMFC dynamic voltage model according to a PEMFC principle, and converting a differential equation into a state equation in a standard form;
and 2, step: based on the state equation in the step 1, giving a general form that the PEMFC dynamic voltage model contains external interference;
and 3, step 3: a pure certainty viewpoint is adopted, a penalty function method is applied to construct a robust regularization least square estimation problem, and a robust Kalman filter is designed;
and 4, step 4: using a robust Kalman filter as a residual signal generator, and giving a system initial value required by the filter to obtain an output value predicted by a system model;
and 5: adding an actuator fault into the PEMFC dynamic voltage model, and comparing the obtained predicted value with the actual value by using the operation method in the step 4 to generate a residual sequence;
step 6: introducing an evaluation function threshold fault detection method, analyzing the statistical characteristics of residual signals, and constructing a decision function and a decision rule;
and 7: and 6, monitoring the operation process of the system according to the decision function and the decision rule in the step 6, and carrying out fault detection.
2. The robust kalman filter based proton exchange membrane fuel cell fault detection method of claim 1, wherein the PEMFC dynamic voltage model output voltage is expressed as:
Vcell＝n(Enerst-ηact-ηcons-ηohmic) (1)
wherein n represents the number of cells, VcellIs a cell voltage, EnerstIs a Nernst voltage, ηactTo activate the overpotential,. etaconsIs a concentration overpotential, etaohmicOhmic overpotential;
Figure FDA0003511405600000011
wherein the content of the first and second substances,
Figure FDA0003511405600000012
an RC circuit comprising an equivalent capacitor and an equivalent resistor is used as a battery equivalent circuit, and the RC circuit is expressed as follows:
Figure FDA0003511405600000021
Figure FDA0003511405600000022
wherein, VCdIs an equivalent voltage, CdIs an equivalent capacitance, taucIs a time constant, RactTo activate polarization loss, RconConcentration polarization loss; selecting
Figure FDA0003511405600000029
As state variables, IdFor current, as a control variable, the linearized continuous system model of the PEMFC is:
Figure FDA0003511405600000023
wherein the content of the first and second substances,
Figure FDA0003511405600000024
3. the robust kalman filter based proton exchange membrane fuel cell fault detection method of claim 1, wherein the PEMFC dynamic voltage model in step 2 contains external disturbances in the general form of:
Figure FDA0003511405600000025
wherein A isz＝eAT，
Figure FDA0003511405600000026
xkRepresents a state variable, ukRepresents a control input, ykRepresenting the output, ωkAnd upsilonkRespectively, process noise and observation noise, and delta a, delta B and delta C are respectively uncertain parameters.
4. The proton exchange membrane fuel cell fault detection method based on the robust kalman filter according to claim 3, wherein the specific process of designing the robust kalman filter in the step 3 is as follows:
s3.1: the uncertain parameters in the PEMFC dynamic voltage model are expressed as follows:
Figure FDA0003511405600000027
wherein, E1、E2、E3、F1、F2、F3Is a constant matrix of known appropriate dimensions, Δ1、Δ2、Δ3The matrix is any compression matrix, delta A, delta B and delta C are respectively uncertain parameters, and I is a unit matrix;
s3.2: at each step k, an a priori estimate is assumed
Figure FDA0003511405600000028
Measurement output ykAnd a control input ukKnown, a min-max constraint optimization problem can be obtained, when the system is most affected by uncertainty, the quadratic cost function is the smallest, and the objective function is as follows:
Figure FDA0003511405600000031
s3.3: the following mapping relationship is defined:
Figure FDA0003511405600000032
then system equation (7) can be rewritten as follows:
Y+δY＝(D+δD)X+W (11)
the uncertainty is written in the form:
Figure FDA0003511405600000033
s3.4: the robust regularized least squares estimate is expressed as:
Figure FDA0003511405600000034
s3.5: introducing a penalty function, and rewriting the objective function (9) as:
Figure FDA0003511405600000035
wherein the content of the first and second substances,
Figure FDA0003511405600000036
s3.6: assuming a priori estimation errors
Figure FDA0003511405600000037
Has an error covariance of P-W has an error covariance of Q, order
Figure FDA0003511405600000038
A determined solution of the objective function (14)
Figure FDA0003511405600000039
The following were used:
Figure FDA00035114056000000310
wherein the content of the first and second substances,
Figure FDA00035114056000000311
Figure FDA00035114056000000312
is a non-negative scalar parameter obtained as a solution to the optimization problem:
Figure FDA00035114056000000313
the objective function Γ (λ) is given as follows:
Γ(λ)＝||z(λ)||2+||Hz(λ)-K||2+λ||FHz(λ)-FK||2 (18)
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003511405600000041
s3.7: using approximate calculations
Figure FDA0003511405600000042
Solving the robust regularized least squares estimation problem, where ξ > 0, then x's robust estimation
Figure FDA0003511405600000043
And estimate error
Figure FDA0003511405600000044
The covariance P of (a) can be given by the following symmetric permutation matrix:
Figure FDA0003511405600000045
wherein the content of the first and second substances,
Figure FDA0003511405600000046
s3.8: from this, the robust kalman filter can be derived as follows:
Figure FDA0003511405600000047
wherein the content of the first and second substances,
Figure FDA0003511405600000048
5. the proton exchange membrane fuel cell fault detection method based on robust kalman filter of claim 1, wherein when the PEMFC voltage model is added to the actuator fault, the external disturbance and fault are included in the form of:
Figure FDA0003511405600000051
wherein A isz＝eAT，
Figure FDA0003511405600000052
xkRepresents a state variable, ukRepresenting a control input, ωkAnd upsilonkRespectively process noise and observation noise, fkIndicating actuator failure, xkThe state variable is represented by a number of variables,
Figure FDA0003511405600000053
for state estimation, δ a, δ B, δ C are uncertainty parameters, respectively.
6. The robust kalman filter-based proton exchange membrane fuel cell fault detection method according to claim 1, wherein the residual sequence generated in the step 5 is:
Figure FDA0003511405600000054
wherein r iskAs residual sequence, ekIndicating an error.
7. The proton exchange membrane fuel cell fault detection method based on the robust kalman filter according to claim 1, wherein the evaluation function threshold fault detection method introduced in the step 6 specifically comprises:
predefining a suitable threshold value JthAnd an evaluation function
Figure FDA0003511405600000055
The residual evaluation function is:
Figure FDA0003511405600000056
the threshold value is:
Figure FDA0003511405600000057
where M is the end time of the entire run and α is a given constant.
8. The proton exchange membrane fuel cell fault detection method based on the robust kalman filter of claim 7, wherein the decision logic for determining whether the system has a fault in the step 6 is as follows:
given the constant α, fault detection can be implemented by the following decision logic:
Figure FDA0003511405600000058
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