energies Article
Application of the Sensor Selection Approach in Polymer Electrolyte Membrane Fuel Cell Prognostics and Health Management Lei Mao *
ID
, Ben Davies and Lisa Jackson
Department of Aeronautical and Automotive Engineering, Loughborough University, Loughborough LE11 3RX, UK;
[email protected] (B.D.);
[email protected] (L.J.) * Correspondence:
[email protected]; Tel.: +44-0782-121-9160 Received: 24 July 2017; Accepted: 14 September 2017; Published: 29 September 2017
Abstract: In this paper, the sensor selection approach is investigated with the aim of using fewer sensors to provide reliable fuel cell diagnostic and prognostic results. The sensitivity of sensors is firstly calculated with a developed fuel cell model. With sensor sensitivities to different fuel cell failure modes, the available sensors can be ranked. A sensor selection algorithm is used in the analysis, which considers both sensor sensitivity to fuel cell performance and resistance to noise. The performance of the selected sensors in polymer electrolyte membrane (PEM) fuel cell prognostics is also evaluated with an adaptive neuro-fuzzy inference system (ANFIS), and results show that the fuel cell voltage can be predicted with good quality using the selected sensors. Furthermore, a fuel cell test is performed to investigate the effectiveness of selected sensors in fuel cell fault diagnosis. From the results, different fuel cell states can be distinguished with good quality using the selected sensors. Keywords: PEM fuel cell; PHM; sensor selection; fault diagnosis; prognosis
1. Introduction Due to characteristics such as zero-emissions and high efficiency, fuel cell technology has been engineered for a range of applications, including automotive, stationary power stations, and consumer devices. However, the fuel cell reliability and durability are still two main barriers for its wider application, which leads to a series of studies on fuel cell prognostics and health management (PHM). From previous studies [1–3], PHM analysis requires several stages, including data collection, data processing, condition monitoring, diagnostics, prognostics, and decision support. From a literature review, it is observed that most fuel cell PHM studies focus on the diagnostic stage, which can be loosely divided into two groups: model-based methods and data-driven techniques. Although several studies employ a model-based method for fuel cell diagnostics, i.e., developing a fuel cell model, and identifying fuel cell faults from residuals between model outputs and actual measurements [4–8], there are complexities in developing an accurate fuel cell model containing complete sets of failure modes. Data-driven approaches are more widely used for fuel cell diagnostics, that is, extracting the features by applying signal processing techniques to the sensor data, and discriminating fuel cell faults with extracted features [9–13]. Compared to fuel cell diagnostics, fewer studies have been devoted to fuel cell prognostics, and among these studies, training data from a fuel cell system is required to generate the input–output relationship of the fuel cell model for the prediction of future performance [14–18]. It can be concluded from the literature review that with commonly used fuel cell diagnostic and prognostic approaches, the performance relies largely on the quality of the fuel cell sensor measurements. Considering the fact that sensors may express different sensitivities to fuel cell Energies 2017, 10, 1511; doi:10.3390/en10101511
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performance change, and environment/measurement noise is usually contained in the collected measurements, more sensor measurements may not provide better performance, thus it is necessary to find the optimal sensors providing reliable results with the minimum computation cost. From a literature review, several sensor selection approaches have been applied in different systems [19–22], but their applications in fuel cell system PHM have not been fully investigated. In this paper, sensor selection approaches are applied to find optimal sensors for fuel cell diagnostics and prognostics, and the performance of these optimal sensors in fault diagnosis and prognosis is evaluated using test data from a polymer electrolyte membrane (PEM) fuel cell system. Section 2 presents the developed fuel cell model and validates its performance in representing fuel cell behavior. Based on the model, the sensitivity matrix relating sensor measurements and model parameters is generated. In Section 3, several sensor selection approaches are used to find optimal sensors based on their sensitivity, and the performance of selected sensors in predicting fuel cell performance is evaluated using an adaptive neuro-fuzzy inference system (ANFIS). Section 4 further evaluates the performance of optimal sensors in identifying fuel cell faults, with test data from a practical fuel cell system. From the findings, conclusions are given in Section 5. 2. Development of PEM Fuel Cell Model and Generation of Sensitivity Matrix 2.1. Development of PEM Fuel Cell Model In this study, sensitivity analysis is used for the sensor selection algorithms, to determine the relationship between sensor outputs and fuel cell failure modes. However, determination of such a relationship using experimental analysis will be very difficult, time-consuming and expensive, as various fuel cell failure modes should be created. Therefore, numerical analysis is taken herein to perform the sensitivity analysis, where a fuel cell model is developed, and model parameters are selected to represent fuel cell failure modes based on the fuel cell failure mechanisms (since different fuel cell failure modes can affect various model parameters and thus the fuel cell performance). With this method, the sensor sensitivities to various fuel cell failure modes can be obtained without complex experimental analysis. Moreover, as sensor sensitivity is obtained by calculating the variation in sensor measurements due to the unit change of model parameter, the results can be used in different fuel cell systems at various operating conditions. Figure 1 depicts the block diagram of the developed fuel cell model. It can be seen that four modules are used in the fuel cell model to express various behavior of the fuel cell, including anode and cathode mass flow modules determining the flow, pressure, and mass of reactant gases at the anode and cathode sides; the membrane hydration module calculating the membrane resistance and water across the membrane; the stack temperature module updating stack temperature using the first law of thermodynamics; and the stack voltage module determining stack voltage based on results from the other three modules. More details about the developed fuel cell model can be found in previous studies [18,23,24]. From the model, the fuel cell stack voltage can be calculated as: Vcell = En − Vact − VFC − Vtrans − Vohm
(1)
where Vcell is the single cell voltage, En is the reversible voltage, Vact , VFC , Vtrans , Vohm are the activation loss, fuel crossover loss, mass transport loss, and Ohmic loss, respectively, which can be obtained in different modules in the developed model.
in previous studies [18,23,24]. From the model, the fuel cell stack voltage can be calculated as: V
=E −V
−V
−V
−V
(1)
where V is the single cell voltage, E is the reversible voltage, V , V , V , V are the activation loss, fuel crossover loss, mass transport loss, and Ohmic loss, respectively, which can be Energies 2017, 10, 1511 3 of 13 obtained in different modules in the developed model.
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Figure Figure1.1.Block Blockdiagram diagramof ofthe thedeveloped developedfuel fuelcell cellmodel. model.
The performance of the developed fuel cell model is evaluated with test data from the fuel cell The performance of the developed fuel cell model is evaluated with test data from the fuel cell system in a previous study [24]. With the fuel cell parameters listed in Table 1, the fuel cell model system in a previous study [24]. With the fuel cell parameters listed in Table 1, the fuel cell model can can be developed, and by determining the model parameters, including internal and exchange be developed, and by determining the model parameters, including internal and exchange current current densities, mass transport coefficients, membrane resistance, etc., the losses in Equation (1) densities, mass transport coefficients, membrane resistance, etc., the losses in Equation (1) can be can be calculated, and fuel cell voltage can then be determined with Equation (1). With this calculated, and fuel cell voltage can then be determined with Equation (1). With this procedure, procedure, the polarization curves from the model can be obtained and compared with that from the polarization curves from the model can be obtained and compared with that from the test; the test; the results are shown in Figure 2. the results are shown in Figure 2. Table 1. Input parameters for the fuel cell model [24]. Table 1. Input parameters for the fuel cell model [24].
Parameter (Unit)
Value
Parameter Number(Unit) of fuel cells
Value54
ActiveNumber electrode areacells of single cell (cm ) of fuel ActiveHydrogen electrode area of single cell (cm2 ) flow rate stoichiometry Hydrogen Airflow flowrate ratestoichiometry stoichiometry Air flow rate stoichiometry 60
model data test data
50 Voltage (v)
5446.5 46.51.15 1.152.0 2.0
40 30 20 10 0
0
5
10
15 20 Current (A)
25
30
35
Figure Comparison polarization curves from model and test. Figure 2. 2. Comparison ofof polarization curves from thethe model and test.
It can be observed from Figure 2 that the polarization curves from the tested fuel cell can be It can be observed from Figure 2 that the polarization curves from the tested fuel cell can be simulated using the developed model with good quality; the difference of the polarization curve simulated using the developed model with good quality; the difference of the polarization curve results between simulated and test data is less than 1%. results between simulated and test data is less than 1%. 2.2. Generation Sensitivity Matrix 2.2. Generation of of Sensitivity Matrix Withthe thedeveloped developedfuel fuelcell cellmodel, model,the thesensor sensorsensitivity sensitivitytotofuel fuelcell cellperformance performancecan canbebe With determined. For this purpose, several model parameters critical to the fuel cell performance are determined. For this purpose, several model parameters critical to the fuel cell performance selected based on previous studies of fuel cell failure modes and corresponding failure mechanisms are selected based on previous studies of fuel cell failure modes and corresponding failure [25–27]. From the results, three model parameters are determined, includingincluding membrane resistance, mechanisms [25–27]. From the results, three model parameters are determined, membrane electrochemical surface area (ECSA), and liquid water inside the fuel cell; the variation in these parameters will cause different fuel cell failure modes. With determined model parameters, the corresponding sensor sensitivity can be calculated. In the analysis, a unit change (1%) is applied to the model parameters, and the variations in fuel cell responses (sensor measurements) can be obtained, which can be expressed with Equation (2). Rj − Rj
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resistance, electrochemical surface area (ECSA), and liquid water inside the fuel cell; the variation in these parameters will cause different fuel cell failure modes. With determined model parameters, the corresponding sensor sensitivity can be calculated. In the analysis, a unit change (1%) is applied to the model parameters, and the variations in fuel cell responses (sensor measurements) can be obtained, which can be expressed with Equation (2). Sij =
Rj2 − Rj1 Pi2 − Pi1
(2)
where P is the selected model parameter, R is the sensor output, 1 and 2 represent values before and after applying the certain change, Sij is the jth sensor sensitivity for the ith model parameter. It should be noted that multiple fuel cell failure effect is not considered herein, thus in each case, only one health parameter is to be changed. 2017, 10, 1511 4 of 13 Table 2 With Energies Equation (1), sensor sensitivities to various fuel cell parameters can be determined. lists the sensors used in the analysis, while Figure 3 depicts the sensor sensitivities to different fuel With Equation (1), sensor sensitivities to various fuel cell parameters can be determined. Table 2 cell parameters. lists the sensors used in the analysis, while Figure 3 depicts the sensor sensitivities to different fuel cell parameters.
Table 2. Sensors used in the analysis. Table 2. Sensors used in the analysis.
Number Number
Sensor Sensor Cell Cellvoltage voltage(V) (V) Stack (K) Stacktemperature temperature (K) Anode inlet Anode inletflow flow(kg/s) (kg/s) Cathode inlet Cathode inletflow flow(kg/s) (kg/s) Anode outletflow flow(kg/s) (kg/s) Anode outlet Cathode outletflow flow(kg/s) (kg/s) Cathode outlet Compressortemperature temperature Compressor (K)(K) Coolant inletflow flow(kg/s) (kg/s) Coolant inlet Inletwater watertemperature temperature Inlet (K)(K) Outletwater watertemperature temperature Outlet (K)(K)
s1 s1 s2 s2 s3 s3 s4 s4 s5 s5 s6 s6 s7 s7 s8 s8 s9 s9 s10s10
-3
8
4
Sensitivity
Sensitivity
6
2
0
s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 Sensor
(a) Sensor sensitivity to membrane resistance
x 10
6 4 2 0
0 s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 Sensor (b) Sensor sensitivity to cell active area
0.02
Sensitivity
0.015 0.01 0.005 0
0 s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 Sensor
(c) Sensor sensitivity to liquid water inside the cell Figure 3. Sensor sensitivity to different fuel cell parameters.
Figure 3. Sensor sensitivity to different fuel cell parameters. It can be seen from Figure 3 that several sensors, such as anode inlet flow, compressor temperature, and coolant inlet flow, have zero sensitivities to the model parameters, indicating that the variation of fuel cell performance due to these parameters cannot change these sensor measurements. Therefore, these sensors should not be used in fuel cell diagnosis and prognosis.
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It can be seen from Figure 3 that several sensors, such as anode inlet flow, compressor temperature, and coolant inlet flow, have zero sensitivities to the model parameters, indicating that the variation of fuel cell performance due to these parameters cannot change these sensor measurements. Therefore, these sensors should not be used in fuel cell diagnosis and prognosis. 3. Sensor Selection Algorithm and Its Performance in PEM Fuel Cell Performance Prediction From results in Section 2, the sensors can be ranked based on their sensitivities, and the sensor selection method proposed in [18] is used herein to find optimal sensors. Its performance in predicting fuel cell performance will be investigated using test data from a PEM fuel cell system. The proposed sensor selection approach in [18] considers both sensor sensitivity and sensor resistance to measurement noise, thus the selected sensors should be more sensitive to the fuel cell performance change and more resistant to the measurement noise. This selection can be made based on Equation (3).
{δP} = (ST S)
−1 T
S {δR} = G{δR}
(3)
where S is the sensitivity matrix, {δR} is the variation in sensor measurements, and {δP} is the perturbations in health parameters. In the selection process, all possible sensor set combinations are considered, and the noise resistance of each sensor set, i.e., {δR} in Equation (3), is evaluated as follows. Random noise is generated (1% of the sensor measurement is used herein) and applied to the studied sensor set, the corresponding fuel cell parameter variations {δP} can be calculated using Equation (3). This process is then repeated a certain number of times (10 in this study), and the standard deviation of each fuel cell parameter can be calculated and used to form the index SD below. SD = σ1 σ2 . . . σp
(4)
where p represents the number of fuel cell parameters, and the overall error can be used to evaluate the noise resistance (NR) of the selected sensor set. NR = µSD + σSD /µSD
(5)
From the above analysis, one sensor set with the best noise resistance is selected from each sensor set size, and the results are listed in Table 3. Table 3. Sensors with the best noise resistance capability from different sizes [18]. Size of Sensor Set
Sensor Set with the Best Noise Resistance Capability
1
Stack temperature
2
Stack temperature, cathode outlet flow
3
Stack temperature, cathode outlet flow, cathode inlet flow
4
Stack temperature, cathode outlet flow, cathode inlet flow, water inlet temperature
5
Stack temperature, cathode outlet flow, cathode inlet flow, water inlet temperature, water outlet temperature
6
Stack temperature, cathode outlet flow, cathode inlet flow, water inlet temperature, water outlet temperature, anode outlet flow
In the study, the adaptive neuro-fuzzy inference system (ANFIS) is used to evaluate the performance of selected sensors, and its general structure is shown in Figure 4. More details about ANFIS can be found in previous research [14,15,17]. In the analysis, the inputs of the ANFIS are the measurements from selected sensors, and the output is the fuel cell voltage. As ANFIS is the multi-step prediction algorithm, the training data
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must be used for the prediction. In this study, the first two-thirds of the data samples are used to train the ANFIS system, while the last one-third of the data samples are used to validate the performance of selected sensors. It should be mentioned that the PEM fuel cell data from IEEE 2014 data challenge [28] is used herein for searching the optimal sensors, which includes a total of 16 sensors collected from the fuel cell system, including fuel cell voltage, current, inlet and outlet Energies 2017, 10, 1511 6 of 13 flow/temperature at anode/cathode, etc. Energies 2017, 10, 1511
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Figure 4. Adaptiveneuro-fuzzy neuro-fuzzy inference structure. Figure 4. Adaptive inferencesystem system(ANFIS) (ANFIS) structure. 4. Adaptive neuro-fuzzy inference (ANFIS) structure.based on Table 3, and In the evaluationFigure analysis, the size of the sensor set issystem increased gradually
Figure 4. Adaptive neuro-fuzzy inference (ANFIS) structure. In the evaluation analysis, the size of the sensor setsystem is increased gradually based on Table 3, the optimal sensors can be determined when further improvement cannot be observed with increase In the evaluation analysis, the size of thewhen sensor further set is increased gradually based on Table 3, and and the optimal sensors can be determined improvement cannot be observed with of sensor setInsize. the evaluation analysis, the size of the sensor set is increased gradually based on Table 3, and the optimal sensors can be determined when further improvement cannot be observed with increase increase of sensor set size. Figure 5 evaluates the performance ofwhen sensor sets improvement in Table 3, incannot termsbeofobserved mean prediction error the optimal sensors can be determined further with increase of sensor set size. Figure 5ofevaluates the performance of sensor Tableset 3, in terms of mean prediction error sensor set size. and computational time. It can be seen clearly sets that in sensor 3 (contains three sensors listed in and Figure 5 evaluates the performance of sensor sets in Table 3, in terms of mean prediction error Figure 5can evaluates the clearly performance ofsensor sensor sets 3in(contains Table 3, inreasonable terms of mean prediction error Table 3) can represent theseen fuel cell performance accurately with computational time.3) can computational time. It be that set three sensors listed in Table and computational time.time. It can be seen clearly that sensor setset3 3(contains three listed in and computational It can be seen clearly that sensor (contains three sensors sensors listed in Figure depicts the prediction results using selected sensors. Itreasonable can be seen that with selected represent the63) fuel cell performance accurately with reasonable computational time. Figure 6time. depicts the Table can represent the fuel cell performance accurately with computational Table 3) can represent the fuel cell performance accurately with reasonable computational time. sensors, reliable prediction cansensors. be results made It after the proper training. prediction results using selected can be seen that with sensors, reliable prediction Figure 6 depicts the prediction using selected sensors. It Itselected can that selected Figure 6 depicts the prediction results using selected sensors. canbebeseen seen that with with selected sensors, reliable prediction can can be made after thethe proper training. can be made after the proper training. sensors, reliable prediction be made after proper training. 0.08
800
600
0
0
0.04
0.04
600 600
400
400
400
0.02 0.02
200 200
0.02
1 0
1
Computation Computationtime time(s) (s)
0.04
0.06 0.06
200
1
2
2
2
3 3 44 3 4 sensor number sensor setset number
55
5
Computation time (s)
800 800
0.06 Mean prediction error (V)
Mean prediction error (V)
Mean prediction error (V)
0.08 0.08
00
066 6
sensor set number
Figure 5. Prediction performance and computational time of different sensor sets.
Figure 5. Prediction performance and computational time of different sensor sets.
S tac k v oltage (v )
3.4 3.4
S tac k v oltage (v )
S tac k v oltage (v )
5. Prediction performanceand and computational computational time of different sensorsensor sets. sets. FigureFigure 5. Prediction performance time of different
3.3 3.3
3.4 3.3 3.2
3.2 3.2 3.1 3.1 3.1
33
3
Actual Prediction Actual
Actual 200 Prediction Prediction 200 200
400
400 400
600 Time (h)
800
1000
600 800 1000 600 800 1000 Time (h) Figure 6. Prediction performance of selected sensors blue dashed line separates the Figure 6. Prediction performance of selected sensors (the vertical vertical blue dashed line separates the Time (h)(the and validation training andtraining validation stages). stages).
Figure 6. Prediction performance of selected sensors (the vertical blue dashed line separates the
Figure 6. Prediction performance of selected sensors (the vertical blue dashed line separates the training and validation stages). training and validation stages).
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4. 4. Performance Performance of of Selected Selected Sensors Sensors in in PEM PEM Fuel Fuel Cell Cell Fault Fault Diagnosis Diagnosis 4.1. 4.1. Description Description of of PEM PEM Fuel Fuel Cell Cell Test Test In section, aa PEM PEM fuel fuel cell cell test test will will be be designed designed to to investigate investigate the the performance performance of of selected selected In this this section, optimal sensors in identifying fuel cell faults. For this purpose, a test rig with capability of optimal sensors in identifying fuel cell faults. For this purpose, a test rig with capability of 80 80 W W is is used, which contains contains aa fuel fuelcell cellstack, stack,air airand andhydrogen hydrogensupply supplysystems, systems,and anda acooling cooling system, which used, which system, which is is depicted in Figure 7. depicted in Figure 7.
Figure 7. Fuel cell test rig.
In thestudy, study,a cell a cell with active 100 used,iswhich is manufactured Pragma 2 iscm In the with active areaarea of 100ofcm used,iswhich manufactured by PragmabyIndustries Industries usingmaterials the same and materials and technologies as commercial such aspolymer Nafion using the same technologies as commercial PEM fuel PEM cells,fuel suchcells, as Nafion polymer electrolyte membrane, platinum nano-particle catalyst, carbon diffusion materials, silicone electrolyte membrane, platinum nano-particle catalyst, carbon diffusion materials, silicone sealing sealing and graphite flow fieldTable plates. Table 4 lists the technical of the cell gaskets,gaskets, and graphite flow field plates. 4 lists the technical details ofdetails the PEM fuelPEM cell fuel test and test and Table lists theused sensors used thethe test for the following Table 5 lists the5sensors in the testinfor following analysis. analysis. Table details of of the the polymer polymer electrolyte electrolyte membrane membrane (PEM) (PEM) fuel fuel cell cell system. system. Table 4. 4. Technical Technical details
Parameter Parameter Membrane thickness (μm) ActiveMembrane area (cm )thickness2 (µm) Active area (cm ) Platinum loading (mg/cm ) Platinum loading (mg/cm2 ) Gas diffusion (μm) Gasthickness diffusion thickness (µm)
Value Value 25 25 100 100 0.2 0.2 415 415
Table 5. Sensors used in in the the fuel fuel cell cell test. test. Table 5. Sensors used
Sensor VoltageSensor Voltage Anode outlet pressure Anode outlet pressure Cathode inlet flow Cathode inlet flow Anode relative humidity Anode relative humidity CathodeCathode inlet pressure inlet pressure
Sensor Anode inlet flow Anode inlet flowpressure Cathode outlet Cathode outlet pressure Anode inlet pressure Anode inlet pressure Cathode relative humidity Cathode relative humidity Stack temperature Stack temperature Sensor
As the PEM fuel cell test is used to investigate the performance of the selected sensor in fault As the PEM fuel cell test is used to investigate the performance of the selected sensor in fault diagnosis, fuel cell fault should be “activated” during the test. Fuel cell flooding is selected in the diagnosis, fuel cell fault should be “activated” during the test. Fuel cell flooding is selected in the current study, as water management is extremely important in the PEM fuel cell normal operation, current study, as water management is extremely important in the PEM fuel cell normal operation, and fuel cell flooding can cause fast degradation to the system performance [29]. During the test, the and fuel cell flooding can cause fast degradation to the system performance [29]. During the test, PEM fuel cell stack is firstly operated at the nominal operating condition, then the stack the PEM fuel cell stack is firstly operated at the nominal operating condition, then the stack temperature temperature is reduced gradually to accelerate the liquid water accumulation and thus flooding, is reduced gradually to accelerate the liquid water accumulation and thus flooding, which can be which can be confirmed with a clear fuel cell voltage drop. Finally, the temperature is increased to confirmed with a clear fuel cell voltage drop. Finally, the temperature is increased to remove the remove the flooding effect and recover the fuel cell performance. Figure 8 illustrates this procedure flooding effect and recover the fuel cell performance. Figure 8 illustrates this procedure with load with load current density and fuel cell stack voltage, where the periods between about 1000 and 1400 s, and 3000 and 3300 s are the time when the polarization curve is collected. It should be
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current density and fuel cell stack voltage, where the periods between about 1000 and 1400 s, and 3000 mentioned that the fuel cell voltage drop at the beginning of the test is due to the instability of the and 3300 s are the time when the polarization curve is collected. It should be mentioned that the fuel fuel cell system; after the certain time (about 300 s in the test), the fuel cell system reaches the stable cell voltage drop at the beginning of the test is due to the instability of the fuel cell system; after the operation stage. certain time (about 300 s in the test), the fuel cell system reaches the stable operation stage.
Temperature (°C)
50 40 30 20 10
0
2000
4000
6000 8000 Time (s)
10000
12000
(a) Stack temperature
1
Voltage (V)
0.8 0.6 0.4 0.2
0
1000
2000 Time (s)
3000
4000
(b) Voltage Figure8.8.Fuel Fuelcell celltemperature temperatureand andcorresponding correspondingstack stackvoltage voltageduring duringthe theoperation. operation. Figure
Moreover, the performance of the developed model shown in Figure 1 in simulating fuel cell Moreover, the performance of the developed model shown in Figure 1 in simulating fuel cell performance under the flooding scenario is illustrated. It is known that with fuel cell flooding, the performance under the flooding scenario is illustrated. It is known that with fuel cell flooding, accumulated liquid water will block the catalyst layer, gas diffusion layer and flow channel; this can the accumulated liquid water will block the catalyst layer, gas diffusion layer and flow channel; be simulated with the developed model by increasing the mass transport coefficients, which can this can be simulated with the developed model by increasing the mass transport coefficients, increase the mass transport loss in Equation (1). Figure 9 depicts the comparison of the which can increase the mass transport loss Vtrans in Equation (1). Figure 9 depicts the comparison of polarization curves from the test and the developed model. It can be seen that by updating the the polarization curves from the test and the developed model. It can be seen that by updating the model parameters (mass transport coefficients herein), the developed model can simulate the fuel model parameters (mass transport coefficients herein), the developed model can simulate the fuel cell cell performance in the flooding scenario with good quality. performance in the flooding scenario with good quality. In the next section, the performance of optimal sensors in fuel cell fault diagnosis will be In the next section, the performance of optimal sensors in fuel cell fault diagnosis will be investigated using data-driven approaches, and the results will be compared with those using all investigated using data-driven approaches, and the results will be compared with those using all available sensors. available sensors.
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Test data Test data Model data Model data
Voltage (V) Voltage (V)
0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 00
1010
2020 3030 4040 2 2 Current density (A/cm ) Current density (A/cm )
5050
Figure 9. 9. Comparison of polarization curves under the flooding scenario. Figure Comparison polarization curves under the flooding scenario. Figure 9. Comparison ofof polarization curves under the flooding scenario.
4.2. PEM Fuel Cell Fault Diagnosis 4.2. PEM Fuel Cell Fault Diagnosis 4.2. PEM Fuel Cell Fault Diagnosis Since sensor measurements collected from the fuel cell forfor the Since sensor measurements collected from thePEM PEM fuel cellsystem system areused used thefault fault Since sensor measurements collected from the PEM fuel cell system are usedare for the fault diagnosis, diagnosis, data-driven diagnostic approaches are used in the study. Due to the collection ofof diagnosis, data-driven diagnostic approaches are used in the study. Due to the collection data-driven diagnostic approaches are used in the study. Due to the collection of information from information from multiple sensors, kernel principal component analysis (KPCA) is used to reduce information from multiple sensors, kernel principal analysis (KPCA)the is dimension used to reduce multiple sensors, kernel principal component analysiscomponent (KPCA) is used to reduce of the dimension of collected dataset. Compared to principal component analysis (PCA), KPCA the dimension of collected dataset. Compared to principal component analysis (PCA), KPCAcan can collected dataset. Compared to principal component analysis (PCA), KPCA can give better performance give better performance in nonlinear systems [30]. Wavelet packet transform is then applied to bettersystems performance in nonlinear [30]. Wavelet packet transform is then applied to ingive nonlinear [30]. Wavelet packet systems transform is then applied to extract the wavelet coefficients extract the wavelet coefficients and generate features, and singular value decomposition extract the wavelet coefficients and generate features, and singular value decomposition (SVD)is is and generate features, and singular value decomposition (SVD) is utilized to determine the (SVD) features utilized to determine the features containing the most useful information for the state classification. utilized to determine the features containing the most useful information for the state classification. containing the most useful information for the state classification. More details about these approaches More about these approaches can bebe found studies [13,31]. Figure 1010 depicts More details these approaches can found inprevious previous studies [13,31]. Figure depictsthe the can bedetails found inabout previous studies [13,31]. Figure 10 in depicts the flowchart of data-driven approaches flowchart of data-driven approaches used herein. flowchart of data-driven approaches used herein. used herein.
Figure 10. Flowchart ofof data-driven approaches in PEM fuel cell fault diagnosis. Figure 10.10. Flowchart of data-driven approaches inin PEM fuel cell fault diagnosis. Figure Flowchart data-driven approaches PEM fuel cell fault diagnosis.
The diagnostic performance using all available sensors listed inin Table 5 is firstly investigated; asas The diagnostic performance using all available sensors Table 55 is investigated; The diagnostic performance using all available sensors listed Table isfirstly firstly investigated; the purpose of the analysis is to identify the fuel cell flooding, only the test data at higher load the purpose of the analysis is to identify the fuel cell flooding, only the test data at higher load as the of the analysis is to identify the fuel cell flooding, only the test data at higher load current current density is isstudied, i.e., the system steady state InInthe current density studied, i.e., thefuel fuelcell cell systemoperates operates underthe the steady statecondition. condition. the density is studied, i.e., the fuel cell system operates under theunder steady state condition. In the analysis, analysis, each sensor is isdivided segments with 700 points, analysis, each sensormeasurement measurement dividedinto into segments with 700sample sample points,which which each sensor measurement is divided into segments with 700 sample points, which corresponds to corresponds totoabout operation. The selection ofof points is isbased onon the corresponds about3The 3min min operation. The selection 700sample sample points based the about 3 min operation. selection of 700 sample points is700 based on the degradation rate from degradation flooding (0.39 inincause the state can degradation ratefrom fromthe the flooding (0.39V/h); 3min minoperation operation theflooding flooding state can causea a the flooding rate (0.39 V/h); 3 min operation inV/h); the3flooding state can a voltage drop ofcause about voltage 0.019 lead degradation and voltage dropofcannot ofabout about 0.019 V,which whichcannot cannot leadtotosignificant significantperformance performance degradation and can 0.019 V, drop which lead toV,significant performance degradation and can thus be regarded as can the thus be regarded as the early/medium stage fault. Moreover, three states are defined in the study: thus be regarded as the early/medium stage fault. Moreover, three states are defined in the study:
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early/medium stage fault. Moreover, three states are defined in the study: voltage drop less than 5% is voltage drop less than 5% is defined as normal state, voltage drop between 5% and 10% is defined as defined as normal state, voltage drop between 5% and 10% is defined as transition state, while voltage transition state, while voltage drop larger than 10% is defined as flooding state. drop larger than 10% is defined as flooding state. The data-driven diagnostic procedure shown in Figure 10 is applied to the dataset containing The data-driven diagnostic procedure shown in Figure 10 is applied to the dataset containing all available sensors, and the diagnostic results are shown in Figure 11. It should be noted that with all available sensors, and the diagnostic results are shown in Figure 11. It should be noted that with KPCA, the original dataset is projected to the first two principal directions, thus the diagnostic KPCA, the original dataset is projected to the first two principal directions, thus the diagnostic results results of these two principal directions can be obtained. of these two principal directions can be obtained.
0.7 Feature 2
0.6 0.5 0.4
Normal Transition Flooding
0.3 0.2
0.35
0.4 Feature 1
0.45
0.5
(a) The 1st principal direction
0.7
Feature 2
0.6 0.5 0.4
Normal Transition Flooding
0.3 0.2 0.2
0.25
0.3 Feature 1
0.35
0.4
(b) The 2nd principal direction Figure Diagnosticresults results using available sensors. Figure 11.11.Diagnostic using allall available sensors.
It can be seen from the above figure that using all available sensors, the three states cannot be It can be seen from the above figure that using all available sensors, the three states cannot be classified clearly, and the test data samples representing normal and flooding states do not cluster classified clearly, and the test data samples representing normal and flooding states do not cluster together, indicating that more sensor information may not provide better diagnostic performance; together, indicating that more sensor information may not provide better diagnostic performance; this further highlights the necessity of using selected sensors for reliable fault diagnosis. this further highlights the necessity of using selected sensors for reliable fault diagnosis. Figure 12 depicts the diagnostic results using the selected optimal sensors from Section 3. For Figure 12 depicts the diagnostic results using the selected optimal sensors from Section 3. For the the purpose of better comparison, the same diagnostic procedure is used and the original dataset purpose of better comparison, the same diagnostic procedure is used and the original dataset containing containing three sensor measurements is projected into the first two principal directions. three sensor measurements is projected into the first two principal directions.
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(b) The 2nd principal direction Figure 12. Diagnostic results using the selected dataset. Figure 12. Diagnostic results using the selected dataset.
From the above figure, all three states can be classified clearly by using the selected sensors, From above figure, allcan three states caneffectively be classified clearly by sensors. using the selected transition sensors, indicatingthe that fuel cell faults be identified with selected Moreover, indicating that fuel cell can faultsbecan be identified effectively with that selected sensors. Moreover, transition and flooding states discriminated, which means by using selected sensors and a and flooding states can be discriminated, which means that by using selected sensors and a data-driven data-driven diagnostic procedure, fuel cell faults at different levels can also be identified, which will diagnostic procedure, fuel cell faults at different levels identified, which will be beneficial be beneficial for better understanding of the fuel cell can statealso andbedesign of mitigation strategies. for better understanding of the fuel cell state and design of mitigation strategies. 5. Conclusions 5. Conclusions This paper investigated the application of the sensor selection approach in fuel cell PHM. The This paper investigated the application of the sensor selection approach in fuel cell PHM. performance of a sensor selection technique in predicting PEM fuel cell performance was studied. The performance of a sensor selection technique in predicting PEM fuel cell performance was studied. Moreover, the performance of selected sensors in PEM fuel cell fault diagnosis was investigated Moreover, the performance of selected sensors in PEM fuel cell fault diagnosis was investigated using test data from a PEM fuel cell system, and the results are compared with those using all using test data from a PEM fuel cell system, and the results are compared with those using all available sensors. available sensors. The sensor selection approach used in this study is based on the sensor sensitivities and sensor The sensor selection approach used in this study is based on the sensor sensitivities and sensor resistance to measurement noises; thus, a selected sensor set would have better sensitivity to the resistance to measurement noises; thus, a selected sensor set would have better sensitivity to the PEM fuel cell performance variation and can better resist measurement noise. Results show that with PEM fuel cell performance variation and can better resist measurement noise. Results show that selected sensors, reliable fuel cell performance can be predicted, and compared to predictions using with selected sensors, reliable fuel cell performance can be predicted, and compared to predictions more sensors, computational time can be reduced significantly using selected sensors while a using more sensors, computational time can be reduced significantly using selected sensors while a reliable prediction can still be obtained. Moreover, with data-driven approaches which are reliable prediction can still be obtained. Moreover, with data-driven approaches which are commonly commonly used for system fault diagnosis, the optimal sensors can provide better diagnostic used for system fault diagnosis, the optimal sensors can provide better diagnostic performance than performance than that with all the sensors, and fuel cell faults at different levels can be classified with good quality; as computational time can be reduced significantly using fewer sensors, the
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that with all the sensors, and fuel cell faults at different levels can be classified with good quality; as computational time can be reduced significantly using fewer sensors, the sensor selection techniques can be applied in practical PEM fuel cell systems for on-line health monitoring purposes. Acknowledgments: This work is supported by grant EP/K02101X/1 for Loughborough University, Department of Aeronautical and Automotive Engineering from the UK Engineering and Physical Sciences Research Council (EPSRC). Authors also acknowledge Intelligent Energy for its close collaboration in providing necessary information for the paper. Author Contributions: Lei Mao developed PEM fuel cell model and performed numerical analysis, analyzed the data, and wrote the paper; Ben Davies designed and performed the experiments; Lisa Jackson contributed analysis ideas and polished the paper. Conflicts of Interest: The authors declare no conflict of interest.
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