Selection of optimal sensors for predicting performance of polymer electrolyte membrane fuel cell

(cid:1) Performance of sensor selection algorithms in PEM fuel cell prognosis is studied. (cid:1) Sensor sensitivity to fuel cell failures is calculated for the sensor selection. (cid:1) Proposed selection approach considers sensor sensitivity and noise resistance. (cid:1) Reliable prediction can be made with optimal sensors from proposed approach. In this paper, sensor selection algorithms are investigated based on a sensitivity analysis, and the capability of optimal sensors in predicting PEM fuel cell performance is also studied using test data. The fuel cell model is developed for generating the sensitivity matrix relating sensor measurements and fuel cell health parameters. From the sensitivity matrix, two sensor selection approaches, including the largest gap method, and exhaustive brute force searching technique, are applied to ﬁ nd the optimal sensors providing reliable predictions. Based on the results, a sensor selection approach considering both sensor sensitivity and noise resistance is proposed to ﬁ nd the optimal sensor set with minimum size. Furthermore, the performance of the optimal sensor set is studied to predict fuel cell performance using test data from a PEM fuel cell system. Results demonstrate that with optimal sensors, the performance of PEM fuel cell can be predicted with good quality.


Introduction
In the last few decades, with the fast application of fuel cells in many areas, including stationary power, automotive, and consumer electronics, the reliability and durability of fuel cells during their operation have attracted more attention, leading to several studies in the field of diagnostics and prognostics of fuel cells.
From previous research, a series of studies have been devoted for fuel cell fault diagnostics to detect and isolate fuel cell faults, including model-based approaches and those with a data-driven framework. With model-based approaches, a numerical model is developed, which should express the fuel cell system performance with consideration of the failure mechanisms, and residuals between model outputs and actual measurements can be used to identify and isolate the fuel cell faults [1e10]. For data-driven techniques, signal processing techniques are applied to the sensor measurements to extract features expressing fuel cell performance, and by classifying these features, different fuel cell failure modes can be determined, such as fuel cell flooding, drying out, carbon corrosion, etc. [11e21].
Compared to fuel cell fault diagnosis, only limited research has been performed in fuel cell prognostics to predict the fuel cell performance and its remaining useful life (RUL). Several studies [22e24] proposed an adaptive neuro-fuzzy inference system (ANFIS) to predict the fuel cell system performance, which combined the advantages of a neural network and fuzzy logic system. With the developed ANFIS, fuel cell outputs, such as voltage and efficiency, could be predicted. Moreover, particle filtering approach has also been applied to update the state of the fuel cell system [25], and with predicted fuel cell voltage and threshold values, the remaining useful life (RUL) could be decided.
It can be noticed that the training process is required in most studies to predict the fuel cell performance, thus the prediction performance relies largely on the quality of sensor measurements. As a set of sensors is usually installed in the practical fuel cell system, including sensors at the fuel cell anode and cathode sides for collecting different information such as temperature, flow rate, pressure, humidity, etc., and these sensors may have different sensitivities to the fuel cell performance variation, it is not necessary to involve all these sensors in the analysis, which may increase the computation time, fuel cell system complexity and cost. Moreover, the existence of environment/measurement noise may also mask the contributions of sensors, especially those with low sensitivity. On this basis, a sensor selection algorithm should be applied to find the optimal sensors, which can provide reliable predictions with minimum computation time.
According to previous research, several studies have investigated selection of the optimal sensor set for health management of various systems, and the algorithms for sensor selection include generation of an objective function with performance requirements [26e28], and evaluation of sensor performance using sensitivityrelated analysis [29]. However, although several studies have been carried out to investigate the sensitivity of PEM fuel cell parameters [30e34], including stack temperature, pressure, relative humidity, etc. on the PEM fuel cell performance, few studies have been devoted to the sensor selection technology for fuel cell health management which requires further investigation with the wide application of fuel cells in practical applications.
This paper presents the approaches for selecting optimal sensors based on the sensitivity analysis, and the capability of optimal sensors in predicting PEM fuel cell performance is also studied. Section 2 determines the fuel cell health parameters which are critical to the PEM fuel cell performance. In section 3, the fuel cell model is developed and its performance is validated using test data. Based on the developed fuel cell model, the sensitivity matrix is generated to relate sensor measurements and fuel cell health parameters, which is described in section 4. Section 5 presents three sensor selection approaches, including the largest gap method, exhaustive brute force searching method, and the proposed approach considering both sensor sensitivity and noise resistance, the selection results from these techniques are also compared in this section. In section 6, the performance of optimal sensors in predicting PEM fuel cell performance is studied using test data from a PEM fuel cell system. From the findings, conclusions will be given in section 7.

Determination of fuel cell health parameters
Before evaluating sensor sensitivities to fuel cell performance variation, the health parameters should be selected, which can represent different fuel cell failure modes. Theoretically, the number of health parameters should be minimized to reduce the computation cost. Based on previous studies [35e37], some typical failure modes of the fuel cell and corresponding health parameters can be determined, which are listed in Table 1.
From Table 1, it can be seen that some health parameters can express more than one failure mode, such as ECSA, the amount of water inside the fuel cell, etc., which indicates that extra information is required to isolate the degraded components when performing fault diagnostics with these health parameters.
Moreover, as performing sensitivity analysis using experimental studies is time-consuming and costly, a numerical fuel cell model is developed in this study to determine the relationship between health parameters and sensor measurements. From previous studies [38], as membrane and electrodes are the most critical components in PEM fuel cells, the health parameters related to these components are selected in the analysis, including membrane resistance, internal current, and ECSA. Moreover, since fuel cell flooding can cause the most rapid performance degradation [39], the amount of water inside the fuel cell is also included in this study. Therefore, the health parameters selected in sensitivity analysis include membrane resistance, internal current, ECSA, and the amount of water inside the fuel cell.

Development of fuel cell model and its performance validation
In this paper, a numerical fuel cell model is developed to perform the sensitivity analysis. In the model, the anode and cathode are modelled separately as lumped volumes, the mass of each gas is calculated from the 1st order differential mass balances in Eqs. (1)e(5), fuel cell temperature is calculated using a single thermal capacitance model shown in Eq. (6), and fuel cell voltage can be calculated with Eq. (7) using results from Eqs. (1)e(6). More details can be found in Refs. [40e42]. The block diagram of the fuel cell model is depicted in Fig. 1 where m is the mass of gas species, W is the mass flow rate, in shows the inlet species, out shows the outlet species, react is the electrochemical reaction energy, and trans is the transport loss. Energy balance m stack C ps dT dt ¼ Q react À Q elec þ Q in À Q out À Q loss (6) where T is the fuel cell stack temperature, T 0 is ambient temperature (293 K in the model), the m s is the mass of fuel cell stack, C ps is the specific heat, is the entropy change of hydrogen, _ m H2 in is the inlet hydrogen mass flow rate), Q elec ¼ V stack I stack is the electrical power generated by the fuel cell stack, Q in ¼ Q H2in þ Q N2in þ Q O2in þ Q H2o liquid in þ Q H2o vapour in and Q out ¼ Q N2out þ Q O2 out þ Q H2o vapour out are the heat flows into and out of the fuel cell stack, Q loss ¼ h stack A stack (T stack ÀT 0 ) is a term to represent the small amount of energy lost from the fuel cell stack surface (h stack stack convective heat transfer coefficient, A stack is the stack area), H v is the enthalpy of water vapour.
With results from the above equations, the fuel cell voltage can be calculated as follows.
where V cell is the single cell voltage, E n is the reversible voltage, V trans ¼ m trans :e ntrans:i , V ohm ¼ i.R membrane are the activation loss, fuel crossover loss, mass transport loss, and Ohmic loss, respectively (R is universal gas constant, a is charge transfer coefficient, F is Faraday constant, i oc is exchange current density at cathode, i n is the interal current density, m trans and n trans are the mass transport loss voltage coefficients, R membrane is the membrane resistance), which can be calculated using results from Eqs. (1)e (6). It should be mentioned that several assumptions are used for the model development. At the anode side, the nitrogen diffusion through the membrane is not considered in the model; the temperature in the anode and cathode volumes is assumed as the same as the stack temperature; uniform temperature distribution is assumed throughout the stack; and products exiting the stack is assumed at the stack temperature.
With the developed model, the cell voltage can be determined in the 'stack voltage' module using Eq. (7) with results from other modules, hydration is calculated in the 'membrane hydration' module, the anode and cathode mass balance equations are calculated in the 'anode model' and 'cathode model' with Eqs.
(1)e(5), and energy balance is determined in the 'stack temperature' module using Eq. (6). It should be mentioned that the current is fed into the model and is the determining factor in the calculations. The 'membrane hydration' module uses the results of the mass balance equations to calculate the resistance of the membrane, and feeds back data into the anode and cathode mass balance modules. The determined resistance values feed directly into the 'stack voltage' module, while the 'stack temperature' module takes outputs from all of the other modules for its calculations.
Before performing the sensitivity analysis, the performance of the developed fuel cell model is validated using test data from a fuel cell system. In this study, the fuel cell tested in Ref. [41] can be simulated by configuring model parameters listed in Table 2. With the configured fuel cell model, the polarization curve at different operating conditions can be obtained and compared with that in the reference paper [41], which is depicted in Fig. 2. It should be noted that the parameter values from semi-empirical model in Ref. [41], including internal and exchange current densities, mass transport coefficients, etc. are used in the developed fuel cell model to simulate the tested PEM fuel cell.
From the results, the measured polarization curves from the tests at different operating conditions can be simulated with good quality with the developed fuel cell model, and the difference between numerical and test data is less than 2%, which is obtained by calculating the difference between the simulated fuel cell voltage and test voltage at same current densities.
With the validated fuel cell model, the relationship between sensor measurements and fuel cell health parameters can be determined by generating a sensitivity matrix, which can also be used to evaluate the sensor resistance to measurement noise.

Generation of sensitivity matrix
In this section, the sensitivity matrix relating fuel cell sensor  measurements to health parameters will be determined using the developed fuel cell model. In the analysis, a certain change (1% increase used herein) is applied to the fuel cell health parameters in the numerical model, and the variations in fuel cell responses (sensor outputs) are obtained. It should be noted that sensors used in this paper are determined with consideration of sensor availability in the practical fuel cell system and the physical fuel cell model, including cell voltage, inlet and outlet flow at the anode and cathode, stack temperature, etc., which are listed as sensor outputs in Table 3. Moreover, in order to determine the sensor sensitivity to each health parameters, in the analysis, only one health parameter is to be changed in each case. The results are then transferred to the sensitivity values using Eq. (8), and the sensitivities of fuel cell sensors to selected parameters are listed in Table 3.
where S represents the sensitivity value, R is the sensor reading, P is the selected fuel cell health parameter, 1 and 2 represent values before and after applying the certain change, Sij is the jth sensor sensitivity for the ith health parameter. It should be mentioned that the sensor sensitivities to internal current are not listed in Table 3, as all the sensors will give zero sensitivities to the internal current variation. The reason proposed is that the internal current value is much smaller compared to the other health parameters (3.55 Â 10 À41 A/cm 2 used in the model), thus its change doesn't lead to a clear variation in the sensor outputs. Hence, in this study, the effect of internal current will not be further considered.
For comparison purposes, the sensitivity values of fuel cell voltage is normalized to a unit value, and sensitivities of the other sensors to the same health parameter (each column in Table 3) will be changed accordingly. By doing so, the sensitivity of each sensor to various health parameters can be compared directly, and the results are listed in Table 4.
It can be seen that several sensors, including anode inlet mass flow meter, compressor temperature sensor, and coolant inlet mass flow meter, have zero sensitivities to all the health parameters, indicating that these sensors could not make contributions in predicting the fuel cell performance, therefore, they should be excluded from the optimal sensor set.
From results in Table 4, the sensors can be ranked based on their sensitivity values, which can express their responses to fuel cell performance due to different failure modes. The results can be used for selecting the optimal sensors in the following section.

Investigation of sensor selection approaches
In this section, three sensor selection approaches will be applied based on the generated sensitivity matrix, including the largest gap method, exhaustive brute force search technique, and the proposed sensor selection algorithm. The details and results of these selection approaches will be presented in the following parts.

The largest gap method
The largest gap method has been applied to find the size of optimal sensor set for several systems in previous studies [43]. In this method, the sensors should be ranked based on the sensitivity variance values, which can express sensor capability of discriminating various failure modes. Moreover, the size of optimal sensor set can be determined by finding the largest value of ratios between two neighbouring variances. Table 5 lists the sensors and corresponding sensitivity variance (variance of each row in Table 4), and the ratios of two neighbouring variances are depicted in Fig. 3. It should be noted that sensors with zero sensitivities to all the failure modes are not included in the analysis.
It can be seen from Fig. 3 that although the largest gap exists between sensor 1 and sensor 4, only 1 sensor cannot provide complete information of the fuel cell system (shown in Fig. 6(a)), thus the second largest gap is used in this study, and the optimal sensor set contains 4 sensors (s1, s4, s5 and s2 listed in Table 5).

Exhaustive brute force searching method
In this section, the optimal sensors will be selected by searching all the possible sensor combinations. It should be mentioned that this approach is very time-expensive, thus it should not be used in the practical applications, and use of this approach herein is to validate the proposed sensor selection method presented in the next section.
In the analysis, the performance of various sensor sets is evaluated with the adaptive neuro-fuzzy inference system (ANFIS), and test data from a PEM fuel cell is used for the searching process.

Description of fuel cell test data
In the analysis, the PEM fuel cell test data from IEEE 2014 data challenge are used, which is open source data [44]. Sensor measurements from the fuel cell system include fuel cell voltage (shown in Fig. 4(a)), current (shown in Fig. 4(b)), anode and cathode inlet and outlet flow, pressure, and temperature. It should be mentioned that during the fuel cell operation, constant current is applied, which gives the steady state of the fuel cell system. Moreover, fuel cell fault is not observed, which means the degradation of fuel cell performance is due to fuel cell aging.

Description of the adaptive neuro-fuzzy inference system
In this study, an adaptive neuro-fuzzy inference system (ANFIS) is used to evaluate the performance of the selected sensors, which has already been proved to be effective in predicting fuel cell performance [22e24]. ANFIS is a multi-layer feed forward neural network, which combines fuzzy rule to improve its inference ability. A typical ANFIS is shown in Fig. 5, which includes five layers. Layer 1 is the fuzzification layer which performs fuzzification to the incoming inputs. For example, two inputs (x 1 ,x 2 ) and 4 membership functions (P 11 , P 21 , P 12 , P 22 ) are applied in Fig. 5, formulating 16 rules (2 4 ) (if-then rule), and the output from layer 1 can be written as in Eq. (9), Where m A j i is the fuzzy rule associated with ith input and jth fuzzy rule, y 1 i is the ith output at layer 1, a i , b i and c i are the parameters in the membership function, which will be adjusted during the training phase.
In layer 2, the firing strength of the fuzzy rule will be generated, with output y 2 i from layer 2, which is described in Eq. (10)  Fig. 3. Distribution of the ratio of two neighbouring sensitivity variance (where si/sj is the variance ratio between si and sj listed in Table 5).
Layer 3 is usually defined as the normalization layer, the neurons at this layer receive inputs from all neurons at layer 2 and calculate the normalized firing strength, which can be expressed as y 3 i in Eq. (11) where u i is the firing strength of the rule.
Layer 4 is called the defuzzification layer, each neuron at this layer receives outputs from layer 3 as well as the original inputs of the system (x 1 ,x 2 ) for the calculation, with output calculated by Eq. (12) where c j 1 , c j 2 and c j 3 are consequent parameters of the jth fuzzy rule, which will be updated during the training process.
With outputs from layer 4, the system output can be calculated with Eq. (13) In the analysis, the inputs of the ANFIS are the measurements from selected sensors, and the output is the fuel cell voltage. The first 2/3rd of the data samples are used to train the ANFIS system, while the last 1/3rd of the data samples are used to validate the performance of selected sensors.

Determination of optimal sensor set
In the analysis, the sensor used in the fuel cell system can be selected from all possible sensors used in the test (with total number of 16, which is listed in Table 6). Based on the above sensor selection results, four sensors are selected for predicting the fuel cell performance. The objective function is defined with the difference between actual fuel cell voltage and corresponding prediction, which can be expressed as: where v i is the actual fuel cell voltage, and p i is the corresponding prediction.
The optimal sensor set can be determined by minimizing Eq. (14) with the smallest size of sensor set. Table 7 lists the optimal sensor sets with minimized objective function, it should be noted that several sensor sets have similar objective function values, indicating these sensor sets can provide similar prediction performance.
It can be seen from Table 7 that sensor set with only three sensors can give reliable prediction of fuel cell voltage. When compared to the results in section 5.1, water inlet temperature is not included in the optimal sensor set, although it has higher sensitivity than the cathode inlet flow, this indicates that the sensitivity alone is not enough for determination of optimal sensor set. Moreover, several temperatures can be included in the optimal sensor set (inlet/outlet temperatures at anode/cathode in Table 7) to replace the stack temperature, which cannot be measured directly in practical fuel cell system.

The proposed sensor selection approach
From above results, it can be seen that with only the sensitivity analysis, the optimal sensor set with minimum size cannot be obtained. On the other hand, the time-expensive exhaustive brute force searching method is not suitable in practical fuel cell system with many sensor candidates.
On this basis, the environment/measurement noise resistance of sensor is also used in the sensor selection process, and the optimal sensors will be determined based on the sensor sensitivity and noise resistance.
In this study, the noise resistance of sensors is evaluated based on the generated sensitivity matrix shown in Table 4, which can be express with Eq. (15).

fdRg ¼ SfdPg
where S is the sensitivity matrix, {dR} is the variation in sensor measurements, and {dP} is the perturbations in health parameters. With inversion of the sensitivity matrix S, the health parameter perturbation can be related through a gain matrix G to the sensor output variation by: The evaluation of noise resistance of these sensors can be performed using Eq. (16). A set of (say n sets) response errors are generated randomly to express the measurement noise, which is a set of ±2% of the sensor measurements. With the subset of gain matrix G (formed using selected sensors), the corresponding health parameter errors (n sets) can be calculated using Eq. (16). From the health parameter errors, a statistical analysis is performed. For Table 6 Available sensors from the fuel cell system.
where p represents the number of health parameters, and the overall error can be used to express the noise resistance of the selected sensor set (NR), Based on above results, the procedure of proposed sensor selection method can be proposed. With analysis results of fuel cell failure modes and their effects, the health parameters critical to the fuel cell performance can be determined. The sensitivity matrix Table 8 Sensors with the best noise resistance capability from different sizes.

Size of sensor set
Sensor set with the best noise resistance capability  between fuel cell health parameters and sensor measurements is then generated, with either the fuel cell model or test data. For sensor sets with different size, one sensor set is selected from each size using Eq. (18), which should have the best noise resistance capability. ANFIS is then used to evaluate the performance of these sensor sets, and the optimal sensor set can be determined based on the criteria that the fuel cell performance can be predicted with good quality using the minimum number of sensors. Using Eq. (18), the noise resistance of various sensor sets can be evaluated, and the sensor set having the best noise resistance capability from each size can be determined, which are listed in Table 8. It should be mentioned that the cathode outlet temperature is used herein to replace the stack temperature in the table, which has been validated in section 5.2.
The performance of sensors set in Table 8 is evaluated using ANFIS, with similar procedure described in section 5.2, the fuel cell performance can be predicted with different sensor sets and the results are shown in Fig. 6. Moreover, the mean prediction error and computation time for each sensor set is depicted in Fig. 7.
From the results in Fig. 7 it can be seen that with increase of sensors, the prediction accuracy can be improved, when more than three sensors is used, the clearly prediction improvement cannot be observed, but the computation time is increased significantly. Therefore, from the proposed approach, the optimal sensor set with three sensors should be selected to predict the fuel cell performance.
However, it can be seen that from prediction results in Fig. 6, two points cannot be predicted (around 800 h and 900 h), even with increased number of sensors in the analysis. The reason is that at these points, sudden voltage drop is observed, which is due to disconnection of the load current, thus these points do not represent the aging process of the fuel cell system, and cannot be learned and predicted using ANFIS.
It should be noted that the proposed sensor selection algorithm only considers the prediction performance of sensors, while in practical fuel cell system, some other properties, including sensor reliability, sensor cost, and sensor transfer function, should also be included for the selection of sensors in the system, this can be performed by generating an objective function with these factors defined as constraints in the future work.

Capability of optimal sensors in predicting PEM fuel cell performance
In this section, the capability of optimal sensors in predicting fuel cell performance is studied using the test data from a PEM fuel cell system, more details about the test set-up and fuel cell test parameters can be found in Ref. [44]. In this study, two constant current loading conditions are selected for the analysis, which are depicted in Fig. 8(a) and (b), where constant current of 0.7 A/cm 2 is used in Fig. 8(a), and a constant current of 0.7 A/cm 2 with high frequency (5 kHz) current ripples (±10% of the constant value) is used in Fig. 8(b) [44].
Similar to the analysis in section 5.2, the ANFIS is used to predict the evolution of the fuel cell voltage using the optimal sensors. In the analysis, the same training/validation data sample ratio is used to train the ANFIS and predict fuel cell voltage, where the results are depicted in Fig. 8(c) and (d).
It can be observed that with optimal sensors, the trained ANFIS system can predict the fuel cell stack voltage with good quality at two different loading conditions, this can be seen from the mean prediction errors listed in Table 9. However, it should be noted that the maximum prediction error cannot be used to evaluate the performance of optimal sensors, since some valleys in fuel cell voltage curve cannot be learned and predicted correctly (voltages at about 800 h and 900 for the 1st loading condition, and voltages at about 100 h and 130 h for the 2nd loading condition), as they do not represent the actual fuel cell system aging process.

Conclusion
This paper investigates the sensor selection approaches for PEM fuel cell performance prediction, based on the sensitivity analysis.

Table 9
Mean prediction errors using optimal sensors at different loading currents.

Loading condition
Mean prediction error (V) 1 0.0089 2 0.0103 The optimal sensors can provide the reliable PEM fuel cell prediction performance with the minimum computation cost.
In the analysis, a numerical model of the fuel cell is developed and its performance is validated with test data. With the developed model, sensitivity matrix relating sensor measurements and fuel cell health parameters can be generated. Based on the sensitivity matrix, two approaches are applied to determine the optimal sensor set, including the largest gap method, and exhaustive brute force search method. From the results, a sensor selection approach is proposed to determine the optimal sensors, which considers both sensor sensitivity and noise resistance. Moreover, the prediction performance of optimal sensors is validated using test data from a PEM fuel cell system at different loading conditions. Results demonstrate that with optimal sensors, reliable fuel cell performance can be predicted with more effective computation cost. In the future work, the prediction performance of optimal sensors in dynamic loading condition will be investigated, which may consider the current variation effect in the selection process.