Implementation of sensor based on neural networks technique to predict the PEM fuel cell hydration state

Journal of Energy Storage 27 (2020) 101051

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Implementation of sensor based on neural networks technique to predict the PEM fuel cell hydration state

T

⁎

Fatima Zohra Aramaa, Khaled Mammarb, Slimane Laribia,c, , Ammaar Necaibiac, Touhami Ghaitaouia,c a

Laboratoire de Développement Durable et d'information (LDDI), faculté des Science et de la Technologie, Université Ahmed Draia, Adrar, Algeria Department of Electrical and Computer Engineering, University of Béchar, Bp 417, Algeria c Unité de Recherche en Energies Renouvelables en Milieu Saharien, URERMS, Centre de Développement des Energies Renouvelables, CDER, 01000, ADRAR, Algérie b

A R T I C LE I N FO

A B S T R A C T

Keywords: PEMFC Neural networks Sensor model Flooding Drying

Proton exchange hydrogen fuel cells have the potential to produce clean and environmentally friendly energy. However, this technique should be adapted to technical challenges, such as performance and durability prior to its marketing. These challenges are closely related to water management. In this research, a PEM fuel cell simulation model was designed for water management. This model consisted of a voltage evolution model based on electrochemical and dynamics gases. It also comprised a model of water activity to estimate the relative humidity. Meanwhile, in identifying the PEMFC hydration state, impedance was estimated by the humidity sensor model, which was based on neural network technology for diagnosis. This model predicted the changes of behaviour in the step response of load demand and the rate of water which flowed into the fuel cell. In the case of flooding or drying, the proposed neural network sensor model was executed through the estimation of internal resistance and biasing resistance values at high and low frequencies. These frequencies corresponded to the model of PEMFC electrical performance. As a result, it was found that the efficacy of this new neural network sensor model led to improved PEMFC hydration and a controlled humid airflow in the fuel cell. Overall, it was indicated that the proposed model can be used in the control system to improve water management by adjusting the relative humidity of supplied air.

Abbreviations PEMFC NNT EIS

proton exchange membrane fuel cell artificial neural networks electrochemical impedance spectroscopy

1. Introduction Recently, renewable energy has gained significant interests. The replacement of fossil fuels with clean sustainable renewable energy carriers is necessary, especially in a highly polluted environment due to greenhouse gases emissions and global warming. Therefore, hydrogen gas is considered as one of the most important elements used to develop an energy system which is independent of fossil energy carriers for long-term energy storage [1–2]. Furthermore, the chemical energy stored in the form of hydrogen gas could be easily converted into electrical energy through fuel cells without involving the emission of

carbon dioxide [1–10]. Consequently, there are various challenges present for the development and use of these new technologies to reach their large-scale marketing. Besides, water management is considered as one of the most challenging aspects of fuel cells which require solution [3–6]. Although optimal hydration is required for the fuel cells to function properly, the excess/or lack of water in the cell could lead to yield losses [7–9]. This study focuses on water management issues which affect PEMFC in real-time during its operation. These issues would lead to degradation and long-term failure in PEMFC's performance with lifespan modification. In this case, the diagnostic methods of PEMFC development were implemented by many researchers to identify fuel cell flooding and drying phenomena [10–19]. One of the most popular electrochemical techniques in the diagnosis of the PEMFC failure modes is the impedance spectroscopy, which can resolve various problems including inappropriate water management. This technique is regarded as a characterization tool for fuel cells and

⁎ Corresponding author at: Laboratoire de Développement Durable et d'information (LDDI), faculté des Science et de la Technologie, Université Ahmed Draia, Adrar, Algeria. E-mail address: [email protected] (S. Laribi).

https://doi.org/10.1016/j.est.2019.101051 Received 12 May 2019; Received in revised form 28 October 2019; Accepted 29 October 2019 2352-152X/ © 2019 Elsevier Ltd. All rights reserved.

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Nomenclature Vcel Enerst Vact Vcon VOhmic Istack RNNT_int RNNT_pol T fc Jn PH2 PO2 Pw Psat qwin qH2in qO2in qH2out qO2out qH2r qO2r qwr CO2

D F n R Rd Rm Rp Q S tm Z ZCPE Zw j

cell voltage (V) thermodynamic potential (V) activation overvoltage (V) concentration overvoltage (V) ohmic overvoltage (V) fuel cell operating current (A), internal resistance at high frequency measured by artificial neural networks humidity sensor model (Ω) biasing resistance at low frequency measured by artificial neural networks humidity sensor model (Ω) temperature (K) current density (A/cm2) H2 partial pressure, (atm) O2 partial pressure, (atm) water vapour pressure (atm) saturated vapour pressure (atm) molar humid airflow (mol/s) hydrogen inlet flow rates (mol/s) oxygen inlet flow rates (mol/s) hydrogen outlet flow rates (mol/s) oxygen outlet flow rates (mol/s) hydrogen usage flow rates (mol/s) oxygen usage flow rates (mol/s) water production flow rates (mol/s) oxygen concentration in the cathode active layer (mol m−3)

diffusion coefficient (m2s−1) faraday constant (A s mol−1) number of electrons perfect gas constant (J mol−1 K−1) electrical resistance (Ω) membrane resistance (Ω) polarisation resistance (Ω) parameter of the CPE active area (m²) membrane thickness (m) fuel cell impedance (Ω) CPE impedance warburg impedance (Ω) imaginary number

Greek letters λa α τd ω δ ξi λ σm φ δ

stoichiometry of air power of the CPE time constant of diffusion (s) pulsation (rad s−1) diffusion layer width (m) parametric coefficient water membrane content membrane conductivity (Ω /cm) relative humidity (%) diffusion layer width (m)

Christophe Lin-Kwong-Chon et al. [23]. suggested a neural network based on the control of adaptive learning applied to the fuel cell system state of health. Meanwhile, Yousfi et al. [24]. presented a method to diagnose PEMFC drying and flooding problem. This method is based on the comparison and analysis between two residues generated by the PEM fuel cell in the real operation. It is also based on the parameters calculated by the neural network in normal operation to detect the PEMFC health state. Another study by Yousfi Steiner [14]. suggested that PEMFC flooding defect could be detected by comparing the decrease in experimental pressure and estimation of pressure with the artificial neural network, which is formed with experimental data in the absence of fuel cell flooding. This method was successfully tested under different experimental conditions, including non-flooding and deliberated flooding. Kim et al. [25]. investigated the PEM fuel cell health state through the recognition diagnosis approach of the Hamming neural network to determine appropriate model parameters. Furthermore, Silva et al. [26]. proposed a new theoretical method found in the adaptive neuro-fuzzy inference systems to estimate the output voltage diminution caused by the degradation of the PEMFC nominal operating conditions. On the other hand, Ali. Mohammadi et al. [27]. suggested a method based on artificial neural networks and the harmonic analysis to identify and classify the faults produced in PEMFC and DC / DC converter, including drying and flooding. These issues usually occurred in the fuel cell under the effects of variations in operating conditions. Additionally, Ali Mohammadi et al. [28]. suggested a diagnostic approach of the PEM fuel cell, which consisted of two steps. A 3D PEMFC model sensitive for different faults was first created for high drying, flooding, and strong flooding to estimate different local parameters. It was followed with development of two-layer feed-forward artificial neural network (NNT), which localises each defect in different segments of the same cell. Wu et al. [29]. also proposed a method to identify the type of PEMFC fault, which could be either drying, membrane flooding, or normal. This identification is based on residual generation and the backward propagation of PEMFC neuron network model into “the faulttolerant control strategy (SFTC)”. Jemeï et al. [30]proposed a dynamic

electrochemical batteries. Fouquet et al. [15] presented an accurate approach in the evolution of the impedance spectrum based on the identified failures. This approach revealed three forms of the spectrum based on the volume of water presented in the cell. Specifically, the first spectrum was carried out in normal operation. The second spectrum was performed in dry operation, while the third spectrum was conducted in a flooded operation. A study by Mason et al. [20]. suggested a dynamic electromechanical analysis to examine PEMFC performance during hydration transients and floods. Furthermore, PEMFC resistance was measured using impedance spectroscopy according to the imposed constraints characteristics. Bouaicha et al. [21]. developed a new modelling approach which enables the estimation of PEMFC dynamic operation including various phenomena occurring inside the fuel cell. Meanwhile, in identifying the starting point of PEMFC flooding, Orazem et al. [22]. suggested a robust fuel cell diagnosis with the use of impedance spectroscopy coupled and a measurement model based on error analysis. Although knowledge of numerous internal parameters during cells operation is required in the control and diagnosis of fuel cell defects, the insufficient tool is a primary challenge in state-of-health monitoring. In transport applications, the manufacturers and fuel cell users aim to reduce the number of equipment used to monitor and control the simple development of diagnostic methods. Accordingly, non-intrusive and easy control parameters are used. Notably, the black box models are characterized by their capacity to identify the minimum of input variables and evaluate the output values. Besides the recognition properties of speed and ease of implementation compared to physical models, the models could also use mathematical equations to describe the physical phenomena occurring in every part of PEMFC. In this case, accurate identification of internal PEMFC parameters is required. Among these black box models, the artificial neural networks possess various advantages, such as the ability to process and apply the nonlinear functions without identifying the physical mechanisms. Several studies were conducted based on the Neural Networks method in PEM fuel cells diagnosis [23–32]: 2

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neural network to control PEMFC system process. In the same area, Laribi et al. [31]. developed at theoretical model based on neural networks to diagnose the occurrence of flooding and drying of the PEM fuel cell. Shao et al. [32]. proposed artificial neural networks method to diagnose faults and improve the stability and reliability of PEM fuel cell systems. Primarily, this research aims to identify and implement a new sensor model based on artificial neural networks, which could diagnose and predict PEMFC hydration state. For the existing impedance spectra, this NNT sensor model could estimate the internal resistance measured at high frequency (RNNT_int), including the biasing resistance measured at low frequency (RNNT_pol) values due to its high sensitivity to flooding and drying of fuel cell [31]. Besides, the inputs of this model are the operating time and relative humidity of the reactive gases, which are calculated by a water activity model. The results illustrated the impact of water incorporated into the reactive gases and the efficiency of the proposed NNT sensor to determine the fuel cell hydration state.

1 1 ⎞⎞ ⎛ σm = (0.00519λ − 0.00324)exp ⎜1268 ⎛⎜ − ⎟ ⎟ 303 T fc (K ) ⎠ ⎝ ⎠ ⎝

Accordingly, λ refers to the membrane water content expressed by the following equation by Springer:

0.043 + 17.81ϕ − 39.85ϕ2 + 36ϕ3, 0 ≤ ϕ ≤ 1 λ=⎧ ⎨ 1≤ϕ≤3 14 + 1.4(ϕ − 1) ⎩

2. PEM fuel cell model

The water vapour partial pressure Pw(atm)is related to the absolute pressure at the

0.420 + λa ψ ⎞ ⎟ Psat = Pexit ⎜⎛ λ (1 ⎝ a + ψ) + 0.210 ⎠

(1)

(2)

qwin ⎛ ⎞ ψ=⎜ qO2 in + qrest ⎟ ⎝ ⎠

Vcon

⎜

⎨q = ⎩ rest

(4)

(13)

(0.420 + λψ) Pexit

φ=

Pwout λ (1 + ψ) + 0.210 = 5120 Psat (Tair (K )) 105 exp 13.7 − T (K )

(

(

air

))

(14)

To determine the relationship between flow and partial pressure, all individual gases were separated based on the ideal gas equation.The model was developed by Y. El-Sharkh et al. in [40,41]. Following are the equations which represent the state:

⎟

tm + Rc ) σm

λ . Istack 4.F λ.I 3.76 4 stack .F

qrest: The molar flow of the non-oxygen (N2) in the air The relative humidityφ (%) defined by Eq. (9) could be described as follows (14) [37,39]:

(5)

According to the equation, B: Parametric coefficient J: Current density of the fuel cell The ohmic overvoltage represents the voltage loss due to the resistance against proton flow in the electrolyte [6]:

Vohmic = Istack (

(12)

⎧ qO2 in =

(3)

The concentration voltage loss was calculated as follows: :

J ⎞ = −B. ln ⎛1 − Jmax ⎠ ⎝

(11)

In the case of the atmospheric fuel cell, the pressure at the output of the stack Pexitis equal to the atmosphere. λa : Air stoichiometry Ψ: The ratio between the molar flow produced by the air in the PEMFC input qwin and the oxygen molar flow at the fuel cell input qO2in is represented as follows:

Based on the equation above,Istack : Current fuel cell operating (A) ξi : Parametric coefficientsCO2: Concentration of oxygen was defined as the following equation:

Po2 5, 08.106. e (−498/ T )

(10)

output of the stack Pexit(atm), as represented by the following equation:

Accordingly, PO2 and PH2 represent the partial pressures of hydrogen and oxygen (atm) respectively. T refers to the cell operation temperature (K). Vact represents the activation voltage loss

Co2 =

(9)

5120 ⎞ ⎞ ⎟⎟ Psat = 105 exp ⎜⎛13.7 − ⎜⎛ ⎝ Tair (K ) ⎠ ⎠ ⎝

Enerst refers to the Nerst voltage, which is defined as [35]:

Vact = −[ξ1 + ξ2. T + ξ3. T . (Co2) + ξ 4 ln (Istack )]

Pwout Psat (Tair )

The saturated vapour pressure Psat(atm) depends on the temperature and the approaches which are experimentally related to the Rankine formula [37,38].

Since the last decades, there has been an increasing concern regarding the developed fuel cell model. Determining the objectives prior to using any fuel cell model is essential. The objectives would define the criteria of this model use, namely speed, precision, flexibility, graphical interface, and implementation in software. In this study, the implementation of fuel cell model for water management was suggested due to the mass transport and thermal behaviour caused by the dynamics of water management. The basic output voltage produced by the single PEMFC cell was provided by [6,33,34]:

Enerst = 1, 229 − 0.85. 10−3 (T − 298, 15) 1 + 4, 31. 10−5. T . ⎡ln (PH2) + ln (PO2) ⎤ 2 ⎦ ⎣

(8)

Accordingly, φ represents the relative humidity. L. Boulon et al. [37]. proposed a model to examine and determine the fuel cell relative humidity. The impact of air supply on hydration and water management issues in the fuel cell system was studied, the relative humidityφof the gas outlets is incorporated into Eq. (9) through the calculation of the ratio between the partial pressure of vapour Pw and the saturated vapour pressure Psat at the temperature Tair(K).

φ=

Vcell = ENerst − Vact − Vohm − Vcon

(7)

(6)

Accordingly,tm representsmembrane thickness. The proton membrane conductivity was highly dependent on the hydration rate (water activity). The empirical formula, which defined the Nafion 117 conductivity σm (λm,Tfc) (Ωcm)−1 as a function of water content, was adopted experimentally from Springer et al. [36]:

d RT (PH 2) = (q − q H 2out − q H 2r ) dt Van H 2in

(15)

d RT (PO2) = (q − qO2out − qO2r ) dt Van O2in

(16)

d RT (Pw ) = (−q wout − q wr ) dt Van

(17)

Accordingly: Pw: The partial pressure of gases inside the cellqH 2in , qO2in : The inlet flow rates of hydrogen and oxygenqH 2out , qO2out , qwout : The outlet flow 3

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Accordingly, Zw refers to the impedance of Warburg which, represented by the following equation:

rates of gases and water vapourqH 2r , qO2r andqwr : The usage and production of gases and water. The electrochemical relationships are presented through the following equations [37]:

qH2 r = 2qO2 r = qwr =

N0. Ifc 2. F

= 2. Kr . Istack

Z w (jω) = Rd

(19)

qO2 out = KO2 PO2

(20)

qwout = Kw Pw

(21)

2

1/ KH 2 (q − 2Kr Istack ) 1 + τH 2 s H 2

Accordingly,τH 2 =

⎧ τd = δ D ⎪ RTδ Rd = 2 2 n F SCD ⎨ ⎪ ZCPE (jω) = 1 Q (jω)α ⎩

Van R. T . KH 2

1/ K O2 . (qO2in − 2. Kr . Istack ) 1 + τO2. S Van R . T . K O2

ZT (jω) = Rm +

(22)

(29)

3.2. Developing an NNT PEMFC humidity sensor model A growing body of literature acknowledged the importance of artificial neural networks, which were considered suitable technology innovations used to solve estimation and prediction problems. It is used to expand the range of potential applications in different domains due to the functionality of the neural network black box. Therefore, the selection of neural network architecture plays a crucial role in the development of a neural network model. This study focuses on the neural networks with various types of feed-forward non-curly which includes one input layer, two hidden layers, and one output layer. The transfer function used in the hidden layer was a sigmoid-type function defined by the following equation by [31,43–45]:

(23)

(24) (25)

f (u) =

1 1 + e−(d . u)

(30)

Based on the equation above, d represents the slope of the curve. The hidden layer input was defined by Eq. (31) below [31,43–45]: n

u=

∑ (wij xi + bi) (31)

j=1

Accordingly, n represents the inputs of the neurons corresponding to the input signal xi. Meanwhile, wij represents the weight of the Table 1 Model parameters [6,30,36,37].

3. Neural networks impedance sensor of PEM fuel cell 3.1. . Modelling PEM fuel cell impedance model The simplest representation of the fuel cell impedance model was mainly used as an electrical Randles, which consisted of Ohmic resistance Rm, polarization resistance Rp, the impedance of Warburg, and the constant phase element (CPE),as shown in Fig. 3. The general equation of the PEMFC impedance Zcell was developed by [15,31,39,42]:

1 ZCPE + (1/(RP + Z w ))

1 Q (jω)α + (1/(RP + Z w ))

This PEMFC impedance included the value of α which ranged from 0.5 to 1.

In this section, the performance of the proposed semi-experimental mathematical model of the fuel cell was tested through the simulation of equations in the MATLAB environment. These changes result in significant impacts on the specifications and parameters used for the development of PEMFC model, as seen in Table 1. Based on Figs. 1 and 2, the result of the voltage/current density characteristics as a function of the relative humidity is shown in a 3D form, where the polarisation and power curve could be classified into three zones: The relative humidity rate in the flooding area is higher than 100%. As a result, a complete evacuation on water could not be performed, causing the fuel cell to become flooded. Meanwhile, the relative humidity rate in the drying area is lower than 100% due to the dry air effect on the fuel cell membrane,resulting in the defect case and the possibility of irreversible degradation. Notably, the relative humidity rate in the optimal area is approximately 100%. To illustrate, the amount of water in the inlet air and the water produced through anelectrochemical reaction is equal to the water amount in the outlet air. In this zone, the maximum volumes of voltage and power are produced by the fuel cell, as shown in Figs. 1 and 2.

Zcell (jω) = Rm +

(28)

The total PEMFC impedance was illustrated in [15,31,39,42]:

Similarly, this equation can be written as follows:

IncludingτO2 =

(27)

The time constant of diffusion τd, the resistance Rd, and the constant phase element impedance are represented by the following equations respectively:

Accordingly,KH2represents the hydrogen valve molar constant [kmol/(atm s)], withKO2referring to the oxygen valve molar constant (kmol/(atm s)).N0represents the number of fuel cell series in the stack, whileIstackrepresents stack current (A). Furthermore,Krrefers to the constant at = N0 Kmol/ (s.A), followed by F which refers to the Farady 4F constant at 9,684,600 C/Kmol. Notably, the replacement of Eqs. (18) and (19) in Eq. (15) was according to the implementation ofLaplace transformation and isolation, which are illustrated as follows:

PO2 =

C τd

(18)

qH2 out = K H2 PH2

PH 2 =

tanh (jω (τd ))

Parameters

Values

Temperature T L Jmax Jn B λa Aair stoichimetry Active area S ζ1 ζ2 ζ3 ζ4 Number of cells N0 Hydrogen valve constant KH2 Oxygen valve constant KO2 Hydrogen time constant, τH2 Oxygen time constant, τO2 Hydrogen –Oxygen flow ratio rH-O

(K) 178 μm 1.5 A/cm2 1.2 A/cm2 0.016 V 2 56.6 cm2 −0.948 0.00286 + +0.0002.lnA+(4.3.10−5)lnCH2 7.6 × 10−5 −1.93 × 10−4 343 4.22 × 10−5 kmol/(s.A) 2.11 × 10−5 kmol/(s.atm) 3.37 (s) 6.74 (s) 1.168 0.996×10−6 kmol/(s.A)

Kr constant =

(26) 4

N0 4F

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Fig. 1. PEMFC polarization curve.

connection between the neurons in the hidden layer.bi refers to the neuron bias. With the linearity in the output layer function, the neural network sensor mathematical model is represented by the following equation [31,43–45]: N

yk u =

N

⎛

N

⎞

∑ (w 0ij ui + bi) = ∑ w 0ij f ⎜∑ (wij xi + bi) ⎟ j=1

j=1

⎝ j=1

⎠

Fig. 3. Randles cell with CPE impedance.

(32)

Fig. 2. PEMFC power variation as a function of current density and relative humidity. 5

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Accordingly, yk, represents the output signal from kth output neuron, whilew0kirepresents the weight of ith output ui to thekth neuron in the output layer. In this study, the NNT sensor model bias values and weight were updated based on the dynamic gradient descent algorithm [45]. The input layer part of the neural network consists of three neurons. Specifically, the first neuron is connected to relative humidity, while the second neuron is linked to the time of operation. The third neuron is connected to frequency. This is followed by the hidden layer, which is composed of two hidden sublayers with twenty neurons under the first sublayer and 10 neurons under the second sublayer. Furthermore, the output layer part consists of two neurons, each is connected to RNNT_int and RNNT_pol. Fig. 4 presents the neural network sensor model architecture used in this study. After the parameters of the database, architect, activation function, and iterations number were determined, the learning phase was conducted by the back-propagation algorithm to adapt the weights and thresholds (biases). Subsequently, the optimization criterion could be fulfilled, followed by the development of a simulation structure. The tangent hyperbolic sigmoid transfer function ("tansig") was used to estimate the parameters of the hidden layers and the linear transfer function ("purelin"), which were applied in the output layer. The parameters used during the neural network learning phase are shown in Table 2. The mean squared error is presented in Fig. 5a. After 100,000 iterations, a significantly low value of the mean squared error of the NNT sensor model was obtained, which was equal to 1.5977 × 10−18. Based on Fig. 5b, the Pearson correlation coefficient R amounted to one (1), indicating the learning reliability of the NNT sensor model.

Table 2 Physical parameters of flooding and drying PEMFC model [15]. Time(sec)

RH(%)

Rm(Ω)

Q(Ssα)

Rp(Ω)

Rd(Ω)

τd(sec)

U(V)

500 3700 500 3700

100 100 10 10

0.00398 0.00416 0.00512 0.0088

1.109 0.936 0.952 0.62

0.008 0.0163 0.0099 0.013

0.0034 0.0312 0.0051 0.0101

0.0872 0.0947 0.1155 0.1835

4.18 3.3 4.06 3.35

4. Results and discussion The proposed model of PEM fuel cell was used in Matlab/Simulink, as shown in Fig. 7 and the parameters presented in Table 1. The complete model consisted of a fuel cell elementary, the unit for calculating of partial pressures of hydrogen and oxygen, the relative humidity calculation unit as the current required by the load, the volume of water injected into the reactive gases (airflow), and the operating temperature. In addition, the neural networks relative humidity sensor model is a black box which predicts the hydration fuel cell state, which could be either flooding or drying. This sensor could identify the impedance spectra with impedance criteria (RNNT_int, RNNT_pol),which defines PEMFC hydration state. As shown in Fig. 8a, based on the test of the proposed model with a step-change in the injection of water into the fuel cell airflow (qwin), a variation of results was found in the relative humidity of air at the cathode with a similar shape as the water injected. These results areshown in Fig. 8b. Fig. 9a and b illustrate the fuel cell dynamic electrical responses. Each response was in terms of voltage and power respectively, resulting from the abrupt changes in the relative humidity including the change in the volume of water injected into the fuel cell airflow as a function of the operating time. As seen in Fig. 8, as for the time interval from 0 to 500 s, the relative humidity amounted to 50% during the same period, with the voltage presented in Fig. 9a and the power presented in Fig. 9b. An increase could be seen from the estimated internal resistance at high frequency with the NNT sensor model (RNNT_int) (Fig. 10a), the estimated biasing resistance at low frequency (RNNT_pol) (Fig. 10b) by the NNT sensor model,and the Nyquist diagram surface (Fig. 10c). Between the interval of 500 and 1000 s, an abrupt change in relative humidity was recorded to range from50% to 150%. In this case, a similar increase in voltage and power was observed. This was followed byan increase in RNNT_int, RNNT_pol and Nyquist diagram surface resistances. This was explained through the increase in the fuel cell membrane ionic conductivity due to the membrane saturation with water, which is a prerequisite to a good ionicconductivity and an improvedfuel cell efficiency. With in 1000 s, the relative humidity decreased from 150% to 100%. This was followed by anincrease in RNNT_int resistance, voltage, and power. Meanwhile,the RNNT_pol resistance and Nyquist diagram surface resistance were reduced. Moreover, within 1500 s, the relative humidity decreased from over 100% to 30%. It was observed that the decrease in voltage and power was due to thedecrease in the relative humidity. This reduction resulted in membrane dryness, leading to PEMFC destruction. Therefore, it can be concluded that fuel cell efficiency with relative humidity is almost 100%, as seen in Figs. 1 and 2. Fig. 10d illustratesthe fuel cell impedance spectra as a function of

3.3. NNT PEMFC humidity sensor model validation When the neural network learning was identified, the test phase of the results was conducted based on the comparison between the results obtained by the NNT humidity sensor model and the experimental results in the literature [15], as shown in Fig. 6. In the case of PEMFC flooding, the essential input parameters are shown in Fig. 8 by Fouquet et al. [15]. In these parameters, the relative humidity rate is higher thanφ = 100%, with an operating time amounting to 1600 s within a frequency range from 0.1 Hz to 1 kHz. As for PEMFC drying, the input parameters are based on literature, as shown in Fig. 10 [15]. These parameters comprise a relative humidity of φ = 20% and operating time of approximately t = 1600 s=, with in a frequency range from 0.1 Hz to 1 kHz. In a normal case of PEMFC, the input parameters shown in Fig. 8 are presented by Fouquet et al. [15,46], where the time amounted to approximately 200 s and relative humidity of approximatelyφ = 100% in a range of frequency from 0.1 Hz to 1 kHz. The quantitative comparison of the estimated NNT sensor model resistances and the resistances recorded through EIS experiment method by Fouquet et al. [15]. are presented in Table 3. The resistors comparison results in Table 3 and Fig. 6 illustrated the comparison between the model simulation and the experimental results. It was indicated from the comparison between the proposed NNT sensor model simulation and experimental results for each test that the proposed model was reliable.

Fig. 4. PEMFC model of neural networks humidity sensor.

6

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Fig. 5. NNT humidity sensor model training performance, (a) Mean squared error. (b) Pearson correlation coefficient R.

instance of this situation was the increase in the water content in the membrane, which resulted in the flooding of the fuel cell.

relative humidity in Fig. 8b and the operating time. In this case,the Nyquist impedance spectra surfaces were influenced by the relative humidity. As a result, it was found that the measured resistance at a high frequency of fuel cell was inversely related to relative humidity, while the measured resistance at a low frequency was directly related tothe Nyquist surfaces. Finally, the sensor model based on artificial neural networks could predict the fuel cell hydration state through the basic parameters (RNNT_int, RNNT_pol).The high sensitivity of the parameters to thehumidity is as follows:

5. Conclusion This study aims to develop a PEMFC semi-experimental mathematical model to assess water activity in the fuel cell under different operating conditions. The proposed model comprised a new improved sensor model based on artificial neural networks, which improved the diagnostic and prediction of PEMFC hydration state. The NNT PEMFC humidity sensor model was tested through the comparison between PEMFC electrical performances flooding and drying cases. The relevance of results was supported by the current findings for both basic parameters (RNNT_int, RNNT_pol). These findings highlighted the parameters high sensitivity to humidity, which proved the efficacy of this new sensor model in improving the PEMFC hydration state detection and controlling the humid airflow in the fuel cell. Overall, it was indicated that this sensor could be used in the control system to improve

• The increase in the R •

NNT_int estimated by the NNT sensor model indicated a decrease inthe air relative humidity at the cathode. An instance of this situation was the decrease in the water content in the membrane. Therefore, the PEMFC membrane internal resistance increased,which resulted in fuel cell drying. The RNNT_pol estimated by the NNT sensor model increased, indicatingthat the air relative humidity at the cathode increased. An

Fig. 6. NNT humidity sensor model validation of the PEMFC. 7

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Table 3 Quantitative comparison of the estimated NNT sensor model resistances and the resistances recorded by EIS experiment method of Fouquet et al. [15].

Flooding case Nominal case Drying case

REIS _ int (Ω) [15]

REIS _ pol (Ω) [15]

RNNT _ int (Ω)

RNNT _ pol (Ω)

0.0041 0.0040 0.006898

0.0356 0.0154 0.02372

0.004006 0.003986 0.00686

0.03586 0.01538 0.02325

Fig. 7. PEM fuel cell block diagram.

Fig. 8. A Proposed change in the step to test the PEMFC block diagram. (a)Water quantity variation injected into fuel cell airflow, (b) Airflow relative humidity variation in the fuel cell.

Declaration of Competing Interest

the humid air supply for water management. It was indicated from the results that the NNT sensor model could be generated easily through the Nyquist diagram spectrums for any cases of flooding or fuel cell drying. However, the control of the molar humid airflow in the fuel cell was not highlighted in this study. Therefore, it is recommended that more studies develop a more specific algorithm for the base of control for this model for the implementation of an intelligent control unit for water management.

All authors have participated in (a) conception and design, or analysis and interpretation of the data; (b) drafting the article or revising it critically for important intellectual content; and (c) approval of the final version This manuscript has not been submitted to, nor is under review at, another journal or other publishing venue.The authors have no affiliation with any organization with a direct or indirect financial interest in the subject matter discussed in the manuscript

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Fig. 9. PEMFC dynamic electrical responses; (a) Voltage. (b) Power.

Fig. 10. Fuel cell diagnostics criteria; (a) Internal resistance measured at high frequency (RNNT_int); (b) Biasing resistance measured at low frequency (RNNT_pol); (c) Nyquist impedance spectra surfaces; (d) PEMFC impedance spectra.

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