Accurate Estimation of PEMFC State of Health Using Modified Hybrid Artificial Neural Network Models

The integration of renewable energy including hydrogen energy become economically and environmentally become necessary worldwide. The fuel cell technology is widely utilized in many applications, for instance,in the last years, there were about 8,000 fuel cell electric vehicles (FCEV) in the U.S, 3,600 in Japan, 5,000 in South Korea, 2,500 in Europe, and 110 in China, and there have been 44 hydrogen refueling stations in the U.S, 112 in Japan, 34 in South Korea, 140 in Europe and 12 stations in China. [1]. On the other hand, the specialized market of hydrogen technologies claims that over 56 thousand hydrogen fuel cell cars were sold at the end of 2022 worldwide and the number of hydrogen refueling station is more than 800 in 2022: (European Hydrogen Refuelling Stations in 2022 - Tuv Sud– Hydrogen Central (hydrogencentral.com)).

There are various applications areas for fuel cells: Banks, infrastructure in cities, Hospitals, Telecommunication companies, Laptops, Chargers systems and radio/communication devices, etc. Generally, the applications of fuel cells can be categorized into three main areas: Stationary power generation, Portable and Transportation). The mean features are classified in Table 1[1].

Table 1. PEM fuel cell features [1]

The research and development in the polymer electrolyte membrane fuel cell describes the importance of this technology. The fuel cell converts the electrical energy from hydrogen chemical energy according to the Equation 1:

O₂ + 2H₂ → 2H₂O + energy + Heat              (1)

The electrochemical reaction is decomposed by the oxidation of hydrogen and the reduce of oxygen as expressed in the half reduction of Equation 2, 3:

$\mathrm{H}_2 \rightarrow 2 \mathrm{H}^{+}+2 e^{-}$Anode                            (2)

$\mathrm{O}_2+4 \mathrm{H}^{+}+4 e^{-} \rightarrow \mathrm{H}_2 \mathrm{O}$ Cathode                      (3)

The protons in the membrane passes to the cathode; whilst, the electrons conducts inside external charge to the cathode side, this process is displayed in Figure 1.

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Figure 1. Basic PEM Fuel Cell process

The (SOH) and the service life of fuel cell are related to the fault diagnosis strategy of the PEMFC system. In addition, The most popular challenging in the fuel cell are focused around the water management, the produced water inside the fuel cell should be more than the water of evacuation and evaporation to confirm the membrane hydrated under each operating conditions of fuel cell. Moreover, the ratio of pressure drop to flow rate and the flooding degree has been used as an indicator to diagnose the state of health of the fuel cell. Therefore, it’s logically to diagnose the failure modes and control the state of health of the fuel cell during different operating conditions, the fault diagnosis can be isolate and correct in time. The optimal water man- agement ensures the best functioning as well as increasing the service life of the fuel cell.

Numerous methods have been proposed to identify and diagnose the state of fuel cell’s health, i.e. semi-empirical, empirical, physical, analytical and the black-box models [2]. In the literature, most common technique to di agnose the fuel cell is the electrochemical impedance spectroscopy (EIS) in order to make the hydration monitoring [3], which characterizes the values of the impedance parameters based on the Randles model of constant phase elements (CPE) through estimating the flooding and drying state in the fuel cell system. In general, the randles model is used to extract the parame- ter feature from the EIS, and this model consists of three elements, namely Rm, Rp and Zw. The fuel cell’s internal resistance is represented by Rm. The polarization resistance Rp characterizes the oxygen reduction reaction. The limitation of mass transfer represented by Zw. Moreover, the parame- ters shown in [4] are directly affected by charge transfer, mass transfer and membrane resistance, which are used as characteristics to select the defect in different FC health states.

One of the promising method based PEMFC diagnostics, becoming im- portant for researchers, is the artificial neural networks (ANNs), it provides many advantages compared to other traditional techniques that require a large number of instruments. Where, several works have empirically demonstrated the effectiveness of the ANNs method to diagnose and analyze the state of health of the fuel cells. It should be noted that ANNs were used in a large scale real-world applications in various domains, such as fingerprint and speaker identification, image analysis, spectroscopy, etc. The presented ANN model by this author used a combined strategies based on Electrochem- ical Impedance Spectroscopy measurement and the stack voltage singularity measurement and classification, which facilitates and optimize the perfor- mance of the water management [4].The main idea behind using ANNs for PEMFC diagnostic is that neural network approach presents a high sensitiv- ity to identify the parameters of the Randles model and capable to predict response of voltage under a sudden change in relative humidity [5].

To this end, in this paper, we suggest to employ the ANNs so we can summary the contribution of our work as follows:

- A fast prognostic tool to predict the output voltage loss in the PEMFC.

-The neural network method proposed could be effective to predict the degradation caused by poor water management of the fuel cell (i.e. Flooding, Drying).

The rest of this paper is organized as follows. Section 2 related work, Section 3 EIS model, Section 4 ANN model (test and simulation), Section 5 results and discussion.

Among the most common methods used to characterize and analyze electrochemical devices is the electrochemical impedance spectroscopy method. Many researchers have used the (EIS) to illustrate the impedance response features by injecting disturbed alternative current into PEMFC, which allows to extract the parameters of Randles model from the obtained signal, (e.g., double layer capacity, charge transfer resistance, membrane resistance, and the constant phase elements (CPE), etc.). The most applications of (EIS) for diagnosing and monitoring the lifetime of fuel cell are based on a Ran- dles circuit measurement. Figure2 displays an equivalent circuit of PEMFC model.

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Figure 2. Equivalent circuit of PEMFC model [18]

The equivalent impedance of Randles circuit is calculated as: [10;18;19].

$Z_{c e l l}(j w)=R_m+\frac{1}{Z_{C P E} \quad+\left(1 /\left(R_P+Z_W\right)\right)}$                    (4)

The Warburg impedance is represented as follows:

$Z_W(j w)=R_d \frac{\tanh \sqrt{\left(j w\left(\tau_d\right)\right)}}{C \sqrt{\tau_d}}$                     (5)

The constant (τd), (Rd) and impedance of constant phase element (ZCPE) are expressed as follows, respectively:

$\left\{\begin{array}{c}\tau_d=\frac{\delta^2}{D} \\ R_d=\frac{R T \delta}{n^2 F^2 S C D} \\ Z_{C P E}(j w)=\frac{1}{Q(j w)^\alpha}\end{array}\right.$              (6)

Accordingly, the PEM fuel cell impedance is given by the following equation [18] :

$Z_T(j w)=R_m+\frac{1}{Q(j w)^\alpha+\left(1 /\left(R_P+Z_W\right)\right)}$                    (7)

where $\alpha=0.5$ when the CPE is the Warburg impedance, and $\alpha=1$ for ideal capacitance [20;21].

In order to study the EIS resistances, we focus on the analysis of the Nyquist plot. The equivalent circuit of Randles-type is used to analyze the impedance response at low and high-frequency in semicircle of the Nyquist plot.

More details about these parameters are given in Table 3.

Table 3. Physical parameters of fuel cell in different state [24]

Through the proposed method, we give (qwin) variation during deferent time’s period under Matlab for each simulation, from 0 to 500 s at normal operating conditions, from 500 s to 3800 s at flooding conditions and from 4000 s to 8000 s at drying conditions, where we can observe the effects of this variation in the parameters of Randles model obtained by the first sub-NNT. Figure 7 a to d displays and compares the results attained using the first sub-ANN as following:

Between the two intervals [0 - 500 s] and [3800 - 4000 s], the parameters of Randles model are constant which means the system is operating under nor- mal operating conditions while the qwin remains constant at (2 ∗ 10−5)mol/s.

During the flooding state the value of qwin is 5mol/s inside the PEM fuel cell. We notice that the values of Rp and Rd increase within 500 to 3800 s.

An increase gradually of the (Rm, Rp and Rd) could be seen after 4000 s, during this phase qwin is decreased to 0.2 mol/s in order to illustrate the effect of membrane dryness. 

Figure 7e illustrates the fuel cell voltage during each time period. The fuel cell voltage’s response is given by secondsub-ANN to display the vari- ations effect of the parameters of Randles model for the state of health of the fuel cell. In the period of 0 s to 500 s (i.e., normal conditions), we can observe that the fuel cell’s voltage remains constant, besides, the Resistances of Randles model conserve its values, this means the effectiveness of the fuel cell.

7a.png

(a)

7b.png

(b)

7c.png

(c)

7d.png

(d)

7e.png

(e)

Figure 7. a-d) parameters of Randles model during different state. e) fuel cell voltage during different state

In addition, we find a drop in the fuel cell voltage during the second test (flooding case). The drop voltage refers the increase of membrane ionic conductivity as shown in Figure  7 e. Moreover, within 4000 s the progressive voltage drop is clearly visible, which correlates with a gradual  increase in (Rm, Rp and Rd).

Depending on these results, the reduction of the voltage is directly related to water content accumulate inside the channels of the Fuel Cell owing to the affection of water content on the membrane conductivity. When the RH increases, the conductivity of membrane also increases, consequently the slow decrease in the FC voltage is influenced by the flood phase.

To sum up, the proposed method could estimate the state of hydration based on the relative humidity variation into PEMFC and the change of the randles model parameters. Therefore, the used artificial neural network in this study helps to know how humidity affects fuel cell voltage.

Accurate the state of health is critical in practical applications which is important to avoid the frequent mistakes that occur owing to poor water management inside the fuel cell membrane. Therefore, in this paper, we have developed a new sensor model using AI technology to determine the overall performance and resistance to PEMFC losses during different oper- ating conditions. Based on the experimental data extracted from [24], the first sub-ANN model is trained to obtain the parameters of the Randles model, and based on the achieved outputs; the second neuralnetwork model is trained to obtain the fuel cell voltage output. Moreover, we can use the combination between the analysis of the parameters of Randles model and the drop output voltage pattern of the fuel cell to improve SOH diagnosis in both cases: flooding and drying. Overall, our model can contribute to get good diagnosis without the requirement for costly tools. Moreover, the pro- posed method will be considered for predicting the degradation of PEMFCs in future research works. Further studies needs tobe addressed to develop a more specific control algorithm for this model to implement an intelligent water management controller based on another method of estimating overall performance and resistance to PEMFC losses during different operating con- ditions, with potential targets for reconfiguration control and/or preventive maintenance.