Degradation prediction model for proton exchange membrane fuel cells based on long short-term memory neural network and Savitzky-Golay filter

Proton exchange membrane fuel cell (PEMFC) as a promising green power source, can be applied to vehicles, ships, and buildings. However, the lifetime of the fuel cell needs to be prolonged in order to achieve a wide range of applications. Consequently, the prediction of the health state draws attention lately and is critical to improving the reliability of the fuel cell. Since the degradation mechanism of the fuel cell is not fully understood, the data-driven method is very suitable for designing degradation prediction models. However, the data-driven method usually requires a lot of data, which is difficult to be obtained. To solve the issues, we propose a degradation prediction model for PEMFC based on long short-term memory neural network (LSTM) and Savitzky-Golay filter in this paper. First, we select the monitoring parameters for building the degradation prediction model by analyzing the degradation phenomenon of the fuel cell. Then, Savitzky-Golay filter is utilized to smooth out the selected data, and the sliding time window is used to generate training samples. Finally, the LSTM is applied to establish the degradation prediction model. Moreover, the dropout layer and mini-batch method are adopted to improve the model generalization ability. We use an actual aging data of the fuel cell to verified the proposed degradation prediction model. The results demonstrate that the proposed model can precisely predict the fuel cell degradation. It is worth mentioning that the determination coefficient (R²) of the test set based on the model trained by 25% of data is 0.9065.     

A novel online degradation model for proton exchange membrane fuel cell based on online transfer learning

A novel online degradation prediction model is proposed to prognosticate the future degradation trend (FDT) of proton exchange membrane fuel cell (PEMFC) stack in this paper. In order to overcome the fact that existing FDT prediction methods of PEMFC stack based on data-driven model rely on the assumption that the operating conditions of the training data and testing data need to be consistent, an end-to-end prediction algorithm based on the combination of transfer learning and transformer neural network, referred to as TLTNN, is proposed to predict the FDT of PEMFC stack. Besides, in order to demonstrate the effectiveness and superiority of the proposed method in prognostics tasks of PEMFC stack FDT, the prediction performance is validated on the PEMFC test system. The results show that the RMSE, MAE and MAPE values of the predicted degradation voltage are 0.00598 V, 0.004842 V and 0.1518%, respectively, which indicates that the proposed TLTNN strategy based on transfer online learning can be used to predict the degradation voltage of PEMFC stack and the superiority of the proposed method is better, thus solving the problem that the distribution of training and test data must be the same in traditional machine learning models.     

Fuel cell health prognosis using Unscented Kalman Filter: Postal fuel cell electric vehicles case study

The Proton Exchange Membrane Fuel Cell (PEMFC) health monitoring and management are of critical importance for the performance and cost efficiency of Fuel Cell Electric Vehicle (FCEV). Prognostics play an important role in improving the lifetime and reducing maintenance costs of PEMFC by predicting the degradation trend. In this paper, the degradation prediction of PEMFC is based on a novel model-driven method which combines the Unscented Kalman Filter (UKF) algorithm with the proposed voltage degradation model. The experimental data originated from the FCEVs which achieve postal delivery mission in the real road are used for construction and validation of the proposed model-driven prognostic method. At our best knowledge, this is the first application which uses field-based data for FC health prognosis. The influence of different lengths of measured voltage data on degradation prediction of PEMFC, and the degradation prediction performance of PEMFC in different FCEVs are also investigated by the proposed method. Test results show that the proposed model-driven method is able to accurately estimate the voltage degradation trend of PEMFC in the FCEV. When more data are applied to learning the degradation of PEMFC, the mean Relative Error (RE) in the prediction phase will decrease. Especially, when the learning data exceeds 45 h, the mean RE in prediction phase is reduced to 0.68%. Considering that the maximum mean RE in the prediction phase is 2.03% for 3 postal FCEVs, the proposed method can be applied in the degradation trend prediction of PEMFC in FCEV under real conditions.     

A hybrid remaining useful life prognostic method for proton exchange membrane fuel cell

Proton Exchange Membrane Fuel Cell (PEMFC) has become a promising power source with wide applications to many electronic and electrical devices. However, even if it is a competitive energy converter, PEMFC still suffers from its limited lifespan. Prognostics appear to be a good solution to helping take actions to extend its lifetime. Considering both advantage and disadvantage of model-based and data-driven based prognostic methods, this study proposes a hybrid prognostic method for PEMFC based on a data-driven method, least square support vector machine (LSSVM) and a model-based method, regularized particle filter (RPF). The main contributions of the proposed method include: 1) It can provide not only an estimated value but also an uncertainty characterization of RUL with a probability distribution; 2) It has a better capability to capture the nonlinearities in degradation data and a lower reliance on PEMFC degradation model; 3) The RPF method improves the standard particle filter algorithm by reducing the degeneration phenomenon and loss of diversity among the particles. Effectiveness of the proposed method is verified based on PEMFC dataset provided by FCLAB Research Federation. The results indicate that the proposed hybrid method can effectively combine both advantages of data-driven and model-based methods, providing a higher accuracy of RUL prediction for PEMFC.     

A novel health indicator for PEMFC state of health estimation and remaining useful life prediction

Proton Exchange Membrane Fuel Cell (PEMFC) is a promising renewable energy, while still limited by the short life duration. To postpone the end of life, approaches of health management and prognostic (PHM) are applied into the cells. The stack voltage and impedance are often used as the health indicator (HI) for estimating state of health (SoH) and predicting remaining useful life (RUL). However, on one hand, on-line measurement of impedance is hardly realizable while downtime measure costs a lot. On the other hand, a single HI based on voltage or impedance is difficult to express the degradation of PEMFC precisely. To tackle this problem, this paper develops a fusion HI and a prognostic methodology for PEMFC SoH estimation and RUL prediction. Moreover, geodesic distance is employed to estimate SoH. Afterwards, a 2nd order Gaussian degradation model is built to complete the RUL prognostics based on unscented particle filter (UPF). In the experiment, both mahalanobis distance and geodesic distance are employed to estimate the SoH based on the presented HI. Besides, a rational model is applied to predict the RUL compared with the proposed Gaussian model. Finally, the results show the efficiency and effectiveness of the SoH estimation and RUL prediction approaches based on the proposed HI.     

Determination of fuel utilisation and recirculated gas composition in dead-ended PEMFC systems

This work presents a fundamental theory and methods for understanding the gas composition dynamics in PEMFC anode fuel supply compartments operated dead-ended with recirculation. The methods are applied to measurement data obtained from a PEMFC system operated with a 1 kW short stack.We show how fuel utilisation and stack efficiency, two key factors determining how well a fuel supply system performs, are coupled through the anode gas composition.The developed methods allow determination of the anode fuel supply molar balance, giving access to the membrane crossover rates and the extent of recirculated gas exchanged to fresh fuel during a purge. A methane tracer gas is also evaluated for estimating fuel impurity enrichment ratios.The above theory and methods may be applied in modelling and experimental research activities related to defining hydrogen fuel quality standards, as well as for developing more efficient and robust PEMFC system operation strategies.     

Hydrogen consumption minimization method based on the online identification for multi-stack PEMFCs system

The proton exchange membrane fuel cell (PEMFC) stacks are not widely used in the field of transportation industry, due to their limited power. Thus, the PEMFC stacks usually connected in parallel or series to meet the load demand power in high-power applications. The hydrogen consumption of multi-stack fuel cells (MFCs) system is related to the efficiency and output power. In addition, the efficiency of PEMFC depends on the applied voltage and other parameters. Consequently, the hydrogen consumption of system changes with varying load, because the system parameters are also varying. It makes reducing the fuel consumption of system a challenging assignment. In order to achieve the goal of minimizing fuel consumption of parallel-connected PEMFCs system, this paper proposes a novel power distribution strategy based on forgetting factor recursive least square (FFRLS) online identification. The FFRLS algorithm is based on data-driven and uses real-time data of the system to improve the estimation accuracy of PEMFC system parameters. On the test bench of parallel-connected PEMFCs system consists of two 300 W PEMFC stacks, PEMFC stack controller, DC/DC converters, and DSP controller etc., a multi-index performance test and comparative analysis are carried out. The results showed that, the performance of proposed power allocation strategy has been successfully validated. In addition, compared with the power average and daisy chain algorithms, the proposed online identification power distribution method can get more satisfactory results. Such as, reducing the hydrogen consumption and improving efficiency.     

Investigation of PEMFC fault diagnosis with consideration of sensor reliability

Despite the wide range of applications for the polymer electrolyte membrane fuel cell (PEMFC), its reliability and durability are still major barriers for further commercialization. As a possible solution, PEMFC fault diagnosis has received much more attention in the last few decades. Due to the difficulty of developing an accurate PEMFC model incorporating various failure mode effects, data-driven approaches are widely used for diagnosis purposes. These methods depend largely on the quality of sensor measurements from the PEMFC. Therefore, it is necessary to investigate sensor reliability when performing PEMFC fault diagnosis.In this study, sensor reliability is investigated by proposing an identification technique to detect abnormal sensors during PEMFC operation. The identified abnormal sensors will be removed from the analysis in order to guarantee reliable diagnostic performance. Moreover, the effectiveness of the proposed technique is investigated using test data from a PEMFC system, where fuel cell flooding is observed. During the test, due to accumulation of liquid water inside the PEMFC, the humidity sensors will give misleading readings, and flooding cannot be identified correctly with inclusion of these humidity sensors in the analysis. With the proposed technique, the abnormal humidity measurements can be detected at an early stage. Results demonstrate that by removing the abnormal sensors, flooding can be identified with the remaining sensors, thus reliable health monitoring can be guaranteed during the PEMFC operation.     

Degradation prediction of proton exchange membrane fuel cell using auto-encoder based health indicator and long short-term memory network

As durability of proton exchange membrane fuel cell (PEMFC) remains as the main obstacle for its larger scale commercialization, predicting PEMFC degradation progress is thus an effective way to extend its lifetime. To realize reliable prediction, a novel health indicator (HI) extraction method based on auto-encoder is proposed in this paper, with which PEMFC future voltage can be predicted by long short-term memory network (LSTM). The effectiveness and robustness of proposed approach is investigated with test data simulating vehicle operation conditions, and accurate prediction performance can be observed, with the maximum root mean square error (RMSE) of 0.003513. Moreover, by comparing with two commonly prognostic methods including attention-based gated recurrent unit network and polarization model-LSTM, the proposed method can provide better predictions under various operating conditions. Furthermore, with the proposed method, the degradation mechanism of PEMFC can also be analyzed. Therefore, the proposed prognostic method can predict reliable PEMFC degradation progress and its corresponding degradation mechanisms, which will be beneficial in practical PEMFC systems for taking appropriate strategies to guarantee PEMFC durability.     

Coupling flow channel optimization and Bagging neural network to achieve performance prediction for proton exchange membrane fuel cells with varying imitated water-drop block channel

The proton exchange membrane fuel cell (PEMFC) flow channel structure obviously affects the reaction gas distribution and electrochemical reactions. In this study, the imitated water-drop block heights and widths within the channel are optimized for better PEMFC performance. A machine learning-based Bagging neural network is applied for the first time to predict PEMFC output performance based on different block structure parameters. First, the proposed imitated water-drop block height and width are optimized by changing parameters. Then, a database is established. Finally, after the Bagging model is validated, the performance is compared with the back-propagation (BP) neural network. Results indicate that the mass transfer and the electrochemical reaction are improved under the optimal width and height of imitated water-drop block for PEMFC. The Bagging prediction model uses less training data to obtain high-precision prediction results in 10 s. The performance prediction model can effectively improve the efficiency of channel optimization.     

Lifetime prediction for proton exchange membrane fuel cell under real driving cycles based on platinum particle dissolve model

Despite the great progress of proton exchange membrane fuel cell (PEMFC) vehicle, the durability and cost of PEMFC still remain challenges. In this paper, a lifetime prediction model of PEMFC is developed by considering the platinum (Pt) electrochemical surface area (ECSA) degradation caused by steady power and transient power. The direct and continuous relationship between lifetime and real driving cycles is built by the proposed model. Firstly, the steady ECSA degradation model is deduced, and both the chemical and electrochemical dissolution of Pt particles are considered in the catalyst layer. The ECSA loss rate for steady power condition can be calculated by this model. Secondly, transient ECSA loss formula is obtained by fitting experimental data of PEMFC. This transient ECSA loss formula is used to calculate the ECSA loss rate under power changes condition. Thirdly, by applying the power voltage relationship, for a given power, the voltage can be calculated and applied to the two ECSA degradation models. Finally, the lifetime prediction method of PEMFC is proposed, and it is verified by PEMFC under three different driving cycles. Experimental test results show that the proposed lifetime prediction model accurately predict the lifetime of PEMFC under different driving cycles. The proposed method in this paper is more accurate compared with the method which divides the degradation into 4 conditions.     

Estimation of crack propagation in polymer electrolyte membrane fuel cell under vibration conditions

In transportation applications, the main reasons of mechanical damage in polymer electrolyte membrane fuel cell (PEMFC) are road-induced vibrations and impact loads. The most vulnerable place of these cells is the interface between membrane and catalyst layer in the membrane electrode assembly (MEA). Hence, studies on mechanical strength of PEMFC should focus on that interface. The objective of present study lies in the fact that employing a prediction method to investigate the damage propagation behavior of vibration applied PEMFC using artificial neural network (ANN). The data available in the literature are used to constitute an ANN model. Three-layer model; input, hidden and output, are used for construction of ANN structure. Initial delamination length (a), amplitude (A), frequency (ω) and time (t) are used as input neurons whereas delamination length is output. Levenberg–Marquardt algorithm is selected as learning algorithm. On the other hand, number of hidden layer neuron is decided with the use of different neuron numbers by trial and error method. It is concluded that prediction capability of ANN model is in allowable limits and model can be suggested as efficient way of delamination length estimation.     

Degradation prediction model of PEMFC based on multi-reservoir echo state network with mini reservoir

The durability of the proton exchange membrane fuel cell (PEMFC) has always been a major obstacle in its commercialization process and effective degradation prediction can improve this problem to a certain extent. Data-driven degradation prediction model is one of the most effective prediction methods available, which is able to ignore the structure of the PEMFC itself and rely solely on the data to make predictions, greatly simplifying the prediction process. Echo state network (ESN), as one of the data-driven methods, has received much attention for its low computational complexity and fast convergence in the degradation prediction of PEMFC. In this paper, the multi-reservoir echo state network with mini reservoir (MRM) degradation prediction model of PEMFC is proposed. The structure of MRM is that the main reservoirs are stacked in a layer and the mini reservoir is in the next level to collect and organize the main reservoir states. In addition, in order to improve the prediction accuracy, this paper firstly uses Savitzky-Golay (SG) filter to process the original data, and then investigates the influence of two important parameters, the number of main reservoirs and the number of main reservoir neurons, on the prediction accuracy and finds the optimal number of main reservoirs and main reservoir neurons for this model using particle swarm optimization (PSO) algorithm. Finally, the effectiveness of the model is verified on different lengths of training sets under both static and dynamic conditions. The results show that the model has higher accuracy and better robustness in the PEMFC degradation prediction compared with other models.     

Classification,summarization and perspective on modeling techniques for polymer electrolyte membrane fuel cell

Proton Exchange Membrane Fuel cell (PEMFC) model is helpful to understand the physical and chemical properties of the PEMFC and predict the performance of the PEMFC under different working conditions. Moreover, it can also provide essential references for evaluating new designs, new materials, and new control strategies. This paper specifically discusses PEMFC modeling at different scales, including single cell scale, stack scale and system scale. In addition, the main modeling approaches of the PEMFC are introduced in-depth, including mechanism approach, empirical approach, semi-empirical approach, equivalent circuit approach, and data-driven approach. The relationship between modeling approaches and different modeling scales is also discussed. At the same time, according to the different characteristics of the model, the modeling research in the last decade is summarized. On this basis, the development trend of the PEMFC modeling research is further analyzed by the statistical analysis method.     

A novel PEM fuel cell remaining useful life prediction method based on singular spectrum analysis and deep Gaussian processes

Accurate remaining useful life (RUL) prediction of proton exchange membrane fuel cells (PEMFCs) can assess the reliability of fuel cells to determine the occurrence of failures and mitigate their operational risk. However, is it quite challenging to design a high-precision prediction method because the implicit degradation details of PEMFCs are difficult to learn well from the measurement data with high-frequency noise. Recognizing this, a novel RUL prediction method based on singular spectrum analysis (SSA) and deep Gaussian process (DGP) is proposed in this paper. The SSA-based method is firstly employed to preprocess the measurement data, which can strengthen the effective information of PEMFC degradation data at the same time remove the noise and spikes that interfere with degradation prediction. As a deep structural model, DGP has strong feature learning ability which can represent the nonlinear details of degradation data and give more accurate prediction results. At the same time, it serves as a probabilistic model that can provide the confidence interval to enhance reliability of RUL prediction. The effectiveness of the proposed method is evaluated by experimental data of the PEMFCs under steady-state conditions, and the results show that the SSA-DGP method has higher accuracy and reliability than conventional methods.     

Neuro-evolutionary approach applied for optimizing the PEMFC performance

A multi-objective optimization strategy, based on stacked neural network–genetic algorithm (SNN–GA) hybrid approach, was applied to study the C/PBI content on a high temperature PEMFC performance. The operating conditions of PEMFC were correlated with power density and electrochemical active surface area for electrodes. The structure of the stack was determined in an optimal form related to the contribution of individual neural networks, after applying an interpolation based procedure. Multi-objective optimization using SNN as model and GA as solving procedure provides optimal working conditions which lead to a high PEMFC performance. Simulation results were in agreement with experimental data, both for model validation and system optimization (the C/PBI content in the range of 17–21%).     

Effectiveness of PEMFC historical state and operating mode in PEMFC prognosis

As a high efficiency and environmental friendly energy conversion technique, proton exchange membrane fuel cell (PEMFC) system faces challenges of limited durability and performance decay during long-term operation. Prognosis estimates the remaining useful life (RUL) of the system, from which maintenance policy can be scheduled to extend its useful life. However, parameters related to either PEMFC historical state or operating mode are used in most existing PEMFC prognostic studies, while their effects on PEMFC predictions are not clarified, this brings great challenge in selecting appropriate parameters for reliable PEMFC prognosis in practical applications subjected to complex operating conditions. In this paper, the effectiveness of PEMFC historical behavior and operating mode on PEMFC future performance at both static and non-static conditions are investigated, using back propagation neural network (BPNN) and adapted neural fuzzy inference system (ANFIS), respectively. From the findings, PEMFC historical state and operating mode make varying contributions to PEMFC prognostic results at different operating scenarios. At static operating condition, PEMFC predictions are dominated by its historical state, since constant operating mode is applied in this scenario, thus reliable prediction can be made by using only parameters representing PEMFC historical state. However, at non-static operating condition, the varying operating mode makes more contribution to the PEMFC predictions, and accurate prognosis should be provided by including variables representing varying operating mode in the prognostic analysis. The results can be beneficial in selecting appropriate parameters in prognostic analysis at practical PEMFC applications, where complex operating conditions may be experienced.     

Experimental characterization of PEM fuel cells by micro-models for the prediction of on-site performance

This paper presents the results of an experimental analysis performed on a miniaturized, 6 W_e Proton Exchange Membrane Fuel Cell (PEMFC) system, integrated with on-site hydrogen production by electrolysis; in particular, the effects of environmental parameters such as the external temperature and the humidity on the performance of fuel cells are investigated. PEMFC systems are zero-emissions power technologies when they are fed with pure hydrogen (at concentration higher than 97%); also, being the only results of system operation the produced electricity and some pure water, when produced by renewable sources hydrogen can be considered an attractive alternative to fossil fuels and may concur to the reduction of pollutant and greenhouse gas emissions deriving by combustion processes. A miniaturized, few watts capacity system may represent a safe and unexpensive solution to perform analysis and predict the on-site performance of larger FC applications. The micro-model used for the experimental characterization is a module of a flexible, larger scale system, which is briefly described in the paper; the entire system is equipped with Nafion 112 membranes, two electrolysers, hydrogen storage devices and a Photovoltaic (PV) panel. The results presented in this paper are only a first set of results; others are expected to be obtained in the future by an outdoor monitoring campaign of the entire system, needed to allow an effective prediction of the on-site performance for stand-alone PEMFC systems fed by solar energy. After having simplified the analysis by excluding the parameters that the experimental data revealed to be less influent, at the end of this paper the characterization of the PEMFC system is completed by introducing a semi-empirical model, derived by graphic analyses and data regressions.     

Remaining useful life prediction of PEMFC based on cycle reservoir with jump model

Accurate prognosis of limited durability is one of the key factors for the commercialization of proton exchange membrane fuel cell (PEMFC) on a large scale. Thanks to ignoring the structure of the PEMFC and simplifying the prognostic process, the data-driven prognostic approaches was the commonly used for predicting remaining useful life (RUL) at present. In this paper, the proposed cycle reservoir with jump (CRJ) model improves the ESN model, changes the connection mode of neurons in the reservoir and speeds up the linear fitting process. The experiment will verify the performance of CRJ model to predict stacks voltage under static current and quasi-dynamic current conditions. In addition, the reliability of the CRJ model is verified with different amount of data as the training and test sets. The experimental results demonstrate that the CRJ model can achieve better effect in the remaining useful life prognosis of fuel cells.     

Fault diagnosis of PEMFC systems based on an auxiliary transfer network

Data-driven fault diagnosis methods require huge amounts of expensive experimental data. Due to the irreversible damage of severe fault embedding experiments to proton exchange membrane fuel cell (PEMFC) systems, rare available data can be obtained. In view of this issue, a fault diagnosis method based on an auxiliary transfer network (ATN) is proposed. This method uses two parallel neural networks (main and auxiliary neural network) and a prediction fusion module to realize fault diagnosis. The auxiliary neural network is a fault diagnosis classifier pretrained based on both slight and severe fault simulative data, and its weights are transmitted into the ATN structure and frozen. After that, the main neural network is trained based on a large number of slight fault experimental data and a small number of severe fault experimental data. Through ATN, the main neural network learns the abstract features of severe faults under the guidance of auxiliary neural network, and realizes the transfer learning from simulation-based fault diagnosis classifier to experiment-based fault diagnosis classifier. Through testing, the accuracy and precision of ATN-based fault diagnosis classifier with LSTM as both main and auxiliary neural network reaches 0.993 and 1.0 respectively, which is higher than the common data-driven methods.