Multistep prediction of remaining useful life of proton exchange membrane fuel cell based on temporal convolutional network

ABSTRACT

Proton-exchange membrane fuel cells (PEMFCs), as potential energy converters with broad application prospects, have low durability owing to several factors that make it difficult to quantify the degradation of PEMFC components. The accurate prediction of the remaining useful life (RUL) can help users understand the degradation status of PEMFCs and adopt reasonable maintenance strategies to improve durability. This paper proposes an RUL prediction framework based on a temporal convolutional network (TCN). First, an equivalent circuit model of the PEMFC is established, and complex nonlinear least squares regression is used to fit the model to estimate the polarization resistance. Then, the prediction framework and joint degradation indicator of the TCN are constructed to predict the RUL. The TCN is compared with four models: linear regression, Holt–Winters, seasonal autoregressive integrated moving average, and Prophet. The results show that the TCN performs significantly better in terms of all the predictive metrics, including the root-mean-squared error which is at least 13.43% lower than those of the four models. The RUL prediction accuracy of the TCN is at least 7.76% higher than that of the four models. Except at 800 h, the average RUL accuracy of TCN is 92.20%. This confirms that the TCN (double variables) can accurately predict the RUL of PEMFCs.

KEYWORDS:

• Proton-Exchange membrane fuel cell
• remaining useful life
• temporal convolutional network
• equivalent circuit
• multistep prediction

Abbreviations

PEMFC	=	Proton-exchange membrane fuel cell
RUL	=	Remaining useful life
TCN	=	Temporal convolutional network
CNLS	=	Complex nonlinear least squares
EIS	=	Electrochemical impedance spectroscopy
θ	=	Nine parameters of the equivalent circuit
MAE	=	Mean absolute error
RMSE	=	Root mean squared error
MAPE	=	Mean absolute percentage error
SMAPE	=	Symmetric mean absolute percentage error
Pre7	=	Seven EIS curves before the measurement of the polarization curve
Post8	=	Eight EIS curves after measurement of the polarization curve
SARIMA	=	Seasonal autoregressive integrated moving average
${\mathrm{K}}_{\mathrm{s}}$	=	convolution kernel size
k	=	Filter size
${\mathrm{t}}_{\mathrm{p}}$	=	Prediction time point
TL	=	Training length
CPE	=	constant phase angle element
FLT	=	Failure life threshold
$\mathrm{Z}\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}$	=	The total impedance of the equivalent circuit (mΩ)
$w$	=	Frequency (Hz)
$\mathrm{Z}\mathrm{r}$	=	Polarization resistance (mΩ)
L1, L2	=	Two inductor elements of the equivalent circuit (mH)
$\mathrm{R}\mathrm{o}\mathrm{h}\mathrm{m}$	=	Ohmic resistance element of equivalent circuit (mΩ)
$\mathrm{R}1,\mathrm{R}2,\mathrm{R}3$	=	Three resistance elements of the equivalent circuit (mΩ)
φ	=	Number between 0 and 1
Q	=	Numerical value of the admittance (S secφ)
Pre7_R	=	Seven polarization resistance values of Pre7 (mΩ)
Post8_R	=	Eight polarization resistance values of Post8 (mΩ)
d	=	Hole size of convolution kernel
N1	=	Layer length
Lr	=	Receptive field length
N	=	Current prediction time point
H	=	Predicting length

Acknowledgement

We thank the FCLAB Lab for the open source data on PEMFCs

Disclosure statement

We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled, “Multistep prediction of remaining useful life of proton exchange membrane fuel cell based on Temporal Convolutional Network.”

Credit author statement

Mingzhang Pan: Funding acquisition, Project administration;

Pengfei Hu: Methodology, Writing – original draft, Visualization, Software;

Ran Gao: Writing – Review & Editing;

Ke liang: Supervision, Investigation

Supplementary material

Supplemental data for this article can be accessed on the publisher’s website.

Additional information

Funding

This work was supported by the Dean Project of Guangxi Key Laboratory of Petrochemical Resource Processing and Process Intensification Technology [no. 2020K009] Mingzhang Pan.