Aging state prediction for supercapacitors based on heuristic kalman filter optimization extreme learning machine Dezhi Li a , Shuo Li a , Shubo Zhang b , Jianrui Sun c , Licheng Wang d , Kai Wang a, * a School of Electrical Engineering, Weihai Innovation Research Institute, Qingdao University, Qingdao, 266000, China b School of Electronic Engineering, Dublin City University, Dublin, D09 V209, Ireland c Shandong Wide Area Technology Co., Ltd, Dongying, 257081, China d School of Information Engineering, Zhejiang University of Technology, Hangzhou, 310023, China article info Article history: Received 17 May 2021 Received in revised form 3 March 2022 Accepted 15 March 2022 Available online 19 March 2022 Keywords: Extreme learning machine Supercapacitors Aging state Heuristic kalman filter Particle swarm optimization abstract With the advancement of wind energy, solar energy, and other new energy industries, the demand for energy storage systems are worth increasing. Supercapacitors gradually stand out among many energy storage components due to their advantages of high power density, fast charging and discharging speed, and long life. Predicting the capacity of supercapacitors from historical data is a highly non-linear problem, subject to various external and environmental factors. In this work, we propose an opti- mized forecasting model-an extreme learning machine (ELM) model coupled with the heuristic Kalman filter (HKF) algorithm to forecast the capacity of supercapacitors. ELM is preferred over traditional neural networks mainly due to its fast computational speed, which allows efficient capacity forecasting in real- time. Our HKF-ELM model performed significantly better than other data-driven models models that are commonly used in forecasting life of supercapacitors. The performance of the proposed HKF-ELM model was also compared with traditional ELM, Kalman filtering model, ELM optimized by the particle swarm optimization (PSO-ELM) and Kalman filter extreme learning machine models (KA-ELM). Different per- formance metrics, i.e., Root Mean Squared Error (RMSE), Mean Square Error (MSE) and R 2 determination coefficient were used for the comparison of the selected models. The aging life of supercapacitors in different environments were also performed using the proposed approach. The results revealed that the proposed approach is superior to traditional data-driven models in terms of prediction aging life of supercapacitors and it can be applied in real-time to predict state of health (SOH) based on the previous charge and discharge data of supercapacitors. In particular, considering RMSE of forecasting, the pro- posed HKF-ELM model performed 77.62% better than the traditional ELM model, 77.46% better than the PSO-ELM model, 87.40% better than the traditional Kalman filter model, 82.51% better than the KA-ELM model in forecasting aging life of supercapacitors. The novelty of the proposed approach lies in the way the fast computational speed of ELMs has been combined with the accuracy gained by tuning hyper- parameters using HKF. Fewer setting parameters, lower time cost and higher prediction accuracy have been need in our methodology compared to available models. Our work presents an original way of performing aging life of supercapacitors forecasting in real-time in industry with highly accurate results which are much better than pre-existing life forecasting models. © 2022 Elsevier Ltd. All rights reserved. 1. Introduction Supercapacitors (SCs) as energy storage devices with superior performance have attracted more attention with the necessity of storing renewable energy [1]. Among the energy storage systems (ESSs), including the batteries [2e4], SCs [5], superconductors [6], and the flywheels, the SCs are rapidly applied to the energy system of electric vehicles [7]. SCs have been widely used in power grid load quality regulation and chaotic carrier frequency modulation due to their small size, high power density, and repeatability in charge and discharge [8]. According to different energy storage mechanisms, super- capacitors are divided into Electric Double Layer Capacitor (EDLC), pseudocapacitor (PC), and Hybrid Capacitor (HC) [9]. The electric * Corresponding author. E-mail addresses: wangkai@qdu.edu.cn, wkwj888@163.com (K. Wang). Contents lists available at ScienceDirect Energy journal homepage: www.elsevier.com/locate/energy https://doi.org/10.1016/j.energy.2022.123773 0360-5442/© 2022 Elsevier Ltd. All rights reserved. Energy 250 (2022) 123773