Unified Univariate-Neural Network Models for Lithium-Ion Battery State-of-Charge Forecasting Using Minimized Akaike Information Criterion Algorithm
Asadullah Khalid, Arif I. Sarwat
Abstract
Lithium-Ion batteries require step-ahead information to apply contingency plans to prevent them from operating beyond their safe operation thresholds in grid storage and electric vehicle applications. Recently, machine learning techniques have been increasingly applied to forecast one such battery information metric, State-of-Charge % ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SOC</i> ). Conventional standalone machine learning techniques applied in recent works suffer from an accuracy standpoint and thus have been replaced by high-fidelity hybrid machine learning techniques. Existing works on hybrid techniques either perform in-sample predictions, provide limited information of the underlying model, or do not consider varying charging-discharging rate (C-rate) dynamics of the battery. To address this issue, this article presents unified <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SOC</i> forecasting models using a Minimized Akaike Information Criterion ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${m}$ </tex-math></inline-formula> -AIC) algorithm. Initially, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${m}$ </tex-math></inline-formula> -AIC algorithm is used in a standalone manner to precisely tune and search ARIMA (Autoregressive Integrated Moving Average) terms’ order automatically to accurately forecast the battery’s current, voltage, and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SOC</i> parameters in a univariate manner at a lower C-rate from given C-rates. The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${m}$ </tex-math></inline-formula> -AIC algorithm based univariate models’ ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m-AIC</i> ) accuracy is further enhanced by first modeling and unifying with Multilayer Perceptron (MLP) and then with Nonlinear Autoregressive Neural Network with external input (NARX) neural networks respectively using the previously forecasted parameters (from <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m-AIC</i> ). This results in unified-MLP ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">u-</i> MLP) and unified-NARX ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">u-</i> NARX) models which provide higher accuracy out-of-sample <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SOC</i> forecasting at the lower C-rate for different optimizer variants. Results show that the proposed <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">u-</i> MLP and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">u-</i> NARX models reduce the mean squared error to 0.1048% and 0.0175% in comparison to their standalone counterparts which show the lowest corresponding error values of 0.271% and 0.0236% respectively. Furthermore, an additional reference univariate model, Holt-Winters Exponential Smoothing (HWES), is analyzed (by replacing <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m-AIC</i> ) for a comparative performance evaluation in both standalone and unified manners. Recommendations for usage of the preferred respective models in either manner for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SOC</i> forecasting are also presented based on epochs and error values.