Functional principal component analysis via regularized Gaussian basis expansions and its application to unbalanced data

Prediction of Lithium-Ion Battery Capacity by Functional Principal Component Analysis of Monitoring Data

The lithium-ion (Li-ion) battery is a promising energy storage technology for electronics, automobiles, and smart grids. Extensive research was conducted in the past to improve the prediction of the remaining capacity of the Li-ion battery. A robust prediction model would improve the battery performance and reliability for forthcoming usage. In the development of a data-driven capacity prediction model of Li-ion batteries, most past studies employed capacity degradation data; however, very few tried using other performance monitoring variables, such as temperature, voltage, and current data, to estimate and predict the battery capacity. In this study, we aimed to develop a data-driven model for predicting the capacity of Li-ion batteries adopting functional principal component analysis (fPCA) applied to functional monitoring data of temperature, voltage, and current observations. The proposed method is demonstrated using the battery monitoring data available in the NASA Ames Prognostics Center of Excellence repository. The main contribution of the study the development of an empirical data-driven model to diagnose the state-of-health (SOH) of Li-ion batteries based on the health monitoring data utilizing fPCA and LASSO regression. The study obtained encouraging battery capacity prediction performance by explaining overall variation through eigenfunctions of available monitored discharge parameters of Li-ion batteries. The result of capacity prediction obtained a root mean square error (RMSE) of 0.009. The proposed data-driven approach performs well for predicting the capacity by employing functional performance measures over the life span of a Li-ion battery.

A note on variable selection in functional regression via random subspace method

Variable selection problem is one of the most important tasks in regression analysis, especially in a high-dimensional setting. In this paper, we study this problem in the context of scalar response functional regression model, which is a linear model with scalar response and functional regressors. The functional model can be represented by certain multiple linear regression model via basis expansions of functional variables. Based on this model and random subspace method of Mielniczuk and Teisseyre (Comput Stat Data Anal 71:725–742, 2014), two simple variable selection procedures for scalar response functional regression model are proposed. The final functional model is selected by using generalized information criteria. Monte Carlo simulation studies conducted and a real data example show very satisfactory performance of new variable selection methods under finite samples. Moreover, they suggest that considered procedures outperform solutions found in the literature in terms of correctly selected model, false discovery rate control and prediction error.