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Longevity and safety of lithium-ion batteries are facilitated by efficient monitoring and adjustment of the battery operating conditions. Hence, it is crucial to implement fast and accurate algorithms for State of Health (SoH) monitoring on the Battery Management System. The task is challenging due to the complexity and multitude of the factors contributing to the battery degradation, especially because the different degradation processes occur at various timescales and their interactions play an important role. Data-driven methods bypass this issue by approximating the complex processes with statistical or machine learning models. This paper proposes a data-driven approach which is understudied in the context of battery degradation, despite its simplicity and ease of computation: the Multivariable Fractional Polynomial (MFP) regression. Models are trained from historical data of one exhausted cell and used to predict the SoH of other cells. The data are characterised by varying loads simulating dynamic operating conditions. Two hypothetical scenarios are considered: one assumes that a recent capacity measurement is known, the other is based only on the nominal capacity. It was shown that the degradation behaviour of the batteries under examination is influenced by their historical data, as supported by the low prediction errors achieved (root mean squared errors from 1.2% to 7.22% when considering data up to the battery End of Life). Moreover, we offer a multi-factor perspective where the degree of impact of each different factor is analysed. Finally, we compare with a Long Short-Term Memory Neural Network and other works from the literature on the same dataset. We conclude that the MFP regression is effective and competitive with contemporary works, and provides several additional advantages e.g. in terms of interpretability, generalisability, and implementability., Comment: 45 pages, 7 figures, 3 tables

When applying principal component analysis (PCA) for dimension reduction, the most varying projections are usually used in order to retain most of the information. For the purpose of anomaly and change detection, however, the least varying projections are often the most important ones. In this article, we present a novel method that automatically tailors the choice of projections to monitor for sparse changes in the mean and/or covariance matrix of high-dimensional data. A subset of the least varying projections is almost always selected based on a criteria of the projection's sensitivity to changes. Our focus is on online/sequential change detection, where the aim is to detect changes as quickly as possible, while controlling false alarms at a specified level. A combination of tailored PCA and a generalized log-likelihood monitoring procedure displays high efficiency in detecting even very sparse changes in the mean, variance and correlation. We demonstrate on real data that tailored PCA monitoring is efficient for sparse change detection also when the data streams are highly auto-correlated and non-normal. Notably, error control is achieved without a large validation set, which is needed in most existing methods., Comment: 26 pages, 13 figures

We consider the problems of variable selection and estimation in nonparametric additive regression models for high-dimensional data. In recent years, several methods have been proposed to model nonlinear relationships when the number of covariates exceeds the number of observations by using spline basis functions and group penalties. Nonlinear {\it monotone} effects on the response play a central role in many situations, in particular in medicine and biology. We construct the monotone splines lasso (MS-lasso) to select variables and estimate effects using monotone spline (I-splines). The additive components in the model are represented by their I-spline basis function expansion and the component selection becomes that of selecting the groups of coefficients in the I-spline basis function expansion. We use a recent procedure, called cooperative lasso, to select sign-coherent groups, that is selecting the groups with either exclusively non-negative or non-positive coefficients. This leads to the selection of important covariates that have nonlinear monotone increasing or decreasing effect on the response. We also introduce an adaptive version of the MS-lasso which reduces both the bias and the number of false positive selections considerably. We compare the MS-lasso and the adaptive MS-lasso with other existing methods for variable selection in high dimensions by simulation and illustrate the method on two relevant genomic data sets. Results indicate that the (adaptive) MS-lasso has excellent properties compared to the other methods both by means of estimation and selection, and can be recommended for high-dimensional monotone regression., Comment: 19 pages, 4 figures and 7 tables

We propose a new approach to safe variable preselection in high-dimensional penalized regression, such as the lasso. Preselection - to start with a manageable set of covariates - has often been implemented without clear appreciation of its potential bias. Based on sequential implementation of the lasso with increasing lists of predictors, we find a new property of the set of corresponding cross-validation curves, a pattern that we call freezing. It allows to determine a subset of covariates with which we reach the same lasso solution as would be obtained using the full set of covariates. Freezing has not been characterized before and is different from recently discussed safe rules for discarding predictors. We demonstrate by simulation that ranking predictors by their univariate correlation with the outcome, leads in a majority of cases to early freezing, giving a safe and efficient way of focusing the lasso analysis on a smaller and manageable number of predictors. We illustrate the applicability of our strategy in the context of a GWAS analysis and on microarray genomic data. Freezing offers great potential for extending the applicability of penalized regressions to ultra highdimensional data sets. Its applicability is not limited to the standard lasso but is a generic property of many penalized approaches., Comment: This paper has been withdrawn by the authors because of a mistake

The immense increase in the generation of genomic scale data poses an unmet analytical challenge, due to a lack of established methodology with the required flexibility and power. We propose a first principled approach to statistical analysis of sequence-level genomic information. We provide a growing collection of generic biological investigations that query pairwise relations between tracks, represented as mathematical objects, along the genome. The Genomic HyperBrowser implements the approach and is available at http://hyperbrowser.uio.no.