arXiv subjects

Mark Cary

Publications and source records attributed to Mark Cary.

3 recordsLinked to original sources

arXiv2026

A Repeated Measurements Approach to $SoH$ Battery Modelling of Cyclic Aged Data in a Laboratory Environment

This document describes the application of a first order linearised nonlinear repeated measurements approach to the analysis of battery cell ageing profiles generated under controlled conditions in a laboratory. The primary advantage of the model is it reflects the obvious structure in the data. Consequently, it is a two-component of variance model: variation within ageing profiles (measurement noise) and variation among ageing profiles (test-to-test or cell-to-cell) variation. Novel regularised iterative generalised least squares parameter identification schemes, with optimal hyper-parameter re-estimation, are used to identify the hierarchical nonlinear model. The training data comprised $SoH$ profiles for 10 cells aged at various constant discharge and charge current cycles at a fixed chamber environmental temperature of 25 [$^\circ$C]. Each cell $SoH$ profile is modelled using a simple power law expression, whereas the variation in ageing parameters is modelled using a single knot cubic B-spline. $SoH$ is accurately predicted to $\pm 0.191\%$ for $SOH \in [0,20]$.

stat.ME↗

arXiv2026

Regularised Iterative Generalised Least Squares with Optimal Selection of the Hyper-Parameter for Identifying Nonlinear Phenomenological Models

In some fields currently dominated by empirical approaches, such as state of health (SoH) prediction for lithium-ion batteries, phenomenological models motivated by quasi-physical thinking contain parameters to be estimated from experimental data. Often the structure of such models yields fully or partially confounded parameters, which are difficult or even impossible to estimate reliably. To preserve the desired model formulation and simultaneously improve the numerical conditioning for the problem we introduce a ridge regression scheme. An automated method is provided, based on information theoretic measures of model performance, which optimises the ridge regression hyper-parameter at each iteration. The formulae presented require fixed point iteration to solve for the hyper-parameter. Given a suitable starting value, analysis demonstrates convergence is very rapid. The optimal hyper-parameter selection mechanism is incorporated within an efficient regularised iterative generalised least squares mechanism, capable of fitting both heteroscedastic and serially correlated data as required. Simulation confirms the efficacy of the overall method.

stat.ME↗

arXiv2026

fSRD: Fuzzy Spectral Region Decomposition -- Automated Multi Operator Koopman Representations via an Adaptive Spectral Learning Architecture

Highly nonlinear chaotic dynamical systems remain difficult to model due to fundamental trade-offs between complexity, expressivity, and data efficiency. Modern machine learning methods achieve strong predictive performance but often rely on a-priori system knowledge or curated data with limited interpretability. Koopman operator theory offers a promising direction via linear representation in an infinite-dimensional observable space. However, many data-driven Koopman methods seek globally valid operators for which useful finite-dimensional spectral embeddings remain difficult to identify under these constraints. To overcome associated limitations, we introduce Fuzzy Spectral Region Decomposition (fSRD), a fully automated learning framework for estimating finite Koopman representation via multiple operators. The proposed method realizes a data-adaptive framework for assembling locally invariant embeddings, termed Invariant Decomposition. fSRD achieves highly accurate linear reconstructions of nonlinear systems while learning finite-dimensional representations of their induced evolution operators, bridging interpretable operator-theoretic models with expressive data-driven sequence learning. These embeddings are adaptively constructed via a global fuzzy tree model, drawing inspiration from fuzzy neural architectures to learn the induced dynamics while prioritizing parsimonious solutions. Empirical results across canonical chaotic systems (e.g., Lorenz and Duffing) and high-dimensional real-world data demonstrate strong predictive accuracy, interpretability, and robust expressivity across data-rich and data-limited regimes, highlighting the method's generality.

cs.LG↗