Path-based splitting methods for SDEs and machine learning for battery lifetime prognostics

In the first half of this Thesis, we present the numerical analysis of splitting methods for stochastic differential equations (SDEs) using a novel path-based approach. The application of splitting methods to SDEs can be viewed as replacing the driving Brownian-time path with a piecewise linear path, producing a ‘controlled-differential-equation’ (CDE). By Taylor expansion of the SDE and resulting CDE, we show that the global strong and weak errors of splitting schemes can be obtained by comparison of the iterated integrals in each. Matching all integrals up to order p+1 in expectation will produce a weak order p+0.5 scheme, and in addition matching the integrals up to order p+0.5 strongly will produce a strong order p scheme. In addition, we present new splitting methods utilising the ‘space-time’ L´evy area of Brownian motion which obtain global strong Oph1.5q and Oph2q weak errors for a class of SDEs satisfying a commutativity condition. We then present several numerical examples including Multilevel Monte Carlo. In the second half of this Thesis, we present a series of papers focusing on lifetime prognostics for lithium-ion batteries. Lithium-ion batteries are fuelling the advancing renewable-energy based world. At the core of transformational developments in battery design, modelling and management is data. We start with a comprehensive review of publicly available datasets. This is followed by a study which explores the evolution of internal resistance (IR) in cells, introducing the original concept of ‘elbows’ for IR. The IR of cells increases as a cell degrades and this often happens in a non-linear fashion: where early degradation is linear until an inflection point (the elbow) is reached followed by increased rapid degradation. As a follow up to the exploration of IR, we present a model able to predict the full IR and capacity evolution of a cell from one charge/discharge cycle. At the time of publication, this represented a significant reduction (100x) in the number of cycles required for prediction. The published paper was the first to show that such results were possible. In the final paper, we consider experimental design for battery testing. Where we focus on the important question of how many cells are required to accurately capture statistical variation

Algorithms for Fault Detection and Diagnosis

Due to the increasing demand for security and reliability in manufacturing and mechatronic systems, early detection and diagnosis of faults are key points to reduce economic losses caused by unscheduled maintenance and downtimes, to increase safety, to prevent the endangerment of human beings involved in the process operations and to improve reliability and availability of autonomous systems. The development of algorithms for health monitoring and fault and anomaly detection, capable of the early detection, isolation, or even prediction of technical component malfunctioning, is becoming more and more crucial in this context. This Special Issue is devoted to new research efforts and results concerning recent advances and challenges in the application of “Algorithms for Fault Detection and Diagnosis”, articulated over a wide range of sectors. The aim is to provide a collection of some of the current state-of-the-art algorithms within this context, together with new advanced theoretical solutions

A Study of Computationally Efficient Advanced Battery Management: Modeling, Identification, Estimation and Control

Lithium-ion batteries (LiBs) are a revolutionary technology for energy storage. They have become a dominant power source for consumer electronics and are rapidly penetrating into the sectors of electrified transportation and renewable energies, due to the high energy/power density, long cycle life and low memory effect. With continuously falling prices, they will become more popular in foreseeable future. LiBs demonstrate complex dynamic behaviors and are vulnerable to a number of operating problems including overcharging, overdischarging and thermal runaway. Hence, battery management systems (BMSs) are needed in practice to extract full potential from them and ensure their operational safety. Recent years have witnessed a growing amount of research on BMSs, which usually involves topics such as dynamic modeling, parameter identification, state estimation, cell balancing, optimal charging, thermal management, and fault detection. A common challenge for them is computational efficiency since BMSs typically run on embedded systems with limited computing and memory capabilities. Inspired by the challenge, this dissertation aims to address a series of problems towards advancing BMSs with low computational complexity but still high performance. Specifically, the efforts will focus on novel battery modeling and parameter identification (Chapters 2 and 3), highly efficient optimal charging control (Chapter 4) and spatio-temporal temperature estimation of LiB packs (Chapter 5). The developed new LiB models and algorithms can hopefully find use in future LiB systems to improve their performance, while offering insights into some key challenges in the field of BMSs. The research will also entail the development of some fundamental technical approaches concerning parameter identification, model predictive control and state estimation, which have a prospect of being applied to dynamic systems in various other problem domains

Optimising investments in battery storage and green hydrogen production

Energy systems are undergoing a transition towards low-carbon alternatives, but intermittent renewable sources like wind and solar pose challenges. Battery storage and hydrogen technologies, offer potential solutions with numerous benefits. They can enhance grid stability, improve power quality, and decarbonise industries like heavy manufacturing, heating, and shipping. Both batteries and hydrogen complement renewables by storing excess power and using curtailed energy. To drive the widespread adoption of low-carbon energy technologies, it is crucial to establish its economic viability. This research focuses on optimising the revenues of low-carbon energy investments, specifically battery storage and green hydrogen production. It explores three key areas: determining the optimal usage of these technologies, identifying the best deployment locations, and addressing uncertainties. In terms of usage, the research analyses various case studies and modelling techniques. It applies optimisation models to energy markets, examines community-owned battery projects, and combines machine learning with optimisation models to maximise battery revenues across different market segments. Additionally, the research explores the optimal investment and usage of PEM electrolysers within wind farms to produce green hydrogen, using optimisation models and real options analysis