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This is a preprint of a manuscript submitted for publication.Good state of charge estimation in lithium-sulfur batteries (Li-S) is vital, as the simplest convention methods commonly used in lithium-ion batteries - open-circuit voltage measurement and 'coulomb counting' - are often ineffective for Li-S. Since Li-S is a new battery chemistry, there are few published techniques. Existing techniques based on the extended Kalman filter and the unscented Kalman filter have shown some promise, existing work has explored only one of many possible estimator architectures: a single filter based on a pre-calibrated behavioural reparameterization of an equivalent circuit network whose parameters vary as a function of state of charge and temperature. Such filters have been shown to be reasonably effective in practical cases, but they can converge slowly if initial conditions are unknown, and they can become inaccurate with changes in current density. It is desirable to understand whether other possible estimator architectures offer improved performance. One such alternative architecture is the 'dual extended Kalman filter', which uses voltage and current measurements to estimate into a short-term dynamic circuit parameters then uses the outputs of this in a slower-acting state-of-charge estimator. This paper develops a `behavioural' form of the dual extended Kalman filter, and applies this to a lithium-sulfur battery. The estimator is adapted with a term to model circuit current dependence, and demonstrated using pulse-discharge tests and scaled automotive driving cycles and more for partially discharged batteries. Compared to the published state-of-the-art, the new estimators can be almost 30% for batteries that are initially partially discharged; the new estimators also converge faster. The resulting estimators have the potential to be extended to state-of-health measures, and the 'behavioural' circuit reparameterization is likely to be of use for other battery chemistries beside lithium-sulfur..

Presentation given at ICLSB 2019. Abstract follows:It is well known that lithium sulfur cells have a distinctive open-circuit voltage profile: at high states of charge there is a ‘high plateau’, starting at around 2.35 V, and at low states of charge there is a flatter ‘low plateau’ at near constant voltage. This presentation will discuss the implications this profile might have for the prediction of the work that cell is capable of doing before it is fully discharged, which is vital for real-world applications. This presentation will introduce a family of techniques that has been developed for the creation of low-complexity dynamic models [1,2] and their application in state estimation algorithms embedded within real-life battery management systems using extended Kalman filters, unscented Kalman filters and particle filters [3,4] or adaptive neuro-fuzzy inference systems (ANFIS) [5]. So far, algorithms for management of lithium-sulfur have all been based on state of charge, rather than ‘remaining energy’. In a practical application, the real information the end user needs is an answer to the question ‘how much work can I still do?’ The work done by a cell is the product of the terminal voltage and the current delivered to the load, and a Coulomb-based metric, dependent on current alone, is only a proxy for this. In this presentation, we explore the question ‘how accurate is state of charge as a predictor of remaining useful work?’ In this presentation, the title question is addressed, both using theoretical and simulation studies comparing a lithium-ion cell [6] from the literature with a model of development-grade industrial lithium sulfur cell [1] and through the analysis of experimental data collected from the same lithium-sulfur cell. In the theoretical studies, it is observed that with low currents, state of charge is a good predictor of remaining useful work in both the lithium-ion cell and the lithium-sulfur one, but that where the remaining useful work predictions for the lithium-ion cell are least accurate at the mid-discharge point, the remaining useful work predictions for the lithium-sulfur cell were least accurate near to the transition between the high and low plateau. The results of the theoretical analysis were supported by an analysis of the experimental data. From these results, no significant motivation was been identified for refactoring estimation algorithms in terms of state of energy. At the time this abstract is prepared, work to consider the accuracy of prediction of remaining useful work at higher loads is underway, and the results of this will also be presented at the conference. [1] Propp K, Marinescu M, Auger DJ, O'Neill L, Fotouhi A, Somasundaram K, Offer GJ, Minton G, Longo S, Wild M & Knap V (2016) Multi-temperature state-dependent equivalent circuit discharge model for lithium-sulfur batteries, Journal of Power Sources, 328 (October) 289-299. Dataset/s: 10.17862/cranfield.rd.c.3292031 [2] Fotouhi A, Auger DJ, Propp K, Longo S, Purkayastha R, O'Neill L & Walus S (2017) Lithium-Sulfur cell equivalent circuit network model parameterization and sensitivity analysis, IEEE Transactions on Vehicular Technology, 66 (9) 7711-7721. [3] Propp K, Auger DJ, Fotouhi A, Longo S & Knap V (2017) Kalman-variant estimators for state of charge in lithium-sulfur batteries, Journal of Power Sources, 343 (March) 254-267. Dataset/s: 10.17862/cranfield.rd.3834057 [4] Knap V, Auger DJ, Propp K, Fotouhi A & Stroe D-I (2018) Concurrent real-time estimation of state of health and maximum available power in lithium-sulfur batteries, Energies, 11 (2133) 1-23. [5] Fotouhi A, Auger D, Propp K & Longo S (2018) Lithium-sulfur battery state-of-charge observability analysis and estimation, IEEE Transactions on Power Electronics, 33 (7) 5847-5859. [6] Antaloae C, Marco J & Assadian F (2012) A novel method for the parameterization of a Li-ion cell model for EV/HEV control applications. IEEE Transactions on Vehicular Technology, 61(9), 3881–3892. https://doi.org/10.1109/TVT.2012.2212474

Additional file 1: Figure S1. Examples showing the measurement of displacement SNR for a typical study (a) and for a stimulated case of low SNR (b). Table S1. Mean and standard deviation of radia strain for healthy volunteers and patients

Additional file 2: Figure S1. Bland–Altman plots for global (A) and segmental (B) radial strains at end systole of basal, mid-ventricular, and apical slices computed using the conventional user-assisted and the fully-automated DL methods. Table S1. Mean and standard deviation of radia strain for healthy subjects and patients

Background\ud \ud Segmental extent of infarction assessed by late gadolinium enhancement (LGE) imaging early post‐ST‐segment elevation myocardial infarction (STEMI) has utility in predicting left ventricular functional recovery.\ud \ud Hypothesis:\ud \ud We hypothesized that segmental circumferential strain with displacement encoding with stimulated echoes (DENSE) would be a stronger predictor of infarct transmurality than feature‐tracking strain, and noninferior to extracellular volume fraction (ECV).\ud \ud Study Type:\ud \ud Prospective.\ud \ud Population:\ud \ud Fifty participants (mean ± SD, 59 ± 9 years, 40 [80%] male) underwent cardiac MRI on day 1 post‐STEMI.\ud \ud Field‐Strength/Sequences:\ud \ud 1.5T/cine, DENSE , T1 mapping, ECV , LGE.\ud Assessment\ud \ud Two observers assessed segmental percentage LGE extent, presence of microvascular obstruction (MVO), circumferential and radial strain with DENSE and feature‐tracking, T1 relaxation times, and ECV.\ud \ud Statistical Tests:\ud \ud Normality was tested using the Shapiro–Wilk test. Skewed distributions were analyzed utilizing Mann–Whitney or Kruskal–Wallis tests and normal distributed data using independent t ‐tests. Diagnostic cutoff values were identified using the Youden index. The difference in area under the curve was compared using the z‐statistic.\ud \ud Results:\ud \ud Segmental circumferential strain with DENSE was associated with the extent of infarction ≥50% (AUC [95% CI], cutoff value = 0.9 [0.8, 0.9], −10%) similar to ECV (AUC = 0.8 [0.8, 0.9], 37%) (P = 0.117) and superior to feature‐tracking circumferential strain (AUC = 0.7[0.7, 0.8], −19%) (P