Gaussian process regression for forecasting battery state of health

Accurately predicting the future capacity and remaining useful life of batteries is necessary to ensure reliable system operation and to minimise maintenance costs. The complex nature of battery degradation has meant that mechanistic modelling of capacity fade has thus far remained intractable; however, with the advent of cloud-connected devices, data from cells in various applications is becoming increasingly available, and the feasibility of data-driven methods for battery prognostics is increasing. Here we propose Gaussian process (GP) regression for forecasting battery state of health, and highlight various advantages of GPs over other data-driven and mechanistic approaches. GPs are a type of Bayesian non-parametric method, and hence can model complex systems whilst handling uncertainty in a principled manner. Prior information can be exploited by GPs in a variety of ways: explicit mean functions can be used if the functional form of the underlying degradation model is available, and multiple-output GPs can effectively exploit correlations between data from different cells. We demonstrate the predictive capability of GPs for short-term and long-term (remaining useful life) forecasting on a selection of capacity vs. cycle datasets from lithium-ion cells.Comment: 13 pages, 7 figures, published in the Journal of Power Sources, 201

Gaussian Process Regression for In-situ Capacity Estimation of Lithium-ion Batteries

Accurate on-board capacity estimation is of critical importance in lithium-ion battery applications. Battery charging/discharging often occurs under a constant current load, and hence voltage vs. time measurements under this condition may be accessible in practice. This paper presents a data-driven diagnostic technique, Gaussian Process regression for In-situ Capacity Estimation (GP-ICE), which estimates battery capacity using voltage measurements over short periods of galvanostatic operation. Unlike previous works, GP-ICE does not rely on interpreting the voltage-time data as Incremental Capacity (IC) or Differential Voltage (DV) curves. This overcomes the need to differentiate the voltage-time data (a process which amplifies measurement noise), and the requirement that the range of voltage measurements encompasses the peaks in the IC/DV curves. GP-ICE is applied to two datasets, consisting of 8 and 20 cells respectively. In each case, within certain voltage ranges, as little as 10 seconds of galvanostatic operation enables capacity estimates with approximately 2-3% RMSE.Comment: 12 pages, 10 figures, submitted to IEEE Transactions on Industrial Informatic

The Role of Monotonicity in the Epistemic Analysis of Strategic Games

It is well-known that in finite strategic games true common belief (or common knowledge) of rationality implies that the players will choose only strategies that survive the iterated elimination of strictly dominated strategies. We establish a general theorem that deals with monotonic rationality notions and arbitrary strategic games and allows to strengthen the above result to arbitrary games, other rationality notions, and transfinite iterations of the elimination process. We also clarify what conclusions one can draw for the customary dominance notions that are not monotonic. The main tool is Tarski's Fixpoint Theorem.Comment: 20 page

Freak Waves in Random Oceanic Sea States

Freak waves are very large, rare events in a random ocean wave train. Here we study the numerical generation of freak waves in a random sea state characterized by the JONSWAP power spectrum. We assume, to cubic order in nonlinearity, that the wave dynamics are governed by the nonlinear Schroedinger (NLS) equation. We identify two parameters in the power spectrum that control the nonlinear dynamics: the Phillips parameter $\alpha$ and the enhancement coefficient $\gamma$. We discuss how freak waves in a random sea state are more likely to occur for large values of $\alpha$ and $\gamma$. Our results are supported by extensive numerical simulations of the NLS equation with random initial conditions. Comparison with linear simulations are also reported.Comment: 7 pages, 6 figures, to be published in Phys. Rev. Let

Black hole hunting in the Andromeda Galaxy

We present a new technique for identifying stellar mass black holes in low mass X-ray binaries (LMXBs), and apply it to XMM-Newton observations of M31. We examine X-ray time series variability seeking power density spectra (PDS) typical of LMXBs accreting at a low accretion rate (which we refer to as Type A PDS); these are very similar for black hole and neutron star LMXBs. Galactic neutron star LMXBs exhibit Type A PDS at low luminosities (~10^36--10^37 erg/s) while black hole LMXBs can exhibit them at luminosities >10^38 erg/s. We propose that Type A PDS are confined to luminosities below a critical fraction of the Eddington limit, $l_c$ that is constant for all LMXBs; we have examined asample of black hole and neutron star LMXBs and find they are all consistent with $l_c$ = 0.10+/-0.04 in the 0.3--10 keV band. We present luminosity and PDS data from 167 observations of X-ray binaries in M31 that provide strong support for our hypothesis. Since the theoretical maximum mass for a neutron star is \~3.1 M_Sun, we therefore assert that any LMXB that exhibits a Type A PDS at a 0.3--10 keV luminosity greater than 4 x 10^37 erg/s is likely to contain a black hole primary. We have found eleven new black hole candidates in M31 using this method. We focus on XMM-Newton observations of RX J0042.4+4112, an X-ray source in M31 and find the mass of the primary to be 7+/-2 M_Sun, if our assumptions are correct. Furthermore, RX J0042.4+4112 is consistently bright in \~40 observations made over 23 years, and is likely to be a persistently bright LMXB; by contrast all known Galactic black hole LMXBs are transient. Hence our method may be used to find black holes in known, persistently bright Galactic LMXBs and also in LMXBs in other galaxies.Comment: 6 Pages, 6 figures. To appear in the conference proceedings of "Interacting Binaries: Accretion, Evolution and Outcomes" (Cefalu, July 4-10 2004

Spectral evolution and the onset of the X-ray GRB afterglow

Based on light curves from the Swift Burst Analyser, we investigate whether a `dip' feature commonly seen in the early-time hardness ratios of Swift-XRT data could arise from the juxtaposition of the decaying prompt emission and rising afterglow. We are able to model the dip as such a feature, assuming the afterglow rises as predicted by Sari & Piran (1999). Using this model we measure the initial bulk Lorentz factor of the fireball. For a sample of 23 GRBs we find a median value of Gamma_0=225, assuming a constant-density circumburst medium; or Gamma_0=93 if we assume a wind-like medium.Comment: 4 pages, 3 figures. To appear in the proceedings of GRB 2010, Annapolis November 2010. (AIP Conference proceedings

The ground state of a class of noncritical 1D quantum spin systems can be approximated efficiently

We study families H_n of 1D quantum spin systems, where n is the number of spins, which have a spectral gap \Delta E between the ground-state and first-excited state energy that scales, asymptotically, as a constant in n. We show that if the ground state |\Omega_m> of the hamiltonian H_m on m spins, where m is an O(1) constant, is locally the same as the ground state |\Omega_n>, for arbitrarily large n, then an arbitrarily good approximation to the ground state of H_n can be stored efficiently for all n. We formulate a conjecture that, if true, would imply our result applies to all noncritical 1D spin systems. We also include an appendix on quasi-adiabatic evolutions.Comment: 9 pages, 1 eps figure, minor change

The SSS phase of RS Ophiuchi observed with Chandra and XMM-Newton I.: Data and preliminary Modeling

The phase of Super-Soft-Source (SSS) emission of the sixth recorded outburst of the recurrent nova RS Oph was observed twice with Chandra and once with XMM-Newton. The observations were taken on days 39.7, 54.0, and 66.9 after outburst. We confirm a 35-sec period on day 54.0 and found that it originates from the SSS emission and not from the shock. We discus the bound-free absorption by neutral elements in the line of sight, resonance absorption lines plus self-absorbed emission line components, collisionally excited emission lines from the shock, He-like intersystem lines, and spectral changes during an episode of high-amplitude variability. We find a decrease of the oxygen K-shell absorption edge that can be explained by photoionization of oxygen. The absorption component has average velocities of -1286+-267 km/s on day 39.7 and of -771+-65 km/s on day 66.9. The wavelengths of the emission line components are consistent with their rest wavelengths as confirmed by measurements of non-self absorbed He-like intersystem lines. We have evidence that these lines originate from the shock rather than the outer layers of the outflow and may be photoexcited in addition to collisional excitations. We found collisionally excited emission lines that are fading at wavelengths shorter than 15A that originate from the radiatively cooling shock. On day 39.5 we find a systematic blue shift of -526+-114 km/s from these lines. We found anomalous He-like f/i ratios which indicates either high densities or significant UV radiation near the plasma where the emission lines are formed. During the phase of strong variability the spectral hardness light curve overlies the total light curve when shifted by 1000sec. This can be explained by photoionization of neutral oxygen in the line of sight if the densities of order 10^{10}-10^{11} cm^{-3}.Comment: 16 pages, 10 figures, 4 tables. Accepted by ApJ; v2: Co-author Woodward adde