Orbits for eighteen visual binaries and two double-line spectroscopic binaries observed with HRCAM on the CTIO SOAR 4m telescope, using a new Bayesian orbit code based on Markov Chain Monte Carlo

We present orbital elements and mass sums for eighteen visual binary stars of spectral types B to K (five of which are new orbits) with periods ranging from 20 to more than 500 yr. For two double-line spectroscopic binaries with no previous orbits, the individual component masses, using combined astrometric and radial velocity data, have a formal uncertainty of ~0.1 MSun. Adopting published photometry, and trigonometric parallaxes, plus our own measurements, we place these objects on an H-R diagram, and discuss their evolutionary status. These objects are part of a survey to characterize the binary population of stars in the Southern Hemisphere, using the SOAR 4m telescope+HRCAM at CTIO. Orbital elements are computed using a newly developed Markov Chain Monte Carlo algorithm that delivers maximum likelihood estimates of the parameters, as well as posterior probability density functions that allow us to evaluate the uncertainty of our derived parameters in a robust way. For spectroscopic binaries, using our approach, it is possible to derive a self-consistent parallax for the system from the combined astrometric plus radial velocity data ("orbital parallax"), which compares well with the trigonometric parallaxes. We also present a mathematical formalism that allows a dimensionality reduction of the feature space from seven to three search parameters (or from ten to seven dimensions - including parallax - in the case of spectroscopic binaries with astrometric data), which makes it possible to explore a smaller number of parameters in each case, improving the computational efficiency of our Markov Chain Monte Carlo code.Comment: 32 pages, 9 figures, 6 tables. Detailed Appendix with methodology. Accepted by The Astronomical Journa

Prognostics

Knowledge discovery, statistical learning, and more specifically an understanding of the system evolution in time when it undergoes undesirable fault conditions, are critical for an adequate implementation of successful prognostic systems. Prognosis may be understood as the generation of long-term predictions describing the evolution in time of a particular signal of interest or fault indicator, with the purpose of estimating the remaining useful life (RUL) of a failing component/subsystem. Predictions are made using a thorough understanding of the underlying processes and factor in the anticipated future usage

Optimal observational scheduling framework for binary and multiple stellar systems

The optimal instant of observation of astrophysical phenomena for objects that vary on human time-sales is an important problem, as it bears on the cost-effective use of usually scarce observational facilities. In this paper we address this problem for the case of tight visual binary systems through a Bayesian framework based on the maximum entropy sampling principle. Our proposed information-driven methodology exploits the periodic structure of binary systems to provide a computationally efficient estimation of the probability distribution of the optimal observation time. We show the optimality of the proposed sampling methodology in the Bayes sense and its effectiveness through direct numerical experiments. We successfully apply our scheme to the study of two visual-spectroscopic binaries, and one purely astrometric triple hierarchical system. We note that our methodology can be applied to any time-evolving phenomena, a particularly interesting application in the era of dedicated surveys, where a definition of the cadence of observations can have a crucial impact on achieving the science goals.Comment: Accepted for publication to PASP. 23 pages, 2 Tables, 9 Figures, 2 Appendice

Uncertainty in PHM

Uncertainty plays an important role in diagnostics, prognostics, and health management of engineering systems. The presence of uncertainty leads to an imprecise understanding of the behavior of such systems; as a result, this may adversely affect the results of diagnostics and prognostics. In particular, this may lead to an inaccurate estimation of the remaining useful life, which in turn affects operational decision-making. While several researchers have recognized the importance of uncertainty in prognostics and health management (PHM), there has not been a significant amount of research work that addresses the impact of uncertainty in different PHM activities. This is challenging because there are various sources of uncertainty that affect PHM, their interactions are not fully understood, and therefore, it is an arduous task to perform different PHM activities by systematically accounting for these sources of uncertainty. However, when this can be accomplished, it would be possible to estimate the uncertainty and confidence in the results of diagnostics and prognostics, and quantify the risk involved in prognostics-based decisionmaking

Computation of time probability distributions for the occurrence of uncertain future events

The determination of the time at which an event may take place in the future is a well-studied problem in a number of science and engineering disciplines. Indeed, for more than fifty years, researchers have tried to establish adequate methods to characterize the behaviour of dynamic systems in time and implement predictive decision-making policies. Most of these efforts intend to model the evolution in time of nonlinear dynamic systems in terms of stochastic processes; while defining the occurrence of events in terms of first-passage time problems with thresholds that could be either deterministic or probabilistic in nature. The random variable associated with the occurrence of such events has been determined in closed-form for a variety of specific continuous-time diffusion models, being most of the available literature motivated by physical phenomena. Unfortunately, literature is quite limited in terms of rigorous studies related to discrete-time stochastic processes, despite the tremendous amount of digital information that is currently being collected worldwide. In this regard, this article provides a mathematically rigorous formalization for the problem of computing the probability of occurrence of uncertain future events in both discrete- and continuous-time stochastic processes, by extending the notion of thresholds in first-passage time problems to a fully probabilistic notion of “uncertain events” and “uncertain hazard zones”. We focus on discrete-time applications by showing how to compute those probability measures and validate the proposed framework by comparing to the results obtained with Monte Carlo simulations; all motivated by the problem of fatigue crack growth prognosis

Dynamic Average Consensus with Anti-windup applied to Interlinking Converters in AC/DC Microgrids under Economic Dispatch and Delays

This work proposes an application of dynamic average consensus in interlinking converters of AC/DC microgrids with a distributed anti-windup for dealing with steady-state errors from communication delays. The proposed controller consists of a PI control that looks after the power-sharing between interlinking converters while achieving a global incremental cost consensus. The controller uses an observer (by dynamic average consensus) for estimating the average power of the interlinking converter cluster; this method represents an alternative formulation to conventional single-integrator consensus. An anti-windup with reset scheme is proposed to reduce steady-state errors in presence of fixed time delays. Stability analyses are also presented as well as simulations. Both show that the proposed controller successfully balances the power between interlinking converters being comparable with similar approaches in the literature

Multiple-imputation-particle-filtering for Uncertainty Characterization in Battery State-of-Charge Estimation Problems with Missing Measurement Data: Performance Analysis and Impact on Prognostic Algorithms

The implementation of particle-filtering-based algorithms for state estimation purposes often has to deal with the problem of missing observations. An efficient design requires an appropriate methodology for real-time uncertainty characterization within the estimation process, incorporating knowledge from other available sources of information. This article analyzes this problem and presents preliminary results for a multiple imputation strategy that improves the performance of particle-filtering-based state-of-charge (SOC) estimators for lithium-ion (Li-Ion) battery cells. The proposed uncertainty characterization scheme is tested, and validated, in a case study where the state-space model requires both voltage and discharge current measurements to estimate the SOC. A sudden disconnection of the battery voltage sensor is assumed to cause significant loss of data. Results show that the multipleimputation particle filter allows reasonable characterization of uncertainty bounds for state estimates, even when the voltage sensor disconnection continues. Furthermore, if voltage measurements are once more available, the uncertainty bounds adjust to levels that are comparable to the case where data were not lost. As state estimates are used as initial conditions for battery End-of-Discharge (EoD) prognosis modules, we also studied how these multiple-imputation algorithms impact on the quality of EoD estimates

Residual-based scheme for detection and characterization of faults in lithium-ion batteries

This work proposes a real-time scheme to monitor the occurrence of faults and perform fault characterization. Faults, in this context, correspond to changes in the parameters of the system being monitored. The method relies on the concept of Analytical Redundancy Relation (ARR), which can be defined as the evaluation of the mathematical constraints of the physical model of the system given the real, noisy measurements. The algorithm consists of two modules: a detection strategy that relies on the regular application of an ARR-based hypothesis test in discrete time-steps; and an optimization procedure to estimate the changes undergone after a fault. By selecting a set of feasible solutions from the output of the optimization algorithm, the method also sheds some light on the uncertainty associated to the estimated quantities. The methodology is tested on simulated data of lithium-ion batteries in unmanned aerial vehicles