Wind turbine condition assessment through power curve copula modeling

Power curves constructed from wind speed and active power output measurements provide an established method of analyzing wind turbine performance. In this paper it is proposed that operational data from wind turbines are used to estimate bivariate probability distribution functions representing the power curve of existing turbines so that deviations from expected behavior can be detected. Owing to the complex form of dependency between active power and wind speed, which no classical parameterized distribution can approximate, the application of empirical copulas is proposed; the statistical theory of copulas allows the distribution form of marginal distributions of wind speed and power to be expressed separately from information about the dependency between them. Copula analysis is discussed in terms of its likely usefulness in wind turbine condition monitoring, particularly in early recognition of incipient faults such as blade degradation, yaw and pitch errors

Bayesian Methods for Analysis and Adaptive Scheduling of Exoplanet Observations

We describe work in progress by a collaboration of astronomers and statisticians developing a suite of Bayesian data analysis tools for extrasolar planet (exoplanet) detection, planetary orbit estimation, and adaptive scheduling of observations. Our work addresses analysis of stellar reflex motion data, where a planet is detected by observing the "wobble" of its host star as it responds to the gravitational tug of the orbiting planet. Newtonian mechanics specifies an analytical model for the resulting time series, but it is strongly nonlinear, yielding complex, multimodal likelihood functions; it is even more complex when multiple planets are present. The parameter spaces range in size from few-dimensional to dozens of dimensions, depending on the number of planets in the system, and the type of motion measured (line-of-sight velocity, or position on the sky). Since orbits are periodic, Bayesian generalizations of periodogram methods facilitate the analysis. This relies on the model being linearly separable, enabling partial analytical marginalization, reducing the dimension of the parameter space. Subsequent analysis uses adaptive Markov chain Monte Carlo methods and adaptive importance sampling to perform the integrals required for both inference (planet detection and orbit measurement), and information-maximizing sequential design (for adaptive scheduling of observations). We present an overview of our current techniques and highlight directions being explored by ongoing research.Comment: 29 pages, 11 figures. An abridged version is accepted for publication in Statistical Methodology for a special issue on astrostatistics, with selected (refereed) papers presented at the Astronomical Data Analysis Conference (ADA VI) held in Monastir, Tunisia, in May 2010. Update corrects equation (3

Functional approach for excess mass estimation in the density model

We consider a multivariate density model where we estimate the excess mass of the unknown probability density $f$ at a given level $\nu>0$ from $n$ i.i.d. observed random variables. This problem has several applications such as multimodality testing, density contour clustering, anomaly detection, classification and so on. For the first time in the literature we estimate the excess mass as an integrated functional of the unknown density $f$. We suggest an estimator and evaluate its rate of convergence, when $f$ belongs to general Besov smoothness classes, for several risk measures. A particular care is devoted to implementation and numerical study of the studied procedure. It appears that our procedure improves the plug-in estimator of the excess mass.Comment: Published in at http://dx.doi.org/10.1214/07-EJS079 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org