Wave Sequential Data Assimilation in Support of Wave Energy Converter Power Prediction

Integration of renewable power sources into grids remains an active research and development area, particularly for less developed renewable energy technologies such as wave energy converters (WECs). WECs are projected to have strong early market penetration for remote communities, which serve as natural microgrids. Hence, accurate wave predictions to manage the interactions of a WEC array with microgrids is especially important. Recently developed, low-cost wave measurement buoys allow for operational assimilation of wave data at remote, site specific locations where real-time data have previously been unavailable. We present the development and assessment of a wave modeling framework with real-time data assimilation capabilities for WEC power prediction. The availability of real-time wave spectra from low-cost wave measurement buoys allows for operational data assimilation with the ensemble Kalman filter technique within a hybrid modeling procedure whereby physics-based numerical wave models are combined with data-driven error models that aim to capture the discrepancy in prescribed boundary conditions. With that aim, measured wave spectra are assimilated for combined state and parameter estimation while taking into account model and observational errors. The analysis allows for more accurate and precise wave characteristic predictions at the locations of interest. Initial deployment data obtained offshore Yakutat, Alaska, indicated that measured wave data from one buoy that were assimilated into the wave modeling framework resulted in improved forecast skill in comparison to traditional numerical forecasts

Sequential Monte Carlo smoothing with application to parameter estimation in non-linear state space models

This paper concerns the use of sequential Monte Carlo methods (SMC) for smoothing in general state space models. A well-known problem when applying the standard SMC technique in the smoothing mode is that the resampling mechanism introduces degeneracy of the approximation in the path space. However, when performing maximum likelihood estimation via the EM algorithm, all functionals involved are of additive form for a large subclass of models. To cope with the problem in this case, a modification of the standard method (based on a technique proposed by Kitagawa and Sato) is suggested. Our algorithm relies on forgetting properties of the filtering dynamics and the quality of the estimates produced is investigated, both theoretically and via simulations.Comment: Published in at http://dx.doi.org/10.3150/07-BEJ6150 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Online data processing: comparison of Bayesian regularized particle filters

The aim of this paper is to compare three regularized particle filters in an online data processing context. We carry out the comparison in terms of hidden states filtering and parameters estimation, considering a Bayesian paradigm and a univariate stochastic volatility model. We discuss the use of an improper prior distribution in the initialization of the filtering procedure and show that the regularized Auxiliary Particle Filter (APF) outperforms the regularized Sequential Importance Sampling (SIS) and the regularized Sampling Importance Resampling (SIR).Comment: Submitted to the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

Online Expectation-Maximization Type Algorithms For Parameter Estimation In General State Space Models

In this paper we present new online algorithms to estimate static parameters in nonlinear non Gaussian state space models. These algorithms rely on online Expectation-Maximization (EM) type algorithms. Contrary to standard Sequential Monte Carlo (SMC) methods recently proposed in the literature, these algorithms do not degenerate over time

A comparison of inferential methods for highly non-linear state space models in ecology and epidemiology

Highly non-linear, chaotic or near chaotic, dynamic models are important in fields such as ecology and epidemiology: for example, pest species and diseases often display highly non-linear dynamics. However, such models are problematic from the point of view of statistical inference. The defining feature of chaotic and near chaotic systems is extreme sensitivity to small changes in system states and parameters, and this can interfere with inference. There are two main classes of methods for circumventing these difficulties: information reduction approaches, such as Approximate Bayesian Computation or Synthetic Likelihood and state space methods, such as Particle Markov chain Monte Carlo, Iterated Filtering or Parameter Cascading. The purpose of this article is to compare the methods, in order to reach conclusions about how to approach inference with such models in practice. We show that neither class of methods is universally superior to the other. We show that state space methods can suffer multimodality problems in settings with low process noise or model mis-specification, leading to bias toward stable dynamics and high process noise. Information reduction methods avoid this problem but, under the correct model and with sufficient process noise, state space methods lead to substantially sharper inference than information reduction methods. More practically, there are also differences in the tuning requirements of different methods. Our overall conclusion is that model development and checking should probably be performed using an information reduction method with low tuning requirements, while for final inference it is likely to be better to switch to a state space method, checking results against the information reduction approach