Estimation of Time-Varying Autoregressive Symmetric Alpha Stable
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In the last decade alpha-stable distributions have become a standard model for impulsive data. Especially the linear symmetric alpha-stable processes have found applications in various fields. When the process parameters are time- invariant, various techniques are available for estimation. However, time-invariance is an important restriction given that in many communications applications channels are time-varying. For such processes, we propose a relatively new technique, based on particle filters which obtained great success in tracking applications involving non-Gaussian signals and nonlinear systems. Since particle filtering is a sequential method, it enables us to track the time-varying autoregression coefficients of the alpha-stable processes. The method is tested both for abruptly and slowly changing autoregressive parameters of signals, where the driving noises are symmetric-alpha-stable processes and is observed to perform very well. Moreover, the method can easily be extended to skewed alpha-stable distributions.
A Comparison of Filter-based Approaches for Model-based Prognostics
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Model-based prognostics approaches use domain knowledge about a system and its failure modes through the use of physics-based models. Model-based prognosis is generally divided into two sequential problems: a joint state-parameter estimation problem, in which, using the model, the health of a system or component is determined based on the observations; and a prediction problem, in which, using the model, the state-parameter distribution is simulated forward in time to compute end of life and remaining useful life. The first problem is typically solved through the use of a state observer, or filter. The choice of filter depends on the assumptions that may be made about the system, and on the desired algorithm performance. In this paper, we review three separate filters for the solution to the first problem: the Daum filter, an exact nonlinear filter; the unscented Kalman filter, which approximates nonlinearities through the use of a deterministic sampling method known as the unscented transform; and the particle filter, which approximates the state distribution using a finite set of discrete, weighted samples, called particles. Using a centrifugal pump as a case study, we conduct a number of simulation-based experiments investigating the performance of the different algorithms as applied to prognostics.
Combining Model-Based and Feature-Driven Diagnosis Approaches – A Case Study on Electromechanical Actuators
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Model-based diagnosis typically uses analytical redundancy to compare predictions from a model against observations from the system being diagnosed. However this approach does not work very well when it is not feasible to create analytic relations describing all the observed data, e.g., for vibration data which is usually sampled at very high rates and requires very detailed finite element models to describe its behavior. In such cases, features (in time and frequency domains) that contain diagnostic information are extracted from the data. Since this is a computationally intensive process, it is not efficient to extract all the features all the time. In this paper we present an approach that combines the analytic model-based and feature-driven diagnosis approaches. The analytic approach is used to reduce the set of possible faults and then features are chosen to best distinguish among the remaining faults. We describe an implementation of this approach on the Flyable Electro-mechanical Actuator (FLEA) test bed.