Detection and Prognostics on Low-Dimensional Systems

This paper describes the application of known and novel prognostic algorithms on systems that can be described by low-dimensional, potentially nonlinear dynamics. The methods rely on estimating the conditional probability distribution of the output of the system at a future time given knowledge of the current state of the system. We show how to estimate these conditional probabilities using a variety of techniques, including bagged neural networks and kernel methods such as Gaussian process regression (GPR). The results are compared with standard method such as the nearest neighbor algorithm. We demonstrate the algorithms on a real-world dataset and a simulated dataset. The real-world dataset consists of the intensity of an NH₃ laser. The laser dataset has been shown by other authors to exhibit low-dimensional chaos with sudden drops in intensity. The simulated dataset is generated from the Lorenz attractor and has known statistical characteristics. On these datasets, we show the evolution of the estimated conditional probability distribution, the way it can act as a prognostic signal, and its use as an early warning system. We also review a novel approach to perform GPR with large numbers of data points.