Monotonic regression filters for trending deterioration faults

This paper describes optimal nonlinear filtering algorithms for recovering trends of system performance variables (fault intensities) from noisy sensor data. A key underlying assumption for the algorithms is that the performance can only deteriorate with time, never improve. This assumption describes accumulating damage to the system components. Mathematically, the trend is obtained as a maximum likelihood estimate of an orbit in a hidden Markov model from the noisy output data. The empirical signal model and the overall problem setup are very close to optimal Kalman filtration. The main difference is that instead of a Gaussian noise driving the random model of the fault a one sided exponentially distributed noise is assumed. Such a statistical model leads to a nonlinear batch filter. The trend is estimated by solving a quadratic programming problem. Unlike Kalman filters that can be implemented through recursive computations, the developed algorithms run in a batch mode. Though being more complex computationally, the developed trending algorithms demonstrate the performance superior to Kalman filters in the fault trending applications.