How good is your predictor? Expanding confidence intervals to define probability densities on adaptive parameters

A method is proposed to measure the performance of linear predictors as they track non-stationary stochastic processes. Classical linear regression techniques are combined with a novel use of instantaneous error to define the likelihood that the coefficients of a linear predictor adequately capture a system´s state. The resultant probability measure serves as a metric of predictor performance: a probability near unity indicates that the predictor is performing well, while a probability near zero indicates the state of the system is poorly captured by the coefficients. The approach is extended to trace coefficients, weighted by these probabilities, as they move about in a space of possible states. The probability measure provides an instantaneous confidence measure of the route that the system proceeds upon within that space: a likelihood roadmap of the state of the system through time. Specifically, the method is applied to the important problem of predicting the vibration signature of rotorcraft gearboxes as they mechanically fail. Actual data from US Navy drivetrain teststands are used to validate the method and underlying assumptions