A Modified Whiteness Test for Damage Detection Using Kalman Filter Innovations
Deviations from whiteness in the innovations of a Kalman filter indicate that the filter is not optimal for the given data. Accepting that the disturbances are stationary and white lack of optimality derives from the fact that the values of some parameters have changed between the time the filter was formulated and the present. The parameters that define the filter come from system properties and from the statistics of the disturbances. For the filter to perform effectively as a fault detector it is necessary to ensure that deviations from whiteness are not due to variations in the statistics of the noise. This paper examines the mathematical relation between the covariance function of the innovations and the changes in the disturbance statistics. It is shown that the effect of changes in the noise statistics on the discriminating metric can be minimized by shifting the range of lags for which the metric is evaluated. The fact that the modified whiteness test can retain adequate sensitivity to damage is illustrated numerically.
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