Methods of Identifying Correlated Model Parameters with Noise in Prognostics

In physics-based prognostics, model parameters are estimated by minimizing the error or maximizing the likelihood between model predictions and measured data. When multiple model parameters are strongly correlated, it is challenging to identify individual parameters by measuring degradation data, especially when the data have noise. This paper first presents various correlations that occur during the process of model parameter estimation and then introduces two methods of identifying the accurate values of individual parameters when they are strongly correlated. The first method can be applied when the correlation relationship evolves as damage grows, while the second method can be applied when the operating (loading) conditions change. Starting from manufactured data using the true parameters, the accuracy of identified parameters is compared with various levels of noise. It turned out that the proposed method can identify the accurate values of model parameters even with a relatively large level of noise. In terms of the marginal distribution, the standard deviation of a model parameter is reduced from 0.125 to 0.03 when different damage states are used. When the loading conditions change, the uncertainty is reduced from 0.3 to 0.05. Both are considered as a significant improvement.