Analysis versus synthesis for trending gas-path measurement time series

Gas-path measurements used to assess the health condition of an engine are corrupted by
noise. Generally, a data cleaning step occurs before proceeding with fault detection and
isolation. Classical linear filters such as the EWMA filter are traditionally used for noise
removal. Unfortunately, these low-pass filters distort trend shifts indicative of faults,
which increases the detection delay. The present paper investigates two new approaches
to nonlinear filtering of time series. On the one hand, the synthesis approach reconstructs
the signal as a combination of elementary signals chosen from a predefined library. On
the other hand, the analysis approach imposes a constraint on the shape of the signal
(e.g., piecewise constant). Both approaches incorporate prior information about the signal
in a different way, but they lead to trend filters that are very capable at noise removal
while preserving at the same time sharp edges in the signal. This is highlighted through
the comparison with a classical linear filter on a batch of synthetic data representative of
typical engine fault profiles.