Application of soft-DTW for Time Series Data Averaging Inside a Rotating Detonation Combustor

Applications of high-speed diagnostics can help understand the structure and dynamics
of detonation waves in RDCs. Phase averaging can be applied to resolve the circumferential
detonation structure. However, a high level of stochasticity has been observed in RDC
experimental data. As a result of this variability, when several data samples are averaged using
the conventional arithmetic mean, data features can be distorted or overlooked. This can easily
lead to an erroneous characterization of the wave structure and flow field inside an RDC. In
order to obtain a more accurate representation of the underlying data, this work investigates
the application of three different averaging techniques: the Euclidean distance based arithmetic
mean, the DTW Barycenter Averaging (DBA) and soft-DTW barycenter. Results show that the
Euclidean barycenter does not capture well the sharpness of the detonation front while the DTW
Barycenter Averaging absorbs the idiosyncrasies of the data resulting in a discontinuous average
that is not characteristic of any of the time series. Soft-DTW based averaging overcomes these
limitations through the introduction of a smoothing parameter and yields a more representative
average of RDC time series data. In addition, soft-DTW based averaging is less sensitive to
small perturbations in the data and can construct a representative average of the data from
fewer data samples