  Triple decomposition is a useful analytical method for extracting the mean
value, organized coherent motion, and stochastic part from a fluctuating
quantity. Although the pressure-sensitive paint (PSP) method is widely used to
measure the pressure distribution on a surface, the PSP data measuring near
atmospheric pressure contain significant noise. Here, we perform triple
decomposition of noisy PSP data. To construct phase-averaged data representing
an organized coherent motion, we propose a relatively simple method based on a
multi-dimensional scaling plot of the cosine similarity between each PSP datum.
Then, the stochastic part is extracted by selecting phase-averaged data with an
appropriate phase angle based on the similarity between the measurement and
phase-averaged data. As a data-driven approach, we also reconstruct the
pressure distribution based on the triple decomposition and the pressure data
at sparse optimal sensor positions determined from the proper orthogonal
decomposition modes of the stochastic part. The optimal sensor positions are
determined as a combinatorial optimization problem and are estimated using
Fujitsu computing as a service digital annealer. Based on the results obtained,
the root mean square error between the pressure measured by a pressure
transducer and the reconstructed pressure obtained by the proposed method is
small, even when the number of modes and sensor points is small. The
application of PSP measurement is expected to expand further, and the framework
for calculating triple decomposition and sparse representation based on the
decomposition will be useful for flow analysis.
