Triple decomposition is a powerful analytical method for a deep understanding of the flow structure by extracting the mean value, organized coherent motion, and stochastic part from a fluctuating quantity. Here, we perform the triple decomposition of the spatial two-dimensional data, especially pressure-sensitive paint (PSP) data, since the PSP method is widely used to measure the pressure distribution on a surface in wind tunnel testing. However, the PSP data measuring near atmospheric pressure contain significant noise, and this makes it difficult to conduct the decomposition. 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, and the PSP data are successfully decomposed. Moreover, we consider sparse optimal sensor positions, in which the data are effectively represented, based on the stochastic part as a data-driven approach. The optimal sensor positions are determined as a combinatorial optimization problem and estimated using Fujitsu computing as a service digital annealer. We reconstruct the pressure distribution from the pressure data at the optimal sensor positions using the mean value, organized coherent motion, and stochastic part obtained from the triple decomposition. 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 detailed flow analysis.
