Data mining of a clean signal from highly noisy data based on compressed data fusion: A fast-responding pressure-sensitive paint application

Abstract

A data mining approach based on compressed data fusion is developed to extract a clean signal from highly noisy data and it has been successfully applied to flow measurement using fast-responding pressure-sensitive paint (fast PSP). In this approach, spatially resolved but noisy full-field data are fused with clean but scattered data to reconstruct full-field clean data. The fusion process is accomplished based on a compressed sensing algorithm, which has shown significantly improved performance compared with low-dimensional analysis. This is because, in low-dimensional analysis such as proper orthogonal decomposition (POD), the selection criteria of proper POD modes for reconstruction are usually based on subjective observation and the mode coefficients can be severely distorted by noise, which restricts the applications of this method to complicated flow phenomena and leads to a low-quality reconstruction. The solutions to these two problems can be expressed via mathematical optimization by determining the optimal coefficients to reconstruct clean data using the most relevant POD modes. Here, compressed sensing is used as a suitable solution to explore the sparse representation of scattered clean data based on the POD modes obtained from noisy full-field data. A high-quality reconstruction can be obtained using the optimized coefficients. The new method is first demonstrated by using fabricated patterns, demonstrating a reduction of 75% in the reconstruction error compared with POD analysis. It is thereafter successfully applied to recover the unsteady pressure field induced by a cylinder wake flow at low speed. Fast PSP measurement and microphones are used to obtain full-field but noisy pressure field data and scattered but clean data, respectively. In the cases of single and step cylinders, the reconstruction errors are approximately 5% and 25%, respectively, and the accuracy of reconstruction depends on the low dimensionality of the flow phenomena and the total number of microphone sensors. The current technique provides a reliable method to recover clean signals from strong noise, with significant potential for applications to flow measurement, control, and monitoring.