No abstract

This paper deals with the problem of blind source separation (BSS), where observed signals are a mixture of delayed sources. In reference to a previous work, when the delay time is small such that the first‐order Taylor approximation holds, delayed observations are transformed into an instantaneous mixture of original sources and their derivatives, for which an extended second‐order blind identification (SOBI) approach is used to recover sources. Inspired by the results of this previous work, we propose to generalize its first‐order Taylor approximation to suit higher‐order approximations in the case of a large delay time based on a similar version of its extended SOBI. Compared to SOBI and its extended version for a first‐order Taylor approximation, our method is more efficient in terms of separation quality when the delay time is large. Simulation results verify the performance of our approach under different time delays and signal‐to‐noise ratio conditions, respectively.

To accurately measure the near-wall flow by particle image velocimetry (PIV) is a big challenge, especially for the slip boundary condition. Apart from high-precision measurements, an appropriate PIV algorithm is important to resolve the near-wall velocity profile. In our study, single-pixel algorithm is employed to calculate the near-wall flow, which is demonstrated to be capable of accurately resolving the flow velocity near the slip boundary condition. Based on the synthetic particle images, the advantages of the single-pixel algorithm are manifested in comparison with the conventional window correlation algorithm. Specially, the single-pixel algorithm has higher spatial resolution and accuracy, and lower systematic error and random error for the case of slip boundary condition. Furthermore, for experimental verification, micro-PIV measurements are conducted over a liquid-gas interface and the single-pixel algorithm is successfully applied to the calculation of near-wall velocity under the slip boundary condition, especially the negative slip velocity. The current work demonstrates the advantage of the single-pixel algorithm in analyzing the complex flow under the slip boundary condition, such as drag reduction, wall skin friction evaluation and near-wall vortex structure measurement.

Accurate particle image velocimetry (PIV) measurement near the wall is of great significance in many fields. However, it is challenging for conventional PIV algorithms to deal with the near-wall flow, especially under the slip boundary condition. In general, the conventional window correlation method cannot accurately calculate the flow velocity at any location that is less than half size of the interrogation window away from the boundary. For steady or periodic flow, the single-pixel ensemble correlation method can estimate the velocity very near the wall, but a large number of image pairs are required, which greatly comes at a great computational cost. In this paper, a new method based on window deformation (WD) is proposed to estimate the velocity profile of near-wall flows. Furthermore, a multi-pixel ensemble correlation (MPEC) method is proposed based on the single-pixel method, which improves accuracy and significantly reduces the computational cost relative to the single-pixel method. Both methods are validated by synthetic particle images and experiments. The current work extends the PIV methodology for accurately measuring the near-wall flows, especially under the slip boundary condition, which will benefit the research on boundary layer, drag reduction, microfluidics, etc.