Abstract
Techniques for the experimental determination of velocity fields such as particle image velocimetry (PIV) can often be hampered by spurious vectors or sparse regions of measurement which may occur due to a number of reasons. Commonly used methods for detecting and replacing erroneous values are often based on statistical measures of the surrounding vectors and may be influenced by further poor data quality in the region. A new method is presented in this paper using Linear Stochastic Estimation for vector replacement (LSEVR) which allows for increased flexibility in situations with regions of spurious vectors. LSEVR is applied to PIV dataset to demonstrate and assess its performance relative to commonly used bilinear and bicubic interpolation methods. For replacement of a single vector, all methods performed well, with LSEVR having an average error of 11% in comparison to 14% and 18% for bilinear and bicubic interpolation respectively. A more significant difference was found in replacement of clusters of vectors which showed average vector angle errors of 10°, 9° and 6° for bilinear, bicubic and LSEVR respectively. Error in magnitude was 3% for both interpolation techniques and 1% for LSEVR showing a clear benefit to using LSEVR for conditions that require multiple clustered vectors to be replaced.
Highlights
In the field of fluid mechanics, experimental techniques for the measurement of velocity play a crucial role
The currently presented work introduces the two-point statistical technique, linear stochastic estimation (LSE) as an alternative vector post-processing routine to identify and replace spurious vectors in grid velocity vector fields such as those obtained through particle image velocimetry (PIV) measurements without the need for multiple iterations or user defined parameters
The two techniques are complementary given that proper orthogonal decomposition (POD) may identify coherent motions, represented as lower order, higher energy modes, while LSE can effectively estimate these structures from a reduced dataset
Summary
In the field of fluid mechanics, experimental techniques for the measurement of velocity play a crucial role. Due to the significance placed on experimentally obtained velocity measurements, research on alternative methods for both improved detection and replacement of spurious vectors is on-going. The same proposed techniques may both detect spurious vectors and offer a replacement Statistical based approaches such as the penalized least-squares method [10] or Kriging regression [11] are two such techniques. Wang et al [12] uses low-order POD modes to construct a reference velocity field allowing for outlier detection and correction using an iterative approach, assuming instantaneous spurious vectors will not influence the lower order modes. The currently presented work introduces the two-point statistical technique, linear stochastic estimation (LSE) as an alternative vector post-processing routine to identify and replace spurious vectors in grid velocity vector fields such as those obtained through PIV measurements without the need for multiple iterations or user defined parameters. The performance of the technique is compared to the widely used interpolation approach
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