On the feasibility of selective spatial correlation to accelerate convergence of PIV image analysis based on confidence
- PDF / 4,632,822 Bytes
- 14 Pages / 595.276 x 790.866 pts Page_size
- 62 Downloads / 161 Views
RESEARCH ARTICLE
On the feasibility of selective spatial correlation to accelerate convergence of PIV image analysis based on confidence statistics M. Edwards1 · R. Theunissen2 · C. B. Allen1 · D. J. Poole1 Received: 31 January 2020 / Revised: 14 August 2020 / Accepted: 10 September 2020 / Published online: 1 October 2020 © The Author(s) 2020
Abstract This paper presents a method which allows for a reduced portion of a particle image velocimetry (PIV) image to be analysed, without introducing numerical artefacts near the edges of the reduced region. Based on confidence intervals of statistics of interest, such a region can be determined automatically depending on user-imposed confidence requirements, allowing for already satisfactorily converged regions of the field of view to be neglected in further analysis, offering significant computational benefits. Temporal fluctuations of the flow are unavoidable even for very steady flows, and the magnitude of such fluctuations will naturally vary over the domain. Moreover, the non-linear modulation effects of the cross-correlation operator exacerbate the perceived temporal fluctuations in regions of strong spatial displacement gradients. It follows, therefore, that steady, uniform, flow regions will require fewer contributing images than their less steady, spatially fluctuating, counterparts within the same field of view, and hence the further analysis of image pairs may be solely driven by small, isolated, nonconverged regions. In this paper, a methodology is presented which allows these non-converged regions to be identified and subsequently analysed in isolation from the rest of the image, while ensuring that such localised analysis is not adversely affected by the reduced analysis region, i.e. does not introduce boundary effects, thus accelerating the analysis procedure considerably. Via experimental analysis, it is shown that under typical conditions a 44% reduction in the required number of correlations for an ensemble solution is achieved, compared to conventional image processing routines while maintaining a specified level of confidence over the domain. Graphic abstract
* M. Edwards [email protected] 1
Aerospace Engineering, University of Bristol, Bristol, UK
Environmental Modelling Unit, VITO NV, Mol, Belgium
2
List of symbols 𝛼 Level of confidence as a percentage 𝜈 Number of degrees of freedom, N − 1 u Ensemble mean horizontal displacement
13
Vol.:(0123456789)
222 Page 2 of 14
𝜎u , 𝜎v Population standard deviation of the displacement hk Spacing between vectors for the kth iteration, in pixels K Total number of WIDIM iterations N Number of images in the ensemble Su , Sv Sample standard deviation of the displacement t Critical value from the Student’s t distribution u, v Displacement components z∗ Critical value from the standard normal distribution CDF Cumulative density function CI Confidence interval PDF Probability density function
1 Introduction Particle image velocimetry (PIV) is used extensively to experimentall
Data Loading...
