Sub-pixel displacement measurement in Digital Image Correlation using Particle Swarm Optimization

Sub-pixel displacement measurement in Digital Image Correlation (DIC) is an optimization problem in search of a point of the deformed image where has the maximum correlation coefficient value to the point of the reference image. Particle Swarm Optimization (PSO) is a novel swarm intelligence algorithm which has great prospect in multidimensional nonlinear optimization because of its advantages of high convergence rate, global search effectiveness, robustness and having few parameters. In this paper, PSO is first applied into DIC to get sub-pixel displacement fields with our aim of proving the feasibility of this method. Two displacements and four deformation gradients for a subset of DIC can all be taken into PSO, while we only take the first two displacements into calculation in consideration of rigid body translation. With set iterative time 20, an accuracy of 0.005 pixels has been achieved between two computer-simulated images by using basic PSO algorithm. In order to limit positions of particles within small areas and thus reduce iterative calculation, an improved integer pixel displacement search method called Grid Method is put forward for accurate integer pixel displacement measurement. Besides, through empirical study, Inverse Function Decreasing Inertia Weight has been proposed and other parameters of PSO have been discussed concerning DIC correlation coefficient function while we attempt to minimize the iterative calculation. We compare the proposed parameters with commonly used PSO parameters and find that PSO with the proposed parameters has much higher convergence rate. So Inverse Function Decreasing Inertia Weight and the set parameters are recommended for use in the PSO method of DIC.