Robust profile alignment based on penalised-spline smoothing

In quality engineering practice, profiles that are used for quality monitoring or evaluation are sometimes unaligned due to engineering constraints. In such cases, profiles have to be registered (aligned) through shifting, time warping or coordinate alignment such that samples are comparable and easy to handle. Among the different registration algorithms, time warping, or alignment of profiles with unequal lengths, is a challenging task. In quality engineering, a typical phenomenon observed in profile alignment is that neighbours of an aligned pair have a high possibility of being similar, which means that a large jump in a warping path is less likely. In this article, a penalised-spline smoothing method is proposed for profile alignment to handle this problem. The newly proposed nonparametric alignment strategy attempts to capture the smoothness and spatially correlated features of warping shifts, and is proven more robust than existing algorithms. A dynamic programming algorithm is developed to obtain the optimal path. Both simulation studies and a real example demonstrate the effectiveness of the proposed method.