Estimating periodic length and defect coordinates from a series of integer values

Abstract Most of existing inspection systems of surface quality equipped on the rolled-strip production lines pay their attentions on detecting and classifying the defects, but they record the defect coordinates in the rolling direction with low-accuracy. It is difficult to make a right judgment on the defective work roll from the recorded defect values. An analytical model has been proposed to exactly identify the periodic length and the defect coordinates from the recorded defect values as a series of integer values. The periodic length is the distance in the rolling direction between two neighboring surface defects and can be applied to identify the defective work roll. The more recorded defect values are available for the analytical model, the more exact periodic length and defect coordinates can be received. In addition, the error-ranges of the identified defect coordinates have been analyzed. It shows that the error-ranges of the identified defect coordinates are piecewise linear with the recorded defect values, and the error-range line is concave downward with high-precision identification being achieved to the defect coordinates at the middle portion.