A method for approximating weave diagrams under heald frame constraint

Abstract

Woven fabric is produced by interlacing the warp yarn and the weft yarn, and their relationship on woven fabric is represented as a weave diagram. In order to produce woven fabric with looms, the necessary number of heald frames can be calculated based on the weave diagram for the woven fabric. However, when the number of available heald frames is limited, it is difficult to produce complex woven fabric. To alleviate this problem, this article proposes a method for approximating weave diagrams under heald frame constraint in terms of the alternating optimization in machine learning. By defining the objective function based on the matrix representation of weave diagram, an alternating optimization method is proposed to generate an approximate weave diagram under the specified number of heald frames. The proposed method is implemented with R language, and evaluated in terms of the performance of the proposed algorithm and woven fabric. Experimental results indicate that the proposed method is effective in generating approximate weave diagrams so that they can be fabricated using looms with a limited number of heald frames.