The hybrid grey-based model for cumulative curve prediction in manufacturing system

The cumulative curve prediction has been widely used in many manufacturing systems to achieve the efficient control and management for production processes. In this paper, the grey model GM(1, 1), a single-variable first-order grey model, which is based on the grey system theory, is proposed to resolve the prediction problem of cumulative curve. To improve the prediction capability of GM(1, 1), the cubic spline function is integrated into GM(1, 1). The newly generated model is defined as 3spGM(1, 1). Then, the particle swarm optimization (PSO) algorithm is applied to 3spGM(1, 1) so that the prediction performance can be further improved. We refer to the optimal version as P-3spGM(1, 1). Finally, a residual compensation approach based on artificial neural network (ANN) is proposed to acquire the best prediction performance. The cumulative curve in the production process is used to validate the proposed models.