Application of a neural network to speed up a mathematical model to calculate strip profiles in flat rolling

Since the sixties, innumerable mathematical models have been developed to simulate flat rolling, specifically, to determine its width-wise profile. Among these, Pawelski, Rasp and others have developed a precise model that accounts for the influence of bending, shearing and flattening of the rolls which are crucial to calculate emergent strip-profiles accurately. This method divides the strip and roll into many stripes, assuming a plane-strain state. For each stripe of the roll and strip, the load and deformation respectively are calculated using an analytical approach. The effects of bending, shearing and flattening are considered through influence coefficients on the rolls. Though good agreement is achieved between the results of this method and those obtained by experience, the program run-time is so large that it must be considered an off-line system. Since the program works iteratively, and since calculation of the influence coefficient matrix for flattening is time-consuming as it must be updated nearly every iteration, improvement in program speed can be achieved by substituting a trained neural network, working as an equal partner in the entire mathematical model. The neural network can be trained in the inverse direction, making possible very fast “inversion” of the flattening matrix. This combined model has better acceptance since it doesn´t appear as a black box, i.e., a model based on neural networks only, and so it can be adapted for online process control. Two feedforward neural networks were designed to cope with the problem of calculating flattening and loading: one for load-to-flattening and the second for inversion. A backpropagation learning rule was used. Substantial reduction in processing time is obtained, without loss of precision, since the flattening calculation step is substituted by a simple sum of polynomials with an appropriate activation function