An integrated algorithm for hinging hyperplanes and its application in distillation process

Hinging hyperplanes (HH) is a kind of piecewise linear approximation methods which is proven to be effective for any continuous linear functions with arbitrary dimensions on compact sets in any given precision. In the open literatures, more attentions are concentrated on the representation capability and the convergence issue of parameter optimization is rarely concerned with, which is important for real world application, especially for real time online modeling. And the application effect by the current parameter optimization method shows that the convergence rate becomes slower and slower along with iterations increase and hard to proceed when parameters are in a neighborhood of optimal point. To cope with this drawback, a novel parameter optimization algorithm is introduced to accelerate the convergence rate, which integrates the Newton´s method with conjugate gradient method. The effectiveness of proposed algorithm is verified by comparison. And then a practical example is given to model the pour point of side-draw of atmospheric column. The accuracy is satisfied for application and convergence rate by the integrated algorithm is accelerated compared with the original one.