On-line optimization of thermomechanical pulping rejects screen using modified sequential simplex method

Abstract

The sequential simplex method (SSM) was blended with the Nelder and Mead method to create two separate simplex methods. The first method is the Equilateral Optimum Following Simplex (EOFS). In this method, the simplex remains equilateral during all steps and changes in size. The other method created in this project is the Non-equilateral Optimum Following Simplex (NOFS). This method is more like the Nelder and Mead method because it has the ability to change its shape when expanding or reducing its size. Both of the methods differ from their predecessor because they are being applied to a system with a moving optimum. Neither the SSM or the Nelder and Mead method have the ability to recognize movement in the location of the optimum. Both methods are excellent at searching for a static optimum, but are incapable of searching for a moving optimum. If either of the SSM or Nelder and Mead methods began to cycle around a single point they would fail to recognize if the optimum moved outside of the current simplex circular area. Both of the methods would continue to focus on the current best point. The best point must be periodically re-evaluated to ensure it isn’t out-dated. When the simplex is ready to contract in both the EOFS and NOFS methods, instead of replacing the worst point, the best point is replaced. This does slow the immediate progress of the simplex, but ensures the long-term success in searching out a moving optimum. Once the simplex methods had been refined on paper, testing each of them in a computer simulation against three types of disturbances was important in determining their potential in an industrial setting. Each simplex method was tested against feed flow, feed fibre distribution and feed consistency disturbances. Computer simulations were run after creating a model of the pressure screen using experimental data obtained from a refined rejects pressure screen at the Thunder Bay, Ontario mill owned by Bowater Inc. Samples were obtained at a variety of operating conditions and analyzed using the Kajaani Fibre Lab to create fibre distributions. These distributions were used to create the model of the screen and the fibre distribution of the feed stream to the screen. The NOFS simplex method performed well when using two different types of performance equations. One equation was based on achieving maximum fibre separation in the screen, while the other was based on obtaining a target fibre distribution. The NOFS method proved to be the most effective method because of its ability to accelerate towards the optimum by changing shape. In some simulations noise was added to determine its effect. Noise caused poor results, but further modifications to the simplex methods would probably solve this problem in future studies.