Making Industrial Processes More Cost Efficient
The microstructure of brass is highly sensitive to annealing conditions as well as its composition. Small variations in annealing temperatures or line speed result in significant variations in mechanical properties as well as grain sizes. A large number of variables influence the microstructure and mechanical properties. As a consequence, it is difficult for operators to decide how to anneal strips of different thicknesses and compositions for achieving a specified grain size.
The relations between the composition of brass and process variables of annealing and the resulting microstructure are complicated. It is not feasible to develop sufficiently accurate and reliable physical models for this process, partly because the phenomena taking place in the process are not well understood. Empirical or semi-empirical modelling, however, does not require the knowledge of the phenomena taking place in the process. It is sufficient to be able to measure the variables of interest. Conventional methods of empirical modelling are linear statistical techniques. Nothing in nature, particularly in materials science, is very linear. Therefore, nonlinear modelling is often a better alternative to linear statistical techniques.
Nonlinear modeling has been in industrial use for more than fifteen years. This new technology benefits the industry in several ways. It has been successfully utilized by various industries for a variety of purposes, particularly for process development. Nonlinear modeling has been successfully used for a large number of processes and materials in several sectors of process industries including metals, polymers and plastics processing, ceramics, concrete, biotechnology, power generation, pulp, paper and board, semiconductor processing, water treatment, chemical production, food processing, etc. The awareness of these techniques is still very limited.
Nonlinear modeling can roughly be defined as empirical or semi-empirical modeling which takes at least some nonlinearities into account. Nonlinear models can be static or dynamic. Nonlinear modeling can be performed in many ways. The simpler ways include polynomial regression and linear regression with nonlinear terms. Nonlinear regression is useful in some situations. The forms of the nonlinearities, however, have to be specified in these older techniques. The new techniques of nonlinear modeling are based on free-form nonlinearities. They include series of basis functions, splines, kernel regression, feed-forward neural networks, etc. Feed-forward neural networks are a set of efficient tools for nonlinear modeling, particularly because of their universal approximation capability.
Nonlinear models of the average grain size of annealed strips
The nonlinear models developed for Aurubis were in the form of feed-forward neural networks with sigmoidal activation functions. The quality of the nonlinear model of grain size was quite good considering that it was developed from plain production data, and that measurements of grain size are done manually and hence are subjective to some extent. The nonlinear model showed correct effects of the input variables, and the correlation coefficient was above 86%. The standard deviation of the prediction error was about 4.2 µm.
Non linear model calculates the effect of speed on average grain size for different annealing temperatures in the vertical zones, keeping other input variables constant, for a certain composition of brass. At higher speeds, temperature has a small effect, while at lower speeds, temperature makes a big difference.
The nonlinear models were implemented in software suitable for use in metal industries. The models were tested by Aurubis and found to be quite good and useful. It is now possible to predict the grain size and hardness of annealed strips before the annealing starts, and the operators can make changes to the line speed, oven temperatures or fan speeds if the predicted hardness is far from its desired value.