Chapter 15
Hydrocyclone Model Using Genetic Programming

Barry Weck
Charles L. Karr

Department of Aerospace Engineering and Mechanics
University of Alabama
Box 870280
Tuscaloosa, AL 35487-0280
e-mail: bweck@eng.ua.edu and ckarr@coe.eng.ua.edu

ABSTRACT

Developing computer models from system data is an important problem. In general, this is a problem of system identification which is the problem of determining the mathematical equations that describe the fundamental behavior of the system being addressed. This problem arises in a wide variety of engineering disciplines, and is important both in process simulation and process control. This chapter describes the use of genetic programming for solving a particular system identification problem from the minerals industry. Specifically, genetic programming is used to determine a functional relationship that describes the behavior of a hydrocyclone, a device used in the minerals industry to achieve mineral separations.

INTRODUCTION

The problem of system identification is the problem of determining the mathematical equations that describe the fundamental behavior of the system being addressed. System identification problems must be solved to achieve a wide variety of goals in an even wider variety of fields. For instance, system identification problems are prominent in the areas of (1) simulation, (2) scheduling and resource allocation, and (3) process control. Such problems exist in almost every engineering and scientific discipline, as well as in business and industrial applications.

The techniques and approaches to solving system identification problems are almost as varied as the disciplines in which these problems appear. These methods range from the traditional first-principles approach to developing artificial intelligence techniques such as neural networks and fuzzy logic. In a first principles approach, the fundamental physics of a system are modeled using governing equations. In the artificial intelligence-based techniques, data depicting the behavior of the system are presented to the technique of choice, and a mathematical relationship describing the characteristics of the system are developed. Certainly, there are other approaches, but since there are almost as many approaches as there are system identification problems, this chapter will focus on a specific area. Namely, the focus of this chapter is on system identification in the minerals industry. The example used is that of developing a computer model of a hydrocyclone separation device.

Here, the system identification problem will be posed as follows. Determine the behavior of a system, f(x), of a particular system given only data depicting system input, x, and the subsequence system output, f. Thus, for the hydrocyclone problem, the input and operating parameters will be considered known, as well as the resulting split size (see discussion on hydrocyclone later in this chapter). Based on a limited number of such data values, the system identification problem is to determine a generalized relationship that can be used to predict the split size based on the input and operating parameters.

Traditional first-principle models are difficult to develop for systems in the minerals industry because the complex chemistry and physics associated with these processes are not fully understood [1]. This is particularly true for hydrocyclones which are characterized by three-phase, three-dimensional flows. However, there is little doubt that the minerals industry can benefit from the application of computer models through the successful solution of system identification problems in the areas of equipment design and process control. Unit processes, including froth flotation, column flotation, grinding, and leaching are currently operated at less than optimum conditions, and the development of accurate computer models represents a major step toward rectifying this situation as discussed in a paper by Karr, Yeager, and Stanley [2]. Efficient (if not optimized) computer models can be used to achieve improved efficiency via their incorporation into adaptive control systems, automated equipment design systems, and scheduling algorithms. Because there is tremendous potential for economic improvements in the separation industry, researchers have begun to focus on the development of computer models of mineral processing systems which are based on artificial intelligence techniques [3, 4]. Two approaches have been found to be particularly effective in developing data-driven computer models: (1) neural networks and (2) fuzzy mathematics with genetic algorithms. Unfortunately, both of these methods have shortcomings.

Neural networks are promising tools for model development in the separation industry. In fact, at first consideration, they seem like a panacea for modeling because the developer is basically required to understand nothing about the relationships between the system parameters. Unlike traditional modeling techniques, neural networks are not “programmed,” rather they are “trained” [5]. Neural networks are presented with input-output data collected from the system and use this data to become proficient predictors of the future input/output response of the system. Although this approach is inviting for a variety of reasons, there is a drawback. Once a neural network has been trained, it is truly a “black box;” the neural network model provides no insight into its predictions. In the complex systems found in the separation industry where safety is a key issue, this limitation can be inadequate. Additionally, this limitation can deem neural networks ineffective in traditional process control algorithms.