Modeling Chemical Process Systems via Neural Computation Naveen V. Bhat, Peter A. Minderman, Jr., Thomas McAvoy, and Nom Sun Wang zyxw ABSTRACT: This paper discusses the use of neural nets for modeling nonlinear chem- ical systems. Three cases are considered: a steady-state reactor, a dynamic pH stirred tank system, and interpretation of biosensor data. In all cases, a back-propagation net is used successfully to model the system. One advantage of neural nets is that they are in- herently parallel and, as a result, can solve problems much faster than a serial digital computer. Furthermore, neural nets have the ability to “learn.” Rather than programming neural computers, one presents them with a series of examples, and from these examples the nets learn the governing relationships in- volved in the training data base. zyxwvutsrqpo Introduction One reason for the recent interest in neural computation is that neural nets hold the promise of solving problems that have here- tofore proven extremely difficult for tradi- tional digital computers. Not only are neural nets parallel computing devices and, there- fore, fast, but they are capable of learning by example. Currently, there are a wide va- riety of neural nets being studied or used in applications. Some of the important ones are the adaptive resonance networks, counter- propagation networks, neocognitrons, Hop- field networks, etc., each of which has its own special applications. However, the most widely used learning neural net is back-prop- agation [I]. Back-propagation is an example of a map- ping network that learns an approximation to a function, zyxwvutsrqponm y equal to f(x), from sample zyxwvutsrq x, y pairs. The fact that the function to be learned is nonlinear presents no problem to a back- propagation net. Representative applications of back-propagation include speech synthe- sis and recognition, visual pattern recogni- tion, analysis of sonar signals, defense ap- plications, medical diagnosis, and learning in control systems. We have used back-prop- agation successfully on a number of prob- lems typical of those found in the chemical/ The authors are with the Department of Chemical Engineering, University of Maryland, College Park, MD 20742. petroleum industry, including sensor inter- pretation [2], dynamic modeling [3], [4], and in learning how to design distillation control systems. This paper draws together the au- thors’ results in these areas and presents some new results on steady-state modeling of a nonlinear chemical reactor. Figure 1 schematically shows an example of a back-propagation neural net used herein. The boxes and circles are neurons, and the lines between the neurons are called inter- connects. As can be seen, a back-propaga- tion net has three layers: input, hidden, and output. Cybenko [5] showed that a contin- uous neural network with two hidden layers and any fixed continuous sigmoidal nonlin- earity, i.e., a back-propagation net, can’ap- proximate any continuous function arbitrar- ily well on a compact set. Although Cybenko’s results do not give any insight into just how large a back-propagation net is required, they do show that the fundamental structure of back-propagation is such that it can model any continuous nonlinear func- tion. validation. Often modeling costs account for over 75 percent of the expenditures in an advanced control project. Since neural nets can learn by example, they may offer a cost- effective method of developing useful pro- cess models. This paper discusses the use of neural nets for modeling nonlinear chemical process systems. Both a steady-state reactor and a dynamic pH continuously stirred tank reac- tor (CSTR) are treated, as well as the use of back-propagation for interpreting biosensor data. It is shown that a back-propagation net is capable of learning the underlying rela- tionships. Once a back-propagation model is available, then it can be used directly on- line, even now. When parallel chips are widely available, back-propagation will be even more attractive. Indeed, the back-prop- agation algorithm can be simulated in a stan- dard digital computer so that no special hard- ware is required for its implementation. After discussing the back-propagation algorithm, the various examples are treated. One of the chief bamers to the more wide- spread use of advanced modeling and control Back-Propagation zyx - techniques in the chemical/petroleum indus- try is the cost of model development and The governing equations for a back-prop- agation net, such as shown in Fig. I, have Scaled zyxwvutsr CA, -CO, \ Scaled CEO Scaled Cco Scaled space time V/F Input Hidden Output layer layer layer BPN zyxwvut for steady-state modeling application. Fig. 1. 24 zyxwvutsrqponm 0272 1708/90/0400-0024 $01 zyxwvutsr 00 0 1990 IEEE IEEE Control Systems Magazine