7.3  NEURAL NETWORK MODELS

Most chemical processes such as chemical reactors and separations systems exhibit nonlinear behavior but such processes are so complex that they require significant engineering time to develop and validate detailed theoretical mathematical models. However, alternatives to the use of nonlinear theoretical models exist. One popular nonlinear empirical modeling approach is called artificial neural networks (ANN). ANN's have been used extensively in recent years to model a wide range of physical and chemical phenomena as well as in other non‑engineering areas such as stock market analysis, chess strategies, speech recognition, and for medical diagnoses.  ANN's are attractive whenever it is necessary to model complex or not‑well understood processes with large input‑output data sets, as well as with models that are too complicated to solve in real-time (Su and McAvoy, 1997; Baughman and Lin, 1995; Ben and Heavner, 1996; Ramchadran and Rhinehart, 1995).  It is analogous to regression in that fitting of ANN's does not require a priori understanding of the process to be modeled.

A multilayer feedforward network structure is one of the most common ANN's, as shown in Fig. 7.12. Nodes are organized into layers (input, output, hidden); each node in the hidden layer is connected to the nodes in adjacent layers via connection weights. These weights are unknown parameters, which are to be estimated based on the data from the process to be modeled. The number of unknown parameters can be quite large (e.g., 50 to 100), and powerful nonlinear programming algorithms are required to fit the parameters to the data using the least squares objective function (Edgar et al., 2001). If enough nodes are utilized, it can be proved that any input‑output process can be simulated accurately by a neural net model (Su and McAvoy, 1997).
			
Figure 7.12. Multilayer Artificial Neural Network with Three Layers

As shown in Fig. 7.13, at each node inputs are collected from other nodes or from bias terms and their strength or magnitude evaluated. These inputs are then summed and compared with a threshold level, and the appropriate output is determined. The connection weight ( Wij ) determines the relative importance of that input. The sum of the weighted inputs is then passed to a nonlinear transformation, as shown in Fig. 7.13. One popular type of transformation has a sigmoidal shape and is shown in the figure, although there are many options available.

The "training" of a neural network involves estimating the unknown parameters; this procedure generally utilizes normal operating data (often large data sets) taken in the operating region where the model is intended to be used. After the parameters are estimated (the net is trained), another large set of data can be used to validate that the model is adequate. Sometimes the resulting ANN model is not satisfactory, and changes in the model structure must be made, often by trial and error. Commercial software packages are available from a number of software vendors that focus on the process industries; such software now makes automatic empirical modeling of complex processes feasible.

Figure 7.13 Signal Diagram for Artificial Neuron

Advanced applications of neural nets have been commercially implemented in the areas of fault detection and diagnosis, sensor errors, and dynamic modeling and control (Su and McAvoy, 1997).  In some cases neural nets have been used to determine controller settings in advanced control systems.

7.3.1  Virtual Sensors

One of the common problems shared by many chemical processes is the inability to measure key process variables non‑invasively and in real‑time, especially the composition of process streams and product properties. The development of new sensors, based on new techniques for analytical chemistry and modern electronic devices using fiber and nonlinear optics and semiconductors, has been an active area. As an alternative, the use of easily measured secondary variables to infer values of unmeasured process variables is now receiving great interest; the term virtual or "soft" sensors (Martin, 1997; Podkulskie, 1997; Brown, 1998), often is used to denote this approach.

Soft sensors have become an attractive alternative to the high cost of accurate on‑line measurements now that companies have greater level of confidence in empirical inferential models such as provided by artificial neural nets. In one interesting example, the Texas environmental regulatory agency now permits such an approach to be used for monitoring emissions from various process units such as power boilers. In this case the assessment is based on direct measurements of selected inputs and outputs, with prediction of some pollutants at the parts per billion level (Martin, 1997).  In the area of materials manufacturing, the real‑time detection of cracks, inclusions, porosity, dislocations, or defects in metallurgical or electronic materials would be highly desirable during processing, instead of after processing is completed and defective products are shipped. Using virtual sensor models that can predict quality control measures, such as the formation and location of defects can greatly reduce the stringent requirements imposed on hardware‑based sensors.