Modeling Examples

This section describes two examples of PLS modeling. The first one describes the model for the reactor already introduced in the previous chapter the second example describes the model for a non-linear process. 

In the previous chapter, the input data of a chemical reactor was analyzed. It was shown that the first variable contained essentially the same information than the second variable. The first variable was therefore deleted and the remaining four input variables can be correlated to the output variable T, in this case the fraction unconverted reactant. The program is saved in file F2304.m, a partial listing is shown below  

The program npls auto-scales the data firsf i.e. from each variable the mean is subtracted and divided by the standard deviation. Then the first 300 data points are used to develop a linear PLS model, the modehng results are shown in Fig. 23.4. 

As can be seen, the model performs reasonably well, as is usually the case during the model development stage. When we now test the model on the remaining 200 data points in 

One could also use the PLS model user interface (Wise et al., 2004)  

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The first is the relational model. Examples are hnear (i.e., models linear in the parameters and neural network models). The model output is related to the input and specifications using empirical relations bearing no physical relation to the actual chemical process. These models give trends in the output as the input and specifications change. Actual unit performance and model predictions may not be very close. Relational models are usebil as interpolating tools. 

The second classification is the physical model. Examples are the rigorous modiiles found in chemical-process simulators. In sequential modular simulators, distillation and kinetic reactors are two important examples. Compared to relational models, physical models purport to represent the ac tual material, energy, equilibrium, and rate processes present in the unit. They rarely, however, include any equipment constraints as part of the model. Despite their complexity, adjustable parameters oearing some relation to theoiy (e.g., tray efficiency) are required such that the output is properly related to the input and specifications. These modds provide more accurate predictions of output based on input and specifications. However, the interactions between the model parameters and database parameters compromise the relationships between input and output. The nonlinearities of equipment performance are not included and, consequently, significant extrapolations result in large errors. Despite their greater complexity, they should be considered to be approximate as well. 

Electronic marketplace/E-commerce In addition to the many databases available and person-to-person contacts, E-commerce in plastics has been conducted through suppliers web sites or the dot-commerce independent web sites that link material buyers with sellers in transactions or auction formats. During the year 2000 five plastic producers/suppliers and various elastomer producers/suppliers created a new and important business model of a joint-venture web site. It provides multiple companies to join forces to do business. This is a strategy some observers call competition and others regard as just another form of selling in. an electronic format. Regardless of how it is perceived, the model will help propel e-commerce into the mainstream of processor procurement due to the size and wealth of the companies involved. The plastic model example is the largest online business-to-business site todate. 

A variety of compound semiconductors have been successfully prepared by this technique. Much of the work concerning ECALE has been concentrated on the deposition of CdTe on An substrates. Notwithstanding the inherent problems of the system (for instance, a 10% lattice mismatch), the formation of CdTe epitaxial layers became a model example of ECALE synthesis. In their pioneering studies, Stickney and co-workers [27, 28] have focused on the deposition of the compound on... 

In both types of problem, solution is usually achieved by means of a step-by-step integration method. The basic idea of this is illustrated in the information flow sheet, which was considered previously for the introductory ISIM complex reaction model example (Fig. 1.4). 

Differences between equations 19.3-19 and 19.3-20 are most significant if samples are collected infrequently. Ultimately, if they lead to substantially different estimates of t and of, it is necessary to verify the results using an appropriate mixing model. Example 19-2 illustrates the method for evaluating t and of from a step response, using both central and backward differencing. 

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