Selection of Independent Model Variables

The process input variables (usually flows) affect the process state variables (usually pressure, level, temperature, concentration) which in turn have an impact on the measured process output such as a quality (for example viscosity). One should then ask oneself the question what part of the process do I want to model the relationship between the process inputs and the quality variable or the relationship between the state variables and the measured quality variable or the relationship between the process inputs and the state variables It would not be logical to model the quality variable as a function of both the process inputs and the state variables. The latter exercise would be one that is not likely to be successful, since the process inputs affect the state variables and the state variables affect the process quality variable. Furthermore, the state variables are usually not mutually independent, for example temperature, pressure and composition. This means that a model that includes the process inputs as well as the state variables as additional inputs, models the effect of the true process inputs multiple times. Therefore a proper selection of the inputs and output(s) of the model is very important. 

An effective way to reduce the number the number of inputs is to transform the input space of mutually dependent variables into a space of independent variables by principal component analysis (PCA). This space is usually much smaller. This transformation forms the basis of the construction of partial least square (PLS) models. Also in many packages for neural-network design a PCA toolbox is present. 

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