Process Model 'Family Tree'

In general, process model or model is a representation of the real system/process. By using a process model, the user can explore the behavior and performance of the real system at a reduced cost, time and risk. In most process models, only the parameters that relevant and related to the problem are made available. Thus, the process model is somehow a simplified and compact version of a real system. The performance of the process model is measured by how much it can actually copied the real one. This criterion is often measured by coefficient of determination (or R2). The closer the R2 value to 1, the more likely the performance of the process model is similar to the original system/process.

The figure above shows what I would call the ‘family tree’ of process model (Note: all the information in the figure does not resemble the entire models that are available in the literature. I just put what I know although I wish I can put all in there. The diagram just serves as a general idea of the process model development). Based on the figure, the there are two nature of process models that are available which are steady state and dynamic. The difference between these two will be cover in the future post. For the time being it is important to know that the dynamic model is the one that are usually used in control system design. Where else, the steady state model is often used in process design and optimization. From the dynamic model, we have three types of dynamic process model which are statistical, mathematical and qualitative.

Statistical Model

Statistical modeling is about relating the variables to one and another based on mathematical equation using statistical tools. This analysis would give a general equation that can ‘fit’ the system behavior and thus represent the real system. The correlation model is developed by quantifying the similarity between the real system and a predicted system. In order to get the predicted system equal to the real system, the adjustment is done based on the regression analysis. The most basic correlation model is the linear line equation y = mx + c. The probabilistic model is based on the probability density function which can determine the ‘density’ of the probability in a bounded region. The most common probabilistic model is the normal distribution which can tell us the probability of a variable taking on a certain value.

Mathematical Model

Actually, most of the modeling development is related to math. The term ‘mathematical model’ is used to highlight the usage of the mathematical concept and language in its development. There are two branch of mathematical modeling which are empirical and mechanistic model. The issue of empirical and mechanistic modeling always draws many attentions. Hence, the advantages and disadvantages of both of the modeling technique will be cover in the future post as it is worth to be discussed.

• Mechanistic Model: The mechanistic model is developed based on the fundamental knowledge and principal of the system/process. Thus, all the theory (e.g. physic, chemistry, transport process, thermodynamic, reaction, mass balance etc) that govern the system will be developed and used in the modeling development. The final model is described as ordinary differential equation (ODE) and partial differential equation (PDE). For easy understanding, ODE and PDE is a set of mathematical equation that can represent the dynamic and behavior of a real system/process. ODE is just considering one dimension of variable whereas PDE is more complex as its includes spatial calculation. The other name for mechanistic model is first principle model.

• Empirical Modeling: Empirical modeling is simply to find a generic relationship between input and output of the system. Thus, the system/process knowledge and operation is not needed in the modeling development. Based on a set of data from the real system, a certain correlation between the input and output is explored. In the final stage, the developed model is presumed to have generalized the real system/process behavior and dynamic. The other name for empirical modeling is black box modeling. The linear or nonlinear application is depend on the order and behavior of the system. If the system is known to have nonlinearities in its response, then a nonlinear modeling is more suitable. In the Figure 1, some examples of linear and nonlinear empirical modeling techniques are shown.

Qualitative Model

Qualitative modeling utilizes a more humane approach as the model is developed according to its ‘true nature’. The ‘true nature’ is something than can preclude the mathematical description such as constrains, physical limitation, saturation, safety etc that happen in the real system/process. A simple qualitative model is the IF-THEN-ELSE model which is developed from the knowledge of experienced operator. Apart from this qualitative process description model, genetic algorithm and qualitative physic theory are developed to further improve the model performance and accuracy. Qualitative transfer function uses a dynamic linkage between the transfer functions to include the system ‘true nature’. The linkage characteristic is influence by the real system behavior. Fuzzy logic model uses algebra and a set of linguistic rule to develop the ill-behave and complex system. The fuzzy logic modeling technique combine a rule based model, probabilistic theory and sets of symbols with interpretation to generate a model.

In the nutshell: There are many type of model that is available with different properties, application and development route. Before using any of these models, it is wise to identify your system/process dynamic and behavior first.