Process Modeling & Optimization 
Using Artificial Neural Networks

There are a lot of methodologies used for modeling a process most of which result in linear models. However, most processes in the real world are non-linear in nature. Since Artificial Neural Networks (ANNs) are non-linear in nature, they are better suited for modeling complex non-linear processes.

Here, we have a non-linear chemical reaction process. The process is characterized by having two reactants mixed together in different proportions (F1 & F2) measured in gallons per minute. The reactants are combined together in a reactor. The reactor pressure (P), temperature (T),  and agitator speed (R) are controllable parameters that affect the outcome of the reaction.

The chemical reaction process produces a product with measurable qualities of (Y1) and (Y2), and a production quantity of (Fo) measured in gallons per minute.

Process Modeling

The objective in process modeling is to build an ANN system that mimics the behavior of the chemical reaction process. The ANN system will have F1, F2, P, T, and R as inputs. The ANN is then trained to produce Y1, Y2, and Fo.

Once training is done, the ANN will behave very similar to the actual process. 

Process Optimization

The objective of the process optimization is to produce a product with desired Y1, Y2, and Fo properties with the most cost effective manner. Since the reaction process is non-linear in nature, there are many permutations of the process reaction inputs (F1, F2, P, T, & R) that will produce our desired outputs (Y1, Y2, & Fo).

The goal of process optimization is to find optimum values for F1, F2, P, T, and R in order to produce our desired product with properties of Y1, Y2, and a flow rate of Fo gallons per minute. The Figure on the right shows the values of the desired product properties.

One way to optimize the process is to perform a Monte Carlo simulation on the ANN process model. The following steps describe the simulation process:

1. Iterate on the acceptable values of F1, F2, P, T, and R.

2. Provide the iterated values of F1, F2, P, T, and R as inputs to the ANN model.

3. If the ANN model produces an output close to our desired process outputs Y1, Y2, and Fo, then we compute the cost associated for this production sample. The cost of production is equal to the cost of F1, F2, P, T, and R. We then store the values of F1, F2, P, T, R, and the cost associated with this sample production.

Repeat steps 1, 2, and 3 until we exhaust the iterations in step 1.

Now, we have a list of acceptable values of F1, F2, P, T, and R that produce our desired Y1, Y2, and Fo product. From the list of all possible input combinations, we pick the one that has the least cost. This corresponds to the optimal inputs of F1, F2, P, T, and R that will result in our desire final product.