Objectives

1. To develop artificial neural network (ANN) models using the MATLAB Neural Net Fitting Toolbox.
   
2. To implement ANN models as soft sensors in Simulink and evaluate their predictive performance.

Problem Statement

In a distillation column, the distillate product impurity (percentage impurity) is strongly influenced by the column tray temperature and the column differential pressure. Figure 1 shows a Simulink representation of the column, where:

• $u_1$ = feed flow rate
  
• $u_2$ = feed heavy component molar fraction
  
• $x_1$ = tray temperature
  
• $x_2$ = differential pressure
  
• $y$ = distillate percentage impurity

Distillation column distillate product impurity (Y) representation in Simulink.

The dynamics of the intermediate variables are given by the following transfer functions:

For tray temperature ($x_1$): $$\begin{array}{}\text{(1)}& x_1(s)=\frac{1}{3s+1}\end{array}$$

For differential pressure ($x_2$): $$\begin{array}{}\text{(2)}& x_2(s)=\frac{0.7s-0.5}{s^2+s+1}\end{array}$$

The relation between impurity and process variables is nonlinear: $$\begin{array}{}\text{(3)}& y=2.5+0.9x_1-0.3x_2-0.1x_1{x}_2+0.05x_1^2-0.06x_2^2\end{array}$$

You wish to develop an ANN model to predict the distillate impurity $y$ as a function of $x_1$ and $x_2$.

For training, use data generated by applying a uniform random number generator (sampling time = 1 unit) to the inputs $u_1$ and $u_2$. For testing, use step input sequences applied to $u_1$ and $u_2$:

• $+1$ unit step in $u_1$ at $t=1$
  
• $-1$ unit step in $u_2$ at $t=20$
  
• $+1$ unit step in $u_2$ at $t=30$
  
• $-1$ unit step in $u_1$ at $t=65$

Methodology

1. ANN Model Development
   • Generate datasets using random inputs for $u_1$ and $u_2$.
     
   • Train two ANN models using the Neural Net Fitting Toolbox:
     • ANN 1: trained on 100 units of data
       
     • ANN 2: trained on 200 units of data
       
   • Vary the number of hidden layers and neurons to find the best model structure.
     
   • Report regression performance (R²), training error, and regression plots.
2. Implementation in Simulink
   • Integrate the trained ANN models into the provided Simulink model of the distillation column.
     
   • Apply the step-change sequence to $u_1$ and $u_2$.
     
   • Compare ANN-predicted impurity against the actual nonlinear relation (Eq. $\text{???}$).
3. Evaluation
   • Assess accuracy of ANN 1 vs ANN 2 based on:
     • Regression performance (R² values)
       
     • Fit of ANN outputs vs actual impurity under step disturbances
       
   • Comment on the impact of training data size on prediction capability.

Report Format

Your report (5 pages maximum) should include the following:

0. Submission Details Include a brief table at the beginning of the report with the following information:

   Lab Title:	Lab 05 - Artificial Neural Networks	Student Name	ID
   Unit:	CHEN4011	Student 1	12345678
   Date:	12 August 2025	Student 2	87654321

1. Objective & Problem Statement Summarize the purpose of ANN modeling and the context of impurity prediction in distillation.

2. Methodology & Implementation

• Describe ANN training procedure (datasets, hidden layers, toolbox functions).
  
• Show regression plots for ANN 1 and ANN 2.
  
• Report number of hidden layers and R² values.
  
• Provide Simulink diagrams used for testing.

3. Results

• Show simulated responses of predicted impurity vs actual impurity under the defined step-change inputs.
  
• Present results for both ANN 1 and ANN 2.
  
• Highlight key differences in prediction accuracy.

4. Analysis and Discussion

• Compare performance of ANN 1 and ANN 2.
  
• Discuss how dataset length and ANN architecture affect prediction accuracy.
  
• Comment on limitations of using ANN as soft sensors in nonlinear systems.

5. Conclusion

• Summarize findings on ANN prediction accuracy.
  
• State which ANN performed best and why.
  
• Discuss broader applications of ANN-based soft sensors in process systems.

Assessment Rubric (20 Marks Total)

No	Section	Marks	Evaluation basis
1.	Objectives & Problem	2	Clarity of problem definition; articulation of objectives
2.	Methodology and Implementation	6	ANN training details; Simulink integration; regression plots and R² reporting
3.	Results	4	Quality, relevance, and labeling of plots; comparison of ANN 1 vs ANN 2 outputs
4.	Analysis and Discussion	6	Insightful interpretation; effect of training size and architecture; limitations
5.	Conclusion and Presentation	2	Coherent summary; quality of writing, formatting, and visual presentation