## 2 Materials and Methods
### Data Collection and Preparation (Sampling Campaigns)
#### 2.1.2 Filtering out the Irrelevant Inputs  
Event-Modeling is a technique for real-time input variable selection in large complex systems [25]. This method is able to group and rank relevant input variables in order of their importance and impact on the model output variable(s). It does not require prior knowledge of the analytical or statistical relationship that may well exist between system input and output variables. This method supports the time-critical dimensionality reduction problem with limited computational resources, which made it suitable for feature extraction and dimensionality reduction in this experiment.  
The event-Modeler algorithm was based on evaluating the relationship between the actual events (model's output variables) to the triggered events' cause (model's input variables). The input/output pairs were used to generate the event-driven incidence matrices (EDIM) element. The application of the ranking ordering clustering (ROC) method resulted in clusters of the most relevant group of input event data (sensors and actuators) against output event data (plant performance indicators). Event tracking, EDIM, and final clustering matrix are presented in Figure 2. As shown in this example, the final clustering table is the normalization of a single event clustering matrix over the sampling time frame.  
Consequently, the algorithm clustered the input/output variables in two groups of highly coupled clusters. i.e., input variables (TDs) 4, 6, and 7 had high impacts on output variables (EDs) 1 and 4 and the same interpretation for the other cluster. A detailed explanation of the event-modeling algorithm and the basic concept is discussed in [25; 26].  
In this experiment, 33 collected process and environmental variables were considered as the event-modeler input variables and coarse return as the output variable. The six highest-ranked (coupled) input variables over output (coarse return) were considered as the most important input variables following the industry expert's approval. The event-modeler correlation results between the input parameters and output (coarse return) are shown in Table A1 in Appendix A. These six inputs were the following; the mill's four parameters of:  
* Fresh feed (FRF): Measured the amount of material that was being fed to the mill [ton/h].
* Mill inlet fill (MIF): Measured the filling level on the first chamber of the mill [%].
* Mill outlet fill outlet (MOF): Measured the filling level on the second chamber of the mill [%]
* Bucket elevator amperage (BEA): Transferred the mill outputs to the separator in amperes [A]. Plus, two separator parameters of:
* Separator Amperage (SEA): This amperage was used by the separator; it was dependent on the amount of incoming load [A].
* Separator Speed (SES): Defined the separator velocity (related with final cement quality, manually set by operators).  
Altogether, these six parameters were the model inputs. In addition, the model output was:  
Figure 2: Event-Modeling technique flowchart.  
* Coarse return (COR) [ton/h].  
The plots of each variable are shown in Figure 3. The plots are normalized for confidential purposes.  
A schematic of the shortlisted mill and separator parameters, including the coarse return feedback loop as presented in Figure 4.  
Figure 4: A schematic of mill and separator parameters and coarse return feedback loop.  
Figure 3: Collected input and output samples over 43,000 min.