In most cases when analysing dynamic systems such as chemical or mineralogical processes, looking at a single snapshot in time is not sufficient to get a realistic view of the behaviour of a system. Different dominating driving forces can often have an impact on the dynamic relationship amongst the system states. Furthermore, processes can operate in different regimes based on available feed and other plant-wide capacity bottlenecks.
The video below demonstrates how the cross-correlation between two variables can change over time. Note how the dominating delay between feed rate and power shifts from +/-20 minutes to zero and even negative values. Deviations from the nominal delay might indicate that a confounding variable is primarily driving the process, or an undesired state in the mill (such as a shift in the centre of gravity of the load).
By retaining some history in the visualisation, a 3D surface plot gives a better view of the dynamic changes that occur. The video below shows correlation graphs in this format.
I plan to clean up the code used for these visualisations. If you think this might be useful to you, get in touch, and I can prioritise it. I am also happy to collaborate on industrial case studies related to interaction analysis or fault detection and diagnosis.