What is Cross-Correlation?

 

Advanced Forensics For Limiting Suspects and Isolating Root-Causes

Do you remember when school kids simply lined up according to height before heading to the library or to gym class? Shortest in the front. Tallest in the back. A quick glance forward and backward is all anyone needed to do to more or less confirm his or her place in the queue. Any outlier (generally the class clown) could be identified and adjusted quickly by the teacher.  Wouldn’t it be nice if the process for isolating and correcting controller issues was that simple?

Indeed, maintaining effective, efficient and safe control is no easy task since control loops rarely line up in serial fashion like second graders. It’s not just that the number of PID control loops at the average production facility significantly outnumbers the number of children in the average elementary class, it’s that the loops themselves along with the relationships that are shared between and among PID loops are highly complex. To cope with the added complexity many practitioners utilize Cross-Correlation as a means of establishing order out of the chaos.

Isolating and correcting controller performance issues often starts with eliminating potential culprits. Cross-Correlation is a tool that is well suited for that specific purpose.

  • A Simple Definition

Cross-Correlation analyzes the relationship between two data series, calculating a value ranging between one (1.0) and negative one (-1.0).  When applied to PID control loops a value of one (1) indicates that two loops share identical dynamics and move in a mirror-like fashion whereas a value of negative one (-1) indicates that the dynamics are shared but the loops move in opposite directions when one zigs, the other zags. As one might suspect, values of most loop pairings fall somewhere between these extremes with many equaling zero (0) and signaling no relationship between the two loops.

  • Time to Line Up

Cross-Correlation is of particular benefit when there are numerous and interacting PID control loops and when the associated calculations take additional time-based values into consideration. These calculations can be difficult to perform on a wide scale without the assistance of software. Control loop performance monitoring (CLPM) software is a growing class of technology that automatically calculates Cross-Correlation values for all control loops within a unit operation. Some even calculate values on a plant-wide basis, assessing the relationship between each and every pair of PIDs throughout a production facility. This lines control loops up according to their correlation value and also based on their respective lead/lag relationship. This further simplifies the process of root-cause analysis.

  • A Practical Example

Consider a tank that maintains level with liquid fed from twelve different lines. If the level’s variability exceeds acceptable tolerances then it would be engineering’s job to isolate the source of the problem and to correct it. In this case there are a dozen loops that are clear suspects – each of the twelve feeder lines. Cross-Correlation provides engineering staff with a rapid and effective means for narrowing the list to a more manageable number. Equipped with the analysis, staff can focus attention on the few loops that have the highest correlation values whether positive of negative.

The average production facility has 100s if not 1000s of PID control loops, and they don’t line up nicely like children.  Cross-Correlation, Power Spectrum and other diagnostic tools enable production staff to analyze large amounts of process data and to uncover valuable insights.

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