Data reconciliation details

Data reconciliation in AVEVA Production Accounting solves constrained, weighted least squares equations.

The basic principle of this technique is weighted least squares error minimization. This is similar to performing a least square fit of a line through data points on a graph. The difference is the reconciled value should meet balance constraints such as mass and/or volume balance requirements. The objective function and balance constraint are presented below:

Figure: The objective function, solved to achieve the objective of minimizing the errors

The following simpler example clarifies the concept of data reconciliation.

To satisfy the material balance (IN = OUT), the reconciled values are calculated by the statistical least square method. X represents the desired, reconciled value for the flow through X1, X2 and X3, which must be equal in this simple example.

In Case I above, we see that with X = 96, we would end up with a sum of squares that is larger than if X is presumed to be 99. This is the essence of what AVEVA Production Accounting does – it finds the value for X (or any reconciled value) that will result in the lowest sum of the squares.

In Case II, a value of 96 would result in the more optimal result, because the initial conditions are different. Case II uses a lower tolerance for v3.

Case III shows what happens if AVEVA Production Accounting is able to determine that one of the measurements is a gross error and therefore does not need to be considered when minimizing the sum of squares. This could happen if the tolerance on v3 were very narrow, or v3’s measure value were much different from the calculated reconciled value for v3.