Data reconciliation and variable classification by null space methods

General steady-state data reconciliation with both measured and un-measured variables is treated through theoretical vector space methods. Instead of solving the initial equality constrained optimization problem, a parametrized regular least squares regression onto the null space of the Jacobian matrix of the constraining equations is performed, yielding adjusted estimates of process variables. Additionally the full structure of the Jacobian, through its singular value decomposition, is exploited in order to state classification rules for the process variables with regards to redundancy and observability as well as to obtain estimates of observable variables. The method is exemplified by applying it to a small process monitoring network for which mass balance provides the physical constraints. Furthermore, the covariance matrix of the adjustments is used in order assist in the design of an improved network with respect to the number of flow-meters required so that reliable estimates of the process variables can be obtained.