Data validation and reconciliation: Difference between revisions

Revision as of 02:31, 27 June 2020

Revision as of 21:48, 20 July 2020

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The term <math>\left(\frac{y_i^*-y_i}{\sigma_i}\right)^2\,\!</math> is called the ''penalty'' of measurement ''i''. The objective function is the sum of the penalties, which will be denoted in the following by <math>f(y^*)=\sum_{i=1}^n\left(\frac{y_i^*-y_i}{\sigma_i}\right)^2</math>.

In other words, one wants to minimize the overall correction (measured in the least squares term) that is needed in order to satisfy the [[constraint (mathematics)|system constraints]]. Additionally, each least squares term is weighted by the [[standard deviation]] of the corresponding measurement. The standard deviation is related to the accuracy of the measurement. For example, at a 95% confidence level, the standard deviation is about twice the accuracy.

===Redundancy===

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Redundancy can be due to [[redundancy (engineering)|sensor redundancy]], where sensors are duplicated in order to have more than one measurement of the same quantity. Redundancy also arises when a single variable can be estimated in several independent ways from separate sets of measurements at a given time or time averaging period, using the algebraic constraints.

Redundancy is linked to the concept of [[observability]]. A variable (or system) is observable if the models and sensor measurements can be used to uniquely determine its value (system state). A sensor is redundant if its removal causes no loss of observability. Rigorous definitions of observability, calculability, and redundancy, along with criteria for determining it, were established by Stanley and Mah,<ref name="Stanley-Mah-1981a">

[https://gregstanleyandassociates.com/CES-1981a-ObservabilityRedundancy.pdf Stanley G.M. and Mah, R.S.H., "Observability and Redundancy in Process Data Estimation, Chem. Engng. Sci. 36, 259 (1981)]</ref> for these cases with set constraints such as algebraic equations and inequalities. Next, we illustrate some special cases: