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{{Short description|A technology to correct measurements in industrial processes}}
'''Industrial process data validation and reconciliation''', or more briefly, '''process data ==Models, data and measurement errors==
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===Error types===
<gallery caption="Random and systematic errors" widths="
File:Normal_no_bias.jpg|Normally distributed measurements without bias.
File:Normal_with_bias.jpg|Normally distributed measurements with bias.
</gallery>
Data originates typically from [[measurements]] taken at different places throughout the industrial site, for example temperature, pressure, volumetric flow rate measurements etc. To understand the basic principles of
# [[random error]]s due to intrinsic [[sensor]] [[accuracy]] and
# [[systematic errors]] (or gross errors) due to sensor [[calibration]] or faulty data transmission.
[[Random error]]s means that the measurement <math>y\,\!</math> is a [[random variable]] with [[mean]] <math>y^*\,\!</math>, where <math>y^*\,\!</math> is the true value that is typically not known. A [[systematic error]] on the other hand is characterized by a measurement <math>y\,\!</math> which is a random variable with [[mean]] <math>\bar{y}\,\!</math>, which is not equal to the true value <math>y^*\,</math>. For ease in deriving and implementing an optimal estimation solution, and based on arguments that errors are the sum of many factors (so that the [[Central limit theorem]] has some effect), data reconciliation assumes these errors are [[normal distribution|normally distributed]].
Other sources of errors when calculating plant balances include process faults such as leaks, unmodeled heat losses, incorrect physical properties or other physical parameters used in equations, and incorrect structure such as unmodeled bypass lines. Other errors include unmodeled plant dynamics such as holdup changes, and other instabilities in plant operations that violate steady state (algebraic) models. Additional dynamic errors arise when measurements and samples are not taken at the same time, especially lab analyses.
The normal practice of using time averages for the data input partly reduces the dynamic problems. However, that does not completely resolve timing inconsistencies for infrequently-sampled data like lab analyses.
This use of average values, like a [[moving average]], acts as a [[low-pass filter]], so high frequency noise is mostly eliminated. The result is that, in practice, data reconciliation is mainly making adjustments to correct systematic errors like biases.
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==History==
,<ref name="Stanley-Mah-1977">G.M. Stanley and R.S.H. Mah, [http://gregstanleyandassociates.com/AIChEJ-1977-EstimationInProcessNetworks.pdf ''Estimation of Flows and Temperatures in Process Networks'', AIChE Journal 23: 642–650, 1977.]</ref><ref>P. Joris, B. Kalitventzeff, ''Process measurements analysis and validation'', Proc. CEF’87: Use Comput. Chem. Eng., Italy, 41–46, 1987.</ref> Quasi steady state dynamics for filtering and simultaneous parameter estimation over time were introduced in 1977 by Stanley and Mah.<ref name="Stanley-Mah-1977"/> Dynamic
▲<ref>P. Joris, B. Kalitventzeff, ''Process measurements analysis and validation'', Proc. CEF’87: Use Comput. Chem. Eng., Italy, 41–46, 1987.</ref> Quasi steady state dynamics for filtering and simultaneous parameter estimation over time were introduced in 1977 by Stanley and Mah.<ref name="Stanley-Mah-1977"/> Dynamic DVR was formulated as a nonlinear optimization problem by Liebman et al. in 1992.<ref>M.J. Liebman, T.F. Edgar, L.S. Lasdon, ''Efficient Data Reconciliation and Estimation for Dynamic Processes Using Nonlinear Programming Techniques'', Computers Chem. Eng. 16: 963–986, 1992.</ref>
==Data reconciliation==
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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 half the accuracy.
===Redundancy===
<gallery caption="Sensor and topological redundancy"
File:sensor_red.jpg|Sensor redundancy arising from multiple sensors of the same quantity at the same time at the same place.
File:topological_red.jpg|Topological redundancy arising from model information, using the mass conservation constraint <math>a=b+c\,\!</math>, for example one can calculate <math>c\,\!</math>, when <math>a\,\!</math> and <math>b\,\!</math> are known.
</gallery>
Data reconciliation relies strongly on the concept of redundancy to correct the measurements as little as possible in order to satisfy the process constraints. Here, redundancy is defined differently from [[Redundancy (information theory)|redundancy in information theory]]. Instead, redundancy arises from combining sensor data with the model (algebraic constraints), sometimes more specifically called "spatial redundancy",<ref name="Stanley-Mah-1977"/> "analytical redundancy", or "topological redundancy".
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
[
Topological redundancy is intimately linked with the [[degrees of freedom (physics and chemistry)|degrees of freedom]] (<math>dof\,\!</math>) of a mathematical system,<ref name="vdi">VDI-Gesellschaft Energie und Umwelt, "Guidelines - VDI 2048 Blatt 1 -
When speaking about topological redundancy we have to distinguish between measured and unmeasured variables. In the following let us denote by <math>x\,\!</math> the unmeasured variables and <math>y\,\!</math> the measured variables. Then the system of the process constraints becomes <math>F(x,y)=0\,\!</math>, which is a nonlinear system in <math>y\,\!</math> and <math>x\,\!</math>.
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\end{align}</math>
i.e. the redundancy is the difference between the number of equations <math>p\,</math> and the number of unmeasured variables <math>m\,</math>. The level of total redundancy is the sum of sensor redundancy and topological redundancy. We speak of positive redundancy if the system is calculable and the total redundancy is positive. One can see that the level of topological redundancy merely depends on the number of equations (the more equations the higher the redundancy) and the number of unmeasured variables (the more unmeasured variables, the lower the redundancy) and not on the number of measured variables.
Simple counts of variables, equations, and measurements are inadequate for many systems, breaking down for several reasons: (a) Portions of a system might have redundancy, while others do not, and some portions might not even be possible to calculate, and (b) Nonlinearities can lead to different conclusions at different operating points. As an example, consider the following system with 4 streams and 2 units.
====Example of calculable and non-calculable systems====
<gallery caption="Calculable and non-calculable systems"
File:calculable_system.jpg|Calculable system, from <math>d\,\!</math> one can compute <math>c\,\!</math>, and knowing <math>a\,\!</math> yields <math>b\,\!</math>.
File:uncalculable_system.jpg|non-calculable system, knowing <math>c\,\!</math> does not give information about <math>a\,\!</math> and <math>b\,\!</math>.
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We incorporate only flow conservation constraints and obtain <math>a+b=c\,\!</math> and <math>c=d\,\!</math>. It is possible that the system <math>F(x,y)=0\,\!</math> is not calculable, even though <math>p-m\ge 0\,\!</math>.
If we have measurements for <math>c\,\!</math> and <math>d\,\!</math>, but not for <math>a\,\!</math> and <math>b\,\!</math>, then the system cannot be calculated (knowing <math>c\,\!</math> does not give information about <math>a\,\!</math> and <math>b\,\!</math>). On the other hand, if <math>a\,\!</math> and <math>
In 1981, observability and redundancy criteria were proven for these sorts of flow networks involving only mass and energy balance constraints.<ref name="Stanley-Mah-1981b">[
===Benefits===
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The individual test compares each penalty term in the objective function with the critical values of the normal distribution. If the <math>i</math>-th penalty term is outside the 95% confidence interval of the normal distribution, then there is reason to believe that this measurement has a gross error.
==Advanced process data
Advanced process data
* complex models incorporating besides mass balances also thermodynamics, momentum balances, equilibria constraints, hydrodynamics etc.
* gross error remediation techniques to ensure meaningfulness of the reconciled values,
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===Thermodynamic models===
Simple models include mass balances only. When adding thermodynamic constraints such as [[First law of thermodynamics|
===Gross error remediation===
[[image:scheme reconciliation.jpg|thumb|350px|The workflow of an advanced data validation and reconciliation process.]]
Gross errors are measurement systematic errors that may [[bias]] the reconciliation results. Therefore, it is important to identify and eliminate these gross errors from the reconciliation process. After the reconciliation [[statistical tests]] can be applied that indicate whether or not a gross error does exist somewhere in the set of measurements. These techniques of gross error remediation are based on two concepts:
* gross error elimination
* gross error relaxation.
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Gross error relaxation targets at relaxing the estimate for the uncertainty of suspicious measurements so that the reconciled value is in the 95% confidence interval. Relaxation typically finds application when it is not possible to determine which measurement around one unit is responsible for the gross error (equivalence of gross errors). Then measurement uncertainties of the measurements involved are increased.
It is important to note that the remediation of gross errors reduces the quality of the reconciliation, either the redundancy decreases (elimination) or the uncertainty of the measured data increases (relaxation). Therefore, it can only be applied when the initial level of redundancy is high enough to ensure that the data reconciliation can still be done (see Section 2,<ref name="vdi" />).
===Workflow===
Advanced
# data acquisition from data historian, data base or manual inputs
# data validation and filtering of raw measurements
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#* gross error remediation (and go back to step 3)
# result storage (raw measurements together with reconciled values)
The result of an advanced
==Applications==
As
==See also==
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{{Reflist}}
* Alexander, Dave, Tannar, Dave & Wasik, Larry "Mill Information System uses Dynamic Data Reconciliation for Accurate Energy Accounting" TAPPI Fall Conference 2007.[http://www.tappi.org/Downloads/Conference-Papers/2007/07EPE/07epe87.aspx]{{Dead link|date=July 2019 |bot=InternetArchiveBot |fix-attempted=yes }}
* Rankin, J. & Wasik, L. "Dynamic Data Reconciliation of Batch Pulping Processes (for On-Line Prediction)" PAPTAC Spring Conference 2009.
* S. Narasimhan, C. Jordache, ''Data reconciliation and gross error detection: an intelligent use of process data'', Golf Publishing Company, Houston, 2000.
* V. Veverka, F. Madron, ''Material and Energy Balancing in the Process Industries'', Elsevier Science BV, Amsterdam, 1997.
* J. Romagnoli, M.C. Sanchez, ''Data processing and reconciliation for chemical process operations'', Academic Press, 2000.
[[Category:Data management]]
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