Data Reconciliation & Gross Error Detection: An Intelligent Use of

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Data Reconciliation & Gross Error Detection An Intelligent Use of Process Data

Shankar Narasimhan and Cornelius Jordache

Publishing Company Houston, Texas

Data Reconciliation & Gross Error Detection Copyright 02000 by Gulf Publishing Cornparty, Houston. Texas. All I-ightsresel-ved. This book, or parts thereof. may not be reproduced in any form without express written permission of the publisher.

Tr, our grtru Professor Richard S. H. Mak, who played

tlze roles of an initiator and a catalyst.

Gulf P ~ ~ b l ~ s hCompany i~ig Book Di\,ision PO. 13ox 260s 1Hou~lnn.l'esas 77252-260s "Since all measurements and observationb ar-e nothing more than approximations to the truth. the same must be t!-ue of 311 c:ilcuiations resting upon them, and thc: highest a m of all cn:npu!2iior!s matie COiICZi71iEs c0i:Cr::ie ~!:cllOnlsila i:lcsr t ? !o ~ approxirnatc, al; ncari)- YLL pr;?c!icab!c. t ~ i!i2 l tr:!ii~. R u t this can be accomplisi~cdin ;lo OCIICS \ri-;~te~:~:; ....................................... Coir!i>ii;a!ic)i-iA Si;lti'ci~\ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pcr-fori!ianci. .'il~-a,u;-:.\ for Ij\.al~iatinsGross fir!-01-!ilcn!i!Ycativil '

si!-,llcgii,s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Coi?ip::i-i,o!~:I: J.i;ri:i;iiz GI-:.,I\\Ei-1-01 !deiitrf'~c;i~ior~ Sira~ezies. . . . . . . . . ; I ? < l I : ! !I ! 1 ' . . . . . . . . . . . . . . . . . .... c:-,\ E,-:(,c [h!e;n\ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S?!l!ii!1~1." . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kc!'~PLI?c~> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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\ -i -// Refs~-cnces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Appendix R: Gralth Theory Fundarr:enfal\. 3-3 Giaphh. PI-cicessGI-,i;;i~s.a:ici Su!;sra;lh\ . . . . . . . . . . . . . . . . . . . 37t. t'at!i.;. Cycles. aiitl C::nnccri~iry . . . . . . . . . . . . . . . . 1 Sp~niiinp'l'recs. I(~-ai?lhes. zrid Cti,?;.~!... . . . . . . . . . . . . . . . . . . . . . :;SO .Ll; Graph Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cutset\. I-undamcniais C~.lrsets.a i d F~ir-ida~ni.rltai C lcie.; . . . . . . . . . . . . ?" I [{efcrence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3K3 ,.>:>

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Forn1uiati:)n f i l l - :>e!:\leasiiri.lnrnt f3i;ica

. . . . . . . . .

Stnrihiical Pi-o;?i.:~iz.oi' T I . I T ~ ~ i\ t i i i ~ i ;rrld ~i the Global Tc\t . . . . . . . . . . . . G c . i l i . i - a l ~Lihi.iih . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 'I'i1c St;ll< o f the ‘ A i ~ t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Siilriiiiai-y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kefel-enL.c\ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2S2

781 289 3 9. c,

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Appendix C: Fundamentals of Probability and Statistics. 384 Randorn Variables 2nd PI-ohabilityDensity Functions . . . . . . . . . . . . . . . 383 Statistical Properties of IZandom Val-iables . . . . . . . . . . . . . . . . . . . . . . . . 589 Ffypothesis Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393

Acknowledaments

Thc authors are indebted to several people who have contributed to the preparation of this book. T h e m a i n contributions c a m e from Prof. N;lrasinlhan's students at the Indian Institute of Technology (1lT)hladras. 'f. Rcnganatllan and J . Prakash. currently doing their doctc?ra! prozrams. prepared the solutions for all examples lvith assislance fr-om Sreerari~Mriguluri. Mnrukuria Rajar~~ouli spent 110ui.s in :he riigtit psepal-ins tlic ~ a b i z sand iigurzs in dil.l'erent ch:i~::eu. Thc s~~ccessfiilccniltleiioii of ii-~i, book was clue to their eftoris. ii:--. S;icl-iln Pat\i.a!-dhan ;1.!1(! S. i'cslir;~\ an;im. faculty at f Jl' M d r a s . pro\~icli.c!critical in~)t!isii? ii:ipro\ c tile 'li!c.us and c!ari:y of- tni: text. Thanks are also due to Liii: RAGE softv.-are cie\~zl:)pment t a r n at E ~ g i ncers India Lirni!cd, R&D Center. c o n s i s i i ~ gi\f Dr. i\ladhukar Gasg. Dr. V. !?a\ ikuliiar. and XIIS. Sheoi-aJ Sin?i! fi-ti~;: ~,~hclir? PI-
The underlying assumptions, char-acteristics. and relative advarttagcs :and disadvantages of various statistica1,tests arc also discussed. FOI-identitying nnultiple gross errors, corl~plexstrategies ar-e requil-ed. A plcttior;~of strategies have been proposed and evaluated in the I-csearch literatur-c.\, special eff'or? has becrr made in Chapter 8 to gi1.e :i ~inificdperspccti\c h classifying the different strategies on the basis of their core pr-inciplzs. \t'e also descr-ibe in detail a typical strategy fronl each of these classes. Chapter 9 treats the problem of gross error identification in dynamic systcr~~s. The efficacy of data reconciliation and gross error detection dependi significantly upon the location of measured variables. Recent attempts to optimally design the sensor network for rnaxinijzing accuracy of data reconciliation solution are described in Chapter 10. Several industrial applications and existent software sysienis for data reconciliation and gross error detection are also discussed in Uhaptc.1- 1 1 . Various aspects related to the benefits of offline and on-line data reconciiiation. the methods n-tostly used and their perfo~manccsare analy~cdhrre. In order to make this book self-sufficier~twith r-espect to the n:xrhi-ma tic:^? background required for- a good undzrstandirl~.:tppzridice> iiii. irlc1udc.d tl~atdescrihe the necessary b a i c co:iccpts fro111linex a!gsi?i:a. %rap11t!:co:v. atid prohabi1i;y ar;d :,ta:isiicai h\;po~hcci.;tc\tiil:.

The Importance of Data Reconciliafion and Gross Error Detection

PROCESS DATA CONDiflONLING METHODS I n aily modern chelnicni p!ant, pctrc~cheiiliiaiprocr3si or refiilel).. h~ndred5oi- eve:; tiiousai~dsof variabiei---silcfi 2s Eo\v r:;:c.s. terr?pei'atu!-cs, pres.;i!i.c;>, ie\.els. ~ : coiiij~o~i:io:~s---31-e d ~ . o L ~ : ~ Inieasured Iz!~ ail,! auio!na:icaliy I-ccoi-dedi'c o f proc
the o\lerall heat transfer coefficient is unknown and has to be estimated from the measured data, this equation may be included and U estirxiated as part of the reconciliation problem. If there is no prior information abotrt U,however, and no feasibility restrictions on it, then inclusion of this constraint does not provide any additional information and estimates of all other variables will be the same regardless of whether this constraint is included or not. Thus, the data reconciliation problem can as well be solved without this constraint and U can subsequently be estimated by the above equation using the reconciled values of flows and temperatures. On the other hand, if U has to be within specified bounds or if there is a good estimate for U from a previous reconciliation exercise (as in the c ~ u d epreheat train example discussed in the previous section, where the esti~ratesof U from the reconciliation solution of the most recent time per-iod can be used as good a pt-iol-i estimates), then the constraint should he included along with the additional information about U as part of the reconciliation problem. The overall heat transfer coefficient can also be related to the physical properties of the streams. their flows, temperatures and the heat exhangel- characte~isticsusing c o ~ ~ e l a t i o r!t~ sis. not aiivisable to use srich a:equatioi~in ths. reconcili:l:ion model since the cc~n-elatio~~ thelnseives s can be quite en-or!eot~sand forcin: the f OV,S arld te~lipera:ui-cs to fii this equation mi): i;:cr-rase the inaccuracy oi'the cs::n?a!es. Ai:othe;. inlportaii! qucstior~is \iit>Cmrrr-0111 (edited by D. E. Seborg and T. F. Edgar). Ne\i York: Engineering Foundation. 1982. 41. Tamhane, A. C., and R.S.H. Mah "Dat;~Reconciliation and GI-oss El-ror Detection in Chemical Process Nctworks." Tc~cl117or1rerr-ics 27 (1985): 409-422.

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and Challenges." J. PI-oc.

44. Mah, R.S.H. Clzemical Process Structures and Irtfonimtiorz Flows. Boston: Butterworths, 1990. 45. Bodington, C. E. Planning, Scheduling and Corztrol bztegratiorz in Process Industries. New York: McGraw-Hill, 1995. 46. Madron, F. Process Plant Performance: Measurenzer~rar~dData Processing for Oprirnizatioiz and Rerroj5t.s. Chichester, West Sussex, England: Ellis Horwood Limited Co., 1992. 47. Veverka, V. V. and Madron, F. Material and Energ?; Balancing in Process Indusiries: From Microscopic Balances t o Large Plants. Amsterdam, The Netherlands: Elsevier, 1997.

M~~~rsurctrre~rr E ~ I - o rarid s El-ror Kcducrio~rTee-hrriqur.~

33

Thus, the relation between the measured value, true value and random erici in the measurement of a variable i is expressed by Equation 1-6. In this chapter, unless otherwise required, we drop the subscript i and rewrite Equation 1-6 as

Measurement Errors and Error Reduction Techniques

where y is the measured value, x is the true value and E is the random error. The random error usually oscillates around zero. Its characteristics can be described using statistical properties of random variables which are described in Appendix C. Its mean o r e.xpected value is therefore given by,

and its var-iaizce

CLASSIFICATION O F MEASUREMENT ERRORS As mentioned in Chapter 1. there are many sources for instrument errors which deterrninc a measurement error in virtually all measured process data. Some of the nleasurernent errors are random snd srnall i ~.lii;doruer-I-CI!-sj. ~vhilc:others are s)stcn~aticand large (gross errot-s). Some authors, joch as Madron / 1 ] and Jiebman et ai. [2], prefer to dsf'ine a separate c l a s ~called .y
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Data Reconciliation & Gross Error Detection: An Intelligent Use of

, Data Reconciliation & Gross Error Detection An Intelligent Use of Process Data Shankar Narasimhan and Cornelius Jordache Publishing Company Houst...

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