Practical diagnosis analysis techniques and behaviour models

Alexandre Simon (EDF/DTG)Thierry Guilloteau (EDF/DTG)

Division Production Ingénierie Hydraulique - DTG Monday, May 12, 2014H-44200965-2014-000190-A2

Statistical models : HST methodFormulation : Yb = f1(t) + f2(z) + f3(S) + ε (Yb can represent displacement,

piezometric level, flow rate, …)Irreversible trend ( time-dependant) : f1(t) = a1 e-t/t0 + a2 t with t0 : characteristic time of exponential decrease

Hydrostatic reversible influence (depends on hydrostatic load ~z): f2(z) = a3 z + a4 z2 + a5

z3 + a6 z4

Seasonal reversible influence (depends on the season S; S=0 1st January and 2π 31st December) : f3(S) = a7 cos(S) + a8 sin(S) + a9 sin(2 S) + a10 cos(2S)

ε : residuals (inaccuracy of the model)

Reference :Willm G., Beaujoint N. (1967). Les méthodes de surveillance des barrages au service de la production hydrauliqued’Électricité de France. Problèmes anciens et solutions nouvelles. In : Proc. of the Ninth International Congress on Large Dams, Istanbul, 1967, pp. 529-550.

Yb

YcDownstream

Rad

ial D

ispl

ace

me

nt in

mm

Division Production Ingénierie Hydraulique - DTG Monday, May 12, 2014H-44200965-2014-000190-A3

Thermal HST (HSTT)

HST approximation: thermal effect is identical each year.Heat or cold waves are not taken into accountImprovement of HST : integration of air temperature (difference of seasonal temperature and then delayed) Used for displacements of arched dams and thin gravity dams.

FG 582-519

-10,0

-8,0

-6,0

-4,0

-2,0

0,0

1990 1991 1992 1992 1994 1995 1996 1996 1998 1999 2000 2000 2002 2003

Date

Dé

pla

ce

me

nt

(mm

)

aval

Pendule

Analyse HST classique sur 10/01/1990 - 24/12/2003

R = 0,97, S' = 1,22

Reference :Penot I., Daumas B., Fabre J.-P. Electricité De France(2005). Monitoring Behavior. In : Water Power & Dam Construction, December 2005, pp. 24-27.

Yb = f1(t) + f2(z) + f3(S) + k*∆ΘR+ε’

Same expression as HST

Thermal sensitivity of the dam

Differencewithseasonaltemperature, and thendelayed

FG 582-519

-10,0

-8,0

-6,0

-4,0

-2,0

0,0

1990 1991 1992 1992 1994 1995 1996 1996 1998 1999 2000 2000 2002 2003

Date

Dépla

cem

ent (

mm

)

aval

Pendule

Analyse HST Thermique sur 10/01/1990 - 24/12/2003

R = 0,99, S' = 0,60

T90 = 19 jours , Coefficient thermique = -0,53 mm/°C

Témoin température de l'air = MONESTIER

Division Production Ingénierie Hydraulique - DTG Monday, May 12, 2014H-44200965-2014-000190-A4

Statistical models : EFR method

Analysis of piezometric levels which do not react instantaneously with water levelCalculation of a « delayed water level » : takes into account the historic of water levelMethod used for analyze of piezometric level in real timeApplied for zoned-earth dams, rockfill dams

Analyses performed since 1992

upstream dow nstream

Im perv ious ea rth (c lay co re )

Perm eab le earth

Perm eab le ea rth

E qu ipo ten tia l o f po re w a ter p ressure

D ra in

F ilte r

V ib ra ting W ire P iezom ete r

Yb = f1(t) + f3(S) + Ze(T0)+Ze

2 (T0) +Ze3 (T0)+Ze

4 (T0) +ε

Same expression as HST

Delayed hydrostatic effect (T0 : characteristic time)

Yb

HST

EFR

Reference : Fabre J.P., 1992, L’analyse retard, note techique EDF-DTG and CIGB2009, BraziliaAdapatation de l’exploitation des barrages pour maîtriser leur sollicitation : exemples de Laouzas, Gage et Grande Pâture

Division Production Ingénierie Hydraulique - DTG Monday, May 12, 2014H-44200965-2014-000190-A5

The need for new models

New models :HST NL : designed for analysis of piezometric levels affected by fracturation of foundation and non-linear phenomena. Effects (irreversible, hydrostatic, seasonal) are dependant (they are not simply added).

HST HY : designed for analysis of drainage flows and for piezometric levels affected by fluctuation (induced by hydrostatic or thermal effects) of permeability. Effects are also dependant.

HST HY and HST NL can be combined : HST HY NL

Artificial Neural Networks : powerful tool, numerical performance and links between explanatory variables are highlighted (same or better than HST HY NL), thresholds and physical limits of phenomena are taken into account

In developmentUse of air, water or concrete temperature in order to analyze displacements of thin arch dams

Division Production Ingénierie Hydraulique - DTG Monday, May 12, 2014H-44200965-2014-000190-A6

Threshold effect : in summer contact (cracking) between dam and foundation is closed : displacements towards the upstream side are bounded NL = different slopes for evaluation of effect

HST NL (Non Linear)

Linear slope

Infiniteasymptote

Infiniteasymptote

Sigmoid curve

threshold

Differentslopes underthreshold

Division Production Ingénierie Hydraulique - DTG Monday, May 12, 2014H-44200965-2014-000190-A7

HST NL

Decrease of dispersion on corrected measurement : 30% (HST to HST NL)

Hydrostatic effect depends on the season

Seasonal effect depends on the hydrostatic load

Division Production Ingénierie Hydraulique - DTG Monday, May 12, 2014H-44200965-2014-000190-A8

HST HY

Used tu analyse piezometric levels which are affected by cracking of foundation.

Principle : a « length of fracturation » LF is a function of hydrostatic load, season and time :

LF = g1(z) + g2(S) + g3(t) (like HST)

The piezometric level NP depends of LF according to the following equation

NP = Nd+(hydrostatic load(z))*LF where Nd is the piezometric level at downstream

Non linear equation because hydrostatic load depends on z and LF depends on S and t.

Hydrostatic load (resp. seasonal effect or irreversible effects) depends on season (resp. hydrostatic and irreversible effects)

DOWNSTREAMUPSTREAM

Central block

FoundationGrout curtain

Hydrostatic load

Drainage

Upstream decompression cracking

Dowstreamcompression : impervious

Reference : Mauris F., Sausse J., Fabre J.-P., Uplift in arch Dam Foundation, Lessons learned from 42 monitored dams in France , 9th ICOLD European Club Symposium, 10-12 April 2013, Venice, Italy

Division Production Ingénierie Hydraulique - DTG Monday, May 12, 2014H-44200965-2014-000190-A9

HST HY : results

Comparison HST versus HST HYPiezometer 3.3 Roselend

Raw MeasurementsHST correctionHST HY correction

years

Pie

zom

etri

cle

vel

DispersionHST : 4.1 mHST HY : 3,4 m

Division Production Ingénierie Hydraulique - DTG Monday, May 12, 2014H-44200965-2014-000190-A10

Artificial Neural Networks ANN (1/2)

PPG4 (piezometric level) is sensitive to hydrostatic load and the state of cracking of the foundation.

Explanatory variables of ANN : z, cosS, sinS, t; other variables of HST can be easily built by ANN ;

39 parameters (against 10 for HST)

Iterative process to converge (200000 iteration for PPG4)

Division Production Ingénierie Hydraulique - DTG Monday, May 12, 2014H-44200965-2014-000190-A11

Artificial Neural Networks ANN (2/2)Dispersion decrease of 40% (HST versus ANN)

April : dam is at its coldest foundation, cracking reaches its maximum, higher slope for hydrostatic load (red)

October : maximum thermal expansion of the dam, state of cracking at its minimum, slope of hydrostatic effect is the slowest

Same effect can be observed on the seasonal effect

HST-corrected data still shows a seasonal aspect correction. This cyclical aspect has disappeared with ANN

Best performance of ANN thanks to the seasonally-dependant hydrostatic effect.

Reference :Simon A., Royer M., Mauris F., Fabre J.P. , Electricité de France, Analysis and Interpretation of Dam Measurements using Artificial Neural Networks, 9th ICOLD European Club Symposium, 10-12 April 2013, Venice, Italy

Division Production Ingénierie Hydraulique - DTG Monday, May 12, 2014H-44200965-2014-000190-A12

Multi-component analyze : PCA Principal Component Analysis

Example of use : displacement measured by pendulums (corrected measurements) ; aim of PCA : reducing number of sensors and identifying links between sensors

Division Production Ingénierie Hydraulique - DTG Monday, May 12, 2014H-44200965-2014-000190-A13

Conclusion

1967 1992 2004 2008-2012

HST EFR HSTT

HST HYHST NLANN

Raw Data are still analyzed (Sometimes HST can not be performed)Thanks to the development of micro-computer EFR was developed in the early 90’sHeat wave in 2003 : development of Thermal HSTAnalysis of state of cracking for arch dams : HST HY NL and ANN