IAEA TECDOC Uncertainty Evaluation in Best Estimate Uncertainty - - PowerPoint PPT Presentation

IAEA TECDOC IAEA TECDOC – – Uncertainty Evaluation in Best Estimate Uncertainty Evaluation in Best Estimate Safety Analysis for Nuclear Power Plants Safety Analysis for Nuclear Power Plants APPROACH AND METHODS TO EVALUATE THE APPROACH AND METHODS TO EVALUATE THE UNCERTAINTY IN SYS UNCERTAINTY IN SYS-

• TH CALCULATIONS

TH CALCULATIONS

• F. D’Auria (UNIPI, I), H. Glaeser (GRS, D), R. R. Schultz (INEEL, US)

DIPARTIMENTO DI INGEGNERIA MECCANICA, NUCLEARE E DELLA PRODUZIONE UNIVERSITA' DI PISA 56100 PISA – ITALY (fax +39-050-8366-65, email dauria@ing.unipi.it)

OECD/CSNI Workshop OECD/CSNI Workshop

Evaluation of Uncertainties in relation to Severe Accidents Evaluation of Uncertainties in relation to Severe Accidents and Level 2 Probabilistic Safety Analysis and Level 2 Probabilistic Safety Analysis

November 7 November 7-

• 9, 2005

9, 2005 – – Aix Aix-

• En

En-

• Provence

Provence, (FRANCE) , (FRANCE)

• Framework for Uncertainty in SYS-TH
• The Origin of Uncertainty
• The Approaches for Uncertainty
• Topics Relevant for Uncertainty Evaluation

(TRUE)

• The CIAU Methodology
• Conclusions

CONTENT CONTENT

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CONSISTENT APPLICATION OF A THERMOHYDRAULIC SYSTEM CODE

Framework Framework for for Uncertainty Uncertainty in SYS in SYS-

• TH

TH

CODE DEVELOPMENT & IMPROVEMENT (1) CODE ASSESSMENT (4) CODE USE (NPP) (5) UNCERTAINTY UNCERTAINTY EVALUATION (6) EVALUATION (6) EXPERIMENTAL DATA (2) PROCEDURES FOR CODE USE (3)

NEEDS FOR UNCERTAINTY

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A) Balance (or conservation) equations are approximate:

• Not all the interactions between steam and liquid are included;
• Equations solved within cylindrical pipes (no geometric discontinuity):

situation not common for NPP. Lacking info to be supplied by code user.

B) Presence of different fields of the same phase: e.g. liquid droplets and film. Only one velocity per phase is considered by codes. C) Geometry averaging at a cross section scale: POROUS MEDIA

• APPROACH. Velocity profiles happen in the reality: OPEN

MEDIA APPROACH (CFD LIKE). D) Geometry averaging at a volume scale: only one velocity vector (each phase) is associated with a hydraulic mesh along its axis.

Different velocity vectors may occur in the reality (inside LP, connection CL-DC)

E) Presence of large and small vortex or eddy. Energy and momentum dissipations not directly accounted.

A large vortex may determine system behaviour (e.g. two-phase natural circulation between hot and cold fuel bundles).

The Origin of Uncertainty The Origin of Uncertainty

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F) The 2nd principle of thermodynamics is not necessarily fulfilled by codes. G) The numerical solution is approximate. Approximate equations are solved by approximate numerical methods.

The ‘amount’ of approximation is not documented.

H) Extensive use is made of empirical correlations:

• Range of validity not fully specified;
• Unavoidably used outside their range of validation;
• Approximately implemented into the code;
• Reference database affected by scatter and errors.

I) Paradox: ‘Steady State’ & ‘Fully Developed’ (SS & FD) flow approximation adopted. However all qualified correlations must be derived under SS & FD conditions. Almost in no region of the NPP those conditions apply.

The Origin of Uncertainty The Origin of Uncertainty

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J) State and material properties are approximate. Specifically true for derivatives of water properties. K) Code User Effect (UE) exists. Two or more groups of users having available the same code and the same input information do not achieve the same results. UE due to:

• nodalization development;
• interpreting supplied information (usually incomplete);
• accepting a steady state performance of the nodalization;
• interpreting transient results, planning sensitivity studies, modifying

(arbitrarily) the nodalization.

L) The computer/compiler installation affects the predictions of a code (computer/compiler effect). Very recent computers, compilers, and code releases did not improve the situation depicted a number of years ago.

The Origin of Uncertainty The Origin of Uncertainty

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M) Nodalization (N) effect exists. The N is the result of a wide range brainstorming process where user expertise, computer power and code manual play a role.

There is a number of required code input values that cannot be covered by logical recommendations: the user expertise needed to fix those may reveal inadequate.

N) Imperfect knowledge of Boundary and Initial Conditions (BIC). Some BIC values are unknown or known with approximation: the code user must add information. O) Severe physical model deficiencies, which are unknown to the code user, cannot be excluded even in the latest versions of the advanced system codes.

The achieved results may flyaway from reality in a way not understandable by the code user.

The Origin of Uncertainty The Origin of Uncertainty

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PRELIMINARY STATEMENTS FOR THE DESIGN OF AN UNCERTAINTY METHOD Uncertainty Origins (UO) from A) to J) embedded into the Code. Effects of UO from K) to M) can be made milder by following Procedures, possibly part of Code Manuals. UO N) and O) have to be carefully considered. Definitely, all UO have to be considered when developing an Uncertainty Method. CURRENT SITUATION A Dozen Methods Available. Reviews Published.

The Approaches to Calculate Uncertainty The Approaches to Calculate Uncertainty

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CLASSIFICATION ADOPTED HEREAFTER Difference between INPUT and OUTPUT PROPAGATION

PROPAGATION OF CODE INPUT “UNCERTAINTIES” PROPAGATION OF CALCULATION OUTPUT “ERRORS”

Alternative Classification

“PURELY” DETERMINISTIC METHOD “PURELY” STATISTIC METHOD USE OF STATISTICS COMBINATIONS OF THE VARIOUS APPROACHES CAN BE PURSUED

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The Approaches to Calculate Uncertainty The Approaches to Calculate Uncertainty

PROPAGATION OF CODE INPUT “UNCERTAINTIES”

THERMALHYDRAULIC SYSTEM CODE

1 1 2 2 n m

Multiple input (n) Multiple output (m)

THE PROPAGATION OF CODE INPUT UNCERTAINTIES IMPLIES THAT THE PROPAGATION OF CODE INPUT UNCERTAINTIES IMPLIES THAT ‘n*’ must be selected with ‘n*’ of the order of 102 and << ‘n’ range of variations and/or Probability Distribution Function (PDF) must be assigned to each of the ‘n*’ parameters

• ‘n’ can be as large as 105
• the dimension of ‘m’ is not a main concern

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The Approaches to Calculate Uncertainty The Approaches to Calculate Uncertainty

PROPAGATION OF CODE INPUT “UNCERTAINTIES”

ERROR BANDS RANGE AND/OR PDF Output Uncertainty

2 1 n*

THERMALHYDRAULIC SYSTEM CODE Input Uncertainty

PATH FOR UNCERTAINTY EVALUATION PATH FOR UNCERTAINTY EVALUATION

DRAWBACKS: DRAWBACKS:

Engineering judgment needed to select:

• ‘n*’ starting from ‘n’
• range and/or PDF for each ‘n*’

The error propagation occurs through the code that, by definition, is an ‘imperfect’ tool

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The Approaches to Calculate Uncertainty The Approaches to Calculate Uncertainty

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THE PROPAGATION OF INPUT UNCERTAINTIES THE PROPAGATION OF INPUT UNCERTAINTIES

Multiple Input Multiple Input n n ~ 10 ~ 105

5

BIC CODE INPUT DECK

1 2 n

Selection Selection of input

• f input

uncertain parameters uncertain parameters n* n* < 10 < 102

2

ID of ID of range range & PDF & PDF per per each each n* n*

Multiple Output Multiple Output m m ~ 10 ~ 103

3

( (typical typical, , uninfluent uninfluent) )

1 2 m

Predicted Predicted NPP NPP transient transient scenario scenario UNCERTAINTY PROPAGATION

RELEVANT EXPERIMENTS Multiple output (m)

2 1 n

THERMALHYDRAULIC SYSTEM CODE Multiple input (n)

2 1 m

ERROR BANDS

PROPAGATION OF CALCULATION OUTPUT “ERRORS” DRAWBACKS: DRAWBACKS:

The process of ‘extrapolation’ of output errors is not based upon fundamental principles It is impossible to distinguish contributions to the output error bands

PATH FOR UNCERTAINTY EVALUATION PATH FOR UNCERTAINTY EVALUATION

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The Approaches to Calculate Uncertainty The Approaches to Calculate Uncertainty

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THE PROPAGATION OF OUTPUT UNCERTAINTIES THE PROPAGATION OF OUTPUT UNCERTAINTIES

Multiple Input Multiple Input n n ~ 10 ~ 105

5

BIC CODE INPUT DECK

1 2 n

Multiple Output Multiple Output m m ~ 10 ~ 103

3

( (typical typical, , uninfluent uninfluent) )

1 2 m

Predicted Predicted NPP NPP transient transient scenario scenario UNCERTAINTY PROPAGATION Relevant Relevant experimental experimental data data Accuracy quantification Accuracy quantification & & criteria for accuracy criteria for accuracy extrapolation extrapolation

Topics Topics Relevant Relevant for Uncertainty Evaluation for Uncertainty Evaluation (TRUE)

(TRUE)

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1) NODALISATION CHOICES

Results from the LBLOCA DEGB DBA Angra-2 analysis: different input decks (nodalisation user choices) produce different effects upon relevant code output parameter, i.e. ΔPCT

2) CODE VERSIONS

Results from the SBLOCA BDBA UMS transient analysis: different code versions (same developer) have a strong impact in the prediction of a relevant uncertainty parameter, i.e. PCT

3) BIFURCATIONS

Results from a bifurcation study related to the SBLOCA BDBA UMS transient analysis. This study is possible with the availability of the Code with Capability of Internal Assessment of Uncertainty (CIAU).

Topics Topics Relevant Relevant for Uncertainty Evaluation for Uncertainty Evaluation (TRUE)

(TRUE)

16/33

NODALISATION CHOICES

UNIPI UNIPI Internal Report Internal Report, 2001 , 2001

50.0 100.0 150.0 200.0 250.0 300.0 Time (s) 200 400 600 800 1000 1200 1400 1600 1800 Temperatutre (K)

WinGraf 4.1 - 05-25-2001

XXX tr02b httemp121200915 X X X X X X X X X X X X X X X X X X X X YYY tr03b httemp121200915 Y Y Y Y Y Y Y YY Y Y Y Y Y Y Y Y Y Y Y ZZZ tr12b httemp121200915 Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z VVV tr13b httemp121200915 V V V V V V V V V V V V V V V V V V V V JJJ tr14b httemp121200915 JJ J J J JJ J J J J J J J J J J J J

PCT PCT obtained with

• btained with the

the same same code code-

• version

version and and different different RPV RPV-

• UP

UP noding noding PCT PCT

Topics Topics Relevant Relevant for Uncertainty Evaluation for Uncertainty Evaluation (TRUE)

(TRUE)

17/33

NODALISATION CHOICES

UNIPI UNIPI Internal Report Internal Report, 2001 , 2001

Two Two problems detected problems detected: : a) a) Reference Reference PCT PCT affected by affected by nodalisation ( nodalisation (choices choices) ) b) b) Δ ΔPCT PCT strongly affected by strongly affected by nodalisation (i.e. a nodalisation (i.e. a given given input input uncertain parameter uncertain parameter is is relevant relevant or

• r not

not depending depending upon upon the the selected selected nodalisation ( nodalisation (see see the the diagram below diagram below) ) The The conclusion conclusion at at item item b) b) is is also also applicable applicable to to different different codes codes. .

• 6 0 0
• 5 0 0
• 4 0 0
• 3 0 0
• 2 0 0
• 1 0 0

1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 1 5 9 1 3 1 7 2 1 2 5 2 9 3 3 3 7 4 1 4 5 4 9 5 3 5 7 6 1

C as e N o. (-) PCT (K) X Y Z

Different Different nodalisations nodalisations

• riginate
• riginate different

different Δ ΔPCT PCT

Topics Topics Relevant Relevant for Uncertainty Evaluation for Uncertainty Evaluation (TRUE)

(TRUE)

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NODALISATION CHOICES

UNIPI UNIPI Internal Report Internal Report, 2001 , 2001

LESSON LEARNED LESSON LEARNED THE PROCESS OF PROPAGATING UNCERTAINTY THROUGH THE PROCESS OF PROPAGATING UNCERTAINTY THROUGH THE CODE THE CODE ( (propagation propagation of code input

• f code input uncertainty

uncertainty) ) IS IS AFFECTED BY THE CODE AND BY THE NODALISATION: AFFECTED BY THE CODE AND BY THE NODALISATION: AN ASSIGNED INPUT UNCERTAIN PARAMETER AN ASSIGNED INPUT UNCERTAIN PARAMETER MAY AFFECT MAY AFFECT Δ ΔPCT IN ONE DIRECTION OR IN ANOTHER PCT IN ONE DIRECTION OR IN ANOTHER DEPENDING UPON THE STRUCTURE OF THE INPUT DEPENDING UPON THE STRUCTURE OF THE INPUT DECK (AND OF THE CODE). DECK (AND OF THE CODE).

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CODE VERSIONS/SAME INPUT DECK

Paper co-authored by UMS participants at BE-2000

Topics Topics Relevant Relevant for Uncertainty Evaluation for Uncertainty Evaluation (TRUE)

(TRUE)

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CODE VERSIONS/SAME INPUT DECK

UNIPI UNIPI Internal Report Internal Report, 1999 , 1999

Topics Topics Relevant Relevant for Uncertainty Evaluation for Uncertainty Evaluation (TRUE)

(TRUE)

EXP XXXX EXP XXXX “OLD” code* YYYY “OLD” code* YYYY “INTERMEDIATE” code* ZZZZ “INTERMEDIATE” code* ZZZZ “NEW” code* VVVV “NEW” code* VVVV * * All All ‘ ‘frozen’ frozen’ code code versions versions

21/33

CODE VERSIONS/SAME INPUT DECK

UNIPI UNIPI Internal Report Internal Report, 1999 , 1999

Topics Topics Relevant Relevant for Uncertainty Evaluation for Uncertainty Evaluation (TRUE)

(TRUE)

LESSON LEARNED LESSON LEARNED CODE VERSIONS CODE VERSIONS (HIGHLY EVALUATEDAND QUALIFIED

(HIGHLY EVALUATEDAND QUALIFIED SYS SYS-

• TH CODE),

TH CODE), WITH THE SAME INPUT DECK,

WITH THE SAME INPUT DECK, HAVE STRONG IMPACT UPON RESULTS HAVE STRONG IMPACT UPON RESULTS AND AFFECT UNCERTAINTY PREDICTION AND AFFECT UNCERTAINTY PREDICTION THEREFORE, ‘DIRECT’ SPECIFIC CODE THEREFORE, ‘DIRECT’ SPECIFIC CODE QUALIFCIATION NEEDED FOR UNCERTAINTY QUALIFCIATION NEEDED FOR UNCERTAINTY EVALUATION EVALUATION

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BIFURCATIONS

UNIPI UNIPI Paper Paper, 2000 , 2000

Topics Topics Relevant Relevant for Uncertainty Evaluation for Uncertainty Evaluation (TRUE)

(TRUE)

SCENARIOS CAN BE IMAGINED WHERE BIFURCATIONS BRING THE TRANSIENT EVOLUTION FAR FROM THE BEST-ESTIMATE DETERMINISTIC PREDICTION, THUS INVALIDATING THE CONNECTED UNCERTAINTY EVALUATION. THEREFORE, A BIFURCATION ANALYSIS MAY REVEAL NECESSARY. STARTING POINTS FOR THE BIFURCATION ANALYSIS ARE: THE IDENTIFICATION OF TYPE ONE AND OF TYPE TWO BIFURCATIONS THE KNOWLEDGE OF THE UNCERTAINTY CHARACTERIZING THE PARAMETERS WHICH AFFECT THE BIFURCATION.

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BIFURCATIONS

UNIPI UNIPI Paper Paper, 2000 , 2000

Topics Topics Relevant Relevant for Uncertainty Evaluation for Uncertainty Evaluation (TRUE)

(TRUE)

2 4 6 8 10 12 14 16 18 20 200 400 600 800 1000 1200

Time (s) Pressure (MPa)

3a sup 3b inf 3a inf 3b sup 3b 3a

Upper Uncertainty Bound Lower Uncertainty Bound UP Pressure (Nominal Calculation)

(Simplified) ‘Tree’ of uncertainty bands resulting from the bifurcation study: Primary System Pressure

24/33

BIFURCATIONS

UNIPI UNIPI Paper Paper, 2000 , 2000

Topics Topics Relevant Relevant for Uncertainty Evaluation for Uncertainty Evaluation (TRUE)

(TRUE)

Standard CIAU application to UMS

400 450 500 550 600 650 700 750 200 400 600 800 1000 1200 Time (s) Temperature (K)

Upper Uncertainty Bound Lower Uncertainty Bound Calc Exp

• 100.0

100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0 900.0 Time (s) 400 600 800 1000 1200 1400 1600 Temperature (K)

XXX ls03 httemp902000910 X X X X X X X X X X X X X X X X X X X X YYY ls1a httemp902000910 Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y ZZZ ls1b httemp902000910 Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z VVV ls2a httemp902000910 V V V V V V V V V V V V V V V V V V V V JJJ ls2b httemp902000910 J J J J J J J J J J J J J J J J J J J J HHH ls2c httemp902000910 H H H H H H H H H H H H H H H H H H H H ### ls2d httemp902000910 # # # # # # # # # # # # # # # # # # # OOO ls3a httemp902000910 O O O O O O O O O O O O O O O O O O O O AAA ls3b httemp902000910 A A A A A A A A A A A A A A A A A A A A BBB ls3c httemp902000910 B B B B B B B B B B B B B B B B B B B B

Time (s) Temperature (K)

Bifurcation CIAU boundaries for UMS UMS results obtained By AEAT (and ENUSA)

25/33

BIFURCATIONS

UNIPI UNIPI Paper Paper, 2000 , 2000

Topics Topics Relevant Relevant for Uncertainty Evaluation for Uncertainty Evaluation (TRUE)

(TRUE)

LESSON LEARNED LESSON LEARNED BIFURCATION STUDY IS POSSIBLE BIFURCATION STUDY IS POSSIBLE BIFURCATION STUDY PRODUCES BIFURCATION STUDY PRODUCES (

(as as expected expected) )

WIDER UNCERTAINTY BANDS WIDER UNCERTAINTY BANDS (

(as as related related to to the the standard standard uncertainty uncertainty study study) )

THE UMS AEAT THE UMS AEAT (

(extreme extreme) ) RESULT IS

RESULT IS (

(basically basically) )

REPRODUCED BY THE CIAU BIFURCATION STUDY REPRODUCED BY THE CIAU BIFURCATION STUDY

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The CIAU Method: the Idea The CIAU Method: the Idea

NPP STATUS NPP STATUS HYPERCUBE TIME INTERVAL “ERROR” DATABASE RELEVANT EXPERIMENTS CODE APPLICATION RESULTS Error filling process NPP UNCERTAINTY NPP UNCERTAINTY PREDICTION PREDICTION Error extraction process NPP CALCULATION NPP CALCULATION &

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ITF Nodalizations Specific experimental data ITF Calculation Accuracy Quantification (°) Accuracy Extrapolation (°) Generic experimental data ASM Calculation a i h j GI FG g c d e f l LN (°) m n YES FG k

(°) Special methodology developed

Stop of the process NO NO Demonstration

• f Similarity (°)

(Phenomena Analysis) (Scaling Laws)

Code

Nodalization and user qualification General Qualification Process b

Uncertainty

Plant nodalization Plant calculation

The CIAU Method: the Engine The CIAU Method: the Engine

The UMAE methodology is the Engine and the Qualification Tool to run the CIAU idea

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The CIAU Method: the Flow The CIAU Method: the Flow-

• Diagram

Diagram

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The CIAU Method: the Application The CIAU Method: the Application

1) The Angra-2 DEGB licensing calculation

The CIAU Method: the Application The CIAU Method: the Application

2) The Kozloduy-3 200 mm break to show similarity of code results

The CIAU Method: the Application The CIAU Method: the Application

3) The Kozloduy-3 500 mm DEGB – support for demonstrating DBA

300 1300 2300 100 200 300 400 500 600 700

Time (s) Temperature (K)

Lower Uncertainty Limit Reference Value Upper Uncertainty Limit

1945 K (PCT in hot rod for code run 6 in Tab. 7-2) 1422 K (PCT in hot rod from ref. [7]) 350 s (all rod quenched from ref. [7]) > 700 s (all rod quenched for code run 6 in Tab. 7-2) – VALUE OUT OF SCALE

BE calc & Lower and Upper

• Unc. Bands

‘Rigorous’ conservatism ‘Driven’ conservatism

Licensing Threshold

CONCLUSIONS CONCLUSIONS

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• UNCERTAINTY ORIGINS IN

UNCERTAINTY ORIGINS IN TH TH-

• SYS

SYS CLASSIFIED. CLASSIFIED.

• “USER EFFECT” AND “CV+J” APPROACH ARE IMPORTANT

SOURCES OF UNCERTAINTY.

• APPROACHES FOR UNCERTAINTY IDENTIFIED.

APPROACHES FOR UNCERTAINTY IDENTIFIED.

• PROPAGATION OF CODE INPUT UNCERTAINTY & PROPAGATION

OF CODE OUTPUT ERROR HAVE BEEN DISTINGUISHED

• TOPICS EMPHASIZED FOR UNCERTAINTY METHOD

TOPICS EMPHASIZED FOR UNCERTAINTY METHOD DEVELOPMENT & APPLICATION DEVELOPMENT & APPLICATION (TRUE) (TRUE) . .

• MATURE UNCERTAINTY METHODS EXIST FOR DBA AND

MATURE UNCERTAINTY METHODS EXIST FOR DBA AND TH TH-

• SYS (ROLE OF 3D NK).

SYS (ROLE OF 3D NK).

NEED TO SPREAD THE TECHNOLOGY

• CIAU

CIAU METHODOLOGY HAS BEEN OUTLINED. METHODOLOGY HAS BEEN OUTLINED.

• THE IDEA
• THE ENGINE
• THE RESULTS FROM APPLICATIONS