Célimène Anglade

Parameter identification:An application of inverse analysis to

cement-based suspensions

UPS-LMDC-INSAFrance

1

Aurélie Papon, Michel Mouret

Viscoplastic Fluids: From Theory to Application

Why are we interested in identification? To link rheological parameters to cementitious

material design To optimize the design regarding handling and

placing context

2

How to observe the behavior of cementitious materials?

Rheometer has to avoid artefacts segregation, migration, sedimentation

Complex velocity field Axial component Circular flow

Specific impeller Helical ribbon or Anchor

LMDC equipped with RheoCAD

3

[Franshahi and al. 05]

Fine particle concentration[CRPP, Bordeaux]

How to process the experimental data? Rheometer returns torques vs rotational speeds Only qualitative information, velocity and stress fields unknown

4Strong hypotheses for simple computation

For quantitative studies:Computation of the rheoCAD flow with COMSOLCoupled with an identification by means of inverse analysis

Cementitious materials: Viscoplastic fluids

Bingham law

Shear-thinning

Shear-thickening

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[Yahia and al., 01], [Papo, 88]

Order of magnitude for cement pastes:

[Cyr, Ph.D, 99]

Numerical modeling

Continuous and homogeneous medium, no slipping Steady-state, incompressible, laminar and adiabiatic Two-dimensional flow

1. Hypotheses

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2. Model Geometry [mm]:

Simplified model to validate the identification process

A flow behavior index variation impact on the curvature

3. Sensitivity study:

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Numerical modeling

A flow consistency index variation impact on the slope

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3. Sensitivity study:

Numerical modeling

A yield stress variation translation

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3. Sensitivity study:

Numerical modeling

Parameter identification1. Principle

10 No experimental torque here, validation on computational data

Parameter identification1. Principle

11 Simulation with COMSOL, assumption of parameter set

Parameter identification1. Principle

12 Choice of an objective function for gap estimation

Parameter identification1. Principle

13 Choice and test of optimization algorithm

Parameter identification2. Objective function

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Parameter identification

Simplex method:

A (m+1) vertex polyhedron « strolling » on objective function surface with m the number of parameters.

Vertices are directed towards objective function minimum.

Only one solution: local or global minimum?

3. Deterministic optimization algorithm

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Parameter 1

Parameter 2

[Nelder and Mead, 65]Example for 2 parameter identification:

Parameter identification3. Stochastic optimization algorithm

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Genetic algorithm:

First population (parameter set collection) created randomly, objective function evaluation for each individual (parameter set).

Formation of new population by crossover and mutation (perturbation) of individuals.

Selection of individual created for building of new population

Much longer as simplex but several solutions.

Parameter 1

Parameter 2

[Holland, 75; Poles, 03]

Parameter identification4. Results

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Results very dependent on the initialization.

(35-25-1) compatible with the device error (0.005 N.m).

Satisfactory triplet? (depending on experimental scatter)

Parameter identification4. Results

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Right triplet comes out from the 4th generation.GA procedure is 8 times longer than the simplex one.

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Objective function is regular,simplex may be adequate.

Parameter identification4. Results Objective function

(N.m)

Conclusions Validation of an identification procedure for numerical

cases

2 kinds of optimization algorithms:

Compromise?

Shape of the objective function is decisive.

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Simplex GAComputational time + -

Quality of the results (fiability, sensitivity, availability) - +

Prospects

21

Célimène Anglade

Parameter identification:An application of inverse analysis to

cement-based suspensions

UPS-LMDC-INSAFrance

22

Aurélie Papon, Michel Mouret

Viscoplastic Fluids: From Theory to Application

Cementitious materials behaviour

In 88, Papo: Herschel-Bulkley minimize the most errors In 01, Yahia et al.: The best for all shear rate De Kee

For small shear rate Herschel-Bulkley

Behaviour law in literature

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Cementitious materials model Model

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Parameter identification

Genetic algorithm:4. Results

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For (25-15-0.5):

Parameter identification

Simplex algorithm on (25-15-0.5):4. Results

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Results are very dependant at the initialization. Good triplet appears only one time.