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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
5
[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
6
2. Model Geometry [mm]:
Simplified model to validate the identification process
A flow behavior index variation impact on the curvature
3. Sensitivity study:
7
Numerical modeling
A flow consistency index variation impact on the slope
8
3. Sensitivity study:
Numerical modeling
A yield stress variation translation
9
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
14
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
15
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
17
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
18
Right triplet comes out from the 4th generation.GA procedure is 8 times longer than the simplex one.
19
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.
20
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
23
Cementitious materials model Model
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Parameter identification
Genetic algorithm:4. Results
25
For (25-15-0.5):
Parameter identification
Simplex algorithm on (25-15-0.5):4. Results
26
Results are very dependant at the initialization. Good triplet appears only one time.