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E.15 ModelUpdating and ShapeEstimation Steps

E.15.1 Model Updating Step

A static and modal model updating verification was performed for a simply supported slab measuring \(20\ \mathrm{m} \times 10\ \mathrm{m}\) with a thickness of \(1.0\ \mathrm{m}\), modeled using shell elements (S4F) and solid elements (C3D8). As shown in the figure, material properties were assigned to four regions, and eigenvalue analysis along with self-weight analysis was conducted to generate artificial measurement data. The verification examined whether, when a single material property was applied in the analysis, the material properties of the four regions used to generate the artificial measurements could be accurately estimated. A total of nine strain sensors were applied.

Figure E.15.1 Application of Material Models (by Color) and Sensor Placement Status

Design Variable Settings and Initial Values

*DesignVariable
stiff, slab1
stiff, slab2
stiff, slab3
stiff, slab4

*Material, TYPE=IsoElasticity, Name=conc
2.5e+10, 0.2, 0, 2500

Static Model Updating Results [Number of Iterations = 4]

################################################
# * Automatic generated file from ModelUpdating
# * Design variables
# stiff, slab1, 0.919989
# stiff, slab2, 0.800017
# stiff, slab3, 1.08001
# stiff, slab4, 1.11997
################################################

*Material, TYPE=IsoElasticity, Name=conc-1
2.29997e+10, 0.2, 0, 2500 

*Material, TYPE=IsoElasticity, Name=conc-2
2.00004e+10, 0.2, 0, 2500 

*Material, TYPE=IsoElasticity, Name=conc-3
2.70003e+10, 0.2, 0, 2500 

*Material, TYPE=IsoElasticity, Name=conc-4
2.79992e+10, 0.2, 0, 2500
  • Very good agreement!!!

Modal Model Updating Results (Stiffness-Only Fitting) [Number of Iterations = 12]

################################################
# * Automatic generated file from ModelUpdating
# * Design variables
# stiff, slab1, 0.915975
# stiff, slab2, 0.795228
# stiff, slab3, 1.09126
# stiff, slab4, 1.12278
################################################

*Material, TYPE=IsoElasticity, Name=conc-1
2.28994e+10, 0.2, 0, 2500 

*Material, TYPE=IsoElasticity, Name=conc-2
1.98807e+10, 0.2, 0, 2500 

*Material, TYPE=IsoElasticity, Name=conc-3
2.72815e+10, 0.2, 0, 2500 

*Material, TYPE=IsoElasticity, Name=conc-4
2.80696e+10, 0.2, 0, 2500
  • Very good agreement!!!

Modal Model Updating Results (Simultaneous Stiffness and Mass Fitting) [Number of Iterations = 69]

################################################
# * Automatic generated file from ModelUpdating
# * Design variables
# stiff, slab1, 0.946149
# stiff, slab2, 0.822749
# stiff, slab3, 1.11071
# stiff, slab4, 1.15184
# mass, slab, 1.02843
################################################

*Material, TYPE=IsoElasticity, Name=conc-1
2.36537e+10, 0.2, 0, 2571.08 

*Material, TYPE=IsoElasticity, Name=conc-2
2.05687e+10, 0.2, 0, 2571.08 

*Material, TYPE=IsoElasticity, Name=conc-3
2.77677e+10, 0.2, 0, 2571.08 

*Material, TYPE=IsoElasticity, Name=conc-4
2.87959e+10, 0.2, 0, 2571.08
  • Not bad

Bayesian Modal Model Updating Results (Stiffness-Only Fitting) [Number of Iterations = 300, Not Converged]

################################################
# * Automatic generated file from ModelUpdating
# * Design variables
# stiff, slab1, 0.917861
# stiff, slab2, 0.804127
# stiff, slab3, 1.08549
# stiff, slab4, 1.10184
################################################

*Material, TYPE=IsoElasticity, Name=conc-1
2.29465e+10, 0.2, 0, 2500 

*Material, TYPE=IsoElasticity, Name=conc-2
2.01032e+10, 0.2, 0, 2500 

*Material, TYPE=IsoElasticity, Name=conc-3
2.71373e+10, 0.2, 0, 2500 

*Material, TYPE=IsoElasticity, Name=conc-4
2.75461e+10, 0.2, 0, 2500
  • Good agreement.
  • But maximum iteration number and tolerance should be calibrated,
  • Computationally expensive, but robust

Bayesian Modal Model Updating Results (Simultaneous Stiffness and Mass Fitting) [Number of Iterations = 300, Not Converged]

################################################
# * Automatic generated file from ModelUpdating
# * Design variables
# stiff, slab1, 1.00128
# stiff, slab2, 0.870686
# stiff, slab3, 1.17542
# stiff, slab4, 1.21895
# mass, slab, 1.08835
################################################

*Material, TYPE=IsoElasticity, Name=conc-1
2.50319e+10, 0.2, 0, 2720.88 

*Material, TYPE=IsoElasticity, Name=conc-2
2.17672e+10, 0.2, 0, 2720.88 

*Material, TYPE=IsoElasticity, Name=conc-3
2.93856e+10, 0.2, 0, 2720.88 

*Material, TYPE=IsoElasticity, Name=conc-4
3.04737e+10, 0.2, 0, 2720.88
  • Good agreement. But maximum iteration number and tolerance should be calibrated,
  • But maximum iteration number and tolerance should be calibrated,
  • Computationally expensive, but robust

Input File

  • S4F.inp
  • S4F-Update.inp

E.15.2 ShapeEstimation Step

Shape estimation was performed for the slab used in Section E.15.1 (a simply supported slab measuring 20 m*10 m with a thickness of 1.0 m).

Input data: updown.dat

# sensorPoint1, sensorPoint2, ...
0.00023509,0.00032888,0.00021655,0.00023181,0.00033321,0.00020855,0.00024429,0.00035479,0.00021098
0.00023509,0,-0.00021655,0.00023181,0,-0.00020855,0.00024429,0.,-0.00021098

Figure E.15.2 Illustrative Example of ShapeEstimation

Input File

  • S4F-ShapeEstimation.inp