1. © 2015 Bentley Systems, Incorporated
Applying Deep Learning to Finite Element Model Calibration
Research Intern: Subrata Saha
Advisor: Zheng Yi Wu

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Needs for Model Calibration
• Adequately represent conditions of in-service infrastructures
– Above- and underground infrastructure systems
• Assess infrastructure performance
– Functionality, capacity, serviceability, safety and deficiency etc.
• Support decision-making for proactive maintenance
– Be preventive instead of reactive

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What is it?
• Start with initial model, e.g. design model
• Adjust model parameters to minimize goodness-of-fit score
• Challenges: intensive computations
FE Solver
Adjust
parameters
Goodness-of-fit
score
Stop?Initial model
Measured
responses
Calibrated model

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Apply Surrogate Model
• Construct a meta-model (approximation), e.g. deep learning, or CMS
• Replace FE full analysis to Improve iterative calibration
FE Solver
Adjust
parameters
Goodness-of-fit
score
Stop?Initial model
Measured
responses
Calibrated modelSurrogate solver

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Apply Deep Learning Solution
Input parameters
FE Model Solver
Goodness-of-fit
Input parameters
Prediction
(DBN DLL)
Goodness-of-fit
Training Dataset DBN Training Trained Model

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(1) UCLA factor building model
(2) 60 decision variables
- 30 for elasticity
- 30 for stiffness
(3) 1357 beams
(4) 30 groups
Dataset

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Command
Combined
Output
Training Set Generation
• Input variables:
– 60
• Output:
– Goodness-of-fit score
• Training dataset
– 6,000
– 12 hours
1. Generate random
number using
uniform distribution
within a certain
range for each of the
decision variables
2. Compute score
using FE solver

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DBN Prediction Accuracy
10
15
20
25
30
35
40
Score
Training samples
Training
Prediction: UCLA FEM Solver score prediction
Target Predicted

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DBN Prediction Accuracy
10
15
20
25
30
35
40
Score
Training samples
Prediction: UCLA FEM Solver score
prediction
Input: hull dimensions and the boat
velocity
10
15
20
25
30
35
40
Score
Training Samples
Training
Prediction: UCLA FEM Solver score prediction
Target Predicted

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DBN Prediction Accuracy
0
5
10
15
20
25
30
35
40
45
Score
Test Samples
Prediction
Prediction: UCLA FEM Solver score prediction
Predicted Target

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Comparison between FEM and DBN Calibrator
RMS error: 0.304611778
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1 6 11 16 21 26 31 36 41 46 51 56
Value
Variable
FEM Calibrator
DBN Calibrator
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1 6 11 16 21 26 31 36 41 46 51 56
Error
Variable
DBN Calibration

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Scores from FEM and DBN Calibrator given top solution
10.63
13.43
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
Top Solution
ObjectiveValue
FEM Calibrator
DBN Calibrator
DBN Calibration

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DBN Tune Calibration
RMS error: 0.306776256
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1 7 12 17 22 27 32 37 42 47 52 57
Value
Variable
FEM Calibrator
DBN Tune
Calibrator
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1 6 11 16 21 26 31 36 41 46 51 56
Error
Variable
Comparison between FEM and DBN Tune Calibrator

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Scores from FEM and DBN Tune given top solution
10.63
11.46
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
Top Solution
ObjectiveValue
FEM Calibrator
DBN Tune Calibrator
DBN Tune Calibration

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Calibration Time
0
5
10
15
20
25
30
35
40
45
50
FEM Calibrator DBN Tune Calibrator
Calibrationtime,hour
FEM Calibrator: 48
hours
DBN Tune Calibrator:
15 hours Training Dataset
Generation: 12 hours
DBN Training: 15 minutes
DBN Predict: 45 minutes
DBN Tune: 2 hours

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Trial vs Fitness Score
10
10.5
11
11.5
12
12.5
13
13.5
0 2000 4000 6000 8000 10000 12000 14000 16000 18000
FitnessValue
No. of Trials
FEM Calibrator DBN Tune Calibrator

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Trial vs Time
0
5
10
15
20
25
30
35
40
45
50
0 2000 4000 6000 8000 10000 12000 14000 16000 18000
Time,hour
No. of Trials
FEM Calibrator DBN Tune Calibrator

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Software

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Thank You!