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revised_slides_subrata_version_5
- 1. © 2015 Bentley Systems, Incorporated
Applying Deep Learning to Finite Element Model Calibration
Research Intern: Subrata Saha
Advisor: Zheng Yi Wu
- 2. 2 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
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
- 3. 3 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
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
- 4. 4 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
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
- 5. 5 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
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
- 6. 6 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
(1) UCLA factor building model
(2) 60 decision variables
- 30 for elasticity
- 30 for stiffness
(3) 1357 beams
(4) 30 groups
Dataset
- 7. 7 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
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
- 8. 8 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
DBN Prediction Accuracy
10
15
20
25
30
35
40
Score
Training samples
Training
Prediction: UCLA FEM Solver score prediction
Target Predicted
- 9. 9 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
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
- 10. 10 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
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
- 11. 11 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
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
- 12. 12 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
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
- 13. 13 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
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
- 14. 14 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
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
- 15. 15 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
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
- 16. 16 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
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
- 17. 17 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
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