1. GRI-Mech Approach Data Collaboration Results
227th ACS National Meeting
April 1, 2004
OPTIMIZATION AND CONSISTENCY OF A REACTION DATASET
GRI-Mech Approach
Data Collaboration
Results
M Frenklach, R. Feeley, A. Packard and P. Seiler
Department of Mechanical Engineering
University of California, Berkeley, CA
Supported by NSF

2. thermochemical
data
GRI-Mech LOOP
experimental
data
trial mechanism

3. GRI-Mech LOOP 2 trial mechanism   active parameters thermochemical
data
GRI-Mech LOOP 2
trial mechanism
training
targets  
active parameters
validation
targets

4. EFFECT SPARSITY (G.E.P. Box)
Usually, only a small number of input and control variables would have a significant effect on the process response(s)

5. statistical surrogates
thermochemical
data
GRI-Mech LOOP 3
trial mechanism
training
targets  
active parameters 
statistical surrogates
validation
targets

6. Optimization Code
Y  Yexpt k Y
surrogate
model

7. Factorial Design of Computer Experiments
ODE
Model y1 y2  x1 x2 T P C
responses
active
variables

8. statistical surrogates
thermochemical
data
GRI-Mech LOOP 4
trial mechanism
training
targets  
active parameters 
statistical surrogates 
optimization
validation
targets

9. Polynomial Fits to Targets
flame speed = P2(k1, k2, k7, k23, …)
• • •
ignition delay = P2(k1, k4, k5, k17, …)
species conc = P2(k3, k4, k7, k12, …)
joint optimization
minimize:

10. statistical surrogates
thermochemical
data
GRI-Mech LOOP 5
trial mechanism
training
targets  
active parameters 
statistical surrogates 
optimization
validation
targets
validation
best current model

11. FURTHER DEVELOPMENTS Realistic Uncertainty in Model Prediction
Given Quadratic Form of the Surrogate Models
we apply Robust Control Theory Techniques
Examples
Realistic Uncertainty in Model Prediction
Collaboration of Data
Consistency of a Dataset

12. A FORMAL LOOK PROCESS Pi is defined: Measured Value yi
Reaction
model
Process 2 P3
Measured Value yi
Uncertainty in Di ui
Model Mi
active variables  measured property
surrogate model

13. DATASET Dataset Units optimization: P3 Process 2 Process 1 Reaction
model
Process 2 P3
optimization:

14. Data Collaboration

15. UNDERLYING CONCEPTS
Dataset
Parameters as
“internal” variables

16. Experiments
“Best”
Parameter
Values
Applications
Mechanism

17. Experiments
“Best”
Parameter
Values
Applications
Model

18. Experiments
“Best”
Parameter
Values
Uncertainty
Applications
Model

19. Experiments
Uncertainty
Assertions
Applications
Model

21. Feasible Set F H F x1 x2 +1 -1

22. MODEL PREDICTION
Process 1
Reaction
model
Process 2 P3

23. MODEL PREDICTION P3
Process 2
Reaction
model
Process 1 P0

24. MODEL PREDICTION

25. Predicting P10 using P1, P2, …, P9
Example (GRI-Mech 3.0 dataset):
Predicting P10 using P1, P2, …, P9

26. u
R10
y10 %

27. Barbara J. Grosz: Collaborative Systems
Harvard University

28. EXTREME OF NON-COLLABORATION
Frozen Core (“read my paper”)
an individual experiment is analyzed in isolation, with a single parameter (typically, most influential) determined by fitting the measurement while having fixed the remaining parameters at their literature recommended values
GRI-Mech 3.0 dataset: 77 units; 102 active variables
“No Solution” exists
in 38 of 77 cases: xi[–1,+1] such that Mj([0,…,0,xi,0,…,0]) = yj
in 5 of 77 cases: xi[–1,+1] such that |Mj([0,…,0,xi,0,…,0])–yj|10%
“Controversy” (9 such cases)
target 66  x44 [0.38, 1.0]
target 67  x44[–1.0, 0.22]

29. BETTER MODES OF DATA ANALYSIS
Free Core (possibly the best of non-collaboration)
an individual experiment is analyzed in isolation, with a single parameter (typically, most influential) determined by fitting the measurement while the remaining parameters are not “frozen” but allowed to lie in the unit hypercube
Full Data Collaboration
The entire knowledge base for the system is used for prediction

30. G H

31. F G H

32. GRI-Mech 3.0 dataset: 77 units, 102 active variables
+ a random prediction process, P0; repeated 100 times
Free-Core Mode
of Analysis
Frequency

33. GRI-Mech 3.0 dataset: 77 units, 102 active variables
+ a random prediction process, P0; repeated 100 time
(Int J Chem Kinet 36:57, 2004)
Free-Core Mode
of Analysis
Frequency
Full Data Collaboration

34. Information LOSS = 1 through 100 runs
GRI-Mech 3.0 dataset: 77 units, 102 active variables
+ a random prediction process, P0; repeated 100 times
Information LOSS =
1 through 100 runs

35. DATASET CONSISTENCY threshold uncertainty such that
for all dataset units i and some x in H

36. Pair-wise Consistency Test of GRI-Mech 3.0 Dataset
dataset unit, i
dataset unit, j
uij *

37. sensitivity of u* to bounds
target OH.1a
target OH.1b
dataset units 

38. CHECKING TARGETS (C.T. Bowman, personal communication)
INITIAL
REVISED
OH.1a
970
700
OH.1b
218
255

39. Modified GRI-Mech 3.0 Dataset
target OH.1b
using target OH.1a = 700 
target OH.1a = 700
target OH.1b = 255

40. SEQUENTIAL ANALYSIS Threshold uncertainty u*
Number of dataset units removed

41. statistical surrogates
thermochemical
data
PrIMe
Library
PrIMe
GRI-Mech procedure 5
trial mechanism
training
targets  
active parameters 
statistical surrogates 
optimization
validation
targets
validation
best current release