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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
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thermochemical data GRI-Mech LOOP experimental data trial mechanism
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GRI-Mech LOOP 2 trial mechanism active parameters thermochemical
data GRI-Mech LOOP 2 trial mechanism training targets active parameters validation targets
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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)
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statistical surrogates
thermochemical data GRI-Mech LOOP 3 trial mechanism training targets active parameters statistical surrogates validation targets
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Optimization Code Y Yexpt k Y surrogate model
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Factorial Design of Computer Experiments
ODE Model y1 y2 x1 x2 T P C responses active variables
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statistical surrogates
thermochemical data GRI-Mech LOOP 4 trial mechanism training targets active parameters statistical surrogates optimization validation targets
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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:
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statistical surrogates
thermochemical data GRI-Mech LOOP 5 trial mechanism training targets active parameters statistical surrogates optimization validation targets validation best current model
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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
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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
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DATASET Dataset Units optimization: P3 Process 2 Process 1 Reaction
model Process 2 P3 optimization:
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Data Collaboration
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UNDERLYING CONCEPTS Dataset Parameters as “internal” variables
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Experiments “Best” Parameter Values Applications Mechanism
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Experiments “Best” Parameter Values Applications Model
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Experiments “Best” Parameter Values Uncertainty Applications Model
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Experiments Uncertainty Assertions Applications Model
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Feasible Set F H F x1 x2 +1 -1
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MODEL PREDICTION Process 1 Reaction model Process 2 P3
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MODEL PREDICTION P3 Process 2 Reaction model Process 1 P0
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MODEL PREDICTION
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Predicting P10 using P1, P2, …, P9
Example (GRI-Mech 3.0 dataset): Predicting P10 using P1, P2, …, P9
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u R10 y10 %
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Barbara J. Grosz: Collaborative Systems
Harvard University
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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]
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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
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G H
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F G H
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GRI-Mech 3.0 dataset: 77 units, 102 active variables
+ a random prediction process, P0; repeated 100 times Free-Core Mode of Analysis Frequency
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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
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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
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DATASET CONSISTENCY threshold uncertainty such that
for all dataset units i and some x in H
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Pair-wise Consistency Test of GRI-Mech 3.0 Dataset
dataset unit, i dataset unit, j uij *
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sensitivity of u* to bounds
target OH.1a target OH.1b dataset units
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CHECKING TARGETS (C.T. Bowman, personal communication)
INITIAL REVISED OH.1a 970 700 OH.1b 218 255
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Modified GRI-Mech 3.0 Dataset
target OH.1b using target OH.1a = 700 target OH.1a = 700 target OH.1b = 255
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SEQUENTIAL ANALYSIS Threshold uncertainty u*
Number of dataset units removed
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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
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