Figure 1
Flammability limits experimental data volume distribution (Molnarne, Schendler and Schröder, 2008).
Figure 2
Influence of inert gas admixtures on explosion region (473.15 K) (Data from Molnarne, Schendler and Schröder, 2008).
Figure 3
Data augmentation method (H2–Air–Ar data at 373.15 K).
Figure 4
Models input feature structures.
Table 1
Process parameters and variables.
| FACTORS | LEVEL 1 | LEVEL 2 |
|---|---|---|
| A. Hidden Layers | • 120,60,30 | • 100,50 |
| B. Solver | • lbfgs | • Adam |
| C. Alpha | •0.00001 | • 0.001 |
| D. Activation Function | • tanh | • ReLU |
| E. Learning Rate | • constant | • adaptive |
Table 2
Optimized model hyperparameters.
| HYPERPARAMETERS | MODEL 1 | MODEL 2 | MODEL 3 | MODEL 4 |
|---|---|---|---|---|
| Hidden layer structure | 120,60,30 | 120,60,30 | 120,60,30 | 120,60,30 |
| Activation function | ReLU | ReLU | tanh | tanh |
| Solver function | adam | lbfgs | adam | adam |
| Alpha | 0,001 | 0,001 | 0,00001 | 0,00001 |
| Learning rate | constant | constant | adaptive | adaptive |
Figure 5
Model 4 mean SHAP values summary plot.
Figure 6
Model’s best hyperparameter performances on models cross-fold validation.
Figure 7
Overall model’s prediction.
Figure 8
Models 3 and 4 LFL prediction deviations (473.15 K).
Figure 9
Models 3 and 4 UFL prediction deviations (473.15 K).
Figure 10
ML performances on FL temperature dependency compared to simpler linear empirical model (equation 1).
Table 3
Apex determination evaluation (473.15 K).
| INERT GAS ADMIXTURES (MOL % INERTS) | |||||
|---|---|---|---|---|---|
| CO2 | H2O | HE | N2 | AR | |
| Experimental Data | 69.6 | 68.1 | 78.1 | 84.0 | 84.5 |
| MODEL PREDICTIONS ABSOLUTE DEVIATIONS (MOL % INERTS) | |||||
| Gasse model (eqs. 2 and 3) | 11.0 | 19.4 | 5.2 | 0.2 | 3.9 |
| Model 3 | 0.6 | 1.2 | 1.3 | 3.4 | 0.4 |
| Model 4 | 0.8 | 1.25 | 0.9 | 3.0 | 0.1 |
Figure 11
Models extrapolation to H2–O2–N2 gas mixtures (293.15 K).
Figure 12
Models’ extrapolation on mixtures with multiple inert gases.
Table 4
Summary of models’ absolute deviations of extrapolation of multiple inert gases diluted H2-air mixtures.
| MIXTURES | ||||
|---|---|---|---|---|
| H2–Air–(25%) N2/(75%) CO2 (673.15 K) | H2–Air–(25%) Ar/(75%) H2O (493.15 K) | |||
| MODELS ABSOLUTE DEVIATIONS | ||||
| MODEL 3 | MODEL 4 | MODEL 3 | MODEL 4 | |
| LFL (mol % H2) | 0.45 | 0.33 | 0.27 | 0.27 |
| UFL (mol % H2) | 0.58 | 0.59 | 0.67 | 0.47 |
| Apex (mol % Inerts) | 2.16 | 0.65 | None | None |