1 Introduction
2 Exploratory Analysis of Firebrand Data
2.1 Source of Data
Independent variables | Value | Description |
---|---|---|
1 | Fence | |
Structural components | 2 | Corner |
3 | Roof | |
1 | Privacy (fence) | |
2 | Lattice (fence) | |
3 | Cedar/plywood (corner) | |
Construction materials | 4 | Cedar/OSB (corner) |
5 | OSB siding/OSB (corner) | |
6 | Recycled rubber (roof) | |
7 | Non-FRT shake (roof) | |
8 | FRT shake (roof) | |
1 | Tree | |
Vegetation | 2 | Grass |
3 | Shrub | |
1 | Loblolly pine (tree) | |
2 | Leyland Cypress (tree) | |
Species | 3 | Little bluestem (grass) |
4 | Chamise (shrub) | |
5 | Saw Palmetto (shrub) | |
1 | Idle (5.36 m/s) | |
Wind speed | 2 | Medium (11.17 m/s) |
3 | High (17.88 m/s) |
2.2 Firebrand Areal Number Density (FAND) and Firebrand Areal Mass Density (FAMD)
2.3 Relationship Between Firebrand Size (Projected Area) and Mass
Wind type | Material type | R\(^2\) | \(\alpha\) |
---|---|---|---|
1 | 1 | 0.862 | 0.714 |
2 | 1 | 0.927 | 0.667 |
3 | 1 | 0.919 | 0.714 |
1 | 2 | 0.859 | 0.714 |
2 | 2 | 0.87 | 0.667 |
3 | 2 | 0.914 | 0.667 |
1 | 3 | 0.694 | 0.714 |
2 | 3 | 0.857 | 0.714 |
3 | 3 | 0.781 | 0.769 |
1 | 4 | 0.821 | 0.714 |
2 | 4 | 0.805 | 0.667 |
3 | 4 | 0.822 | 0.714 |
1 | 5 | 0.914 | 0.714 |
2 | 5 | 0.742 | 0.769 |
3 | 5 | 0.784 | 0.625 |
1 | 6 | 0.836 | 0.667 |
2 | 6 | 0.882 | 0.714 |
3 | 6 | 0.857 | 0.667 |
1 | 7 | 0.82 | 0.769 |
2 | 7 | 0.916 | 0.667 |
3 | 7 | 0.847 | 0.667 |
1 | 8 | 0.903 | 0.714 |
2 | 8 | 0.866 | 0.714 |
3 | 8 | 0.887 | 0.667 |
Wind type | Species type | R\(^2\) | \(\alpha\) |
---|---|---|---|
1 | 1 | 0.896 | 0.667 |
2 | 1 | 0.829 | 0.625 |
3 | 1 | 0.654 | 0.833 |
1 | 2 | 0.864 | 0.667 |
2 | 2 | 0.843 | 0.625 |
3 | 2 | 0.844 | 0.589 |
1 | 3 | 0.49 | 0.667 |
2 | 3 | 0.293 | 0.909 |
3 | 3 | 0.42 | 0.833 |
1 | 4 | 0.836 | 0.625 |
2 | 4 | 0.629 | 0.667 |
3 | 4 | 0.734 | 0.625 |
1 | 5 | 0.569 | 0.833 |
2 | 5 | 0.522 | 0.909 |
3 | 5 | 0.655 | 0.714 |
2.4 Independent Variables
2.5 Hypothesis
2.6 Finding Linear and Non-linear Patterns in Data Separation
3 Machine Learning Framework
3.1 Non-linear Non-parametric Machine Learning Algorithms
3.2 Training and Testing Datasets
3.3 Model’s Performance
Characteristics | FAMD | FAND |
---|---|---|
Accuracy | 94.78 | 93.04 |
CI_Lower | 91.24 | 89.05 |
CI_Upper | 98.85 | 97.69 |
Sensitivity | 94.83 | 96.72 |
Specificity | 94.74 | 88.89 |
PPV | 94.83 | 90.77 |
NPV | 94.74 | 96.00 |
Balanced accuracy | 94.78 | 92.81 |
F1 Score | 94.83 | 93.65 |
MCC | 89.56 | 86.19 |
Characteristics | FAMD | FAND |
---|---|---|
Accuracy | 98.33 | 98.33 |
CI_Lower | 96.57 | 96.32 |
CI_Upper | 100.00 | 100.00 |
Sensitivity | 98.31 | 98.46 |
Specificity | 98.36 | 98.18 |
PPV | 98.31 | 98.46 |
NPV | 98.36 | 98.18 |
Balanced accuracy | 98.33 | 98.32 |
F1 Score | 98.31 | 98.46 |
MCC | 96.67 | 96.64 |
3.4 Model Tuning
3.5 K-Nearest Neighbor (KNN)
(a) FAMD from structural fuels | |||
---|---|---|---|
PLF | PHF | Total | |
ALF | 54 | 3 | 57 |
AHF | 3 | 55 | 58 |
Total | 57 | 58 | 115 |
(b) FAND from structural fuels | |||
---|---|---|---|
PLF | PHF | Total | |
ALF | 48 | 2 | 50 |
AHF | 6 | 59 | 65 |
Total | 54 | 61 | 115 |
(c) FAND from vegetative fuels | |||
---|---|---|---|
PLF | PHF | Total | |
ALF | 54 | 1 | 55 |
AHF | 1 | 64 | 65 |
Total | 55 | 65 | 120 |
(d) FAMD from vegetative fuels | |||
---|---|---|---|
PLF | PHF | Total | |
ALF | 60 | 1 | 61 |
AHF | 1 | 58 | 59 |
Total | 61 | 59 | 120 |
(a) FAMD from structural fuels | |||
---|---|---|---|
PLF | PHF | Total | |
ALF | 43 | 18 | 61 |
AHF | 14 | 40 | 54 |
Total | 57 | 58 | 115 |
(b) FAND from structural fuels | |||
---|---|---|---|
PLF | PHF | Total | |
ALF | 46 | 9 | 55 |
AHF | 8 | 52 | 60 |
Total | 54 | 61 | 115 |
(c) FAND from vegetative fuels | |||
---|---|---|---|
PLF | PHF | Total | |
ALF | 47 | 16 | 63 |
AHF | 8 | 49 | 57 |
Total | 55 | 65 | 120 |
(d) FAMD from vegetative fuels | |||
---|---|---|---|
PLF | PHF | Total | |
ALF | 44 | 29 | 73 |
AHF | 17 | 30 | 47 |
Total | 61 | 59 | 120 |
3.6 Support Vector Machine Radial Kernel
3.7 Area Under the Receiver Operating Characteristic Curve
Model | Dependant variable | Type of fuel | AUROC (%) |
---|---|---|---|
FAND | Structural | 98.41 | |
KNN | FAND | Vegetative | 98.18 |
FAMD | Structural | 99.05 | |
FAMD | Vegetative | 99.65 | |
FAND | Structural | 89.71 | |
SVM-NL | FAND | Vegetative | 87.10 |
FAMD | Structural | 74.53 | |
FAMD | Vegetative | 64.85 |
3.8 Cross Validation
Dependant variable | Type of fuel | Accuracy (%) |
---|---|---|
FAND | Structural | 84.04 |
Vegetative | 76.57 | |
FAMD | Structural | 70.00 |
Vegetative | 63.62 |