Table 4 Performance of forecasting method through BPNN-DE.
From: Concrete crack opening forecasting by back propagation neural network and differential equation
Item | JB-1 with mean −21.67 | JB-3 with mean −18.23 | JB-7 with mean 0.95 | ||||||
|---|---|---|---|---|---|---|---|---|---|
Model | BPNN | BPNN-DE-1TD | BPNN-DE-2TD | BPNN | BPNN-DE-1TD | BPNN-DE-2TD | BPNN | BPNN-DE-1TD | BPNN-DE-2TD |
\({K}_{1}\) | / | 0.005 | 0.005 | / | −0.0200 | −0.0200 | / | −0.11 | −0.11 |
\({K}_{2}\) | / | 0.001 | 0.001 | / | 0.0001 | 0.0001 | / | 0.000005 | 0.000005 |
\({C}{\prime}\) | / | −0.0001 | −0.0001 | / | −0.0008 | −0.0008 | / | −0.0085 | −0.0085 |
TD1 | / | 26 | 26 | / | 23 | 23 | / | 16.5 | 16.5 |
TD2 | / | 26 | 17 | / | 23 | 10 | / | 16.5 | 11 |
The ratio < 20% error | 100% | 100% | 100% | 100% | 100% | 100% | 73.7% | 77.8% | 79.2% |
Average absolute error (% mm) | 0.013% (0.0028) | 0.013% (0.0027) | 0.012% (0.0027) | 0.07% (0.013) | 0.036% (0.007) | 0.034% (0.006) | 14.99% (0.068) | 13.10% (0.060) | 12.62% (0.058) |
Minimum error (% mm) | 0% (0) | 0% (0) | 0% (0) | 0% (0) | 0% (0) | 0% (0) | 0% (0) | 0% (0) | 0% (0) |
Maximum error (% mm) | 0.060% (0.013) | 0.063% (0.014) | 0.063% (0.014) | 0.219% (0.040) | 0.135% (0.025) | 0.127% (0.023) | 85.45% (0.278) | 74.32% (0.264) | 66.86% (0.236) |
R2 | 0.780 | 0.867 | 0.877 | 0.619 | 0.896 | 0.916 | 0.856 | 0.892 | 0.903 |
KGE | 0.838 | 0.926 | 0.936 | 0.700 | 0.912 | 0.956 | 0.897 | 0.914 | 0.951 |
VAF | 0.778 | 0.864 | 0.870 | 0.619 | 0.895 | 0.913 | 0.858 | 0.893 | 0.901 |
Entropy | 4.413 | 10.355 | 10.356 | 6.140 | 10.716 | 10.716 | 8.832 | 10.606 | 10.606 |
MI | 1.24 | 2.48 | 2.46 | 2.31 | 3.58 | 3.59 | 4.88 | 4.98 | 4.99 |
TIC | 132.85 | 131.76 | 131.73 | 138.83 | 137.34 | 136.70 | 137.55 | 137.85 | 138.46 |
