Enhancing Height Predictions of Brazilian Pine for Mixed, Uneven-Aged Forests Using Artificial Neural Networks
Abstract
:1. Introduction
2. Materials and Methods
2.1. Study Areas
2.2. Data
2.3. Modeling Using Artificial Neural Networks (ANNs)
2.4. Statistical Criteria
2.5. Comparison with Other Approaches
3. Results
4. Discussion
5. Conclusion
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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City | State | Latitude | Longitude | Altitude | MAT | AP |
---|---|---|---|---|---|---|
Lages (LGS) | SC | 27°49′ S | 50°19′ W | 986.8 | 15.2 | 1684.7 |
São José do Cerrito (SJC) | SC | 27°39′ S | 50°34′ W | 888.0 | 16.0 | 1690.0 |
São Francisco de Paula (SFP) | RS | 29°26′ S | 50°34′ W | 853.8 | 15.0 | 2016.4 |
Variables | Data | Minimum | Mean | Maximum | Standard Deviation |
---|---|---|---|---|---|
DBH | Training [N = 603] | 9.9 | 42.2 | 97.1 | 16.2 |
HCB | 3.0 | 12.8 | 22.3 | 3.9 | |
SP | 1.0 | 1.7 | 3.0 | 0.8 | |
h | 7.2 | 17.5 | 25.1 | 3.4 | |
DBH | Validation [N = 201] | 11.1 | 42.5 | 93.0 | 16.2 |
HCB | 3.2 | 13.2 | 20.1 | 3.7 | |
SP | 1.0 | 1.7 | 3.0 | 0.8 | |
h | 8.4 | 17.8 | 24.8 | 3.3 |
Data Normalization | Activation Function in the Hidden Layer | Architecture | ANNs | Training | Validation | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
R2 | RMSE | MAE | MAPE | R2 | RMSE | MAE | MAPE | t (p-Value) | ||||
[0, 1] | Logistic Sigmoid | 3-3-1 | 87 | 0.83 | 1.42 | 1.10 | 6.54 | 0.80 | 1.47 | 1.12 | 6.54 | 0.3669 |
3-4-1 | 151 | 0.84 | 1.38 | 1.08 | 6.45 | 0.80 | 1.47 | 1.10 | 6.46 | 0.3669 | ||
3-5-1 | 133 | 0.84 | 1.37 | 1.07 | 6.35 | 0.80 | 1.48 | 1.10 | 6.44 | 0.3222 | ||
3-6-1 | 35 | 0.84 | 1.36 | 1.06 | 6.29 | 0.80 | 1.49 | 1.12 | 6.53 | 0.3925 | ||
3-7-1 | 112 | 0.85 | 1.34 | 1.04 | 6.13 | 0.78 | 1.57 | 1.18 | 6.94 | 0.2157 | ||
3-8-1 | 2 | 0.85 | 1.33 | 1.03 | 6.11 | 0.79 | 1.54 | 1.15 | 6.82 | 0.2076 | ||
3-9-1 | 27 | 0.85 | 1.33 | 1.04 | 6.17 | 0.78 | 1.56 | 1.19 | 7.18 | 0.2782 | ||
[−1, 1] | Tangent Hyperbolic | 3-3-1 | 63 | 0.83 | 1.42 | 1.10 | 6.54 | 0.80 | 1.47 | 1.12 | 6.54 | 0.3669 |
3-4-1 | 186 | 0.83 | 1.38 | 1.08 | 6.47 | 0.80 | 1.48 | 1.10 | 6.47 | 0.3776 | ||
3-5-1 | 142 | 0.84 | 1.36 | 1.06 | 6.32 | 0.79 | 1.51 | 1.13 | 6.62 | 0.3595 | ||
3-6-1 | 76 | 0.84 | 1.36 | 1.05 | 6.27 | 0.80 | 1.48 | 1.11 | 6.43 | 0.3926 | ||
3-7-1 | 21 | 0.84 | 1.35 | 1.05 | 6.25 | 0.79 | 1.52 | 1.14 | 6.78 | 0.3688 | ||
3-8-1 | 85 | 0.85 | 1.32 | 1.03 | 6.11 | 0.78 | 1.55 | 1.20 | 7.13 | 0.3583 | ||
3-9-1 | 88 | 0.85 | 1.32 | 1.03 | 6.10 | 0.78 | 1.55 | 1.18 | 6.91 | 0.4455 |
Output | Description | Symbology | Parameters * |
---|---|---|---|
h [ANNLS–35] | Connection weight between the i-th input neuron and the j-th neuron of the hidden layer | w11 | 3.32816051171092 |
w12 | 5.63564847455494 | ||
w13 | −4.40653201913032 | ||
w14 | 2.68858077614371 | ||
w15 | −1.68221666104095 | ||
w21 | −3.24989570960590 | ||
w22 | −5.77536858770656 | ||
w23 | 3.87689105761618 | ||
w24 | −1.13376891107571 | ||
w25 | 1.25838992740362 | ||
w31 | −321.30491714453200 | ||
w32 | −381.40410414733300 | ||
w33 | 86.20493085148810 | ||
w34 | 88.90641991865460 | ||
w35 | 21.61783043205750 | ||
w41 | −22.89030349033760 | ||
w42 | 410.83399462375600 | ||
w43 | 0.50990767756676 | ||
w44 | −125.55254893517100 | ||
w45 | −36.36394357853860 | ||
w51 | 3.94323030362454 | ||
w52 | 5.80007401299029 | ||
w53 | −0.78654999414145 | ||
w54 | 0.20965400755131 | ||
w55 | −0.14330472749885 | ||
w61 | 4.07529360272997 | ||
w62 | 6.59876667861121 | ||
w63 | −0.08872791410663 | ||
w64 | −2.17397149230597 | ||
w65 | 0.68803696120158 | ||
Bias value of the j-th neuron of the hidden layer | β1 | −3.50954443727372 | |
β2 | 4.05439213215968 | ||
β3 | 196.62632091995300 | ||
β4 | −161.28176733076100 | ||
β5 | −0.68610189401701 | ||
β6 | −1.58674993359591 | ||
Connection weights | v1 | −10.01973417076710 | |
v2 | −10.27312884996830 | ||
v3 | 0.09861299114926 | ||
v4 | 0.04642360435809 | ||
v5 | 8.18137541276566 | ||
v6 | −6.94837517016951 | ||
Bias value of the output neuron | θ | 9.71477261782129 |
Type | Social Position | CL b | Validation * | ||
---|---|---|---|---|---|
RMSE | MAE | MAPE | |||
NL a | SP1 | 1.95 | 1.55 | 8.69 | |
SP2 | 2.71 | 2.18 | 12.47 | ||
SP3 | 2.74 | 2.37 | 14.97 | ||
LDV a | SP1, SP2, SP3 | D1, D2 | 2.41 | 1.93 | 11.21 |
PC-MNLR a | 2.12 | 1.78 | 10.52 | ||
ANNLS-35 | 1.49 | 1.13 | 6.57 |
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Costa, E.A.; Hess, A.F.; Finger, C.A.G.; Schons, C.T.; Klein, D.R.; Barbosa, L.O.; Borsoi, G.A.; Liesenberg, V.; Bispo, P.d.C. Enhancing Height Predictions of Brazilian Pine for Mixed, Uneven-Aged Forests Using Artificial Neural Networks. Forests 2022, 13, 1284. https://doi.org/10.3390/f13081284
Costa EA, Hess AF, Finger CAG, Schons CT, Klein DR, Barbosa LO, Borsoi GA, Liesenberg V, Bispo PdC. Enhancing Height Predictions of Brazilian Pine for Mixed, Uneven-Aged Forests Using Artificial Neural Networks. Forests. 2022; 13(8):1284. https://doi.org/10.3390/f13081284
Chicago/Turabian StyleCosta, Emanuel Arnoni, André Felipe Hess, César Augusto Guimarães Finger, Cristine Tagliapietra Schons, Danieli Regina Klein, Lorena Oliveira Barbosa, Geedre Adriano Borsoi, Veraldo Liesenberg, and Polyanna da Conceição Bispo. 2022. "Enhancing Height Predictions of Brazilian Pine for Mixed, Uneven-Aged Forests Using Artificial Neural Networks" Forests 13, no. 8: 1284. https://doi.org/10.3390/f13081284