Prognoses of diameter and height of trees of eucalyptus using artificial intelligence

Science of the Total Environment 619–620 (2018) 1473–1481

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Science of the Total Environment journal homepage: www.elsevier.com/locate/scitotenv

Prognoses of diameter and height of trees of eucalyptus using artificial intelligence Giovanni Correia Vieira ⁎, Adriano Ribeiro de Mendonça, Gilson Fernandes da Silva, Sidney Sára Zanetti, Mayra Marques da Silva, Alexandre Rosa dos Santos Federal University of Espírito Santo/UFES, PostGraduate Programme in Forest Sciences, Av. Governador Lindemberg, 316, 29550-000 Jerônimo Monteiro, ES, Brazil

H I G H L I G H T S

G R A P H I C A L

A B S T R A C T

• We use artificial neural networks to estimate the growth in DBH and height of eucalyptus trees. • Using new techniques in forestry measurement. • The techniques of artificial intelligence showed accuracy in growth estimation in DBH and total height. • The techniques of artificial intelligence are appropriate in estimating the growth of eucalyptus trees. • The techniques used can be adapted to other areas and forest crops.

a r t i c l e

i n f o

Article history: Received 12 September 2017 Received in revised form 12 November 2017 Accepted 12 November 2017 Available online xxxx Editor: Elena Paoletti Keywords: Artificial neural networks Adaptive neuro-fuzzy inference system Forest measurement Forest inventory

a b s t r a c t Models of individual trees are composed of sub-models that generally estimate competition, mortality, and growth in height and diameter of each tree. They are usually adopted when we want more detailed information to estimate forest multiproduct. In these models, estimates of growth in diameter at 1.30 m above the ground (DBH) and total height (H) are obtained by regression analysis. Recently, artificial intelligence techniques (AIT) have been used with satisfactory performance in forest measurement. Therefore, the objective of this study was to evaluate the performance of two AIT, artificial neural networks and adaptive neuro-fuzzy inference system, to estimate the growth in DBH and H of eucalyptus trees. We used data of continuous forest inventories of eucalyptus, with annual measurements of DBH, H, and the dominant height of trees of 398 plots, plus two qualitative variables: genetic material and site index. It was observed that the two AIT showed accuracy in growth estimation of DBH and H. Therefore, the two techniques discussed can be used for the prognosis of DBH and H in even-aged eucalyptus stands. The techniques used could also be adapted to other areas and forest species. © 2017 Elsevier B.V. All rights reserved.

1. Introduction Forest planning depends on a large quantity of information, emphasizing the prediction and the prognosis of growth and forest yield as the

⁎ Corresponding author. E-mail address: [email protected] (G.C. Vieira).

https://doi.org/10.1016/j.scitotenv.2017.11.138 0048-9697/© 2017 Elsevier B.V. All rights reserved.

most important tools in the generation of this information (Andreassen and Tomter, 2003). Often it is interesting to express the growth and yield of individual trees to get more details. When this happen, regression models are used to estimate the growth in diameter at breast height (DBH) and total height (H), which are components of these models (Andreassen and Tomter, 2003; Clutter et al., 1983; Davis and Johnson, 1987; Martins et al., 2014; Soares and Tomé, 2002). In addition to these

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variables, the estimation of mortality (Monserud and Sterba, 1999; Yang et al., 2003; Yao et al., 2001) and the use of competition indexes (Bella, 1971; Castro et al., 2013; Contreras et al., 2011; Martins et al., 2014; Pukkala and Kolström, 1987) are modeling elements of this kind of model. As examples of using regression models to express the growth and yield of individual trees, we can cite the works of Adame et al. (2008), Crecente-Campo et al. (2012), Lynch and Murphy (1995), Mabvurira and Miina (2002), Martins et al. (2014), Da Silva et al. (2002), Tennent (1982), Vospernik et al. (2010). In search of more efficient methods of estimating growth prognosis and forest yield, the use of artificial intelligence techniques (AIT) has been highlighted. Among all AIT, artificial neural networks (ANN) are an alternative to traditional methods of modeling individual trees, i.e., the statistical regression models (Guan and Gertner, 1991). The ANNs have greater generalizability, less susceptibility to noise and outliers, and the ability to model nonlinear relations unknown to the modeler, among other features (Haykin, 2009) compared to the regression models. These characteristics are important in modeling the growth and yield of forest stands. As examples of studies using ANNs in forest measurement, we can mention the studies of: Aertsen et al. (2010) used ANNs for prediction of site index in Mediterranean mountain forests; Diamantopoulou et al. (2015) used ANNs for estimation of Weibull function parameters for modeling tree diameter distribution; Diamantopoulou (2005) used ANNs as an alternative tool in pine bark volume estimation; Diamantopoulou and Özçelik (2012) used the generalized regression neural network technique has been applied for tree height prediction; Hasenauer et al. (2001) used ANNs of estimating tree mortality of Norway spruce stands; Ioannou et al. (2009) used ANNs to predict the prices of forest energy resources; Ioannou et al. (2011) used ANNs for predicting the possibility of ring shake appearance on standing chestnut trees (Castanea sativa mill.); Leite et al. (2011) used ANNs of estimation of inside-bark diameter and heartwood diameter of Tectona grandis Linn; Moisen and Frescino (2002) used ANNs for predicting forest characteristics; Özçelik et al. (2010); used ANNs of estimation breast height diameter and volume from stump diameter for three economically important species in Turkey; Özçelik et al. (2013) used nonlinear regression and artificial neural network models estimating crimean juniper tree height; Santi et al. (2017) used multifrequency SAR images and inversion algorithm based on ANNs for estimating forest biomass in Mediterranean áreas; Soares et al. (2011) used ANNs of estimation Recursive diameter prediction and volume calculation of eucalyptus trees; Vahedi (2016) used ANNs in comparison with modeling allometric equations for predicting above-ground biomass in the Hyrcanian mixed-beech forests of Iran; Vahedi (2017) used ANNs and traditional models for monitoring soil carbon pool in the Hyrcanian coastal plain forest of Iran. Porras (2007) evaluated the growth in diameter and height of Pinus cooperi in Mexico; Castro et al. (2013), Leite et al. (2011), Da Silva et al. (2009) analyzed the growth in diameter and height for Eucalyptus spp. in Brazil. The application of AIT in modeling of forest growth and yield is mostly restricted to the use of ANN. The use of other techniques such as fuzzy logic and adaptive neuro-fuzzy inference system (ANFIS) is still incipient. These techniques have the potential to improve estimation of growth and yield forest, as presented by satisfactory results in other areas of knowledge (Aish et al., 2015; Dongale et al., 2015; Maier and Dandy, 2000; Mashaly et al., 2015; Sarigul et al., 2003; Zarifneshat et al., 2012). Fuzzy logic is a generalization of classical logic, which enables intermediate values between false and true, being suitable to solve problems that do not have well-defined borders, that is, when the transition from one class to another is smooth and not abrupt (Silvert, 2000; Tanaka, 1997; Zadeh, 1965). In the agricultural arena, fuzzy logic is used for multi-criteria analysis of image, image classification, vegetation mapping, assessment of soil suitability, and planning forest harvesting (Ahamed et al., 2000; Boyland et al., 2006; Fisher, 2010; Jiang and

Eastiman, 2000; Joss et al., 2008; Malczewski, 2002; Oldeland et al., 2010; Phillips et al., 2011; Triepke et al., 2008). The ANFIS consists of a fuzzy inference system (FIS) with a distributed parallel structure, such that the learning algorithms of neural networks are used to adjust the parameters of the FIS. Besides the advantages of fuzzy systems, the ANFIS has the advantage of using the learning ANN (Jang, 1993). In growth and yield diameter at 1.30 m (DBH) and total height (H) models in level of individual trees, generally, the assumption of error independence is not met because the same tree is measured at different ages. The AIT does not guarantee some of the assumptions of regression models, such as normality and independence of errors. Another advantage of using AIT is the possibility to work with qualitative variables, such as yield class and genetic material. Considering the potential of AIT to be used in forest mensuration, this paper proposes the application of ANNs and ANFIS to predict growth in DBH and H of eucalyptus trees. 2. Methodology The methodological steps (Fig. 1) required to perform the prognosis of growth in DBH and H for eucalyptus plantations using artificial intelligence techniques were: 1. Database generation; 2. 3. 4. 5.

Input variables of the proposed methods; Site classification; Methods for prognosis; Evaluation of methods.

2.1. Step 1.1: description of the area and of the database The data used in this study were obtained from eucalyptus plantations (Eucalyptus grandis x Eucalytus urophylla) in the county of Virginópolis, Minas Gerais state, Brazil. The geographical coordinates of the study area are 18°49′50″ S latitude and 42°41′46″ W longitude. The climate classification of the region is Cwa, according to Köppen (Alvares et al., 2013). Were used data of continuous forest inventory from 28 eucalyptus clones. In those inventory were annually measured the variables DBH, H, and the dominant height according to the concept of Assmann (1970), for 398 plots ranging from 200 m2 to 350 m2, totaling 18,432 trees. 2.2. Step 1.2: partitioning of the database The database was divided as follows: 85% of the plots were allocated for the fit of the regression models, training of ANN and ANFIS and 15% of the plots were used to test the accuracy of the three techniques. The data used in the training in the techniques of AI were classified into two sets: one with 70% used for training and one with 15% for validation. Database partitioning in this proportion performs well for large datasets like ours, with small deviations, being common in the literature as in the works of Alshahrani et al. (2017), Gramatikov (2017), Ondieki et al. (2017) and Ridolfi et al. (2014). The validation consists in the division of the database in a group for training and one for validation. The training is interrupts after each iteration to perform the validation, while the validation group error is less than the previous iteration error, the algorithm continues, and when the error increase, the training is complete. 2.3. Step 2. Input variables of the regression models and artificial intelligence techniques The variables used in this study were DBH, H, dominant height, genetic material, basal area, number of trees per hectare, and the competition index independent of the distance. The average values of stand

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Fig. 1. Methodological steps necessary to realize prognosis of the growth of diameter at 1.30 m above the ground (DBH) and total height (H) using artificial intelligence techniques.

variables of the three sites are shown in Table 1 of supplementary material.

2.5. Step 4.1. Prognoses of growth for the DBH and H using regression models

2.4. Step 3. Classification of the production capacity

To estimate the growth in the DBH and H we adjusted three traditional regression models at the level of individual trees found in the literature (Table 1).

The classification of the productive capacity was modeled according to Schumacher and Hall (1933), adjusted to the stands of this study (Eq. 1).  
 1 Log Hd ¼ 3:74397−26:921316 Age

ð1Þ

2.6. Step 4.2. Prognoses of the growth of DBH and H using artificial neural networks

where ðHdÞ is dominant height (m), Age (months) and Log is logarithm neperian. The adjusted model presented all significant parameters (p b 0.01) using the Student's t-test, determination coefficient of 79.55%, and root mean square error (RMSE) of 2.57 m. We used the method of the guide curve to classify the sites (Eq. 2).

The model developed to represent the artificial neuron (Eq. 3 and Fig. 1 of supplementary material) comprises m synapses as the input, which represents the dendrites of the natural neuron, wherein respective weights (Wkj) are assigned to each one of the Xj inputs to simulate synapses (Haykin, 2009). Thereafter, a summation (Σ) is used to obtain the sum of the products of the inputs by respective weights, including a bias (bk) applied externally to increase or decrease net entry of the activation function (Haykin, 2009). The activation function f(x) restricts the neuron output amplitude (Y) (Haykin, 2009).

    
 1 1 − S ¼ exp Log Hd −26:921316 Agei Age

Y ¼ f@

0 ð2Þ

m X

1 W k; j  X j þ bk A

ð3Þ

j¼1

where S is site index (m) and Agei is Age index (months). The Age index used was 72 months. The site classes were: 22 m (low productivity), 30 m (average productivity), and 38 m (high productivity).

For training, 100 networks were adjusted for each architecture using MultiLayer Perceptron – MLP with a hidden layer. We evaluated network architectures ranging from 3 to 30 neurons and activation

Table 1 Regression models for estimating the growth in diameter at 1.30 m (DBH) and total height (H) of individual trees of eucalyptus. Model

Author

1 2

Pienaar and Shiver (1981) Schumacher adapted the Campos and Leite (2013) Adapted by Martins et al. (2014) the Bella (1971), Monserud and Sterba (1999), Mabvurira and Miina (2002)

3

Equation Y2 = Y1(−β0(Ageβ1 1 )) + ε 1 1 − Age Þ þ β2 BAI þ ε LogðY 2 Þ ¼ LogðY 1 Þ þ β1 ðAge 2

Y 2 ¼ Y 1 þ ðβ0 þ

1 β1 ðAge 2

1 − Age Þ 1

1

þ β2 BAI þ β3 SÞ þ ε

Wherein: Y2 = diameter (cm) or height (m) in future Age; Y1 = diameter (cm) or height (m) in current Age; Age2 = future Age (months); Age1 = current Age (months); BAI = basal area index; β0, β1, β2, β3 = model coefficients; e ε = random error.

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Table 2 Input variables used in artificial neural networks – ANN. ANN

Activation functions

Inputs

Outputs

DBH ANN1 ANN2 ANN3 ANN4

Log-sigmoid Hyperbolic tangent sigmoid Log-sigmoid Hyperbolic tangent sigmoid

DBH1, Age1, Age2, DICI, S, Gm DBH1, Age1, Age2, DICI, S, Gm DBH1, Age1, Age2, DICI, S DBH1, Age 1, Age2, DICI, S

DBH2 DBH2 DBH2 DBH2

H ANN1 ANN2 ANN3 ANN4

Log-sigmoid Hyperbolic tangent sigmoid Log-sigmoid Hyperbolic tangent sigmoid

H1, Age1, Age2, DICI, S, Gm H1, Age1, Age2, DICI, S, Gm H1, Age1, Age2, DICI, S H1, Age1, Age2, DICI, S

H2 H2 H2 H2

R2

H2: total future height (m); S: class Site; DICI ¼ DBHi  DBH−2: distance-independent competition index; Gm: genetic material.

functions log-sigmoid (Eq. 4) and hyperbolic tangent sigmoid (Eq. 5) in the hidden layer. In the output layer was used the linear function (Eq. 6). f ðxÞ ¼

1 1 þ e−x

ð4Þ

f ðxÞ ¼

2 −1 1 þ e−2x

ð5Þ

MAE

RMSE

Regression model 1 Regression model 2 Regression model 3 ANN 1 ANN 2 ANN 3 ANN 4 ANFIS 1 ANFIS 2 ANFIS 3

0.9668 0.9646 0.8846 0.9870 0.9871 0.9883 0.9883 0.9872 0.9867 0.9873

Regression model 1 Regression model 2 Regression model 3 ANN 1 ANN 2 ANN 3 ANN 4 ANFIS 1 ANFIS 2 ANFIS 3

0.8857 0.8679 0.4835 0.9572 0.9587 0.9573 0.9572 0.9447 0.9502 0.9498

0.0962 0.2169 1.0198 −0.0227 −0.0209 −0.0177 −0.0294 −0.0255 −0.0360 −0.0430 H (m) 0.3355 0.8503 3.2066 −0.0445 −0.1058 −0.0967 −0.0276 0.0718 −0.1142 −0.1432

0.4745 0.4888 1.0554 0.4155 0.4177 0.4031 0.4069 0.4115 0.4218 0.4222

0.6553 0.6768 1.2223 0.5785 0.5789 0.5496 0.5535 0.5756 0.5880 0.5742

1.2764 1.3866 3.2066 1.0899 1.0700 1.0747 1.0819 1.2676 1.1732 1.1731

1.6638 1.7888 3.5369 1.4256 1.4078 1.4315 1.4278 1.8988 1.5431 1.5523

Wherein: Coefficient of Determination (R2), Mean Bias Error (BEM), a Mean Absolute Error (MAE) e a Root mean square error (RMSE).

ð6Þ

We adopted the supervised training method, using the LevenbergMarquardt algorithm (Hagan and Menhaj, 1996). This method combines the best features of the gradient descent method and GaussNewton method, which provides greater convergence speed compared to the error backpropagation algorithm (Hagan and Menhaj, 1996). A stopping criterion was employed after 1000 epochs for each combination of configurations or an early-stopping rule was applied based on validation. In the early-stopping rule, it is possible to identify overadjustment through validation, where one sample is used for network training and another is used for validation after each iteration (Haykin, 2009). As long as the Mean squared error (MSE) of the validation sample is less than the MSE of the previous iterations, the training of the network is continued, otherwise the training must be terminated, since after that point the network loses its generalization capacity (Fig. 2 of supplementary material). The input and output variables were standardized between [0, 1] for the log-sigmoid activation function and [−1, 1] for the hyperbolic tangent sigmoid (Eq. 7).  X norm ¼

BEM DBH (cm)

Wherein: Age1: current Age (months); I2: future Age (months); DBH1: current diameter at 1.30 height (cm), DBH2: future diameter at 1.30 height (cm); H1: total current height (m);

f ðxÞ ¼ x

Table 4 Statistics used to evaluate the regression models, artificial neural networks – ANN and adaptive neuro-fuzzy inference system –ANFIS to estimate the growth in diameter at 1.30 height – DBH (cm) and total height – H.

X i −X minimum X maximum −X minimum

 ð7Þ

Table 3 Input variables used in the adaptive neuro-fuzzy inference system – ANFIS. ANFIS

Method

Input

Output

DBH 1 2 3

Subtractive clustering Subtractive clustering Grid partition

DBH1, Age1, Age2, DICI, S, Gm DBH1, Age1, Age2, DICI, S DBH1, Age1, Age2, DICI

DBH2 DBH2 DBH2

H 1 2 3

Subtractive clustering Subtractive clustering Grid partition

H1, Age1, Age2, DICI H1, Age1, Age2, DICI, S H1, Age1, Age2, DICI

H2 H2 H2

Wherein: Age1: current Age (months); I2: future Age (months); DBH1: current diameter at 1.30 height (cm), DBH2: future diameter at 1.30 height (cm); H1: total current height (m); H2: total future height (m); S: class site; DICI ¼ DBH i  DBH −2: distance-independent competition index; Gm: genetic material.

where Xi is the value to be standardized, Xminimum is the lowest value of the data set and Xmaximum is the highest value of the data set. This standardization was used to prevent variables of greater magnitude from having a greater influence on the result (Haykin, 2009). The description of the ANN with its activation functions and input and output variables is presented in Table 2. 2.7. Step 4.3 Prognoses of the growth of DBH and H using ANFIS We used the adaptive neuro-fuzzy inference system (ANFIS) that is based on a set of inputs and desired outputs; the tool prepares a fuzzy inference model. We used three membership functions for variables DBH1 and H1; two for each Age1, Age2, and DICI; and a membership function for each site class and clone. The input membership functions were all Gaussian, and the output function was linear. The algorithms used were the grid partition and subtractive clustering. The grid algorithm is limited to a few partition entries, because the number of rules increases exponentially with an increasing number of entries, causing difficulty in processing (Wei et al., 2007). The subtractive clustering proposed by Chiu (1994) groups similar variables to facilitate processing and is suitable for problems with more variables and/or membership functions (Wei et al., 2007). We also used the hybrid training algorithm, compound of backpropagation method, and the least squares method. The backpropagation method is related to the parameter estimates of the input membership functions, while the method of least squares estimates the output the parameters of the membership functions. As a stopping criterion, we used the error to zero and/or the maximum set number of training epochs. The number of epochs for training ranged from 1 to 50, using the number of times that had the lowest error for the test data. The use of two training algorithms is related to the number of system inputs. The starters used are shown in Table 3. 2.8. Step 5. Evaluation of the techniques used To evaluate the accuracy of the techniques were analyzed: the graphs of variables observed versus estimated variables, the coefficient

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Fig. 2. Graphical Analysis the estimated diameter at 1.30 height – DBH (cm) vs. the observed diameter at 1.30 height – DBH (cm) and the estimated total height – H vs. the observed total height – H of regression models 1, 2 and 3.

of determination – R2 (Eq. 8), Mean Bias Error – MBE (Eq. 9), the Mean Absolute Error – MAE (Eq. 10) and the Root Mean Square Error – RMSE (Eq. 11). 2

R2 ¼ 1−

^i Þ Σðyi −y

Σðyi −yi Þ2

ð8Þ

wherein: yi: observed value of the ith variable; ŷi: estimated value of the ith variable; ȳ: mean of the observed values of the variable. Pn

^

i¼1 ðyi −yi Þ

MBE ¼

n

ð9Þ

wherein: yi: observed value of the ith variable; ŷi: estimated value of the ith variable; n: sample size. Pn MAE ¼

^

i¼ j jyi −yi j

n

RMSE ¼

n

3.1. Regression models for the estimation of DBH and H Based on the results shown in Table 1 of supplementary material, ex^ of the DBH in Model 3, all estimated cept for the estimated parameter β 3 parameters were statistically significant (p b 0.05). Analyzing statistical indicators (R2, MBE, MAE, and RMSE) for DBH the Model 1 and Model 2 showed highest accuracy. For the H models, Model 1 showed highest accuracy, followed by Model 2 (Table 4). Regarding the observed values versus estimated values graph by regression models (Fig. 2), we note that Model 1 and 2 showed a smaller dispersion of data with respect to the 1:1 trend line. An underestimation trend was also observed in Model 3 for estimating DBH and H. Therefore, Model 1 and 2 is the most appropriate to estimate the DBH and H because of its higher accuracy, and it does not present trends in the estimates for any size class.

3.2. Artificial neural networks to estimate the DBH and H of eucalyptus trees ð10Þ

wherein: yi: observed value of the ith variable; ŷi: estimated value of the ith variable; n: sample size. ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sP n ^ i¼ j ðyi −yi Þ

3. Results

ð11Þ

wherein: yi: observed value of the ith variable; ŷi: estimated value of the ith variable; n: sample size. For each ANN configuration and ANFIS, we selected those that had the lowest RMSE values.

Based on the simulations, the networks settings were selected (number of neurons in the hidden layer) which had lower RMSE for the prognosis of DBH and H. In the configuration for the prognosis of DBH (Fig. 3a), the neuron number of input layer were 35 and the neurons in the hidden layer that had the lowest RMSE was 8 for the network 1; the neuron number of input layer were 35 and the neurons in the hidden layer that had the lowest RMSE was 23 to the network 2; the neuron number of input layer were 7 and the neurons in the hidden layer that had the lowest RMSE was 6 for the network 3; and the neuron number of input layer were 7 and the neurons in the hidden layer that had the lowest RMSE was 5 into the network 4. To estimate the H, the network configuration (Fig. 3b), which had the lowest RMSE was the network 1 with 35 neurons in the input layer and 8 neurons in the hidden layer. For network 2, were 35 neurons in the input layer and 4 neurons in

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Fig. 3. Root mean square error (RMSE, cm) of artificial neural networks – ANN with different numbers of hidden layer neurons (K) to estimate the diameter at 1.30 height – DBH (cm) and total height – H, wherein the red dots highlight the number of neurons that present lower RMSE for the configurations of artificial neural networks – ANN. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 4. Graphic Analysis the estimated diameter at 1.30 height – DBH (cm) vs. the observed diameter at 1.30 height – DBH (cm) and the estimated total height – H vs. the observed total height – H of configurations of artificial neural networks – ANN 1, 2, 3 and 4.

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the hidden layer. For networks 3 and 4 were 7 neurons in the input layer and 4 neurons in the hidden layer. Analyzing the statistics to assess the accuracy of ANNs (Table 4), it is noted that the analyzed indicators (R2, MBE, MAE and RMSE) to estimate the DBH did not show great variation among the configurations of neural networks of greater accuracy. Among the settings that had the greatest accuracy was Network 3, followed by Network 4. When analyzing the results for overall H, we note similar results to the DBH, except for the MBE statistics. The network with greater accuracy for H was Network 2. Based on graphical analysis of estimated DBH vs. observed DBH (Fig. 4a), is can be noted that Network 4 has the best fit, showing greater dispersion of DBH below 15 cm. For the prognosis of H (Fig. 4b), it is noted that Networks 2 and 4 had better distribution of residuals. In general, it is observed that the data are widely dispersed in relation onto the 1:1 trend line. Greater dispersion of data for the trees with H b 20 m was observed. Therefore, the most appropriate network settings are Networks 3 and 4 for estimating the DBH and Networks 2 and 4 for estimating H because of its higher accuracy. 3.3. Adaptive neuro-fuzzy inference system to estimate the DHB and H of eucalyptus trees Comparing the three ANFIS in terms of accuracy, using as a basis the statistical indicators, it is noted that for DBH, the compared systems showed similar accuracy, as happened to ANNs. Thus, considering the statistics analyzed, one can use any of the three settings to estimate DBH eucalyptus trees. When analyzing the results for H, note that the ANFIS 2 was the one with greater accuracy. Analyzing the estimated DBH vs. observed DBH graph for the ANFIS (Fig. 5a), it is observed that the three systems showed greater dispersion of data for trees with DBH b15 cm. Considering the graphical analysis of observed height vs. estimated height to ANFIS (Fig. 5b), it is noted

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that the data are more dispersed in trendline 1:1 compared to the results of ANNs. We can see greater dispersion for the trees smaller 23 m of H. In general, the ANFIS 1 showed the worst performance, with greater dispersion of observed values versus estimated for the DBH and H of the trees. 4. Discussion Since the growth of individual trees is a function of time (Age of the population) having a nonlinear relationship, the use of this type of AIT modeling is feasible. This fact testifies to the adequacy of these techniques for modeling this kind of relationship, as described by several researchers (Da Silva et al., 2009; Özçelik et al., 2010; Leite et al., 2011, Soares et al., 2011; Diamantopoulou and Özçelik, 2012; Castro et al., 2013). Considering the analyzed statistics (Table 4) and the graphs (Figs. 2, 4 and 5), it is clear that it is feasible the use ANNs and ANFIS to estimate growth of individual eucalyptus trees, becauseboth showed better accuracy in projecting DBH and H of eucalyptus trees compared to regression models. In the work of Martins et al. (2014), which tested regression models for projecting DBH and H of eucalyptus hybrids, determination coefficient values between 0.9586 and 0.9874 for DBH and 0.9428 to 0.9886 for the H were found. When comparing the graphs of observed data vs. estimated data for the evaluated techniques (Figs. 2, 4 and 5), it is observed that the AIT showed less dispersion of data with respect to the 1:1 trend line and lesser trends of overestimation or underestimation of the DBH and H of trees studied. Assessing ANNs from the point of view of activation function, we note that there were no differences in accuracy due to activation functions (Table 4). The activation function is related to the relationships contained in data, convergence speed of the algorithms, and network complexity (Duch and Jankowski, 1999).

Fig. 5. Graphic Analysis the estimated DBH vs. observed DBH and estimated H vs. the observed H, of configurations of adaptive neuro-fuzzy inference system – ANFIS 1, 2 and 3.

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Little variation of the RMSE was observed (Fig. 3) with the number of network neurons. The network configuration is related to the complexity of the problem, and for more complex problems more neurons are needed (Haykin, 2009). Accordingly, the use of less complex networks, i.e., with fewer neurons, has the advantage of higher processing speed without significant loss of accuracy. In general, there was not much accuracy variation with respect to network configurations for DBH and H. The addition of genetic material as a categorical variable did not considerably increase the accuracy of RNAs in estimates of DBH and H. However, this is a variable that must always be evaluated because growth is influenced by the type of genetic material. Regarding the ANFIS, it was observed that there was no significant difference in accuracy with respect to input space separation methods. The grid partition method restricts the number of inputs, because the number of relevant rules increases exponentially with an increasing number of entries, which increases the processing time and may impair the numerical solution of the problem (Wei et al., 2007). With the inclusion of local class variables and genetic material, it was necessary to use the subtractive cluster method. However, similar to what happened with the ANNs, an increase in the accuracy with the use of genetic material as categorical variable was not observed; the same was true for site class. Thus, the AIT analyzed in this work can be used to project the DBH and H of eucalyptus trees, demonstrating that they are suitable alternatives to classical regression methods. 5. Conclusions The ANNs and the ANFIS had higher accuracy than regression models for projecting DBH and total H of eucalyptus trees. Thus, it is reasonable to say that these techniques can be used for the prognosis of growth of DBH and H for individual trees. Also, the site class variables and the genetic material did not provide more accuracy when inset as input variables to the artificial intelligence techniques. Therefore, the two techniques discussed can be used for prognosis of growth of DBH and H in even-aged eucalyptus stands. The methodology can be adapted for use of artificial intelligence techniques in other forest crops. Acknowledgment The authors would like to extend their thanks to the Research and Innovation Support Foundation of the Espírito Santo (FAPES) for the funding through the scholarship (public notice number 21/2012 and 124/2014), the Graduate Program in Forest Science of the Federal University of Espírito Santo. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.scitotenv.2017.11.138. References Adame, P., Hynynen, J., Cañellas, I., del Río, M., 2008. Individual-tree diameter growth model for rebollo oak (Quercus pyrenaica Willd.) coppices. For. Ecol. Manag. 255 (3–4):1011–1022. https://doi.org/10.1016/j.foreco.2007.10.019. Aertsen, W., Kint, V., van Orshoven, J., Özkan, K., Muys, B., 2010. Comparison and ranking of different modelling techniques for prediction of site index in Mediterranean mountain forests. Ecol. Model. 221 (8), 1119–1130 (https://doi.org/10.1016/ j.ecolmodel.2010.01.007). Ahamed, N.T.R., Rao, K.G., Murthy, J.S.R., 2000. GIS-based fuzzy membership model for crop-land suitability analysis. Agric. Syst. 63 (2):75–95. https://doi.org/10.1016/ S0308-521X(99)00036-0. Aish, A.M., Zaqoot, H.A., Abdeljawad, S.M., 2015. Artificial neural network approach for predicting reverse osmosis desalination plants performance in the Gaza strip. Desalination:367240–367247. https://doi.org/10.1016/j.desal.2015.04.008. Alshahrani, M., Soufan, O., Magana-Mora, A., Bajic, V.B., 2017. DANNP: an efficient artificial neural network pruning tool. PeerJ Comput. Sci. 3, e137 (https://doi.org/ 10.7717/peerj-cs.137).

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