An artificial neural network model for predicting compression strength of heat treated woods and comparison with a multiple linear regression model

Construction and Building Materials 62 (2014) 102–108

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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat

An artificial neural network model for predicting compression strength of heat treated woods and comparison with a multiple linear regression model Sebahattin Tiryaki ⇑, Aytaç Aydın Department of Forest Industry Engineering, Faculty of Forestry, Karadeniz Technical University, 61080 Trabzon, Turkey

h i g h l i g h t s  Effects of heat treatment temperature and duration on CS were studied.  CS values were predicted with the ANN and MLR models using the experimental data.  CS values decreased with increasing heat treatment temperature and duration.  ANN showed a better prediction performance compared to MLR.  It was shown that the ANN model save time, and decrease the experimental costs.

a r t i c l e

i n f o

Article history: Received 17 February 2014 Received in revised form 26 March 2014 Accepted 26 March 2014

Keywords: Artificial neural network Heat treatment Compression strength Multiple linear regression

a b s t r a c t This paper aims to design an artificial neural network model to predict compression strength parallel to grain of heat treated woods, without doing comprehensive experiments. In this study, the artificial neural network results were also compared with multiple linear regression results. The results indicated that artificial neural network model provided better prediction results compared to the multiple linear regression model. Thanks to the results of this study, strength properties of heat treated woods can be determined in a short period of time with low error rates so that usability of such wood species for structural purposes can be better understood. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Heat treatment is one of the processes used to improve the various properties of wood [1]. It was reported that heat treatment improves wood properties such as wood durability, dimensional stability and resistance to fungi [2,3]. However, it is a fact that increased temperature and duration during heat treatment adversely influence most of mechanical characteristics of wood [4–6]. The temperature and duration of heat treatment generally varies from 120 °C to 250 °C and 15 min to 24 h, respectively depending on wood species, sample dimensions, moisture content of the sample and intended use [7]. Especially, temperatures over 150 °C applied to wood modify the mechanical, chemical and physical properties of wood gradually [8]. Wood becomes more brittle due to heat ⇑ Corresponding author. Tel.: +90 462 3771515; fax: +90 462 3257499. E-mail addresses: [email protected] (S. Tiryaki), [email protected] (A. Aydın). http://dx.doi.org/10.1016/j.conbuildmat.2014.03.041 0950-0618/Ó 2014 Elsevier Ltd. All rights reserved.

treatment and its strength characteristics are decreased by 10–30% [2]. It was claimed that degradation of the hemicelluloses between microfibrils in cell wall is the main reason of strength loss in wood [9]. This case especially reveals the importance of determining the strength properties of heat treated woods in terms of structural constructions. Several studies were conducted to determine the effects of heat treatment temperature and duration on compression strength (CS) of wood. Unsal and Ayrilmis [10] found that CS parallel to grain of river red gum (Eucalyptus camaldulensis Dehn.) samples decreased about 19.0% as a result of heat treatment at 180 °C for 10 h. Yıldız et al. [11] investigated the mechanical behavior of spruce wood modified by heat. They observed that the CS losses due to heat treatment were 32.44% at 200 °C for 10 h. Korkut [12] detected a reduction of 29.41% for CS of Uludag fir (Abies bornmuellerinana Mattf.) wood at 180 °C for 10 h. Korkut and Budakçı [13] studied on the mechanical properties of rowan (Sorbus aucuparia L.) wood. They determined a reduction of 24.33% for CS of the samples

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exposed to the same treatment time and temperature. Similarly, heat treatment causes varying amounts of weight loss (WL) depending on exposure temperature and time. Zaman et al. [14] reported WL of 6.4%, 7.1% and 10.2% for birch (Betula pendula) treated at 205 °C for 4, 6 and 8 h, respectively. It is a fact that a great number of temperature and duration values need to be tested to determine a change in the mechanical behavior of wood caused by heat treatment. However, conducting comprehensive experiments causes the loss of much time and high costs. Therefore, it is very important to find more economic methods providing desirable results concerning CS of heat treated wood without needing the more experiments requiring much time and costs. For this purpose, artificial neural networks (ANNs) have been widely used in the field of wood science, such as calculating wood thermal conductivity [15], moisture analysis in wood [16], predicting fracture toughness of wood [17], wood recognition system [18], forecasting wood quality [19], drying process of wood [20], and wood veneer classification [21]. ANNs have been also used for predicting some mechanical properties of solid wood and wood composites. Cook and Chui [22] predicted the internal bond strength of particleboard using a radial basis function neural network with an accuracy level of 87.5%. Fernández et al. [23] predicted MOR and MOE values of particleboard by ANN at the accuracy levels of 86% and 87%, respectively. Esteban et al. [24] predicted the MOE of Abies pinsapo Boiss. wood by using ANN with 75.0% accuracy. Esteban et al. [25] predicted bonding strength of plywood using an ANN with 93% accuracy. Demirkır et al. [26] predicted the bonding strength of plywood using an ANN at the accuracy level of 98.0%. Studies on predicting some mechanical properties of wood and wood composites were expressed above. However, there is very limited information on predicting CS of heat treated wood. Ulucan [27] predicted CS of heat treated pine and chestnut woods by ANN at the accuracy levels of 92.59% and 92.04%, respectively. Therefore, the main aim of this study was to design the models having capable of predicting CS in heat treated woods by using the values obtained from the experimental study and thus to obtain more economic and safe results without doing comprehensive tests.

2. Materials and methods 2.1. Materials Oriental spruce (Picea orientalis (L.) Link.), Scots pine (Pinus sylvestris L.), Anatolian chestnut (Castenea sativa Mill.) and Oriental beech (Fagus orientalis Lipsky.), which are commonly utilized in the forest industry sector, were chosen for the materials of the experiment. The samples used in the experiments were all randomly selected from naturally grown woods in the Black Sea region of Turkey. Sample logs obtained from each wood species were allowed to dry naturally to

reduce the moisture. Then, the sample dimensions were trimmed to the appropriate dimensions (20  20  30 mm) for CS experiments. The samples were randomly divided into 48 treatment groups, each having 10 wood samples. Thus, a total of 480 (48  10) experimental samples were used for CS experiments. The samples were conditioned at a temperature of 20 ± 2 °C and 65 ± 5% relative humidity to the moisture content of about 12%.

2.2. Experimental details 2.2.1. Application of heat treatment Heat treatment was applied to the experimental samples in a laboratory type heating oven controlled at an accuracy of ±1 °C under atmospheric pressure. The temperature reached to 130 °C, 150 °C, 170 °C, and 190 °C at a heating rate of 10 °C/min. Once the target temperature had been reached, the temperature was held constant for 2 h, 6 h, and 10 h. After heat treatment process, the samples were conditioned to constant weight at 65 ± 5% relative humidity and at a temperature of 20 ± 2 °C until they reached stable weight according to TS 642 [28]. Prior to the experiments, the dimensions of the samples were measured to the nearest 0.001 mm and their weights were recorded at an accuracy of 0.01 g.

2.2.2. Determination of weight loss (WL) Prior to heat treatment, samples prepared for the experiments were dried in a heating oven at 103 ± 2 °C. Then, oven-dry weight of samples was determined with ±0.01 g sensitivity. After heat treatment, oven-dry weight of the same samples was measured again. WL of samples due to heat treatment was calculated according to Eq. (1). Table 1 gives WL of samples.

WL ð%Þ ¼ 100ðmb  ma Þ=mb

ð1Þ

where mb is the initial oven-dry weight of the sample prior to heat treatment and ma is the oven-dry weight of the same sample after heat treatment.

2.2.3. Determination of compression strength (CS) The universal test device (Mohr + Federhaff + Losenhausen) was used to determine CS values parallel to grain of the wood samples. Determination of CS values was carried out using the samples prepared according to TS 2595 [29] standards. For this purpose, the samples having 20  20  30 mm dimensions were used in CS experiments. The speed of the test machine in the experiments was adjusted to 1.5–2 min for crushing. Then, the force (Fmax) applied on wood samples during crushing was recorded. CS values parallel to grain of samples were calculated by Eq. (2).

rc== ¼ F max =a:bðN=mm2 Þ

ð2Þ

where Fmax is the force applied on wood samples (N), a is the cross-sectional width of test sample (mm), b is the cross-sectional thickness of the test sample (mm). After determining CS, the moisture content of each sample was measured according to TS 2471 [30]. Then, in the event of deviation from 12% moisture content, strength values were corrected (transformed to 12% moisture content) using the following conversion equation:

rc==ð12Þ ¼ rcm== ½1 þ aðM2  12Þ

ð3Þ 2

where rc//(12) is the strength at 12% moisture content (N/mm ), rcm// is the strength at moisture content deviated from 12% (N/mm2), a is the constant value showing relationship between strength and moisture content (a = 0.05 for rc//) and M2 is the moisture content as percentage during the experiment.

Table 1 The experimental (measured) values of CS and WL of samples due to heat treatment. Temperature (°C)

130 130 130 150 150 150 170 170 170 190 190 190

Time (h)

2 6 10 2 6 10 2 6 10 2 6 10

N

40 40 40 40 40 40 40 40 40 40 40 40

Anatolian chestnut

Oriental beech

CS (N/mm2)

Oriental spruce WL (%)

CS (N/mm2)

Scots pine WL (%)

CS (N/mm2)

WL (%)

CS (N/mm2)

WL (%)

37.18 36.13 37.76 38.64 37.05 35.70 35.41 36.07 33.43 33.79 32.93 30.08

2.92 3.84 4.61 3.77 4.93 6.07 4.71 5.90 7.89 6.27 8.59 10.80

58.02 59.20 58.08 58.30 58.29 56.07 55.70 54.44 53.94 54.24 52.11 48.76

3.36 3.95 4.96 4.30 5.74 6.87 5.50 6.97 8.56 7.17 9.04 11.35

58.81 59.08 57.05 56.83 54.97 54.17 54.47 55.45 53.69 53.40 51.65 49.83

3.36 4.72 5.64 4.17 5.56 6.83 5.48 6.85 8.13 7.01 9.88 12.46

67.68 68.60 65.23 65.80 65.81 64.46 65.35 64.45 61.98 63.04 61.14 58.66

4.05 4.89 5.71 4.87 5.67 7.32 5.76 6.93 8.63 7.08 9.18 11.93

Note: training values: italics, validation values: bold, testing values: bold italics, N: number of samples.

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2.3. Prediction tools 2.3.1. Multiple linear regression (MLR) Many problems in engineering and science involve exploring the relationships between two or more variables. Multiple linear regression (MLR) is a linear statistical technique that is very useful for predicting the best relationship between a dependent variable and several independent variables [31,32]. The dependent variable is sometimes called the predictand, and the independent variables the predictors. MLR is based on least squares: the model is fit such that the sum of squares of differences of observed and predicted values is minimized. MLR analysis was carried out by using SPSS 11.5 (Statistical Package for The Social Science). A general MLR model can be formulated as following equation:

Y ¼ b0 þ b1 X 1 þ . . . þ bn X n þ e

ð4Þ

where Y indicates dependent variable, Xi represents independent variables, bi represents predicted parameters, and e is the error term [33]. 2.3.2. Artificial neural networks (ANNs) ANNs can be defined as artificial intelligence modeling techniques. ANNs have a highly inter-connected structure similar to brain cells of human neural networks and consist of the large number of simple processing elements called neurons, which are arranged in different layers in the network. The most widely used ANN type for prediction is Multi-Layer Perception (MLP). MLP is composed of an input layer, an output layer and one or more hidden layers that allow the network to learn relationships between input and output variables [34,35]. The input layer receives the initial values of the variables, the output layer shows the results of the network for the input, and the hidden layer carries out the operations designed to achieve the output [36]. A typical MLP structure is shown in Fig. 1. The MLP Eq. (5) gives the mathematical expression of the output of the MLPs shown in Fig. 1.

Y ¼g hþ

m X j¼1

"

vj

#! n X f ðwij X i þ bj Þ

ð5Þ

i¼1

In Eq. (5), Y is the prediction value of dependent variable; Xi is the input value of ith independent variable; wij is the weight of connection between the ith input neuron and jth hidden neuron; bj is the bias value of the jth hidden neuron; vj is the weight of connection between the jth hidden neuron and output neuron; h is the bias value of output neuron; g() and f() are the activation functions of output and hidden neurons respectively. Another important parameter influencing ANN performance is the number of neurons in the ANN layers. The number of neurons in the input layer must correspond to the number of input (independent) variables, and the number of output neurons is equal to the number of output (dependent) variables in a prediction problem based on cause and effect relationship [37]. However, there is no rule to allow prior decisions to determine the number of neurons in the hidden layer or the number of the hidden layer(s). It was reported that insufficient number of hidden neurons causes difficulties in learning of network whereas excessive number of hidden neurons might lead to unnecessary training time [38]. The only way to obtain the hidden layer is by a process of trial and error [24]. In order for an MLP to accomplish a required task, neural network should be trained with data regarding the problem. The training of an MLP means to determine the best weights of connections between the neurons in order to obtain a minimum difference between measured and predicted value of the dependent variable [36]. Several training (learning) algorithms have been developed. The back-propagation learning algorithm is the most commonly used neural network algorithm and has been used with great success to model numerous engineering applications [39].

Fig. 2. The ANN architecture used as the prediction model for CS. 2.3.2.1. Neural network architecture. The training was carried out by making attempts to establish different ANN models with different network configurations and learning parameters. The models were tested using a test data set which was not utilized for the training processes in order to test the performance of networks. Thus, ANN model given the most sensitive results was targeted. As a result, the ANN model producing the closest values to the measured values for CS was chosen as the prediction model. A three-layered ANN architecture consisting of one input layer, one hidden layer and one output layer selected as the prediction model for CS is presented in Fig. 2. While wood species, time and temperature were considered as network inputs, CS variable was used as network output in the prediction model. Thus, in the ANN model developed for predicting CS, there were three input neurons and one output neuron. As mentioned earlier, there is no general rule for determining the number of neurons in a hidden layer. The optimal number of hidden layer neurons was determined by trying various networks, in order to decide the best network architecture. The best performance of the ANN model, in terms of the performance indicators such as the mean absolute error (MAE), the mean absolute percentage error (MAPE), the root mean square error (RMSE) and the determination coefficients (R2), was obtained for the configuration characterized by 4 neurons in the hidden layer, according to Fig. 2. Thus, the 3 – 4 – 1 neurons configuration was determined as the optimal configuration. In the designed ANN model, the hyperbolic tangent in the hidden layer and the linear transfer function in the output layer were chosen as the activation functions. Levenberg–Marquardt back propagation algorithm was preferred as the training algorithm. 2.3.3. Data preparation The data used in the ANN and MLR models were obtained from experimental study. The ANN model was implemented in the MATLAB Neural Network Toolbox. Experimental data was randomly divided into three groups as training data set (70%), validation data set (15%) and testing data set (15%) for predicting CS because a neural network is generally created in three phases referred to as training, validation and testing. In the ANN and MLR models were used the average of CS values, namely a total of 48 data. Each data is the average of 10 measurements of CS. The ANN model was trained using 34 randomly selected data, while the remaining 14 samples were equally divided for the ANN validation and testing process. On the other hand, all data (namely 48 data) were used for predicting CS values in the MLR model. 2.3.4. Performance evaluation The MAE, MAPE, RMSE and R2 were used to assess the validity of the ANN and MLR prediction models. The models providing the best prediction results for CS was selected as the prediction models. The lower MAE and MAPE and RMSE values represent the more accurate prediction results. The higher R2 values present the greater similarities between measured and predicted values. The MAE, MAPE, RMSE and R2 values were calculated using Eqs. (6)–(9), respectively.

MAE ¼

N 1X jt i  tdi j N i¼1

MAPE ¼

   1 XN ti  tdi   100 i¼1  ti  N

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N u1 X 2 RMSE ¼ t ðti  tdi Þ N i¼1 PN 2 ðti  tdi Þ R2 ¼ 1  Pi¼1 2 N  i¼1 ðt i  tÞ Fig. 1. A typical MLP structure.

ð6Þ

ð7Þ

ð8Þ

ð9Þ

where ti is the measured (experimental) values, tdi is the predicted values, N is the total number of data and t is the average of predicted values.

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heat treatment were 32.44% at 200 °C for 10 h. Korkut et al. [40] determined reduction in CS values in the heat treatment applied to Scots pine wood. In another study, Korkut et al. [41] observed that CS values of Anatolian chestnut deteriorate with increased temperature and duration of heat treatment. Yıldız [42] detected that heat treatment caused a drastic reduction in CS values of beech wood. Similarly, heat treatment causes varying amounts of WL depending on exposure temperature and time. Zaman et al. [14] reported WL of 6.4%, 7.1% and 10.2% for birch (Betula pendula) treated at 205 °C for 4, 6 and 8 h. Hillis [43] reported that the primary reason for the strength loss or WL is the degradation of hemicelluloses, which are less resistant to heat treatment compared to cellulose and lignin. Hemicelluloses degrade firstly due to their low molecular weight and branching structure according to Fengel and Wegener [44]. Therefore, changes or loss of hemicelluloses play an important role in strength properties of wood exposed to heat treatment at high temperatures.

Table 2 Homogeneity groups of CS depending on heat treatment conditions. CS (N/mm2)

Heat treatment conditions

Average

HG

Wood species

Oriental spruce Scots pine Anatolian chestnut Oriental beech

35.34 55.60 54.95 64.35

A B B C

Temperature (°C)

130 150 170 190

55.23 53.84 52.03 49.14

A B C D

Time (h)

2 6 10

53.54 52.96 51.18

A A B

3. Results and discussion 3.2. Predicting CS by ANN and comparison with MLR 3.1. Effects of heat treatment on CS In order to predict CS values of spruce, pine, chestnut and beech woods, the experimental data were grouped into training, validation, and testing data sets. The data sets used in the ANN prediction model, in other words, all CS values for the MLR prediction model, and the WL of samples due to heat treatment are shown in Table 1. The analysis of variance (ANOVA) was carried to determine the effects of heat treatment on CS. According to the ANOVA results, the parameters that influence CS were statistically significant (P < 0.01). In the following, the Duncan test was applied to establish homogenous groups and the results were presented in Table 2. According to the average values of each parameter tested, the averages for all parameters generally exhibited a decrease with increased duration and temperature. In other words, heat treatment reduced CS values of samples. The maximum decrease in CS for all parameters was recorded at heat treatment of 190 °C for 10 h. The lowest CS values obtained were 30.08, 48.76, 49.83 and 58.66 N/ mm2 for spruce, pine, chestnut and beech samples in the same variation, respectively. In addition, WL of samples increased with increasing temperature and time. WL was determined as 10.80%, 11.35%, 12.46% and 11.93% for spruce, pine, chestnut and beech at 190 °C for 10 h, respectively. These values were also recorded as the highest WL percentages in all variations. In general, the results of this study on the effects of heat treatment on CS of spruce, pine, chestnut and beech are compatible with the findings of the previous studies related to the effects of heat treatment on CS. For example; in a study on the effects of heat treatment on CS of spruce wood, Yıldız et al. [11] reported that the CS losses due to

The ANN predicted values of the experimental samples of CS and their percentage errors are given in Table 3. The designed ANN model indicated a good prediction performance. When Table 3 is examined, it can be shown that the prediction values obtained by ANN were determined with very low percentage errors. These levels of errors are satisfactory for predicting CS values. The MAE, MAPE, RMSE, and R2 values used to evaluate the performance of the ANN and MLR models developed in this study are given in Table 4. In decision-making, MAPE values were considered as the most important performance criterion. According to this, the MAPE values were determined as 0.645%, 2.042% and 2.641% in the prediction of CS values for training, validation and testing data sets, respectively. Additionally, the MAPE value was obtained as 7.679% in the prediction of CS with MLR. As seen from the results, the ANN approach has exhibited higher prediction performance than MLR approach based on evaluation criteria and has a sufficient accuracy level in the prediction of CS values. By also applying the MLR analysis on the same data is obtained the MLR model in Eq. (10)

Y ¼ 38:358 þ 8:636X 1  2:011X 2  1:180X 3

ð10Þ

where Y represents dependent variables (CS), and Xi represents independent variables (respectively, wood species, heat treatment temperature, and exposure time). The relationship between the experimental (measured) values and calculated (predicted) values obtained using the ANN and MLR prediction models is shown in Figs. 3 and 4, respectively. In

Table 3 Predicted values of the experimental samples of CS and their percentage errors. Temperature °C

Time (h)

N

CS (N/mm2) Oriental spruce

130 130 130 150 150 150 170 170 170 190 190 190

2 6 10 2 6 10 2 6 10 2 6 10

40 40 40 40 40 40 40 40 40 40 40 40

Anatolian chestnut

Oriental beech

Predicted

Error (%)

Predicted

Scots pine Error (%)

Predicted

Error (%)

Predicted

Error (%)

37.55 37.47 37.37 38.14 37.91 37.60 36.91 36.00 34.30 35.75 32.86 30.07

0.995 3.709 1.033 1.294 2.321 5.322 4.236 0.194 2.602 5.801 0.213 0.033

58.60 58.58 58.52 58.29 57.52 56.15 55.19 54.65 53.88 54.13 52.05 49.41

1.000 1.047 0.758 0.017 1.321 0.143 0.916 0.386 0.111 0.203 0.115 1.333

58.61 58.51 58.12 56.96 55.73 54.89 54.89 54.30 53.45 53.58 51.88 49.45

0.340 0.965 1.876 0.229 1.383 1.329 0.771 2.074 0.447 0.337 0.445 0.763

69.47 68.43 66.82 66.09 65.36 64.60 65.14 64.09 62.30 63.19 60.97 58.63

2.643 0.248 2.438 0.441 0.684 0.217 0.321 0.559 0.516 0.238 0.278 0.051

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Table 4 Performance criteria used for predicting CS by the ANN and MLR models. Model

ANN

MLR

Data

Training data Validation data Testing data All data

Performance criteria MAE

MAPE

RMSE

R2

0.336 0.960 1.071 3.678

0.645 2.042 2.641 7.679

0.432 1.082 1.313 4.508

0.998 0.998 0.997 0.830

the figures, the solid line shows the perfect linear fit between the predicted values and measured values of CS. The determination coefficient (R2) between the measured and predicted values is another important indicator to check the validity of the prediction models. As the R2 values approach 1, prediction accuracy increases. This means that there is a consistent agreement between the measured results and the prediction results. According to Fig. 3, R2 values in training, validation and testing the data set for CS are 0.9979, 0.9975 and 0.9969, respectively. Thus, R2 values obtained in this study with ANN modeling approach are greater than 0.99% for three data sets. This result implies that the model designed is capable of explaining at least 0.99% of the measured data. These values also support the applicability of using ANN. On the other hand, the R2 value was obtained as 83% in the prediction of CS with the MLR model. These results indicated that the used models in both methods can be considered for accurate predictions, since they both have a high explanatory values. However, the ANN model provided very higher prediction results compared to the MLR model. There is limited information on predicting CS of heat treated wood. However, several studies were carried out about some strength properties of wood and wood-based products. R2 values

Fig. 4. Relationship between the measured values and CS values predicted by the MLR model for all data.

obtained in these studies can be summarized as follow: Fernández et al. [45] found R2 values as 0.73 and 0.66 in prediction of MOR and MOE of structural plywood board by ANN, respectively. In the same study, R2 values for regression model were 0.51 and 0.47 in prediction of MOR and MOE, respectively; Eslah et al. [46] predicted R2 values as 0.79 and 0.69 in prediction of MOR and MOE of particleboard by using regression model, respectively. Demirkır et al. [26] obtained a value for R2 of 0.98 in prediction of bonding strength of plywood by ANN; and Esteban et al. [24] predicted a value for R2 of 0.75 in predicting the MOE of solid wood by ANN. Thus, it can be seen that the values of R2 obtained by ANN and MLR models in the present study are higher compared to those obtained by the above mentioned modeling applications for

Fig. 3. Relationship between the measured values and CS values predicted by the ANN model for training data (a), validation data (b), testing data (c) and all data (d).

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model are very close to the experimental measurements. On the other hand, the MLR results showed a higher deviation from experimental measurements as compared to the designed ANN model. From these comparison graphics, it can be clearly claimed that the ANN is properly trained and shows consistency in predicting CS. This situation increases the reliability of the proposed ANN prediction model. It is also demonstrated that a well-trained ANN model can be used to predict CS without needing the more experimental study requiring much time and high experiment costs. 4. Conclusion In this study, CS values of heat treatment woods were predicted by the ANN and MLR models using the experimental results. According to the obtained data, the following was concluded. A significant decrease was generally observed in CS values from the most important mechanical properties of wood with increasing duration and temperature of heat treatment. Also, WL of samples increased with increasing exposure temperature and time. When the measured values were compared with the predicted values obtained by ANN, it was shown that the ANN modeling technique can be successfully used for predicting the CS values of heat treated woods in a quite short period of time with low error rates. Thus, this study allows a preliminary decision about usability for structural purposes of treated woods. In the testing set, the R2 and MAPE values were obtained as 0.997% and 2.641% respectively. These values obtained by using ANN model showed a very higher prediction performance than MLR model. Considering the cost and time consumed for carrying out the experiment, with the use of ANN model, satisfactory results can be predicted rather than measured which thereby reduces the testing time and cost. Consequently, the losses of time, material and costs can be prevented. References

Fig. 5. Comparison of measured and predicted values of CS for training data (a), validation data (b) and testing data (c).

Fig. 6. Comparison of the measured results, the ANN prediction results, and MLR prediction results for all data.

predicting various strength properties of wood and wood-based products. The comparison of measured values and predicted values for CS using ANN are presented as graphically in Fig. 5. Also, the comparison of the measured results, the ANN prediction results, and the MLR prediction results was illustrated in Fig. 6, for all data. Once the graphics presented in Figs. 5 and 6 are examined, it appears that the values calculated by utilizing the ANN prediction

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