Artificial neural networks and multiple linear regression as potential methods for modelling body surface temperature of pig

ABSTRACT

An experiment was conducted to evaluate modelling relationships between pig’s body surface temperature and ambient environment including inside and outside of pig barn. For this purpose, four different artificial neural network (ANN), including Feed Forward Back-propagation (FFB), Layer recurrent (LR), Elman (EL) and Cascade Forward Back-propagation (CFB) with different learning algorithms, transfer functions, hidden layers and neuron in each layer, and multi-linear regression (MLR) models have been performed to predict body temperature of pig. Six two-month-old pigs were studied over a period of 92 days during two years (2017–2018) to develop and evaluate the ANN and MLR models. The performance of the models in predicting pig’s body temperature was determined using statistical quality parameters, including coefficient of determination (R²), root mean square error (RMSE) and mean absolute percentage error (MAPE). The FFB model with the Levenberg-Marquardt training function, Gradient descent weight and bias learning function, Log-sigmoid transfer function and two hidden layers with 20 neurons was found as the best model. Sensitivity analysis indicated that the temperature-humidity index (THI) inside the room is the most influential factor in predicting pig’s body temperature in the MLR/ANN models.

KEYWORDS:

• Ambient environment
• artificial neural networks
• multiple linear regression
• pig’s body temperature
• temperature-humidity index (THI)

1. Introduction

Body temperature is of vital importance for all biological functions of animals. The rate of metabolic processes increases with temperature, but if temperature is elevated beyond a certain threshold limit, biological functions may not work properly (Kessel et al. 2010). Therefore, there is a growing concern in measuring body surface temperature of animals and ambient environment inside and outside of a livestock barn for determining thermal comfort zone. Temperature, relative humidity, ammonia and carbon dioxide concentration are the most pivotal environmental parameters for life and govern the performance and fitness of animal (Rome et al. 1992; Le et al. 2009; Süli et al. 2017). Among above environmental parameters, it is well established that physiological processes are strongly temperature sensitive and mostly occur within a narrow range of body temperatures (Peterson et al. 1993; Zimmerman et al. 1994; Sagonas et al. 2013). The effectiveness of thermoregulation depends, to a large extent, on body temperature (Huey and Stevenson 1979) and ambient environmental conditions inside and outside livestock barn (Cervantes et al. 2018).

As homeothermic animals, pigs preserve relatively constant their body temperature over a certain range of ambient temperature, relative humidity, carbon dioxide concentration etc. (Mader et al. 2006, Jeong 2012; Rezende and Bacigalupe 2015; Basak et al. 2019). Some studies reported that at low ambient temperature and high relative humidity, pigs generate heat through increasing basal metabolism (Adair and Black 2003) and the thermic effect of feed (Levine 2004). At high ambient temperature and low relative humidity pigs use a well-regulated mechanism to dissipate heat to the environment (Morera et al. 2012) preventing excess body heat (Quiniou et al. 2001; Kerr et al. 2003; Sagonas et al. 2013). In addition, Wilson and Crandall (2011) examined that when pigs face heat stress, they increase their heart rate, respiratory frequency and peripheral blood flow to promote loss of heat and also, decrease voluntary feed intake (Huynh et al. 2005; Renaudeau et al. 2010). Morales et al (2016) and Cervantes et al (2017) in their studies evaluated an increment of up to 2.0°C in the body temperature of pigs when exposed to high ambient temperature and low relative humidity in pig barn. From the previous studies, it can be observed that a substantial portion of pig’s body temperature depends on the balance within the ambient environmental parameters, the production of body heat and their capability to dissipate heat. Therefore, pig’s body temperature, as an integrating trait, is affected by several components, either directly or indirectly.

To address this subject, pig’s body temperature can be predicted indirectly using ambient environmental and growth-related parameters. Until now, most of the modelling studies on pig’s body temperature prediction have focused on simple correlation, path analysis, linear and multi-linear regression, stepwise regression, factor analysis and principle component analysis (PCA) (Jang et al. 2015; McClure 2015; Mostaço et al. 2015; Soerensen and Pedersen 2015; Basak et al. 2019), of which a linear relationship between variables and body temperature of pig is assumed. Although these methods would reduce the number of input variables, they are neither sufficient nor comprehensive enough to really show the interactions of ambient environmental conditions and pig’s body temperature. Additionally, they would not be able to capture the highly non-linear and complex relations between pig’s body temperature and other parameters. Unlike linear-based models, artificial neural networks (ANNs), genetic expression (GE), Bayesian classification (BC) or other non-linear models would be appropriate when non-linearity and complex relationships exist among the considered variables (Farjam et al. 2014; Sabzalian et al. 2014; Mansouri et al. 2016; Abdipour et al. 2018, 2019). It has been documented by many studies that non-linear approaches such as ANNs interoperate variable relationships more accurately than other methods and it would be more capable to predict output variables compared to the linear-based methods (Khairunniza-Bejo et al. 2014; Safa et al. 2016; Abdipour et al. 2019). Odabas et al (2014) noted that ANN provides less error and is more capable than MLR or any other linear-based models to find the best pattern of variables.

ANNs have been widely utilized to handle non-linear data processing (Shin et al. 2000). Different architectures of ANN like back propagation neural network (Srivastava 2003), adaptive logic network (Qu et al. 2001), radial basis function network (Boilot et al. 2002), FuzzyAR TMAP (Boilot et al. 2002), self-organizing map network (Sinesio et al. 2000) and time-delay neural network (Zhang et al. 2003) have been applied to analyze data. In food safety research, ANNs have been used in conjunction with electronic nose systems for detection of Escherichia coli in packaged alfalfa sprouts (Siripatrawan et al. 2004; Siripatrawan et al. 2006) and for beef spoilage/contamination detection (Panigrahi et al. 2006; Balasubramanian et al. 2009). Moreover, ANNs and fuzzy logics have been widely used in agricultural field for yield prediction of crops such as wheat, corn, soybean, potato, barley etc. (Alvarez 2009; Mutlu et al. 2011; Moradi et al. 2013; Ahmadi et al. 2014; Odabas et al. 2014; Matsumura et al. 2015; Safa et al. 2016; Fieuzal et al. 2017; Abdipour et al 2019). However, few studies have been conducted in the field of animal science on the prediction of pig’s body temperature, considering ambient environmental parameters inside and outside pig barn using ANN models. Therefore, this study was conducted to develop ANN models that can predict pig’ body temperature giving input variables. The objectives of the present study were to build up and evaluate the predictive performance of ANNs and MLR-based models for predicting body temperature of pig using input variables and also to analyze the sensitivity of the input variables to determine the most and the least influential parameters on pig’s body surface temperature.

2. Materials and methods

2.1 Experimental pig barn

The research was conducted in an experimental pig barn located in the Gyeongsang National University (latitude 35^o9'6.14"N, longitude 128^o5'44.40"E and altitude 44 m). Each experiment pig barn had an average size of 3.3 m (width) × 5.4 m (length) × 2.9 m (height) and 0.05 m thickness of roofs and walls. Galvanized steel was used in the construction of walls and roof was made using expanded polystyrene. These materials were used due to their usefulness in keeping comfortable environment inside the pig barn (Moon et al. 2016). Moreover, the galvanized steel was properly fixed inside and outside with expended polystyrene materials. To circulate air flow within the pig barn, a constantly ventilated exhaust fan and an air inlet damper (Auto-Damper 250, Sanison Co., Ltd., Korea) with an average flow rate of 0.16 m³/s were installed at a height of 1.44 and 1.72 m, respectively above the ground level in the pig barn.

2.2 Experimental design and data collection

In this experiment, six two-month-old Yorkshire breed pigs with an initial body weight of 30.3 ± 0.85 kg (mean ± s.d.) were studied. Two independent experiments were performed from 15 September to 15 December in 2017 and 2018 with the same number of pigs. The experimental period was selected based on the comfortable temperature available in the pig barn during these period. The research team had interacted with pig’s farmers to gather their understanding of weather variability in pig barn. According to Dong et al. (2001), temperatures of 16–25°C are most comfortable for sows in pig barn. Before the beginning of the experiment, a two-week observation phase was implemented to define the best data measuring conditions. On the first day of each experiment, ear tags were implanted for identification in each pig after cleaning and disinfection of the application spot on the skin with isopropyl alcohol. The barn was equipped with drinkers and feeders, and the pigs were restrained with halters for feeding and drinking. The feed was provided twice a day, at 10.00 am and 17.00 pm in an equal amount of feed, and the amounts of feed offered and leftovers of each pig were recorded daily to estimate feed intake. Moreover, the body weights were determined by averaging weights measured on two times in day at study onset.

The body surface temperature of pig was measured using four infrared sensors (IR sensor, model-MI3, Raytek corporation, California, United States of America) at a fixed distance (20 cm) which were positioned perpendicularly to the pig’s body at four different body regions of each pig: left side (LS), right side (RS), forehead (FH) and back side (BS) at the same time (Figure 1). The IR sensor is a non-contact and non-invasive temperature measuring instrument, which has been adopted in a number of studies for measuring body surface temperature of livestock and wildlife animals (GürdiL et al. 2007; Mccafferty and Dominic 2007), for disease detection (Montanholi et al. 2008; Schaefer et al. 2012) and animal welfare (Stewart et al. 2005; Nääs et al. 2014). Since it is unnecessary to touch the pig’s body, infrared (IR) measurement technique considerably reduces the risk of spreading infection. Moreover, in animals, this is advantageous since handling and restraint increase stress, causing effects on core and surface temperatures (Loughmiller et al. 2001; Vianna et al. 2005; Ludwig et al. 2007; Stewart et al. 2010; Magnani et al. 2011 and Warriss et al. 2006). The IR sensor recorded readings every 2 h in a day, from 9.00 am to 17.00 pm and the measured temperature data were automatically transmitted to computer. Furthermore, detailed experimental observations were made on different management systems such as feeding, drinking, manure etc. in day time for a more explanation of the experimental set-up. Livestock environment management systems (LEMS) and weather sensors were installed to record data of temperature, humidity, carbon dioxide, smoke and wind speed in every five-minute intervals inside and outside of pig barn, respectively. However, for this the study we used the equal interval data obtained from IR sensor, LEMS and weather sensor during the experiment period. The LEMS and weather sensors’ data reception were connected to the computer where the data were transmitted for storage.

Figure 1. Schematic diagram for measuring pig’s body temperature using IR sensor.

2.3 Development of artificial neural network

Artificial neural networks (ANNs) are made up of interconnecting artificial neurons, which may be used either to gain an understanding of biological neural networks or to solve artificial intelligence problems without the need to create a model of a real biological system (Bishop 1996; Nadimi et al. 2011). To develop an ANN topology, three main layers, the input, hidden and output layers are required (Figure 2). Each ANN contains neurons or nodes, which are connected to each other by weighted connections according to the required specified architecture and the weighted values are automatically adjusted by training the network according to a specified learning rule until it performs the desired task appropriately (Bishop 1996; Khashei-Siuki et al. 2011). The number of hidden nodes is selected based on the specific problem of the study and typically is determined by trial and error (Tufail et al. 2008). The reliability of the neural network performance is measured by testing the network with several input–output vectors (Bishop 1996). Samarasinghe (2016) discussed the ANN theory and its application for applied sciences and engineering fields. The output of the ANN network was reported by Hydrology (2000) as shown in Equation (1).(1) $y_t={\alpha }_0+\sum _{j=1}^n{\alpha }_{j}f\left(\sum _{i=1}^m{\beta }_{ij}{y}_{t-1}+{\beta }_{0j}\right)+{\epsilon }_t$(1) where y_t is the network output (pig’s body temperature), n is the number of hidden nodes, m is the number of input nodes, f is the transfer function, ${\beta }_{ij}\{i=1,2,\dots ,mj=0,1,\dots ,n\}$ are the weights from the input to hidden nodes, ${\alpha }_j\{j=0,1,\dots ,n\}$ are the vectors of weights from the hidden to the output nodes and α₀ and β_0j denote the weights of arcs leading from the bias terms.

Figure 2. Topology of Feed Forward Back-propagation neural network for log-sigmoid transfer function with 12 neurons (n) in hidden layers to predict pig’s body temperature. W and B of the ANN model are shown weight to hidden layer from input layer, weight to layer, hidden layer to output layer and bias to layer, bias to layer 2 and bias to output layer.

In the present work, different ANN models were developed using the Matlab (R2018a) neural network toolbox. To evaluate the capability of ANNs to predict pig’s body temperature, four different ANN models, including Feed Forward Back-propagation (FFB), Layer recurrent (LR), Elman (EL) and Cascade Forward Back-propagation (CFB) with different learning algorithms, transfer functions, hidden layers and neuron in each layer, were performed. To find the best topology for each ANN model, two hidden layers and neurons in each hidden layer (4–20) were tested through trial and error. The Levenberg-Marquardt training function, Gradient descent weight and bias learning function and the three transfer functions (Log-sigmoid, Linear transfer function (purelin) and Tan-sigmoid) were examined for the hidden and output layers to elucidate which function performed better. A maximum 1000 epochs (iterations) and mean square error (MSE) were used for each run on the training, testing and cross-validation dataset. Finally, the best ANN architecture for desirable output was determined based on the lowest error on the training, testing and validation sets of data. In avoidance of the risk of overtraining and memorization, the convergence of the average of RMSE values during the training, testing and cross-validation stages in different epochs (6–1000) were investigated. The dataset was randomly partitioned into three subsets (65%), (20%) and (15%) for training, testing and validation of the ANNs and MLR, respectively (Abdipour et al. 2018).

2.4 Development of multiple linear regression model

Multiple linear regression (MLR), also known simply as multiple regression, has been used extensively in agricultural fields more than other prediction techniques (Parimala and Mathur 2006; Golkar et al. 2011; Huang et al. 2013; Abdipour et al. 2015; Abdipour et al. 2016; Basak 2019). The goal of MLR is to model the linear relationship between the explanatory (independent) and response (dependent) variables. As a predictive analysis, MLR is based on linear and additive associations of the explanatory variables and attempts to model the relationship between two or more explanatory variables and a dependent variable by the assumption of a linear relationship (Abdipour et al. 2019). Multiple linear regression model was developed according to Equation (2) (Darlington and Hayes 2016):(2) $y_i={\beta }_0+{\beta }_{1\times 1}+{\beta }_{2\times 2}+\cdots +{\beta }_{n\times n}+\epsilon i$(2) where y_i is the body surface temperature, β₀–β_n are the coefficients of regression, X₁–X_n are the input variables and ε is the error associated with the ith observation.

2.5 Model performance and data analysis

The model performance to predict the desired output was determined using four statistical quality parameters, including root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE) and coefficient of determination (R²). They are mathematically expressed as shown from Equations (3)–(6).(3) $\mathrm{RMSE}=\sqrt{{\displaystyle \frac{{\sum }_{i=1}^n{(Oi-Pi)}^2}{n}}}$(3) (4) $\mathrm{MAE}={\displaystyle \frac{1}{n}\sum _{i=1}^n|Oi-Pi|}$(4)

(5) $\mathrm{MAPE}={\displaystyle \frac{1}{n}\sum _{i=1}^n{\displaystyle \frac{|Oi-Pi|}{Oi}\times 100}}$(5) (6) $R^2={\displaystyle \frac{\sum _{i=1}^n(Oi-\overline{\mathrm{O}})(Pi-\overline{\mathrm{P}})}{\sqrt{\sum _{i=1}^n(Oi-\overline{\mathrm{O}}}{)}^2\times \sqrt{\sum _{i=1}^n(Pi-\overline{\mathrm{P}}}{)}^2}}$(6) where n is the number of data, O_i is the observed values, P_i is the predicted values and the bar denotes the mean of the variable. Moreover, a sensitivity analysis was also conducted in this study to observe the effects of independent variables on the output and provide insight into the usefulness of individual variable. Statistical calculations were performed with Statistical Package for the Social Sciences (IBM SPSS Statistics 22.0.0.0, New York, United States of America) and Origin Pro 9.5.5 (OriginLab, Northampton, Massachusetts, United States of America).

3. Results and discussion

3.1 Input variables selection

The selection of input variables is an important consideration in each ANNs and MLR modelling methods to determine the model structure (Table 1). It also affects the weighted coefficient of ANNs and the results of those models (Emamgholizadeh et al. 2015). Although there are different methods to select the best input variables, the correlation coefficient is one of the effective methods for this purpose (Abdipour et al. 2019). It deduces simple relationships between variables, and it would be helpful in identifying the traits by which they have a strong correlation between input and output variable. In the present study, correlation coefficient method has been performed to analyze the relationship between input and output variables. As it is clear from Figure 3, there is positive correlation between pig’s body temperature (PBT) and room temperature (RT), room temperature-humidity index (RTHI), outside temperature (OT), outside temperature-humidity index (OTHI). Similar results were reported by other researchers that RT (Barb et al. 1991; Azim et al. 1996; Prunier et al. 1997; Burri et al. 2009; Basak 2019), RTHI (Bouraoui et al. 2002; Mader 2006; White et al. 2008; Renaudeau et al. 2011; Ross et al. 2015; Basak 2019), OT (Christon 1988; Verstegen and Close 1994), OTHI (Amezcua et al. 2014) are constantly associated with the body temperature of pig. Negative correlation was also observed between PBT and the room relative humidity (RRH), room CO₂ concentration (RCO₂) and the outside CO₂ concentration (OCO₂). In confirmation of the above results, some researchers reported a negative correlation, and had an association between PBT and RRH (Ingram 1965; Brown 2011; Basak et al. 2019), RCO₂ and OCO₂ (Hartung et al. 1994; Arieli and Kerem 1995; Le et al. 2009). However, the outside relative humidity (ORH), age of pig (AG), feed intake (FI) and body weight (BW) showed no significant correlation with PBT. Based on the correlation results, RT, RRH, RCO₂, RTHI, OT, OCO₂ and OTHI were considered as the most important traits for evaluating the ANNs and MLR models because they have a good correlation (r ≥ 0.5) with pig’s body temperature.

Figure 3. Pearson correlation coefficients of input variables with body temperature of pig. AG: age of pig; FI: feed intake; BW: body weight of pig of capsules per plant; OTHI: outside temperature-humidity index; OCO₂: outside CO₂ concentration; ORH: outside relative humidity, OT: outside temperature; RTHI: room temperature-humidity index; RCO₂: room CO₂ concentration; RRH: room relative humidity; RT: room temperature.

Table 1. Summary of the estimated parameters for ANN/MLR models.

Parameters	Range	Mean	Std. deviation
RT (^OC)	9.40–31.60	20.66	4.77
RRH (%)	30.10–87.60	63.92	10.43
RCO2 (ppm)	391–1193	762.15	174.10
RTHI	49.73–82.65	66.72	6.68
OT (^OC)	6.50–36.50	21.48	5.97
ORH (%)	15.10–96.00	46.33	17.61
OCO2 (ppm)	229–374	318.45	23.10
OTHI	46.64–83.10	66.60	7.43
BW (kg)	30.12–141.30	80.48	29.12
FI (gm)	720–2250	1732.58	110.50
AG (day)	65–156	110.50	26.57

Note: RT: room temperature; RRH: room relative humidity; RCO₂: room CO₂ concentration; RTHI: room temperature-humidity index; OT: outside temperature; ORH: outside relative humidity; OCO₂: outside CO₂ concentration; OTHI: outside temperature-humidity index; AG: age of pig; FI: feed intake; BW: body weight.

3.2 Artificial neural network model development and performance

To achieve an efficient model through input variables (RT, RRH, RCO₂, RTHI, OT, OCO₂ and OTHI), four different ANNs models, including Feed Forward Back-propagation (FFB), Layer recurrent (LR), Elman (EL) and Cascade Forward Back-propagation (CFB) with Levenberg-Marquardt training function, Gradient descent weight and bias learning function and the three transfer functions (Log-sigmoid, Linear transfer function (purelin) and Tan-sigmoid) were trained with two hidden layers and neurons in each hidden layer (4–20). In this study, ANN models were performed to identify the relationship between input–output variables aided by hidden layer nodes, which the nodes clarify the conformation of the data measured from experiment. The results of the R² and RMSE for each ANN model with three different transfer functions for training, validation and testing stage are shown in Table 2. As shown in Table 2, the development of FFB model with log-sigmoid transfer function, LR with tan-sigmoid transfer function, EL with tan-sigmoid transfer function and CFB model with log-sigmoid transfer function had the best performance due to the least RMSE and the highest R² in training, validation and testing stages. These models have been used by many researchers to predict the performance of different animals and crops fields (Aarnink and Elzing 1998; Arogo et al. 2003; Grivas and Chaloulakou 2006; Kai et al. 2006; Emamgholizadeh et al. 2015; Abdipour et al. 2018). Regarding the performance of non-linear functions in this study, the relations between input variables and pig’s body temperature may be somewhat non-linear in nature due to higher efficiency. As the results showed, the performance of the ANN models with a linear function such as purelin decreased because of high RMSE values in training, validation and testing stages (Table 2). This reduction in efficiency is probably related to the nature of the function, since linear functions perform a simple linear transformation on the processed input and then carry it to the output layer (Hagan et al. 1996; Abdipour et al. 2019). Compared to other transfer functions, non-linear variations have been used in many studies due to the high prediction accuracy (Alvarez 2009; Ahmadi et al. 2014; Mansouri et al. 2016; Elhami et al. 2017; Mansourian et al. 2017).

Table 2. The performance of the artificial neural network models with different transfer functions to predict body surface temperature of pig.

Network type	Transfer function	Training		Validation		Testing
		R^2	RMSE	R^2	RMSE	R^2	RMSE
Feed Forward Backprop	Log-sigmoid	0.854	1.007	0.862	0.932	0.850	1.008
	Linear (purelin)	0.702	1.467	0.773	1.318	0.691	1.409
	Tan-sigmoid	0.826	1.036	0.835	0.980	0.790	1.197
Layer recurrent	Log-sigmoid	0.843	1.020	0.837	1.007	0.864	0.995
	Linear (purelin)	0.701	1.471	0.736	1.369	0.719	1.343
	Tan-sigmoid	0.862	0.961	0.854	0.949	0.842	1.046
Elman	Log-sigmoid	0.816	1.105	0.824	1.052	0.793	1.161
	Linear (purelin)	0.719	1.421	0.742	1.348	0.619	1.604
	Tan-sigmoid	0.838	1.036	0.833	0.988	0.844	1.042
Cascade-forward	Log-sigmoid	0.841	1.027	0.830	1.016	0.845	1.020
	Linear (purelin)	0.709	1.467	0.709	1.393	0.724	1.337
	Tan-sigmoid	0.828	1.071	0.815	1.074	0.832	1.108

To find the appropriate number of neurons in hidden layers for the selected networks and transfer function, FFB model with log-sigmoid, LR with tan-sigmoid, EL with tan-sigmoid and CFB model with log-sigmoid and different number of neurons in each hidden layer (4–20) were tested through trial and error (Table 3). As the results showed, the FFB model and two hidden layers and 20 neurons in the hidden layer have given the best results in training (RMSE = 0.967 and R²= 0.867), validation (RMSE = 1.003 and R²= 0.859) and testing (RMSE = 0.888 and R²= 0.895) stages. This model with a relatively simple topology had the highest performance to predict pig’s body temperature. Even though the complexity of the model which depends on the nature of the subject and types of input variables, the ANN models with simple topology that achieved in this study are more admired and accepted by the researchers (Zeng et al. 2016; Mansourian et al. 2017; Abdipour et al. 2018; Niazian et al. 2018).

Table 3. The performance of the artificial neural network models with different neurons in hidden layers to predict body surface temperature of pig.

Network type	Neurons in hidden layers	Training		Validation		Testing
		R^2	RMSE	R^2	RMSE	R^2	RMSE
Feed Forward Backprop	4	0.787	1.283	0.766	1.261	0.824	1.110
	8	0.841	1.048	0.824	1.120	0.805	1.154
	12	0.845	1.007	0.872	0.932	0.814	1.008
	16	0.848	0.988	0.857	0.987	0.859	1.055
	20	0.867	0.967	0.859	1.003	0.895	0.888
Layer recurrent	4	0.802	1.202	0.787	1.209	0.794	1.195
	8	0.838	1.052	0.794	1.187	0.788	1.213
	12	0.860	0.961	0.867	0.949	0.843	1.046
	16	0.857	0.974	0.849	1.008	0.858	1.001
	20	0.857	0.970	0.837	1.045	0.855	1.009
Elman	4	0.806	1.187	0.781	1.232	0.745	1.349
	8	0.832	1.077	0.795	1.184	0.807	1.154
	12	0.842	1.036	0.855	0.988	0.844	1.042
	16	0.854	0.983	0.823	1.092	0.841	1.050
	20	0.859	0.962	0.847	1.012	0.868	0.969
Cascade-forward	4	0.799	1.190	0.810	1.192	0.810	1.116
	8	0.839	1.046	0.799	1.141	0.867	1.020
	12	0.852	1.027	0.848	1.016	0.865	1.020
	16	0.861	0.943	0.848	1.015	0.857	0.987
	20	0.845	1.006	0.805	1.061	0.884	0.943

To better understand the distribution of data and the ability of the selected models, the predicted and actual pig’s body temperature values for complete dataset were presented and compared in the scatter plots and box plots (Figures 4–7 and Tables 4 and 5). As shown in the scatter plots obtained from FFB model (Figure 4 and Table 5), the predicted PBT values have a very close distribution pattern with measured PBT values, and both have almost the same pattern with R²= 0.871, RMSE = 0.961 and MAPE = 2.207. Also, based on the box plots results for FFB model (Figure 4(b)), the both measured and predicted datasets with having same statistical parameters, such as the minimum of the sample, lower quartile, median, upper quartile and maximum of the sample, did not show significant difference. Moreover, the lack of outliers (unusual values of data) in the box plot (Figure 4(b)), once again identified the FFB model for log-sigmoid transfer function with 20 neurons in two hidden layers as the best to predict PBT.

Figure 4. Measured and predicted pig’s body temperature in Feed Forward Back-propagation neural network for log-sigmoid transfer function with 20 neurons in hidden layers. (a) Scatter plot of measured and predicted pig’s body temperature. (b) Box plot of measured and predicted pig’s body temperature.

Figure 5. Measured and predicted pig’s body temperature in Layer recurrent neural network for Tan-sigmoid transfer function with 12 neurons in hidden layers. (a) Scatter plot of measured and predicted pig’s body temperature. (b) Box plot of measured and predicted pig’s body temperature.

Figure 6. Measured and predicted pig’s body temperature in Elman neural network for Tan-sigmoid transfer function with 20 neurons in hidden layers. (a) Scatter plot of measured and predicted pig’s body temperature. (b) Box plot of measured and predicted pig’s body temperature.

Figure 7. Measured and predicted pig’s body temperature in Cascade Forward Back-propagation neural network for log-sigmoid transfer function with 16 neurons in hidden layers. (a) Scatter plot of measured and predicted pig’s body temperature. (b) Box plot of measured and predicted pig’s body temperature.

Table 4. The overall performance of the artificial neural network models with different transfer functions to predict body surface temperature of pig.

Network type	Transfer function	MAE	RMSE	MAPE	R^2
Feed Forward Back-propagation	Log-sigmoid	0.772	1.035	2.441	0.851
	Linear (purelin)	1.118	1.440	3.568	0.711
	Tan-sigmoid	0.840	1.111	2.667	0.828
Layer recurrent	Log-sigmoid	0.786	1.051	2.488	0.846
	Linear (purelin)	1.118	1.442	3.572	0.710
	Tan-sigmoid	0.739	0.999	2.345	0.861
Elman	Log-sigmoid	0.872	1.139	2.765	0.819
	Linear (purelin)	1.124	1.440	3.580	0.711
	Tan-sigmoid	0.784	1.047	2.479	0.847
Cascade Forward Back-propagation	Log-sigmoid	0.809	1.061	2.555	0.843
	Linear (purelin)	1.121	1.439	3.574	0.711
	Tan-sigmoid	0.842	1.109	2.676	0.829

Table 5. The overall performance of the artificial neural network models with different neurons in hidden layers.

Network type	Neurons in hidden layers	MAE	RMSE	MAPE	R^2
Feed Forward Back-propagation	4	0.976	1.265	3.091	0.777
	8	0.830	1.094	2.626	0.833
	12	0.798	1.057	2.523	0.844
	16	0.777	1.032	2.465	0.852
	20	0.696	0.961	2.207	0.871
Layer recurrent	4	0.943	1.216	2.980	0.794
	8	0.880	1.140	2.783	0.819
	12	0.774	1.024	2.446	0.854
	16	0.770	1.028	2.441	0.853
	20	0.777	1.032	2.455	0.852
Elman	4	0.950	1.232	3.022	0.789
	8	0.860	1.125	2.711	0.824
	12	0.824	1.079	2.598	0.838
	16	0.782	1.043	2.471	0.849
	20	0.735	0.992	2.324	0.863
Cascade Forward Back-propagation	4	0.919	1.192	2.902	0.802
	8	0.813	1.076	2.574	0.839
	12	0.760	1.024	2.416	0.854
	16	0.741	1.006	2.343	0.859
	20	0.791	1.053	2.514	0.846

3.3 Multiple linear regression model development and performance

The prediction efficiency of regression-based models depends on the existence of linear relationships between input and output variables. Due to their simplicity, MLR models have been used in many studies compared to any other modelling techniques in agricultural sectors (Parimala and Mathur 2006; Karimi et al. 2009; Golkar et al. 2011; Ghoreishi et al. 2012; Huang et al. 2013; Abdipour et al. 2015; Abdipour et al. 2016; Basak 2019). By taking the same inputs and output data which were used for the ANN models, the efficiency of the regression model was evaluated to predict the PBT. The following equation (7) was computed to predict PBT:(7) $\mathrm{PBT}=20.48+0.219\mathrm{RT}-0.037\mathrm{RRH}-0.002\mathrm{RC}{\mathrm{O}}_2+0.040\mathrm{RTHI}-0.257\mathrm{OT}-0.010\mathrm{OC}{\mathrm{O}}_2+0.259\mathrm{OTHI}$(7) where PBT is the pig’s body temperature, RT is the room temperature, RRH is the room relative humidity, RCO₂ is the room CO₂ concentration, RTHI is the room temperature-humidity index, OT is the outside temperature, OCO₂ is the outside CO₂ concentration and OTHI is the outside temperature-humidity index (OTHI).

The predicted PBT value in Equation (7) is a linear combination of the input variables (RT, RRH, RCO₂, RTHI, OT, OCO₂ and OTHI), such that the sum of the squared deviations of the measured and predicted PBT values is minimum. A formula model such as Equation (7) is useful in understanding how PBT changes with RT, RRH, RCO₂, RTHI, OT, OCO₂ and OTHI and what values of these variables are required to achieve the optimal value of PBT. The MLR model was less capable of predicting PBT in training (with R²=0.720, RMSE=1.383 and MAPE=3.423), validation (with R²=0.765, RMSE=1.235 and MAPE=3.045) and testing (R²=0.640, RMSE=1.723, MAPE=4.536) compared to the ANN models. To evaluate the efficiency of the MLR model, the pattern of the distribution of actual and predicted values of PBT for complete dataset was compared on the scatter plot and box plot (Figure 8(a,b)). As shown in the box plot (Figure 8(b)), there is a difference between the actual and predicted values in terms of the minimum of the sample, lower quartile, median, upper quartile and maximum of the sample. Moreover, the existence of outliers can be attributed to the inability of the model to predict PBT properly. Although it is possible to achieve higher-performing regression models, in this study the MLR (with R²=0.710) cannot be considered as an optimum model for predicting PBT.

Figure 8. Measured and predicted pig’s body temperature in Multiple linear regression (MLR) model with seven input variables. (a) Scatter plot of measured and predicted pig’s body temperature. (b) Box plot of measured and predicted pig’s body temperature.

3.4 Comparing ANN and MLR models for predicting PBT

Based on statistical qualitative parameters (i.e. R², RMSE and MAPE), the result of the study showed that all the ANN models provided a more powerful tool than the regression model for predicting PBT. The selected ANN model could predict PBT for training, validation and testing stages with a 20.42, 12.29 and 39.84% increase in R² and a reduction of 30.10, 48.57 and 18.76% in RMSE, respectively, compared to the MLR model. Moreover, the ANN model to the MLR model is also well defined by considering the relatively similar values of the statistical parameters such as median or similar distribution for the actual and predicted values (Figure 4(b) and Figure 8(b)). In addition, a graphical presentation of the actual and predicted values by the ANN and MLR models over a graph (Figure 9) can help to better understand the ability of the two models for predicting PBT. Results obtained from the cumulative distribution function (Figure 9) showed that the predicted PBT values by the ANN model had greater prediction accuracy than the MLR model. As shown in Figure 9, 80% of the data have a residual value between -1 and 1 for the ANN model, whereas it was 55% for the MLR model in the same boundary limit. Moreover, from the S-curve (Figure 9), a significant proportion of the relationships between the input variables and PBT are followed through non-linear relationships, which may also affect the performance of the ANN and MLR models. However, the difference in performance between the ANN and MLR models showed the importance of choosing the best model to predict PBT. The higher ability of the ANN modelling methods compared with the MLR methods to capture the highly non-linear and complex relationship between output and inputs variables has been reported in many studies (Singh et al. 2003; Gholipoor et al. 2013; Khairunniza-Bejo et al. 2014; Mansourian et al. 2017; Abdipour et al. 2019). In general, all of the ANN models had higher efficiency in predicting PBT than the regression model in this study.

Figure 9. Cumulative distribution function calculated from measured and predicted pig’s body temperature. (a) Cumulative distribution function of measured and predicted pig’s body temperature for the ANN. (b) Cumulative distribution function of measured and predicted pig’s body temperature for the MLR.

3.5 Sensitivity analysis of input variables

Sensitivity tests were performed for the both the MLR and ANN models in order to find out the individual effect of the input variables on the predicted PBT value. As shown in Figure 10, the ability of the ANN and MLR models to predict PBT significantly decreased when they were run without RTHI. As illustrated in Figure 10, the ANN and MLR models without RTHI had the lowest R² (0.810, 0.694) and the highest RMSE (1.170, 1.482) and MAPE (2.592, 3.612), respectively. Therefore, RTHI can be said to be the most influential factor in predicting PBT in both models, followed by RT, OTHI, OT, RCO₂, OCO₂ and RRH, respectively. The importance of this variable to determine the PBT has led to the introduction of this variable in many modelling studies as an important indirect indicator to predict PBT (Basak 2019; Prunier et al. 1997; Azim et al. 1996; Barb et al. 1991; Burri et al. 2009; Mader 2006; Ross et al. 2015; White et al. 2008; Renaudeau et al. 2011; Bouraoui et al. 2002; Christon 1988; Verstegen and Close 1994; Amezcua et al. 2014). In addition to RTHI, three next important traits (i.e. RT, OTHI and OT) also had a significant effect to predict PBT in both models. These four traits (RTHI, RT, OTHI and OT) had a positive relationship and account for a total of 78% and 67% of the PBT variation in the ANN and MLR models, respectively. Therefore, they can be considered as the most important indirect indicators in the pig farming to determine the thermal comfort zone.

Figure 10. Sensitivity analysis of the input variables on body temperature of pig in ANN and MLR models. A: The best ANN/MLR model without RT; B: MLR/ANN model without RRH; C: MLR/ANN model without RCO₂; D: MLR/ANN model without RTHI; E: MLR/ANN model without OT; F: MLR/ANN model without OCO₂; G: MLR/ANN model without OTHI.

4. Conclusion

The research was conducted to evaluate modelling relationships between pig’s body temperature and ambient environment inside and outside of a pig barn. In the current study, four different ANN (FFB, LR, EL and CFB) models, along with a MLR model, were developed with seven selected input variable i.e. RT, RRH, RTHI, RCO₂, OT, OCO₂ and OTHI to predict PBT. The results showed a higher performance rate by the ANN models as compared to the MLR model. FFB model with log-sigmoid transfer function and two hidden layers in 20 neurons was selected as the best model to predict the PBT. This priority for ANN models for predicting PBT may be due to the existing non-linear association between body temperature of pig and its components of which the MLR method is unable to explain in its model. These results indicated that the selected ANN model does not suffer from this problem and can assuredly replace multiple linear models such as MLR for predicting PBT. Sensitivity analysis showed the number of temperature-humidity index in room (RTHI) is the most influential factor to predict PBT in the MLR/ANN models, followed by room temperature (RT), outside temperature-humidity index (OTHI), outside temperature (OT), room CO₂ concentration (RCO₂), outside CO₂ concentration (OCO₂) and room relative humidity (RRH), respectively. Therefore, if the temperature-humidity index increases inside the pig barn, it might raise the body temperature of pigs which may create thermal uncomfortable situation in pig barn. Similar to those observed in this study, it can be said that maintaining temperature-humidity index within comfortable limit along with room temperature can be a good approach to addressing the thermal comfort zone in a livestock barn. However, the above-described ambient environmental parameters may not always be the same when associated with body temperature of pig, and also, trying to achieve high prediction efficiency of PBT using the same attributes may lead to changes in the performance of the models. Therefore, more environmental factors as well as other growth factors may be included in models.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Korea Institute of Planning and Evaluation for Technology in Food, Agriculture, Forestry and Fisheries (IPET) through Agriculture, Food and Rural Affairs Convergence Technologies Program for Educating Creative Global Leader, funded by Ministry of Agriculture, Food and RuralAffairs (MAFRA) (717001-7).