Validation of an AutoRegressive Integrated Moving Average model for the prediction of animal zone temperature in a weaned piglet building

Validation of an AutoRegressive Integrated Moving Average Model for the Prediction of Animal Zone Temperature in a Weaned Piglet Building J.A. Ortega, E. Losada, R. Besteiro, T. Arango, M.J. Ginzo- Villamayor, R. Velo, M.D. Fernández, M. R. Rodríguez Version: Accepted manuscript HOW TO CITE Ortega, JA., Losada, E., Besteiro Doval, R., Arango López, T., Ginzo-Villamayor, M.J., Velo Sabín, R, Fernández Rodríguez, MD., Rodriguez Rodríguez, MR. (2018). Validation of an AutoRegressive Integrated Moving Average model for the prediction of animal zone temperature in a weaned piglet building Biosystems Engineering. I74. pp. 231- 238. Elsevier. FUNDING The authors are grateful to the regional government Xunta de Galicia for funding this research through the “Programme of consolidation and structuring of competitive research units” (GPC2014/072). © 2018 IAgrE. Published by Elsevier Ltd. All rights reserved. This manuscript version is made available under the CC-BY-NC-ND 4.0 license 1 Validation of an AutoRegressive Integrated Moving Average Model 1 for the Prediction of Animal Zone Temperature in a Weaned Piglet 2 Building 3 J.A. Ortegaa, E. Losadab, R. Besteiroc, T. Arangoc, M. J. Ginzo-Villamayord, R. Veloc, M.D. 4 Fernandezc, M.R. Rodríguezc* 5 a Xunta de Galicia, Regional Agrarian Office of Lalín, Pontevedra, Spain 6 b Xunta de Galicia, Department of Culture, Education and University Planning, Lugo, Spain 7 c Department of Agroforestry Engineering, University of Santiago de Compostela, Campus 8 Terra, 27002, Lugo, Spain 9 d Department of Statistics, Mathematical Analysis and Optimization, University of Santiago de 10 Compostela, Faculty of Mathematics, Campus Vida, 15782 Santiago de Compostela, Spain. 11 *corresponding author: m[email protected] 12 13 Abstract 14 15 An AutoRegressive Integrated Moving Average model was validated for the 16 prediction of temperatures in the animal zone of conventional weaned piglet barn. The 17 validation period covered seven cycles and recorded values at 10-min intervals for 292 18 days. Average weight was 5.75±0.86 kg at the beginning of the production cycle and 19 18.41±2.12 kg at the end of the cycle. Mean outdoor air temperatures ranged 6.14 to 20 17.85ºC with deviations in the range 2.49ºC to 5.24ºC, which involved marked 21 differences in the operation of the ventilation system. The Mean Average Percentage 22 Error was below 4%, with a mean error of 1ºC. The Root Mean Square Error was in the 23 range 0.77ºC to 1.19ºC, whereas the coefficient of determination ranged between 0.52 24 and 0.81. Despite the changes in environmental conditions and in animal weight and 25 management, the accuracy of the model remained stable with low dispersion of values. 26 2 The model showed good accuracy and reliability covering all the seasons under changing 1 meteorological conditions because it considered the operation of the heating and 2 ventilation systems and changes in animal weight. The residuals obtained from the 3 validation of the seven production cycles were Gaussian distributed, which confirmed the 4 validity of the model. The generated model can be used for more effective environmental 5 control systems that are capable of anticipating events and show a better response, which 6 helps improve energy savings and animal welfare. 7 8 Keywords: weaned piglets; ARIMA; validation; temperature; indoor climate; livestock 9 buildings. 10 11 Nomenclature 12 ARIMA AutoRegressive Integrated Moving Average 13 CFD Computational Fluid Dynamics 14 𝐶𝑂𝑉  covariance of 𝑋 and 𝑋  15 d backshifts for degree of differencing of the ARIMA model structure 16 MAPE Mean Absolute Percentage Error, % 17 ME Mean Error 18 𝑛 number of records 19 p backshifts for lag order of the ARIMA model structure 20 q backshifts for averaging window of the ARIMA model structure 21 R2 coefficient of determination 22 RMSE Root Mean Square Error 23 Sao air outlet section area, m2 24 SD standard deviation 25 3 Tao outdoor air temperature, ºC 1 Taz animal zone temperature, ºC 2 Vao volume of extracted air by the fan, m3 3 Wa body mass of the animals, kg 4 𝑋 value measured at time t 5 𝑋  value predicted by the model at time t 6 𝜎 standard deviation of X 7 𝜎  standard deviation of 𝑋  8 9 1. Introduction 10 The increasingly restrictive environmental and animal welfare regulations for the pig 11 industry, along with the increase in energy demand, have significant effects on farm 12 competitiveness and environment. In this context, the productivity of farms must be 13 improved, which calls for an improvement in energy efficiency and animal welfare. 14 15 In piggeries, a major effort is required during birth and weaning, which are the most 16 sensitive phases of swine production and the phases with the highest energy requirements 17 (Dolz et al., 2015). Weaning in particular is a sensitive phase characterised by 18 simultaneous stresses including separation from the sow, mixing of litters, and changes 19 in diet and environment (Le Dividich & Herpin, 1994; Dong & Pluske, 2007). During 20 weaning, piglet weight triples over a short period, animal welfare demands are strong, 21 and the climatic demands of the piglets show important variations. Consequently, 22 environmental control systems must be adapted to the growth needs of piglets. 23 24 4 Models for the prediction of environmental variables in diverse scenarios require 1 extensive validation before use. Moreover, the global increase in temperature caused by 2 climate change demands flexible and adaptable models that provide error estimates. 3 Similarly, the increasing need for energy efficiency in buildings demands predictive 4 control systems that include environmental models that can be applied to diverse 5 geographical locations. Accordingly, the validation of indoor environment models 6 becomes essential to ensure the accuracy and robustness of the models, and consequently, 7 their use. 8 9 Overall, the literature reveals a lack of validated models for the prediction of 10 environmental variables in livestock buildings. Many models have been developed but 11 not validated at all (Diesch & Froehlich, 1988; Axaopoulos et al., 1992; Lambert et al., 12 2001; Besteiro et al., 2017). Other models have been validated over short periods, which 13 does not ensure the robustness of the model or the incorporation of the effects of animal 14 growth. For instance, Upachaban et al. (2016) validated their model for three days, 15 whereas Liberati and Zappavigna (2007) or Seo et al. (2012), used two days for model 16 validation and Daskalov (1997) used only one day. CFD model validation requires stable 17 boundary conditions and this can shorten validation times even more. For the model 18 developed by Rojano et al. (2016), the total validation time amounted to 26 h 50 min. 19 20 Also, most authors do not considere the heterogeneity of the air volume and assume 21 a perfect gas mixture inside the building. To predict the model output variables, these 22 models have often used a probe or selected a specific reference spot inside the building 23 far from the animal occupied zone, in which air volume is a key factor for environmental 24 control. Guo et al. (2001) placed humidity and temperature probes at 1.6 m height above 25 5 the floor, Daskalov (1997), at 1 m height above the floor, and Cooper et al. (1998) at 1 m 1 below the roof. Yet, other authors have focused on the animal occupied zone (van 2 Wagenberg & De Leeuw, 2003, Upachaban et al., 2016). 3 4 In addition, the input variables are not uniform. Many authors neglected the effects 5 of solar radiation or the contribution of the evaporation of water from manure 6 (Axaopoulos et al., 1992; Lambert et al., 2001). 7 8 The goal of this paper is to extensively validate an AutoRegressive Integrated Moving 9 Average (ARIMA) model for the prediction of indoor temperature in the animal occupied 10 zone of a conventional pig farm. The model, designed by Besteiro et al. (2017), predicts 11 temperature inside a building for weaned piglets in the range 6 to 20 kg live body mass. 12 The model predicts 10-min values and allows for the analysis of complete 40-day rearing 13 cycles, which makes it suitable for use in predictive systems for climate control. 14 Accordingly, the validated model must adapt to the increase in piglet weight and to the 15 changes in the environmental conditions inside the building over the period of interest, 16 which vary from 30 – 32ºC for 5 kg live body mass to 19 – 25ºC for 20 kg live body mass 17 in rooms with plastic slatted floors (Muirhead & Alexander, 1997). The model 18 incorporates predictor variables that are representative of outdoor conditions, operation 19 of the systems and animal weight. The 292-day validation period used allowed for 20 analysis of model accuracy and its robustness. Accuracy was analysed by comparing 21 model-predicted values with real values, whereas robustness was analysed in terms of the 22 capacity of the model to maintain accuracy under different environmental and 23 management conditions. 24 25 6 2. Materials and Methods 1 2 2.1 Model 3 4 The ARIMA method is based on the assumption that past observations can explain the 5 present and future evolution of a time series. In ARIMA models, exogenous variables 6 related to the study dependent variable, known as predictor or independent variables, can 7 be incorporated. There are three basic components to an ARIMA model: Auto-Regression, 8 Integration and Moving Average. The ARIMA model investigated in this paper was 9 designed by Besteiro et al. (2017). The model allowed for the prediction of 10-min values 10 of animal zone temperature for a complete production cycle of approximately 6 weeks. 11 The model included the following predictor variables: (1) the outdoor climate, as defined 12 by outdoor air temperature (Tao), (2) the operation of the ventilation system, as defined 13 by air outlet section area (Sao) and volume of extracted air (Vao) and (3) the body mass of 14 the animals (Wa). The most usual models of pig growth show an underlying exponential 15 fit (Wellock et al., 2003; Vincek et al., 2012). Exponential fit was used for the three 16 weighings performed at three different times: when the animals entered the room, when 17 the animals left the room and at an intermediate growth stage, between days 9 and 22, in 18 order to obtain 10-min values of animal body mass. 19 20 The model shows a 2,1,2, structure (p, d, q), which indicates the highest order of each 21 component, two backshifts for the lag order (p), only one backshift for the degree of 22 differencing (d) and two backshifts for the averaging window (q) of the predicted 23 variable. The model structure shows the maximum backshifts needed for each component 24 of the predicted variable. Table 1 shows the backshifts applied for each component (p, d, 25 q) of the study variables. Thus, the series for all the variables have been differentiated 26 7 from the previous values (d = 1). To predict Taz, we used the first and second backshifts 1 for the autoregressive component and only one backshift for the moving average 2 component. For the predictor variables, we used the current values and one backshift for 3 the autoregressive component. The moving average was not applied to the predictor 4 variables. From among the models developed by Besteiro et al. (2017), Model 4.4 was 5 chosen because it showed a level of significance of 0.055, which allowed for the 6 assumption of the randomness of its residuals at a 95% confidence level. This model was 7 the only model that described the evolution of the variable, insofar as it produced a series 8 of residuals with a structure that was similar to that of Gaussian white noise. 9 10 Table 1. Backshifts for each component, lag order (p), degree of differencing (d), and 11 averaging window (q) of the predicted variable, animal zone temperature (Taz); p 12 and d of predictor variables outdoor air temperature (Tao), air outlet section area 13 (Sao), volume of extracted air (Vao) and animal body mass (Wa) 14 15 Component Taz (ºC) Tao (ºC) Sao (cm2) Vao (m3) Wa (kg) p 1 0 0 1 0 2 1 - - - d 1 1 1 1 1 q 1 - - - - 16 17 2.2 Experimental test 18 19 To obtain the variables required for model validation, experiments were conducted on 20 a commercial pig farm located in Northwest Spain (ED50: 43º10’15’’N 8º 19’ 24’’ W). 21 The farm, which housed weaned piglets of 20 kg live body mass, was representative of 22 the type of farm found in the study area. 23 24 8 The weaner room, with an area of 69.26 m2 and a volume of 164.50 m3, consisted of 1 twelve 2.55 × 1.97 m pens, six on each side of a central aisle. The room was capable of 2 holding a maximum of 300 piglets; in this case, commercial hybrids obtained by mating 3 a Landrance-Large White F1 sow with a German Piétrain boar. The room had completely 4 slatted plastic flooring over a 450 mm deep pit. The ventilation system was composed of 5 a 500 mm helical extractor fan with 480 W power and an outlet section area of 0.20 m2. 6 Fan speed was adjusted by changing the voltage using a digital controller based on 7 temperature. The air outlet section area was modulated by two manually-operated sliding 8 panels according to the age of the animal. Fresh air entered the room through two 0.70 9 m2 windows with air deflectors. The water underfloor heating system was composed of 10 two 1.20 × 0.50 m polyester spreader plates for water. 11 12 To validate the model, seven production cycles with an average duration of 41.71 days 13 were used between the 21st of November, 2011 and the 20th of May, 2013 (Table 2), which 14 did not include the periods used to design the model. The following variables were 15 measured: Taz, Tao, Sao, Vao and Wa. 16 17 Temperatures were measured using an S-THB-M002 sensor (Onset Computer 18 Corporation©, Bourne, MA, USA). Speed of the air extracted through the ventilation 19 system was measured using a HD2903TTC310 (Delta Ohm, Caselle, PD, Italy) active air 20 speed transmitter (Besteiro et al, 2017). Volume of extracted air was calculated from air 21 velocity and fan section according to the method proposed by Hinz and Linke (1998). 22 These variables were sampled every second and recorded at 10-min intervals. Live mass 23 of the animals was obtained by applying the exponential growth model (Nóvak et al, 24 2014, Vincek et al, 2012) using the three weighings performed along the cycle. 25 15 confidence level (Besteiro et al., 2017). As a result of error randomness, no clear trends 1 were found for the errors in predictions. For instance, during the first period, both 2 underestimations (cycles 2, 3, 4) and overestimations (cycles 1, 5, 6) are found (Fig. 1). 3 Important temperature changes (Fig. 2.) often result in underestimations, particularly 4 under high temperatures (Cycle 4), but also in overestimations (Cycle 5) or good fits 5 (Cycle 7). Similarly, different responses have been observed under slight temperature 6 changes (Fig. 3). Consequently, analyzing the errors becomes essential. 7 8 According to the graphical analysis of the distributions of residuals obtained from 9 model validation, residuals tend to be Gaussian (normally) distributed, although the 10 distributions obtained from prediction residuals are not identical to those of Gaussian 11 white noise (Fig. 4). The ME values suggest that the distributions of residuals for the 12 cycles with average temperatures (cycles 4 and 7) are almost centred on zero. By contrast, 13 during the cold cycles (1 and 2), the distribution of histograms was skewed to the right, 14 i.e., temperature is underestimated (positive ME), whereas during the warm cycles (6 and 15 7), the distribution is skewed to the left (negative ME). Accordingly, there appears to be 16 some dependence between residuals and outdoor temperature, which in turn affects the 17 operation of the ventilation system, both included as predictor variables in the model. 18 However, overall the errors were quite symmetrically distributed. For cycles 2 and 6, the 19 central area of the histogram is slightly skewed. This behaviour is more frequent for the 20 values near and below the mean. 21 22 5. Conclusion 23 24 16 The statistical model validated in this paper provides a relevant improvement in terms 1 of accuracy and reliability compared to the existing models because of its extensive and 2 continuous validation under changing meteorological conditions and because it considers 3 the operation of the heating and ventilation systems, as well as changes due to animal 4 body mass. However, the model predicts only the temperature of the building, whereas 5 numerical models can provide a more detailed description under stable conditions for 6 short periods. The residuals obtained from the validation of the seven production cycles 7 can be considered to be Gaussian (normally) distributed, which confirms the validity of 8 the model. The generated model can be used in more effective environmental control 9 systems that are capable of anticipating events and show a better response, which can 10 improve energy savings and animal welfare. 11 12 Acknowledgment 13 14 The authors are grateful to the regional government Xunta de Galicia for funding this 15 research through the “Programme of consolidation and structuring of competitive 16 research units” (GPC2014/072). 17 18 References 19 Axaopoulos, P., Panagakis, P., & Kyritsis, S. (1992). Computer simulation assessment of the 20 thermal microenvironment of growing pigs under summer conditions. Transactions of the 21 ASAE, 35(3), 1005-1009. doi: 10.13031/2013.28694. 22 Besteiro, R., Ortega, J. A., Arango, T., Rodriguez, M. R., & Fernandez, M. D. (2017). ARIMA 23 modeling of animal zone temperature in weaned piglet buildings: design of the model. 24 Transactions of the ASABE, 60(6), 2175-2183. https://doi.org/10.13031/trans.12372. 25 17 Blanes, V., & Pedersen, S. (2005). Ventilation flow in pig houses measured and calculated by 1 carbon dioxide, moisture and heat balance equations. Biosystems Engineering, 92(4), 483-493. 2 https://doi.org/10.1016/j.biosystemseng.2005.09.002. 3 Cooper, K., Parsons, D. J., & Demmers, T. (1998). A thermal balance model for livestock 4 buildings for use in climate change studies. Journal of Agricultural Engineering Research, 5 69(1), 43-52. https://doi.org/10.1006/jaer.1997.0223. 6 Daskalov, P. I. (1997). Prediction of temperature and humidity in a naturally ventilated pig 7 building. Journal of Agricultural Engineering Research, 68(4), 329-339. 8 https://doi.org/10.1006/jaer.1997.0211. 9 Diesch, M. A., & Froehlich, D. P. (1988). Production and environmental simulations in 10 livestock housing. Transactions of the ASAE, 31(5), 1532-1539. doi: 10.13031/2013.30896. 11 Dolz, N., Babot, D., Alvarez-Rodriguez, J., & Forcada, F. (2015). Improving the environment 12 for weaned piglets using polypropylene fabrics above the animals in cold periods. International 13 Journal of Biometeorology, 59(12), 1839-1847. https://doi.org/10.1007/s00484-015-0991-0. 14 Dong, G. Z., & Pluske, J. R. (2007). The low feed intake in newly-weaned pigs: problems and 15 possible solutions. Asian-Australasian Journal of Animal Sciences, 20(3), 440-452. 16 https://doi.org/10.5713/ajas.2007.440. 17 Garcimartin, M. A., Ovejero, I., Sanchez, E., & Sanchez-Giron, V. (2007). Application of the 18 sensible heat balance to determine the temperature tolerance of commercial poultry housing. 19 World's Poultry Science Journal, 63(4), 575-584. https://doi.org/10.1017/S0043933907001626. 20 Guo, H., Lemay, S. P., Barber, E. M., Crowe, T. G., & Chénard, L. (2001). Humidity control for 21 swine buildings in cold climate - Part II: Development and evaluation of a humidity controller. 22 Canadian Biosystems Engineering, 43, 537-546 23 Hinz, T., & Linke, S. (1998). A comprehensive experimental study of aerial pollutants in and 24 18 emissions from livestock buildings. Part 1: Methods. Journal of Agricultural Engineering 1 Research, 70(1), 111-118. https://doi.org/10.1006/jaer.1997.0279. 2 Lambert, M., Lemay, S. P., Barber, E. M., Crowe, T. G., & Chénard, L. (2001). Humidity 3 control for swine buildings in cold climate- Part I: Modelling of three control strategies. 4 Canadian Biosystems Engineering, 43(5), 529-536. 5 Le Dividich, J., & Herpin, P. (1994). Effects of climatic conditions on the performance, 6 metabolism and health status of weaned piglets: a review. Livestock Production Science, 38(2), 7 79-90. https://doi.org/10.1016/0301-6226(94)90052-3. 8 Liberati, P., & Zappavigna, P. (2007). A dynamic computer model for optimization of the 9 internal climate in swine housing design. Transactions of the ASABE, 50(6), 2179-2188. doi: 10 10.13031/2013.24093. 11 Muirhead, M. R., & Alexander, T. J. L. (1997). Managing pig health and the treatment of 12 disease: a reference for the farm. (1st ed.). Shefield. 5M Enterprises Ltd., (Chapter 3). 13 Novák, L., Zeman, L., Novák, P., & Mareš, P. (2014). Modeling the pigs body mass growth and 14 the stressing factors impact on the daily feed intake. Acta Universitatis Agriculturae et 15 Silviculturae Mendelianae Brunensis, 53(5), 105-116. 16 http://dx.doi.org/10.11118/actaun200553050105 17 Rojano, F., Bournet, P. E., Hassouna, M., Robin, P., Kacira, M., & Choi, C. Y. (2016). 18 Computational modelling of thermal and humidity gradients for a naturally ventilated poultry 19 house. Biosystems Engineering, 151, 273-285. 20 https://doi.org/10.1016/j.biosystemseng.2016.09.012. 21 Samer, M., Loebsin, C., Fiedler, M., Ammon, C., Berg, W., Sanftleben, P., & Brunsch, R. 22 (2011). Heat balance and tracer gas technique for airflow rates measurement and gaseous 23 emissions quantification in naturally ventilated livestock buildings. Energy and Buildings, 24 43(12), 3718-3728. https://doi.org/10.1016/j.enbuild.2011.10.008. 25 19 Seo, I. H., Lee, I. B., Moon, O. K., Hong, S. W., Hwang, H. S., Bitog, J. P., Kwon, K. S., Ye, 1 Z., & Lee, J. W. (2012). Modelling of internal environmental conditions in a full-scale 2 commercial pig house containing animals. Biosystems Engineering, 111(1), 91-106. 3 https://doi.org/10.1016/j.biosystemseng.2011.10.012. 4 Schauberger, G., & Pilati, P. 1998. Evaluation of a steady-state balance model to simulate the 5 indoor climate in livestock buildings: A comparison with measurements of a cattle house. 6 Wiener Tierarztliche Monatsschrift, 85(2), 49-55. 7 Upachaban, T., Khongsatit, K., & Radpukdee, T. (2016). Mathematical model and simulation 8 study of a closed-poultry house environment. Mechanical Engineering, 7, 1246-1252. 9 https://doi.org/10.14716/ijtech.v7i7.4744. 10 van Wagenberg, A. V., & de Leeuw, M. T. J. (2003). Measurement of air velocity in animal 11 occupied zones using an ultrasonic anemometer. Applied Engineering in Agriculture, 19(4), 12 499-508. doi: 10.13031/2013.14922. 13 van Wagenberg, A. V., Bjerg, B., Bot, G. P. A., 2004. Measurements and simulation of climatic 14 conditions in the animal occupied zone in a door ventilated room for piglets. Agricultural 15 Engineering International: The CIGR Journal of Scientific Research and Development, 16 Manuscript BC 03 020, Vol VI. 17 Vincek, D., Sabo K., Kušec G., Kralik G., Durkin I., & Scitovski, R. (2012). Modeling of pig 18 growth by s-function–least absolute deviation approach for parameter estimation. Archives of 19 Animal Breeding, 55 (4): 364–74. https://doi.org/10.5194/aab-55-364-2012. 20 Wellock, I. J., Emmans, G. C., & Kyriazakis, I. (2003). Modelling the effects of thermal 21 environment and dietary composition on pig performance: model logic and concepts. Animal 22 Science, 77, 255 - 266. https://doi.org/10.1017/S1357729800058999. 23 24 20 Figure Captions 1 2 Fig. 1. Measured (discontinuous) and simulated (continuous) temperatures in the animal 3 zone for the first three days 4 Fig. 2. Measured (discontinuous) and simulated (continuous) temperatures in the animal 5 zone for periods with important temperature changes 6 Fig. 3. Measured (discontinuous) and simulated (continuous) temperatures in the animal 7 zone for periods with slight temperature changes 8 Fig. 4. Distribution of residuals of temperature in the animal zone (ºC) for the validated 9 production cycles 10