Comparison of neural network models with aerodynamic and empirical models toward real-time estimation of the number of air exchanges per hour of a naturally ventilated greenhouse

Abstract

The feasibility of estimating the number of air exchanges per hour N of a naturally ventilated greenhouse in real time using neural network NN models was evaluated. An aerodynamic AD model and an empirical model were also used to compare different types of model. The value of N for an eight-span Venlo-type greenhouse with roof vents containing no plants was measured using the tracer gas method with CO 2 for 17 d. An AD model derived from Bernoulli's principle, an empirical model, and several NN models in which explanatory variables differed were trained and validated with 4,508 data points subjected to 10-fold cross-validation. We first compared the AD model, the empirical model, and two NN models that used the same explanatory variables in the empirical model, with and without wind direction. The mean accuracy in terms of root mean square error RMSE and coefficient of determination r 2 in the relationship between measured and estimated N values was the highest for the two NN models, followed by the empirical model and AD model. We next compared four NN models. The differences among them included that, as explanatory variable s , only the difference between inside T i and outside T o air temperatures or both T i and T o was used and whether solar irradiance I was used or not. There was a slight improvement in accuracy when using I, irrespective of how air temperature was handled. The NN models thus tended to exhibit a higher degree of accuracy in estimating N of a naturally ventilated greenhouse than the AD and empirical models considered in this study. For the NN model that performed the best in our comparison, a mean RMSE of 1.08 h 1 and a mean r 2 of 0.79 were observed.

Intraseasonal and interseasonal applicability of a neural network model for real-time estimation of the number of air exchanges per hour of a naturally ventilated greenhouse

“…The NN model used to estimate N was the same as that reported by Matsuda et al 2019 , with some exceptions. Measured variables used for the input layer independent variables or the feature vector were U x , U y , R w , R l , T i , T o , and I.…”

“…These were selected because an NN model with these variables and the wind direction as the input layer showed the highest N estimation accuracy in our previous study Matsuda et al, 2019 . As the effect of wind direction on N was not necessarily large Matsuda et al, 2019 , it was removed here. The input layer consisted of these variables measured at the same time as that for N estimation and those measured at 1, 2, 3, 4, and 5 min before the time for N estimation, assuming that the effects of environmental conditions on N can be delayed Matsuda et al, 2019 . For I, R w , and R l , linear interpolation was used to estimate the 1-min data from the 5-min data. The output layer or dependent variable was N. There were two hidden layers between the input and output layers, and each of the two hidden layers had 20 units.…”

“…The output layer or dependent variable was N. There were two hidden layers between the input and output layers, and each of the two hidden layers had 20 units. The hyperparameters used were the same as those reported by Matsuda et al 2019 , except that the batch size was 1,024. The NN model was trained with mini-batch gradient descent using backpropagation.…”

“…There are several methods to calculate N of a naturally ventilated greenhouse Boulard, 2006 . The methods include the tracer gas method with CO 2 Okada and Takakura, 1973;Nederhoff et al, 1985;Boulard and Draoui, 1995 , the energy balance method Kozai et al, 1980;Fernandez and Bailey, 1993 , the water balance method Takakura et al, 2009Takakura et al, , 2017 , and the methods based on aerodynamic Kozai et al, 1980;Sase et al, 1980;Boulard and Baille, 1995;Boulard et al, 1996;Kittas et al, 1997or neural network Seginer et al, 1994Boulard et al, 1997 models. Among them, we have recently shown the potential availability of the NN models with internal and external environmental data and the extent of ventilator openings as the model inputs for real-time N estimation for a naturally ventilated uncropped greenhouse Matsuda et al, 2019 . Using data collected in an uncropped experimental greenhouse in the winter, NN models were trained and validated according to 10-fold cross-validation. The NN models tended to exhibit a higher accuracy in estimating N of the greenhouse than the aerodynamic and empirical models.…”