1. Introduction

2. Materials and Methods

2.1. TRNSYS Generalized Thermal Load Model

In defining the mathematical model of greenhouse thermal load, tree components play an important role: plants inside the space, air in the building and covering material. Unlike construction buildings, greenhouse has a transparent film whose role is to transmit the solar radiation which is then absorbed by soil and plants. In order to obtain energy flow inside a greenhouse, as shown in Figure 1, it is necessary to introduce the following preconditions in order to reduce complexity:

- External atmospheric parameters are constant during the time step calculation (hourly values of outside air parameters do not change)

- There is no condensation inside the building, or in the inner surfaces of film

- Change in temperature and relative humidity inside the building is uniform

Heat flux which is transmitted by convection into the air of the building can be expressed by the following equation [34,35,36]:

$$\dot{q}={\dot{q}}_{surf,i}+{\dot{q}}_{inf,i}+{\dot{q}}_{vent,i }+{\dot{q}}_{gain,i}+{\dot{q}}_{wall,i}$$

(1)

where ${\dot{q}}_{surf,i}$ heat flux transmitted by convection from soil into air, ${\dot{q}}_{inf,i}$ losses due to infiltration, ${\dot{q}}_{vent,i }$ losses due to ventilation, ${\dot{q}}_{gain,i}$ thermal load due to internal sources of energy in the building and ${\dot{q}}_{wall,i}$ heat flux delivered by convection from the walls of the building film into air.

Heat flux which is delivered by radiation to the inner surface of the building film can be represented by the following equitation:

$${\dot{q}}_{wall,r,i}= {\dot{q}}_{sol,i}+ {\dot{q}}_{long,i}+ {\dot{q}}_{plant,i}$$

(2)

where ${\dot{q}}_{wall,r,i}$ is heat flux received by inner surface of the film, ${\dot{q}}_{sol,i}$ shortwave solar radiation that has passed through the film of the building and directly absorbed by the inner surfaces,${\dot{q}}_{long,i}$ long wave solar radiation that is exchanged between the adjacent inner surfaces of the film and ${\dot{q}}_{plant,i}$ heat flux from plants towards the inner surfaces of the film of the building.

Energy balance for the film itself can be expressed by:

$${\dot{q}}_{wall,i}+ {\dot{q}}_{wall,o}+ {\dot{q}}_{wall,r,i}+ {\dot{q}}_{sky,o}=0$$

(3)

where ${\dot{q}}_{wall,i}$ the heat flux that is by convection transmitted from the outside air to the film of the building and ${\dot{q}}_{sky,o}$ heat flux of radiation between the sky and the outer surface of the covering.

To better determine the dynamic thermal behaviour of the building and monitoring of thermal load dependence due to changes in parameters of external environment, heat transfer coefficients from the outside and inside film of the building are also modelled dynamically. To determine the heat transfer coefficient in the outside film of the building, reduced air speed relative to the normal of the described surface must be determined and in line with [37]:

• surface located in direction of wind flow

  

  (4)
• surface located in the leeward (oriented opposite to the direction of wind flow)

  

  (5)

  Where v_l sign represents the local wind velocity towards the observed surface.

Forced convection heat transfer coefficient due to air flow over the outer surface is:

(6)

Heat transfer coefficient on the inner film surfaces of the building depends on the combined convection which occurs in the boundary layer directly to the surface and depends on the position, i.e. whether the surface is vertical or horizontal, temperature differences between inner surface and air in the observed zone, as well as on the number of changes of air inside the zone. Validation of the TRNSYS model was carried out on the basis of measured temperature values during the heating period when parameters of the condition of interior space were monitored. In Figure 2 for five selected days in November a comparison of the air temperature in the house obtained by numerical simulation with the measured values is showed.

Simulation results match well with the measured values and thus it can be concluded that is well positioned and that can be improved by determining the optimal amount of fresh air introduced into the building through natural ventilation in order to create favorable conditions for plant growth during the period from October to May.

Changes in outside air temperature during the year are shown in Figure 2. It can be clearly seen that in winter extremely low temperatures are not pronounced, which favorably affects the heat loss especially at night. Minimum temperature according to TMY in the winter is about -10 °C, and the maximum in summer is up to 35 °C.

2.3. Artificial Neutral Network Structure

The training and model test set were constructed on the calculated data from TRNSYS simulation and real meteoroogical data for given location. Set of 8760 data was divided in train and test in order of 80: 20. Validation data set were selected from measured data in greenhouse for selected days in heating period. The backpropagation algorithm, which was one of the supervised learning techniques, was used for modeling with the hidden layers to improve the prediction rate of the model (Figure 5). The ANNs featured outstanding performance since each neuron calculates the weight factor in two stages. The Levenberg-Marqardt algorithm [38] was used for the learning technique.

Input layer neurons were 4. ANN model is set up on assumption that predicted values of microclimatic parameters–temperature and relative humidity can be improved with real outside conditions. Considering the fact that greenhouses thermal load structure is much more complex than residential building’s due to specific internal gains, ANN model aims to predict microclimatic parameters for specific facility in a simpler way. Output layer neurons were 2–optimal inside temperature and relative humidity. Number of hidden layers and neurons are important factor for model accuracy. Similar researches are mainly based on one hidden layer with number of neurons determined from input and put neurons sum [30] or based on array of n/2, n, 2n, 2n+1 [39]. In the study presented in this paper, optimization of the number of neurons, learning rate and number of epochs was carried out in order to find the optimal model that will have the best accuracy and the least losses compared to the initial model. The choice of model is shown in Table 1.

Due to the reason that ANN model validation was not performed only from the origin data set, but also on the basis of measured real data greenhouse data, the performance measure is given by the linear correlation coefficient, the coefficient of determination, the mean absolute error and the mean square error [32]. The reason for the double validation lies in the fact that the original data set was also formed on the basis of predictions obtained from the TRNSYS simulation, so the goal was to show how good both prediction models are.

The performance measure is usually given by the linear correlation coefficient (r), coefficient of determination (R2), mean absolute error (MAE) and root mean square error (RMSE):

$$r= \frac{n\sum \widehat{y}y- \left(\sum \widehat{y}\right)\left(\sum y\right)}{\sqrt{n\left(\sum {\widehat{y}}^2\right)-{\left(\sum \widehat{y}\right)}^2}\sqrt{n\left(\sum y^2\right)-{\left(\sum y\right)}^2}}$$

(7)

$$R^2=1-\frac{{\sum }_{i=1}^n{\left(y_i-{\widehat{y}}_i\right)}^2}{{\sum }_{i=1}^n{\left(y_i-{\overline{y}}_i\right)}^2}$$

(8)

$$MAE=\frac{1}{n}\sum _{i=1}^n\left|{\widehat{y}}_i-y_i\right|$$

(9)

(10)

where, ŷ is predicted value, y is measured value, y is the mean of measured variables and n is the number of samples.

3. Results and Discussion

Table 1. The chosen models in simulations with relevant parameters.

Table 2. Variation of RMSE, MAE and R2 values for different ANN models.

Table 3. Variation of RMSE, MAE and R2 values for different ANN models.

Table 3. The differences between the input data and the data obtained by prediction.

5. Conclusions

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