Prediction Models for the Plant Coverage Percentage of a Vertical Green Wall System: Regression Models and Artificial Neural Network Models

Abstract

(1) Background: The expansion that most cities have been showing for more than half a century has also brought with it an increase in the density of buildings, most of the time at the expense of green areas. This has led to negative effects, such as overpopulation of cities, rising urban temperatures, pollution of water, air, soil, and others, affecting daily urban life. As a result, specialists from different fields form multidisciplinary teams are looking for solutions to counteract these effects. The subject of visible facades has registered an increased interest among researchers in recent years because they can represent a viable solution that can contribute to increasing the degree of urban comfort. However, for such a system to be effective, it is necessary that the plants used grow and develop harmoniously and ensure the best possible coverage of the facade. The aim of this research is to find an adequate mathematical model that can predict, with a high degree of accuracy, the percentage of plant coverage of a green wall system, which is positioned in the city of Iasi, northeastern Romania. (2) Methods: The models used for this purpose were a multiple linear regression model (MLR) and a model based on a feed-forward artificial neural network (ANN). Four independent variables (soil temperature, soil moisture, week of the year, and cardinal wall orientation) and the interaction between two variables (soil temperature and week of the year) were used for the multiple linear regression model. Artificial neural networks were also trained to estimate the percentage of plant coverage in the analyzed system, and the network with the best mean squared error performance was chosen in doing predictions. For both MLR and ANN models, we constructed confidence intervals for the degree of plant coverage of the system (PCP) for a set of observed values. In the case of the ANN model, the confidence interval was derived via the bootstrap method, which is a resampling with replacement technique used to generate new samples from the original dataset. To the best of our knowledge, the derivation of confidence intervals using a combination of neural networks with the bootstrap method has not been used before, at least for predictions in horticulture. (3) Results: The ANN employed here consisted of one input layer with four neurons, one hidden layer with five neurons, and one output layer with one neuron. The comparison showed that the confidence interval obtained using ANN has a shorter length (and thus it is more accurate) than that obtained by the multiple linear regression model. The choice of the experimental module façade had a significant influence (of magnitude 1.9073) on the plant coverage percentage. An increase of one unit in soil humidity will determine an increase of almost 5.1% in plant coverage percentage, and an increase of 1 °C in soil temperature will determine a decrease of almost 1.21% in plant coverage percentage. The choice of the experimental module façade had a significant influence (of magnitude 1.9073) on the plant coverage percentage. (4) Conclusions: Although both methods showed to be useful in making predictions, the ANN method showed better predictive capabilities, at least when the performance is measured by the mean squared error. This fact may be useful when predicting the percentage of plant coverage of a green wall system with a higher degree of accuracy, in the case of organizing outdoor exhibitions or other similar projects.