# Calculation of the Population of Construction Scaffoldings Using Neural Networks
## 4 Discussion of the Results  
The conducted in situ research allowed for the collection of information concerning the number of used scaffoldings in selected regions of Poland. The obtained research results show a clear seasonality in the use of scaffoldings. It can be observed that in the second and third quarter of the year, there is an increase in the number of scaffoldings in use by an average of approximately 50% when compared to the first and fourth quarters. The largest difference is noticeable in the communes included in groups \(G_{3}\) and \(G_{4}\) (111% and 164%, respectively). These groups had a total of 70 communes and were characterized by a high number of new residential buildings (\(I_{5}\)), and a relatively large area of built-up and urbanized land (\(I_{10}\)). In the communes from group \(G_{2}\), the fluctuation in the amount of scaffolding in use was 37% per year. The smallest fluctuations were observed in group \(G_{1}\) (approximately 20%), which in the Dolnoslaske region included only one commune--Wroclaw--the capital, and the largest city of the region. By analyzing the neural models obtained as a result of the calculations, it can be concluded that all five individual neural network models were characterized by a high quality of adjustment to the analyzed phenomenon (quality of network learning close to one), without showing an excessive adjustment of the network to the training set (quality of network validation close to one). Additionally, the analysis of the learning process graphs (Table 4) clearly shows that the network learning process was correct [27]. A similar and very high quality of matching the results to the empirical values is observed in the case of the developed neural network set (\(R=0.989\); \(R^{2}=0.979\)). The detailed analysis of the developed neural networks allows for the conclusion that all the networks were developed correctly. The sensitivity analysis of all the quantitative and qualitative variables that were used to build the models showed that in each case, all the variables had a significant impact on the final result of the network (the values of the sensitivity coefficient in all the cases were greater than 1.0 [27]), as seen in Figure 8.  
Figure 8: Sensitivity analysis of all the variables that were used to build the network. When analyzing the above chart, it can be noticed that the \(G\) input (group numbers) and the \(I_{1}\) input (number of construction companies carrying out work related to the construction of buildings) had the greatest impact on the final result of the network. This situation is due to the fact that the number of building scaffoldings in use depends to a large extent on the number of construction companies carrying out construction work and on the nature of a given commune--in particular, the degree of its industrialization. Additionally, depending on the type of network, the impact of individual parameters was different. An example can be seen in network number 1, in which the \(G\) parameter had a greater influence on the final result than the \(I_{1}\) parameter. In the case of network number 2, the situation was the opposite--the \(G\) parameter had a smaller impact on the network result than the \(I_{1}\) parameter. In order to verify the developed neural network models, alternative mathematical models were built, with the results generated by both types of models then being compared. Linear regression was used to build the verifying models. As a result of the performed calculations, four different linear models were developed--one for each group of communes. The developed linear models are characterized by a very high degree of matching to reality. This is evidenced by the obtained statistics of \(R_{P}\), \(R^{2}\), and \(R_{S}^{2}\), which were close to one. The developed linear models were used to estimate the number of building scaffoldings in all the analyzed communes, and the obtained results were then compared with the results obtained from the model of the neural network.