## 3 Results
### The Idea of Applying Machine Learning  
In recent years, there has been a noticeable shift toward emphasizing the application of general knowledge surrounding the impact of constraints on the learning process [27]. This shift prompts the question of whether a specific model aligns with these constraints, or if there is a way to ensure that the learner consistently generates models that meet these criteria. When the constraints are purposely enforced on the model, this process is known as the imposition of constraints; conversely, when the model's alignment with constraints is confirmed, this is referred to as the verification of the model [27]. Both aspects, imposition and verification of constraints, have received significant attention in the field of decision trees, which highlights the importance of understanding and integrating constraints effectively in the learning process. Through exploring how learners engage with constraints and how models are developed within these limitations, researchers seek to gain deeper insights into optimizing the learning experience and maximizing the effectiveness of educational tools. This focused approach not only enhances the quality of models generated but also contributes to broader discussions on the role of constraints in shaping the learning environment. By looking into these complexities, educators and researchers can work toward refining methodologies that have better support for learners in overcoming challenges and reaching their full potential within the constraints of the learning process [28]. The problem of the impact of traffic-induced vibrations on buildings and their occupants will be solved as a non-linear classification, with quantitative and qualitative variables. The output value is a qualitative variable predicting the effect of vibrations on humans in four ranges: Y\({}_{1}\), none; Y\({}_{2}\), negligible; Y\({}_{3}\), medium; and Y\({}_{4}\), large. The concept includes the use of ML to predict the potential for traffic vibration to affect the building and its occupants. The vector of input variables is assumed as follows (see Figure 8):  
* X\({}_{1}\): type of slab material;
* X\({}_{2}\): source of vibrations;
* X\({}_{3}\): direction of vibrations;
* X\({}_{4}\): condition of building;
* X\({}_{5}\): distance from road;  
Figure 7: Maximum RMS accelerations for traffic-induced vibrations: (**a**) in the X/Y directions; (**b**) in the Z-direction—measurement of wooden slab (source: authors’ own). * X\({}_{6}\): types of moving vehicles;
* X\({}_{7}\): occurrence of manholes and ruts. Artificial neural networks use the principle of operation of human nerve cells [14]. Neurons process the information, and try to remember it in order to use it in the future. Artificial systems work similarly [8]. Data are presented to the system, then they are processed, and then remembered. The construction of the network begins with the appropriate preparation of the database and its division into a learning set (70%), validation set (15%), and testing set (15%). In the next step, the input and output variables are determined. Then, an algorithm is developed. For the correct operation of the network, it is necessary to select factors that will influence the calculations. Two neural networks with hidden layers, differing in their activation functions, were created for the study. At the output, the expected value concerns information as to whether a person in the building is in the influence zone and whether the level of vibrations exceeds the available threshold or not. To check the correctness of the network, a graph of the learning samples and validation samples with respect to the number of epochs was created for two models, as shown in Figures 9 and 10. As can be seen from Figure 9, the accuracy of samples trained until the sixth epoch increases steadily up to 88.5% and then remains constant until the end of the calculation. However, the accuracy of the validation samples also increases until the sixth epoch, and thereafter it is constant at a value of almost 87%.