International Scientific Journals
of Scientific Technical Union of Mechanical Engineering "Industry 4.0"

Nonlinear dynamical systems arise in numerous scientific and engineering domains, including physics, economics, biology, and control theory. Their complex behavior, sensitivity to initial conditions, and possible chaotic dynamics make accurate modeling and prediction challenging using traditional analytical approaches alone. In recent years, artificial intelligence (AI) techniques have demonstrated strong potential for modeling nonlinear and complex systems through data-driven methods. This paper explores artificial intelligence approaches for modeling nonlinear dynamical systems, focusing on the integration of machine learning techniques with classical mathematical modeling. We consider representative nonlinear systems and analyze how neural networks, regression models, and hybrid AI–mathematical frameworks can be used to approximate system behavior, predict future states, and capture hidden structures in time-series data. Special attention is given to systems exhibiting chaotic behavior, where small perturbations in initial conditions can lead to significant divergence in trajectories. The study presents numerical simulations and comparative analyses between traditional mathematical models and AI-based approaches. The results highlight the advantages of machine learning methods in capturing nonlinear patterns and improving predictive accuracy, especially when analytical solutions are difficult or unavailable. Additionally, we discuss the interpretability of AI models in the context of dynamical systems and outline potential applications in engineering, intelligent control, and data-driven system identification. The proposed framework contributes to the growing intersection between dynamical systems theory and artificial intelligence by demonstrating how AI tools can support the analysis and modeling of complex nonlinear phenomena. This work aims to provide a foundation for future research on hybrid mathematical–AI methods for understanding and predicting complex systems.

This paper presents a method for predicting the performance of compressors in HVAC/R systems using 2-D quadratic spline interpolation. Compared to traditional third-order polynomial interpolation, the spline model provides smoother and more accurate approximations, especially useful when limited manufacturer data is available. Using real-world compressor data, we constructed mathematical models and evaluated their performance through key statistical indicators. Results indicate that the spline-based model yields lower RMSE values with reduced model order, improving its integration in system simulations. This study also provides a comparative analysis against a polynomial-based model developed in earlier research.

This paper talks about how we can use math to create better models based on actual compressor experiments. The goal? To bridge the gap between what we see happening in real life and what we can predict, ultimately helping us optimize HVAC systems for better performance.
Within these systems, parts like compressors, fans, and electrical components play crucial roles. Compressors, especially, are quite dynamic, especially in heat pump setups.
However, the problem is that manufacturers usually only give real-world data on how compressors perform, without detailed models for understanding how they work in different situations. Hopefully in this paper we will try to construct a detailed model in order to be able to evaluate a HVAC system without the necessity of real-world data. Also, we will evaluate two different mathematical models, two dimensional interpolation and approximation in order to see who perform better.

Partial differential equations (PDEs) are differential equations in which there is more than one independent variable. They arise in the modelling of a wide-range of physical phenomena including electromagnetism, fluid flow, elasticity, quantum mechanics and heat conduction. The wave equation serves as a fundamental model for understanding various wave phenomena in physics and engineering. In this paper, we explore the application of Sturm-Liouville problems to solve the wave equation. The results of our investigations not only showcase the accuracy and computational advantages of the Sturm-Liouville method but also shed light on the physical interpretations of the obtained eigenfunctions and eigenvalues. In conclusion, this paper contributes to the body of knowledge regarding the application of SturmLiouville problems in wave equation modeling and analysis. It offers a valuable perspective for researchers, scientists, and engineers seeking efficient and insightful solutions to wave-related challenges. The versatility and effectiveness of the Sturm-Liouville approach make it a compelling tool for gaining deeper insights into wave phenomena and their practical applications.

In this paper we will study an important part of the speech signal processing, the reconstruction of the signal. We will use the Newton interpolation method with a deterministic model and warped frequencies in order, maybe, to get a better reconstruction process of the signal. To determine the efficiency of the method we will use two criteria like: accuracy of reconstruction, noise stability. Then we will test this algorithm using the criteria that we proposed above versus the classic Yen’s algorithm. At the end of our experiment we will see that in noise stability our algorithm performs better but not in the reconstruction accuracy. In overall Yen’s algorithm performs slightly better.

In this paper we will discuss an important topic such as the WER (word error rate). Imagine if we use an ASR system in a real event for approximately one hour or more. We would have a lot of issues like: the quality of the transcription of words, the time of the processing of the words spoken. And so a lot of WER will be produced by this event. The high rate of ASR errors have demanded the necessity to find better techniques in order to correct such errors. The improvement of the system it is a necessity not only to have a better stability of the system but also to prevent the high costs in order to use our resources in the best way as possible.

The rapid spread of COVID-19 disease worldwide has caused a frightening crisis in the health care system in many states. To prevent it, many states have taken various measures, including total blockades. In this paper we have used the logistic growth model to show the increase in the population of the number infected with the Covid-19 virus in Albania. The generalized logistic equation is used to interpret the COVID-19 epidemic data in Albania. The growth rate was calculated using two random data and the expected number of infected people. The predictions of the logistic model are as correct as the data are accurate, and that correct that they can imitate the dynamics of the epidemic. The model clearly shows that there is a correlation between real and projected data. When daily predictions of epidemic size begin to converge, we can say that the epidemic is under control. If we deviate from the forecast curve it may indicate that the  epidemic may get out of control. With a fully valid model, this type of information can be used as an example by policy makers to assess how to take appropriate action.

In this paper we will use different feature extraction approach in order to compare the stability of the Automatic Speech Recognition (ASR) on different SNR noise, in different situations. By using the classic feature extraction like: Mel filter Bank, Fast Fourier Transformation (FFT), Discrete Fourier Transformation (DFT). After we implement this methods for the different situations then we will warp the frequency of this methods directly on the spectrum in order to see if we get better results. The results will be compared with one another using the Word Error Rate algorithm (WER).

The population of the city of Tirana is getting bigger. Transportation in this city has become extremely heavy. Many of its citizens choose to move using their vehicles thus causing an overcrowded traffic. It has happened to all of us to get stuck in the traffic of Tirana, to be late for our destinations and to be stressed by that chaos.
The use of public transport would be a successful way of reducing the traffic. In this paper we have treated Dijkstra Algorithm and its application in railway system of transport for the proposed Tram system for the city of Tirana. Considering the expansion(map) and relief of this city, we think that it is very favorable to build a tram system in this city. The results of this paper help to have a clear idea of the construction of the tram and a prediction of how it will work and how much it can facilitate the traffic in Tirana.

In this paper we evaluate the growth of Automatic Speech Recognition systems in respect to the various forms of spectral analysis ways used. A straightforward analysis of platter and Gammatone filter banks used for spectral analysis compared with the direct use of FFT spectral values is taken into account. This analysis was supported understanding the effectiveness of existing Automatic Speech Recognition systems that are specifically targeted on platter and Gammatone filter banks compared with FFT spectral values. We discover that warping the FFT spectrum directly, instead of using filter bank averaging, provides an additional precise approximation to the sensory activity scales. Direct use of FFT spectral values are even as effective as using either Gammatone or Linear Prediction filter banks, as long as the feature extracted from the FFT spectral values takes into consideration a Gammatone or platter like frequency scale. Computing speech signals using FFT or filter bank spectral features and utilizing a method supported by a sliding block of spectral features, is shown to be simpler in terms of ASR accuracy.