This paper presents the results of modelling the heat transfer process in heterogeneous media with the assumption that part of the heat flux is dispersed in the air around the beam. The heat transfer process in a solid material (beam) can be described by an integer order partial differential equation. However, in heterogeneous media, it can be described by a sub- or hyperdiffusion equation which results in a fractional order partial differential equation. Taking into consideration that part of the heat flux is dispersed into the neighbouring environment we additionally modify the main relation between heat flux and the temperature, and we obtain in this case the heat transfer equation in a new form. This leads to the transfer function that describes the dependency between the heat flux at the beginning of the beam and the temperature at a given distance. This article also presents the experimental results of modelling real plant in the frequency domain based on the obtained transfer function.

This paper presents some recent results in the area of application of fractional order system models. After the introduction to the dynamic systems modelling with the fractional order calculus the paper concentrates on the possibilities of using this approach to the modelling of real-world phenomena. Two examples of such systems are considered. First one is the ultracapacitor where fractional order models turn out to be more precise in the wider range of frequencies than other models used so far. Another example is the beam heating problem where again the fractional order model allows to obtain better modelling accuracy. The theroetical models were tested experimentally and the results of these experiments are described in the paper.

In this article, the modeling of the ultracapacitor using different models of capacity part is shown. Two fractional order models are compared with the integer model of traditional capacitor. The identification was made using the diagram matching technique. Next, the derivation of time domain response of the ultracapacitor and system with the ultracapacitor are presented. The results of frequency domain identification were used to validate the response of the ultracapacitor in time domain. All theoretical results are compared with the response of the physical system with the ultracapacitor.

In this paper, the modeling of the ultracapacitor using fractional order model is shown. The derivation of time domain response of the ultracapacitor and system with the ultracapacitor is presented. The results of frequency domain identification were used to validate the response of the ultracapacitor in time domain. All theoretical results are compared with the response of the physical system with the ultracapacitor. Then the issue of capacity for the ultracapacitors is shown and discussed.

Objective. The primary purpose of this work is to analyze the ability of N-BEATS architecture for the problem of prediction and classification of electrocardiogram (ECG) signals. To achieve this, performance comparison with various types of other SotA (state-of-the-art) recurrent neural network architectures commonly used for such problems is conducted. Approach. Four architectures (N-BEATS, LSTM, LSTM with peepholes, GRU) were tested for performance and dimension reduction problems for different number of leads (2, 3, 4, 6, 12), both in variants consisting of blended branches, allowing retaining accuracy while reducing the computational capacity needed. The analysis was performed on datasets and using metrics from Challenges in Cardiology (CinC) 2021 competition. Main results. Best results were achieved for LSTM with peepholes, then LSTM, GRU and the worst for N-BEATS (challenge metrics respectively: 0.42, 0.40, 0.39, 0.35; for times: 0.0395 s, 0.0036 s, 0.0027 s, 0.0002 s). Commonly used LSTM outperforms N-BEATS in terms of multi-label classification, data set resilience, and obtained challenge metrics. Still, N-BEATS can obtain acceptable results for 2 lead classification (metric of 0.35 for N-BEATS and 0.38 for other networks) and outperforms other solutions in terms of complexity and speed. Significance. This paper features a novel approach of using the N-BEATS, which was previously used only for forecasting, to classify ECG signals with success. While N-BEATS multi-label classification capacity is lower than LSTM, its speed obtaining results with a reduced number of leads (faster by one to two degrees of magnitude) allows for arrhythmias detection and classification while using off-the-shelf wearable devices (Holter monitors, sport bands, etc).