Faculty of Mechanical Engineering

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A Review of Modeling Approaches and Key Parameters in the Simulation of Wastewater Treatment Plants
(MDPI AG, 2026-01-20)
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Fault Diagnosis of Rotating Machinery Using Supervised Machine Learning Algorithms with Integrated Data-Driven and Physics-Informed Feature Sets
(MDPI AG, 2026-03-17)
Ignjatovska, Anastasija Angjusheva
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Shishkovski, Dejan
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Domazetovska Markovska, Simona
This study proposes a supervised machine learning framework for vibration-based fault diagnosis of rotating machinery using integrated data-driven and physics-informed fea-ture sets. A dataset acquired under variable load and multiple operating conditions was used for model training. Parallel signal processing techniques were applied to capture fault-related information across multiple frequency bands including time-domain analy-sis, frequency-domain analysis, baseband analysis, and envelope analysis. From the cor-responding signal representations, statistical, spectral, and physics-based features associ-ated with characteristic fault frequencies were extracted and combined into integrated feature sets. The diagnostic performance of models trained using purely data-driven fea-tures was systematically compared with models incorporating integrated data-driven and physics-informed features. Support Vector Machine, Random Forests, Gradient Boosting, and an ensemble classifier were evaluated using accuracy, precision, recall, and F1-score metrics. The proposed framework employs a two-layer classification strategy, where the first layer performs multiclass fault identification, while the second layer evaluates the presence of imbalance as a coexisting fault. In addition, the influence of different feature groups as well as individual measurement axes and their combinations on diagnostic performance were analyzed. Validation using a new dataset measured in laboratory con-ditions confirmed the robustness and generalization capability of the proposed diagnostic framework.
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A Multimodal Hybrid Piezoelectric–Electromagnetic Vibration Energy Harvester Exploiting the First and Second Resonance Modes for Broadband Low-Frequency Applications
(MDPI AG, 2026-03-27)
Shishkovski, Dejan
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Markovska, Simona Domazetovska
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Pecioski, Damjan
The increasing demand for autonomous wireless sensors in Internet of Things (IoT) ap-plications has intensified research on vibration energy harvesting, particularly in the low-frequency range where ambient vibrations are most prevalent. However, most vibra-tion energy harvesters operate efficiently only at a single resonance mode, resulting in a narrow operational bandwidth and pronounced performance degradation under fre-quency detuning. To address this limitation, this paper proposes a multimodal hybrid pi-ezoelectric–electromagnetic vibration energy harvester that exploits both the first and sec-ond resonance modes of a cantilever-based structure to achieve broadband low-frequency operation. The design is guided by the complementary utilization of strain-dominated and velocity-dominated regions associated with different vibration modes. Numerical model-ing and finite element simulations are employed to investigate the influence of mass dis-tribution, deformation characteristics, and relative velocity on energy conversion perfor-mance. A secondary cantilever carrying the electromagnetic coil is introduced to enhance the relative motion between the coil and the magnetic field, thereby extending the effective operational bandwidth. The experimental results demonstrate increased harvested power, improved energy conversion efficiency, and a significantly broadened effective frequency range compared to conventional single-mode piezoelectric and electromagnetic energy harvesters.
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Energy efficiency of combined compressor-ejector vapor compression systems applied in industrial concentrators
(National Library of Serbia, 2025)
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Gjerasimovska, Natasha
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Sarevski, Vasko
Investigations of the energy characteristics of thermocompression systems applied in industrial concentrators are presented in this paper. A significant increase of the energy efficiency in comparison with traditional industrial concentrators is achieved with the implementation of turbocompressor and/or ejector thermocom-pression. Single stage centrifugal compressors with water (R718) as a refrigerant are especially suitable for application in concentrators for production of fruit or grape concentrates because of the relatively small temperature difference between condensation and evaporation temperatures (Tc – Te). The heat pump cycle in the ejectors is realized with thermocompression of one part of the waste water vapor in the solution, which together with the primary steam from the boiler, or other heat generator, is used as a motive steam for the process of concentration. Several solutions of highly efficient single stage and multistage concentrator systems with turbocompressor and/or ejector thermocompression are proposed. The process of boiling - evaporation of the water from the treated solution in the concentrator is realized at low temperatures, under deep vacuum conditions, which is a guarantee for a high product quality. Due to the low costs of conventional fuels used in the processes of production of concentrate, the products made with these procedures are relatively low-priced, which makes them competitive on the market. A solution of a polygeneration system for production of electricity and thermal energy (steam and hot water) for the needs of technological processes in industrial concentration plants is presented.
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SCALE INVARIANT STOCHASTIC GRADIENT METHOD WITH MOMENTUM
(Matematichki Bilten, Union of Mathematicians of Macedonia, 2023)
Nikolovski, Filip
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Optimization in noisy environments arises frequently in applications. Solving this problem quickly, efficiently, and accurately is therefore of great importance. The stochastic gradient descent (SGD) method has proven to be a fundamental and an effective tool which is flexible enough to allow modifications for improving its convergence properties. In this paper we propose a new algorithm for solving an unconstrained optimization problems in noisy environments which combines the SGD with a modified momentum term using a twopoint step size estimation in the Barzilai-Borwein (BB) framework. We perform a high probability analysis for the proposed algorithm and we establish its convergence under the standard assumptions. Numerical experiments demonstrate a promising behavior of the proposed method compared to the "vanilla" SGD with momentum in noise-free and in noisy environment when the objective function is scaled.
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ON THE CONVERGENCE OF THE PROXIMAL GRADIENT METHOD WITH VARIABLE STEP SIZES
(Union of Mathematicians of Macedonia, 2025)
Nikolovski, Filip
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Composite optimization problems arise frequently in modeling, since the objective function might contain components that do not possess some “nice” properties like differentiability; the case of l1 (LASSO) regularization is one such example. The proximal gradient methods are designed to handle this kind of optimization problems, and can solve them efficiently when the proximal mapping has a closed-form solution. Theoretical analyses of the convergence properties of the proximal gradient method with constant step size have showed sublinear and linear convergence for convex and strongly convex objective functions respectively. In this paper we show that under standard assumptions the same kind of convergence result can be established for the proximal gradient method with variable step sizes in the general setting of bounded step sizes. Further, a recently proposed step size selection for the proximal gradient method with variable step sizes is considered, and the above convergence analysis is implemented for this method.
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Gradient Descent Methods for Regularized Optimization
(Macedonian Academy of Sciences and Arts, 2024)
Nikolovski, Filip
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Regularization is a widely recognized technique in mathematical optimization. It can be used to smooth out objective functions, refine the feasible solution set, or prevent overfitting in machine learning models. Due to its simplicity and robustness, the gradient descent (GD) method is one of the primary methods used for numerical optimization of differentiable objective functions. However, GD is not well-suited for solving l1 regularized optimization problems since these problems are non-differentiable at zero, causing iteration updates to oscillate or fail to converge. Instead, a more effective version of GD, called the proximal gradient descent employs a technique known as soft-thresholding to shrink the iteration updates toward zero, thus enabling sparsity in the solution. Motivated by the widespread applications of proximal GD in sparse and low-rank recovery across various engineering disciplines, we provide an overview of the GD and proximal GD methods for solving regularized optimization problems. Furthermore, this paper proposes a novel algorithm for the proximal GD method that incorporates a variable step size. Unlike conventional proximal GD, which uses a fixed step size based on the global Lipschitz constant, our method estimates the Lipschitz constant locally at each iteration and uses its reciprocal as the step size. This eliminates the need for a global Lipschitz constant, which can be impractical to compute. Numerical experiments we performed on synthetic and real-data sets show notable performance improvement of the proposed method compared to the conventional proximal GD with constant step size, both in terms of number of iterations and in time requirements.
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Statistical Analysis of Urban Noise Measurements Data: Case Study for the City of Skopje
(EuroRegio, 2022)
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Nikolovski, Filip
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Noise from the road transport, particularly from vehicles in urban city areas largely accounts for the general noise level and annoyance of the citizens. The numerous volumes of motor vehicles flow can be treated statistically, which can establish a deeper insight into the contribution of the road noise to the prevalent noise pollution and its' characteristics. According to ISO 362 and ISO 1996:2, the environmental noise level from traffic is highly dependent on the vehicle category regarding the factor of contribution to the overall urban noise level. The purpose of this study is to analyze the dependence between the number and types of vehicles and measured standardized parameters (Leq, LAF and L95) for noise level assessment by implementing a statistical model analysis ofthe collected results. The number and the type of the vehicles is obtained from the States' traffic management and control center for a chosen road in the center of the city, whereas noise level measurements have been conducted with a Bruel&Kjaer sound level meter by using a standardized noise level measurement methodology procedure for the selected period on the given location. This study provides a detailed statistical approach of the collected noise and traffic volume data to obtain conclusions and prediction models for further management of the noise pollution problem in the city.
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КОМПРЕСИРАЊЕ ДИГИТАЛНИ СЛИКИ СО ПРИМЕНА НА SVD РАЗЛОЖУВАЊЕ НА МАТРИЦИ
(Faculty of Natural Sciences and Mathematics, 2017)
Nikolovski, Filip
Во ова излагање се разгледува еден начин за компресирање на дигитални слики, т.е. намалување на количеството меморија која ја зафаќаат сликите. За таа цел се поаѓа од претставувањето на сликите со помош на матрици кои содржат информација за бојата на поединечните пиксели. Користејќи го резултатот дека секоја матрица има единствено разложување по сингуларни вредности (SVD разложување), се конструирa апроксимација на матрицата на сликата која зафаќа помалку меморија од неа. На ваков начин се добива апроксимација и на самата слика. Се покажува дека квалитетот на апроксима-цијата на сликата може да се контролира со ограничување на разликата помеѓу матрицата и нејзината апроксимација. На самиот крај се наведуваат неколку други случаи во кои може да се примени сличен пристап.
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Some application of Grunsky coefficients in the theory of univalent functions
(Walter de Gruyter GmbH, 2025-11-26)
Obradović, Milutin
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