Patrik Flegner

Rotary drilling represents a complex dynamic process in which vibration signals contain significant information regarding the interaction between rock material, drilling tools, and mechanical subsystems of the drilling apparatus. Despite considerable advances in vibration-based diagnostics, there remains a need for methodologies that integrate signal processing, geometric interpretation, and operational-state classification. This paper proposes an approach based on the representation of vibration signals in Hilbert space, where signals are interpreted as vectors in an infinite-dimensional functional space. The proposed methodology utilizes geometric metrics, such as distances, norms, and angular similarities, for the classification of rotary-drilling operational regimes and the analysis of dynamic system behavior. Experimental vibration data were obtained from a laboratory drilling stand during drilling of limestone, granite, and concrete, while auxiliary operational modes of the mechanical system were also analyzed. The results demonstrate that the Hilbert-space representation can distinguish the investigated operating states. The granite-drilling regime exhibited distinct amplitude, energetic, and impulsive vibration characteristics, whereas auxiliary mechanical regimes formed compact geometrical clusters with high mutual similarity. Among the evaluated symptoms, the power spectrum showed the greatest sensitivity to frequency-energy differences across the investigated operating regimes. The evaluated symptoms provided complementary information for distinguishing between the investigated operating regimes. The proposed methodology provides a mathematically consistent framework that may serve as a basis for future vibration-based condition monitoring and predictive maintenance systems.

Rotary rock drilling generates vibration signals that capture the dynamic behavior of the drilling system, the interaction between the tool and the rock, and the progression of tool wear. These signals, traditionally considered undesirable, have become a key source of information for condition monitoring and predictive maintenance. This study experimentally investigates vibration sources and diagnostic indicators using a laboratory horizontal drilling stand equipped with accelerometers and controlled operating regimes. Six regimes were evaluated, ranging from idle operation of individual aggregates (motor, pump, hydrogenerator) to drilling of concrete and granite under defined process parameters. Vibration data were analyzed in the time, frequency, and time–frequency domains using RMS, variance, spectral centroid, spectral entropy, FFT-based spectra, autocorrelation, cross-correlation, and spectrograms. The results confirm the research hypothesis that selected vibration-based indicators correlate with tool degradation. Increased RMS values, higher variance, reduced correlation symmetry, and a shift of spectral energy above 6 kHz reliably reflect wear progression and changes in the dynamic response of the system. Spectrograms further reveal transient phases and redistribution of vibration energy during drilling. The findings demonstrate that vibration measurements enable the identification and separation of vibration sources related to aggregates and processes. The extracted diagnostic features form a basis for intelligent monitoring and predictive algorithms in rotary drilling, supporting advanced condition monitoring strategies within Industry 4.0.

Annealing of steel coils in bell-type furnaces is a critical process in steel production, requiring precise temperature control to ensure desired mechanical properties and microstructure. However, direct measurement of inner coil temperatures is impractical in industrial conditions, necessitating model-based estimation. This study presents a comparative analysis of physics-based and machine learning (ML) approaches for predicting internal temperatures during annealing. A finite difference method (FDM) was developed as a physics-based model and validated against experimental data from both laboratory and industrial annealing cycles. Furthermore, several ML models, including support vector regression (SVR), neural networks (NN), multivariate adaptive regression splines (MARS), k-nearest neighbors (k-NN), and random forests (RFs), were trained on surface temperature measurements to predict inner temperatures. The results demonstrate that the MARS, k-NN, and RF models achieved high prediction accuracy with performance index (PI) values below 1.0 on unseen data, demonstrating excellent generalization capabilities. In contrast, SVR with polynomial kernels and NN exhibited poor performance in specific configurations, highlighting their sensitivity to overfitting and data variability. The findings suggest that combining physics-based models with data-driven techniques offers a robust framework for soft-sensing in annealing operations, enabling improved process monitoring and control.

Hot metal is produced in a blast furnace. Subsequently, the hot metal is loaded from the blast furnace into a torpedo car and transported to the ladle, where the desulfurization process of the hot metal is realized. After desulfurization, the hot metal is poured from the ladle into the oxygen converter. The temperature of the hot metal has an impact on the steelmaking process realized in the oxygen converter. The complex model presented in the article calculates the temperature drop of the hot metal in the torpedo car and the ladle. Predicting the hot metal temperature behavior allows for determining the length of time the hot metal transport requires and thus initiating steelmaking at its required hot metal temperature. This model, based on heat transfer by conduction, convection, radiation, heat accumulation, and chemical reactions, also allows for the monitoring of the hot metal temperature drop in the torpedo car and the ladle, the analysis of the influence of the linings in terms of heat accumulation, the investigation of the desulfurization process in the ladle, and the optimization torpedo and ladle selection in terms of the accumulated heat in the lining for their entry into the hot metal transport process. An absolute and relative error calculation was used to verify the proposed model.

A spectrogram is one of the most effective tools for visualizing dynamic signal changes in industrial processes. In many cases, these signals exhibit certain forms of symmetry—whether in time, frequency, or statistical properties. This paper proposes a novel visualization methodology based on an adaptive nonlinear quantization framework, which intentionally introduces asymmetry to enhance diagnostic-critical features of the power spectrum. Unlike conventional linear quantizers that preserve uniform sensitivity across the range, the nonlinear approach enables selective emphasis of transient or low-energy components, improving visibility under varying signal-to-noise conditions. The design of both symmetric (linear) and asymmetric (nonlinear) quantizers is presented, including their mathematical foundations and visual effects on deterministic, stochastic, and pulsed signals. Entropy-based metrics are used to evaluate information content in the visualized spectrograms. The results demonstrate the proposed technique’s potential for enhancing fault detection, monitoring, and industrial diagnostics.

Hot metal is loaded from the torpedo car to the ladle, where desulfurization is realized. The main aim of the desulfurization process is to reduce the amount of sulfur in hot metal. During this process, the temperature of desulfurized hot metal is changed. The continuous measurement of this temperature during the desulfurization process is not implemented due to the device’s construction and the increasing costs. The temperature is measured only at the beginning and end of this process. For this reason, the paper focuses on the mathematical model proposal for the continuous measurement and the prediction of the desulfurized hot metal temperature. Information about this temperature will provide insight into the course of thermal processes and allow us to predict the temperature before pouring from the ladle into the oxygen converter.

In today’s era, it is important to analyze and utilize various signals in industrial or laboratory applications. Measured signals provide critical information about the controlled system, which can be contained precisely within a narrow frequency range. Many methods and algorithms exist to process such signals in both the time and frequency domains. In particular, signal processing in the frequency domain is primary in industrial practice because dominant components within a specific narrow frequency band are sought. The discrete Fourier transformation (DFT) algorithm is the tool used in practice to find these frequency components. The DFT algorithm provides the full frequency spectrum with a higher number of calculation steps, and its spectrum frequency resolution is low. Therefore, research has focused on finding a method to achieve high-frequency spectrum resolution. An important factor in selecting the technique was that such an algorithm should be implementable on a microprocessor-based system under harsh industrial conditions. Research results showed that the DFT ZOOM method meets these requirements. The frequency zoom has many advantages but requires some modification. It is implemented in high-performance analyzers, but a thorough and detailed description of the respective algorithm is lacking in technical articles and literature. This article mathematically and theoretically describes the modified frequency zoom algorithm in detail. The steps of the frequency zoom, from creating an analytical signal through frequency shifting and decimation to the frequency analysis of the signal, are realized. The algorithm allows for the analysis of a signal with high-frequency resolution in a limited frequency band. A significant modification of DFT ZOOM is that of using the Hilbert transform to create an analytic signal. This resolves the aliasing issue caused by the overlap between fundamental and sideband spectra. Results from processing deterministic and stochastic signals using the modified DFT ZOOM are presented. The presented experimental results contribute to a more detailed frequency analysis of the signal. As part of this scientific research, the issues of frequency zoom were thoroughly addressed, solving the partial problems of this algorithm, both in theory and in the context of signal theory.