Combined study

4 years

doc. Ing. Petr Drexler, Ph.D.

Chairman :
doc. Ing. Petr Drexler, Ph.D.
Councillor internal :
doc. RNDr. Martin Kovár, Ph.D.
doc. Ing. Jan Mikulka, Ph.D.
prof. Ing. Lubomír Brančík, CSc.
doc. Ing. et Ing. Vilém Neděla, Ph.D., DSc.
doc. RNDr. Dana Hliněná, Ph.D.

The doctoral study program "Theoretical Electrical Engineering" is focused on the preparation of high-qualified scientific and research specialists in various areas of theoretical electrical engineering. Particularly, in the theory and applications of electromagnetism, electrical circuits, electro/magnetic measurement methods and signal processing methods. The preparation is supported by the provision of knowledge in related mathematical disciplines such as stochastic processes and statistical methods of systems investigation, systems analysis using functional equations, design of multi-criteria optimization methods, numerical methods for solution of continuous and discrete dynamical systems and others. The aim of the program is to provide a doctoral education to graduates of Master's degree in all these sub-disciplines, to deepen their theoretical knowledge and to develop practical expert skills and to educate them in the methods of scientific work.

Graduates in doctoral study program "Theoretical Electrical Engineering" are able to solve scientific and complex technical innovation tasks in the field of electrical engineering at the theoretical level, as well as its practical use in research, development and production. To solve technical research and development tasks, they are equipped with a complex knowledge of the theory and application of electromagnetic field, electrical circuits, methods of measuring and signal processing and their physical and mathematical description. They are able to use modern computing, measuring and diagnostic techniques in a creative way.
Thanks to the high-quality theoretical education, practical expert skills and specialization in the chosen field, graduates of doctoral study are sought as specialists and executive staff in general electrical engineering. They will apply as researchers in basic or applied research, as specialists and leaders of teams in development, design and operation in research and development institutions and in electrical and electronic manufacturing companies operating in the field of advanced technologies.

Specialists and executive staff in general electrical engineering, researchers in basic or applied research, specialists and leaders of teams in development, design and operation in research and development institutions and in electrical and electronic manufacturing companies operating in the field of advanced technologies

The doctoral study is conducted according to the individual study plan. The individual study plan is prepared by the supervisor in cooperation with the doctoral student at the beginning of the study. The individual study plan specifies all the duties stipulated in accordance with the Study and Examination Rules at the Brno University of Technology, which the doctoral student must fulfill to successfully finish his studies. These responsibilities are scheduled throughout the whole study period; they are scored and they are evaluated at the end of given periods.
The student enrolls and takes examinations of the compulsory courses Numerical Computations with Partial Differential Equations and English for the state doctoral exam; at least two obligatory elective courses relating to the focus of his dissertation and at least two optional courses (English for Post-graduates; Scientific Citing; Solution of Innovational Tasks; Scientific publishing).
The student may enroll for the state doctoral exam only after taking all the exams prescribed by the individual study plan. Before the state doctoral exam, the student prepares a treatise on dissertation thesis, which describes in detail the goals of the thesis, a thorough evaluation of the state of knowledge in the area of the dissertation solved, or the characterization of the methods intended to apply in the solution.
The defense of treatise on dissertation thesis, which is reviewed, is part of the state doctoral exam. In the next part of the exam the student must demonstrate deep theoretical and practical knowledge in the field of electrical engineering, electromagnetic field, circuit theory, methods of measuring electrical and other physical quantities, processing and analysis of signals and mathematical modeling of technical processes. The state doctoral exam has a form of oral presentation and discussion on the treatise on dissertation thesis. In addition, it also includes a discussion on issues of thematic areas related to obligatory and obligatory elective courses.
The doctoral student can apply for the defense of dissertation thesis after passing the state doctoral exam and after fulfilling conditions for termination of the study, such as participation in teaching; scientific and expert activity (creative activity) and at least a monthly study or work internship at a foreign institution or participation in an international creative project.

The doctoral studies of a student follow the Individual Study Plan (ISP), which is defined by the supervisor and the student at the beginning of the study period. The ISP is obligatory for the student, and specifies all duties being consistent with the Study and Examination Rules of BUT, which the student must successfully fulfill by the end of the study period. The duties are distributed throughout the whole study period, scored by credits/points and checked in defined dates. The current point evaluation of all activities of the student is summarized in the “Total point rating of doctoral student” document and is part of the ISP. At the beginning of the next study year the supervisor highlights eventual changes in ISP. By October, 15 of each study year the student submits the printed and signed ISP to Science Department of the faculty to check and archive.
Within the first four semesters the student passes the exams of compulsory, optional-specialized and/or optional-general courses to fulfill the score limit in Study area, and concurrently the student significantly deals with the study and analysis of the knowledge specific for the field defined by the dissertation thesis theme and also continuously deals with publishing these observations and own results. In the follow-up semesters the student focuses already more to the research and development that is linked to the dissertation thesis topic and to publishing the reached results and compilation of the dissertation thesis.
By the end of the second year of studies the student passes the Doctor State Exam, where the student proves the wide overview and deep knowledge in the field linked to the dissertation thesis topic. The student must apply for this exam by April, 30 in the second year of studies. Before the Doctor State Exam the student must successfully pass the exam from English language course.
In the third and fourth year of studies the student deals with the required research activities, publishes the reached results and compiles the dissertation thesis. As part of the study duties is also completing a study period at an abroad institution or participation on an international research project with results being published or presented in abroad or another form of direct participation of the student on an international cooperation activity, which must be proved by the date of submitting the dissertation thesis.
By the end of the winter term in the fourth year of study students submit the elaborated dissertation thesis to the supervisor, who scores this elaborate. The final dissertation thesis is expected to be submitted by the student by the end of the fourth year of the studies.
In full-time study form, during the study period the student is obliged to pass a pedagogical practice, i.e. participate in the education process. The participation of the student in the pedagogical activities is part of his/her research preparations. By the pedagogical practice the student gains experience in passing the knowledge and improves the presentation skills. The pedagogical practice load (exercises, laboratories, project supervision etc.) of the student is specified by the head of the department based on the agreement with the student’s supervisor. The duty of pedagogical practice does not apply to students-payers and combined study program students. The involvement of the student in the education process within the pedagogical practice is confirmed by the supervisor in the Information System of the university.

1. Advanced flight planning methods for unmanned aerial vehicles

   The purpose of the dissertation will be the analysis and application of advanced methods for unmanned aircraft flight and their application to flight path planning. Typical usage scenarios will be analyzed and current flight path planning methods will be proposed to own or optimize various aspects of their operations. Based on the research, metaheuristic algorithms such as genetic algorithms, swarm intelligence, evolutionary strategies and others will be proposed and tested. As part of the research, a software solution capable of optimizing UAV swarm trajectories will be developed. The functionality of the proposed solution will be verified in a simulation environment and will also be tested on physical UAVs. The results of the dissertation will be not only a theoretical analysis of the selected optimization approaches, but also a practical implementation of an efficient trajectory planner for autonomous UAV swarm operations.

   Tutor: Janoušek Jiří, Ing., Ph.D.

2. Advanced methods of numerical modeling in safety problems of progressive electrical installations

   At present, it is possible to expect an increase in the number of dangerous events caused by electrical installation elements due to the higher load on the energy network. The reason is the expansion of electromobility and the use of local energy sources, which results in a two-way flow of energy and a load on the electrical installation to the limit of capacity even in distribution systems without regular control. The aim of the dissertation will be to identify typical problems of security breaches caused by electrical installation elements and distribution systems inside and outside buildings, in cooperation with industrial partners and the Czech Safety Corps. On the basis of real experience, the current numerical modeling methods for heat distribution reconstruction will be designed or optimized for these cases, e.g. devices in switchboards during long-term overload or in the event of a fault, considering the individual characteristics of the environment. The accuracy of the numerical models will be verified by comparing the results with measurements on physical models. Based on the verified model, a methodology for applying the proposal in practice will be drawn up.

   Tutor: Kadlec Radim, Ing., Ph.D.

3. Advanced methods of radiofrequency detection of partial discharges

   One of the key problems of high-power high-voltage transformers is the existence of partial discharges PD in their dielectric oil filling. Radiofrequency methods may provide an efficient tool for observing the PD activity. The possibility of PD-radiated UHF electromagnetic (EM) signal detection is crucial for successful methods application. This signal has a relatively low magnitude and its occurrence is accompanied by a strong impulse-like interference from other discharge processes. On the other side, the PD signal dispose with specific time and frequency properties, which can be utilized for its reliable detection and evaluation. The theme of the Ph.D. study is focused on the research of new approach to PD-radiated EM signals detection utilizing signal’s specific time and frequency properties. The goal is to deepen the knowledge in the problematic of reliable detection and identification of PD activity and increasing the reliability of the high-power high-voltage transformers.

   Tutor: Drexler Petr, doc. Ing., Ph.D.

4. Advanced methods of satellite attitude control in Very Low Earth Orbit

   The aim of this doctoral research is to advance the scientific understanding of satellite attitude and orbit control in the under-explored area of very low Earth orbits (VLEO). The research will be based on current attitude control algorithms utilized in orbital missions but will reflect the specificity of the highly dynamic environment of VLEO. The focus of the thesis will be on integrating multiple strategies into a single solution. Those strategies might include thrust control, aerodynamic control, or the estimation of external disturbances to adapt the control algorithm in real time. The research will also explore robust control strategies to maintain stable orbits under elevated atmospheric drag and drag-induced torques. Methodological contributions will among others include advanced multi-axis control and sensor fusion for environment and satellite state estimation. The results of the research are expected to expand the understanding of the design of VLEO missions and enable efficient satellite operations with long-durations at extremely low attitudes.

   Tutor: Drexler Petr, doc. Ing., Ph.D.

5. Artificial intelligence in signal and image processing

   The aim of the dissertation will be to increase the level of knowledge in the field of processing of one-dimensional and multidimensional signals (images) by modern methods of artificial intelligence (deep learning). It will be mainly about suppression of interference, noise and artifacts arising during their acquisition. Processing of low-level signals acquired by tomographic methods or signals acquired by ELF-THF detection is expected.

   Tutor: Mikulka Jan, doc. Ing., Ph.D.

6. Controllability problems for differential and discrete equations with aftereffect.

   The aim is to solve some controllabity problems on relative and trajectory controllability for systems of discrete equations with aftereffect. It is assumed that criteria of controllability will be derived and relevant algorithms for their solutions will be constructed (including constructions of controll functions). Starting literature – the book by M. Sami Fadali and Antonio Visioli, Digital Control Engineering, Analysis and Design, Elsewier, 2013 and papers by J. Diblík, Relative and trajectory controllability of linear discrete systems with constant coefficients and a single delay, IEEE Transactions on Automatic Control, (https://ieeexplore.ieee.org/document/8443094) 64 (2019), Issue 5, 2158-2165 and by J. Diblík, K. Mencáková, A note on relative controllability of higher-order linear delayed discrete systems, IEEE Transactions on Automatic Control 65, No 12 (2020), 5472-5479, (https://ieeexplore.ieee.org/document/901308900. During study a visit to Bialystok University, Poland, where similar problems are studied, is planned.

   Tutor: Diblík Josef, prof. RNDr., DrSc.

7. Detection and Tracking of Flying Objects

   This thesis focuses on the development of optimization and detection algorithms for tracking flying objects using artificial intelligence algorithms in real-time. The goal is to create advanced algorithms and their implementation in the field of unmanned aerial vehicles (UAVs).

   Tutor: Marcoň Petr, doc. Ing., Ph.D.

8. Electrical Impedance Tomography

   The aim of the dissertation is to increase scientific knowledge in the field of non-destructive analysis of the internal structure of materials by electrical impedance tomography. The expected direction of the dissertation work is the optimization of methods of reconstruction of electrical impedance distribution, the use of multispectral noise and impulse analysis, application and optimization of artificial intelligence and machine learning elements, acceleration of calculations using parallelization of calculations. The design of the methods will be carried out with respect to selected applications, e.g. soil investigation, condition of building structures, etc. in cooperation with specific institutions. Research activities will include modelling of the environment and the measurement system with equivalent circuits, simulation, emulation, measurements on the real environment including evaluation of the influence of the excitation signal frequency on the quality of reconstruction of the electrical properties of the analyzed environment.

   Tutor: Mikulka Jan, doc. Ing., Ph.D.

9. General solutions to weakly delayed linear differential systems and discrete-time signal processing

   The aim will be to derive explicit formulas for general solutions to weakly delayed linear differential systems and discrete systems, to show if its reduction to linear systems of ordinary differential equations and discrete equations is possible, and prove results on conditional stability. To derive results, various mathematical tools will be used, one of them is the Laplace transform. Starting literature – the paper by D. Ya. Khusainov, D. B. Benditkis and J. Diblik, Weak delay in systems with an aftereffect, Functional Differential Equations, 9, 2002, No 3-4, 385-404, J. Diblík, H. Halfarová, J. Šafařík, Formulas for the general solution of weakly delayed planar linear discrete systems with constant coefficients and their analysis, Applied Mathematics and Computation 358 (2019), 363-381, , J. Diblík, H. Halfarová, J. Šafařík, Two-parameters formulas for general solution to planar weakly delayed linear discrete systems with multiple delays, equivalent non-delayed systems, and conditional stability, Applied Mathematics and Computation vol. 459, Art. ID 128270, pp. 1-14, 2023, M. Sami Fadali, A. Visioli, Digital Control Engineering, Analysis and Design,' Third Edition, Academic Press in an imprint of Elsevier, Elsevier, 2019 and recently published new results. During study a visit to Bialystok University, Poland, where similar problems are studied, is planned.

   Tutor: Diblík Josef, prof. RNDr., DrSc.

10. Implementation of new reconstruction methods for quantification of fat fraction in CSE-MRI

    The aim of this study topic is to master selected advanced reconstruction algorithms to address an advanced signal model and their application in the reconstruction of fat fraction from CSE-MRI (chemical shift encoded – MRI) data. The research will focus on existing advanced algorithms for fat fraction reconstruction and the implementation of new methods or combinations with existing approaches to improve the accuracy and speed of reconstruction. All measurements will be conducted on a preclinical 9.4T MRI animal device at UPT, AV ČR in Brno.

    Tutor: Kořínek Radim, Ing., Ph.D.

11. Low-level measurements in the study of fluid behaviour

    The aim of the dissertation will be to investigate the current and propose new or optimization of current methods for low-level measurements of electrical quantities to describe the behavior of fluids primarily during changes in their state of matter (freezing), or to determine the presence and characterization of parameters of precursor nanofilm of water and other compounds. The dissertation will be carried out in collaboration with the Department of Chemistry, Faculty of Science, Masaryk University. It will build on the existing results of measurements of the electric potential of freezing liquids, while deepening the understanding of the behaviour of liquids at very low temperatures. Translated with DeepL.com (free version)

    Tutor: Szabó Zoltán, Ing., Ph.D.

12. Mapping the Earth's Magnetic Field Using Unmanned Aerial Vehicles

    The aim of this dissertation is to systematically explore and analyze current methods for mapping the Earth's magnetic field using unmanned aerial vehicles (UAVs). The work will focus on new methods and approaches for mapping the Earth's magnetic field or materials and on the analysis of magnetic interferences caused by UAVs. The practical part of the dissertation will involve the design and implementation of experiments with UAVs equipped with magnetometers, aimed at verifying the accuracy and reliability of the measured data and proposing recommendations for optimizing measurement procedures. The results of this work will contribute to a better understanding and more efficient use of UAVs in the field of Earth's magnetic field mapping.

    Tutor: Marcoň Petr, doc. Ing., Ph.D.

13. Methodology for measuring very low level signals

    The aim of the dissertation will be to measure signals on the border of physical limits, whether it is the measurement of very small voltages in the order of nV, fA current or special measurements of air ion concentration. The finite element method will be used to correctly distribute the electrostatic charge in the measurement methodology. The goal will be to have proper analog and digital filtering, use advanced noise suppression methods and obtain a very weak useful signal. This includes interdisciplinary research in conjunction with natural scientists and physicians to correlate the measured quantities with possible effects on living organisms. Translated with DeepL.com (free version)

    Tutor: Roubal Zdeněk, Ing., Ph.D.

14. Numerical aspects of solutions of partial differential equations with delay.

    The problem will be focused on the construction of schemes for numerical solution of some types of partial differential equations (the telegraph equation, the heat conduction equation) with a delay in the time argument. We expect to use and develop some numerical algorithms mentioned, for example, in the work by J. Diblik "Representation of solutions of linear discrete systems with constant coefficients and with delays", Opuscula Math. 45, no. 2 (2025), 145-177. Theoretically, the research will be related to the results published in, e.g., J. Diblik, D. Khusainov, O. Kukharenko, Z. Svoboda "Solution of the first boundary-value problem for a system of autonomous second-order linear partial differential equations of parabolic type with a single delay", Abstr. Appl. Anal. 2012, Art. ID 219040, 27 pp. The results will be algorithmized and presented in software form.

    Tutor: Diblík Josef, prof. RNDr., DrSc.

15. Research of properties and applications of noise electromagnetic fields

    Measuring and diagnostic methods based on the interaction of radiated electromagnetic (EM) field with test objects are currently mature and widely used technology. However, the vast majority of systems based on such approach use the concept of generating and evaluating EM fields with certain defined or swept frequency. In this case, it is necessary to take into account the possibility of reactive coupling of the measured object and the measuring device in the near field, which can detriorate the measurement. Conversely, if broadband stochastic signals (noise signals) were used for diagnostics, these problematic coupling could be suppressed. The topic of the study is focused on the research of the use of the concept of diagnostic of materials and electromagnetic structures by the noise field, especially in radiofrequency and microwave domain, its development and experimental verification.

    Tutor: Drexler Petr, doc. Ing., Ph.D.

16. Semi-analytical solution methods of fractional differential equations

    The aim of the dissertation thesis is a proposal of a numerical semi-analytical method which will be based on Adomian decomposition method and integral transformations to solving initial value problems for fractional systems of differential equations with emphasis on analysis of fractional transfer functions and their impulse characteristics. Convergence analysis of the proposed method will be investigated as well.

    Tutor: Šmarda Zdeněk, doc. RNDr., CSc.

17. Tuned nano-structures

    Current research areas include research on sophisticated nanostructures. Scientific work is focused on the design, modeling and experiments with tuned nanostructures in the f=10-500THz range, as well as for the frequency band corresponding to the electron beam. It is possible to focus on three areas. The first focus is on the field of numerical modeling of structures. Based on the real properties of nanomaterials, create a numerical model and analyze the electromagnetic properties of the structure. The second area is focused on the design of methods and methodologies for verifying the results using experiments, measurements and verification of assumptions expected from theoretical descriptions. By modeling using the finite element method, finite volumes (for example, in the ANSYS, ANSOFT, MAXWELL, etc. program), a model of the behavior of mass dynamics is designed. The third area of ​​research is focused on the field of technology. In this focus, research on technologies for the implementation of the designed structures and their feasibility in the experimental part of the topic is expected. The results will serve for the research of special tuned periodic structures as a special part of electron microscope optics. Topics can be addressed separately, it is not a requirement that all of them be addressed by one applicant. The topic is part of the announced CZ grant.

    Tutor: Fiala Pavel, prof. Ing., Ph.D.