Full-time study

4 years

doc. Ing. Petr Drexler, Ph.D.

Chairman :
doc. Ing. Petr Drexler, Ph.D.
Councillor internal :
prof. Ing. Lubomír Brančík, CSc.
doc. RNDr. Martin Kovár, Ph.D.
doc. Ing. Jan Mikulka, Ph.D.
doc. RNDr. Dana Hliněná, Ph.D.
Councillor external :
prof. RNDr. Martin Knor, Ph.D.
prof. RNDr. Ondřej Kalenda, Ph.D.
prof. Ing. Karel Bartušek, DrSc.
prof. Ing. Jan Macháč, DrSc.

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 analysis of pathological brain tissue from MRI data

   The aim of the work is research in the field of classification of biological tissues occurring in the brain and advanced analysis of biomedical images obtained from pathological tissue in the brain.

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

2. 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.

3. Aggregation operators in fuzzy logic

   Fuzzy logic is a form f many-valued logic or probabilistic logic. It has been applied to many fields, from control theory to artificial inteligence. The topic of the thesis is tu study new constructions and properties of fuzzy logic connectives via aggregation operators.

   Tutor: Hliněná Dana, doc. RNDr., Ph.D.

4. Algebraic hyperstructures in autonomous driving

   The dissertation will study possible applications of algebraic hyperstructure theory for autonomous driving and traffic control. It will make use of rough sets, generalizations of automata theory and other algebraic tools used for modeling contexts in which multivalued results of algebraic operations and their approximate descriptions are needed.

   Tutor: Novák Michal, doc. RNDr., Ph.D.

5. Analysis of image reconstruction methods in EIT

   The aim of this work is the analysis of mathematical models for image reconstruction obtained by the electrical impedance tomography from the viewpoint of applicability to individual engineering fields (chemical industry, geology, material engineering and diagnostics, etc.). The output of the work will be a theoretical analysis and optimization of limiting factors of methods in solving selected technical tasks including evaluation of measurement uncertainties (specific conductivity and position of inhomogeneities), computational demands, etc. Specifically, the work will focus on a) optimization of mathematical model parameters with respect to the actual parameters of the physical model, b) regularization methods, c) image processing methods (segmentation of inhomogeneity), d) adaptive meshing methods according to the ongoing results of reconstruction.

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

6. Autonomous drones in gps-denied environments

   The work is focused on the development of data fusion algorithms, artificial intelligence and their testing in order to control autonomous drones without GPS. For correct selection of control signals, it is necessary to process data from sensors in real time. Algorithms must therefore work quickly and adaptably.

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

7. Controllability problems for 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 paper 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) 2158 - 2165, 2019. During study a visit to Bialystok University, Poland, where similar problems are studied, is planned.

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

8. Image modeling and reconstruction in EIT using tools of artificial intelligence and machine learning

   The aim of the dissertation is to create a model for image reconstruction in electrical impedance tomography using machine learning and artificial intelligence. The output of the thesis will be a functional system including a sufficient set of synthetic and real data for learning the proposed models to identify electrical impedance inhomogeneities within an unknown environment. It is also envisaged to create a laboratory tomograph model to obtain real data to reconstruct the specific conductance and possibly optimize the proposed methods for follow-up applied research conducted at DTEEE.

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

9. Multispectral electrical impedance tomography

   The aim of the dissertation is to increase the scientific knowledge in the field of non-destructive analysis of the internal structure of the material with regard to the optimization of methods for solving the inverse problem of reconstruction of electrical quantities, the use of multispectral noise and impulse analysis of the environment under investigation, elements of artificial intelligence and machine learning. The design of the methods will be carried out with respect to specific practical applications, e.g. soil investigation, condition of building structures, etc. The research activity will include modelling of the environment and the measurement system by 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 analysed environment.

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

10. Numerical solution methods of integer and fractional control systems

    The aim of the dissertation thesis is modification of a numerical semi-analytical method based on Adomian decomposition method and integral transformations to solving initial value problems for integer and fractional control systems in the sense of Caputo fractional derivative. Convergence analysis of the proposed method will be investigated as well.

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

11. Optical fiber sensing of electromagnetic transients

    The use of a magneto-optical effect in optical fibers is an attractive option for the design of magnetic field and electric current sensors. Their application is particularly interesting in the case of measurements of strong magnetic fields, or currents reaching values in the range of kiloamperes up to tens of megaamperes. In this context, their application in the diagnostics of plasma discharges in future fusion reactors is highly potential. For successful deployment of these sensors it is highly desirable to have the possibility of testing them during development. Many works have already dealt with the measurement of sensor properties. However, the necessary attention has not been paid to the possibility of testing the dynamic properties of the transducers in the nanosecond and sub-nanosecond regions. Moreover, together with the magnetic fields induced by currents of kiloamperes and above. The dissertation thesis will be devoted to the research of properties and testing of sensors in the nano and sub-nanosecond area. The design and development of a unique testing device is expected.

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

12. 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.

13. Spatial Analysis of the Force Load on a Deformed Developing Spine, and Corrective Force Modelling Applied to Minimize the Scope of a Scoliosis Surgery

    Spinal deformity in children (scoliosis) is a condition whose progression cannot be predicted. The results obtained via conservative therapy are problematic, and a certain degree of curvature requires surgical treatment, including the risk of repeated surgeries and complications. The presently used system of growing rods affects, on the average, 9 spinal segments; these become immobile and influence the excessive stress upon the free segments under fusion, resulting in earlier degenerative changes, back pain at a mature age, restrained bodily activity, and damage to the locomotor system. The project is conceived to propose a novel methodology for minimizing the spurious impacts of the surgical treatment of progressive spinal deformity upon child patients, with 3D modeling to define the mechanical stress distribution within the simulation of the planned intervention. The set of patients to be recruited includes individuals with idiopathic, symptomatologic, and congenital scoliosis progressing despite conservative therapy; all these subjects would otherwise undergo spinal surgery. The project aims to design a surgical solution to correct idiopathic, symptomatologic, and congenital spinal deformities by the osteotomy of 1 vertebra. It will exploit 3D modeling to define the stress on the spine, estimation of the spine development and intervertebral discs regeneration by MRI. The project will be carried out in collaboration with University Hospital in Brno Bohunice.

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

14. Stochastic differential equations in electrical engineering

    By adding some randomness to the coefficients of an ordinary differential equation we get stochastic differential equations. As an example of that is the equation, that describes the current in an RL circuit with stochastic source. Then the solution of the equation is a random process. The subject involves creating stochastic models, numerical solutions of stochastic differential equations and examinations of the statistical estimates of the solutions.

    Tutor: Kolářová Edita, doc. RNDr., Ph.D.

15. The Theory of Nonlinear Acoustics in Relation to Inhomogeneous Locally Periodic Structures

    Nonlinear acoustics is a comparatively modern research discipline, whose primary focus lies within the propagation of acoustic waves in a nonlinear environment, modelling of the parametric acoustic field, and applications stemming from these areas. In this branch of science, major problems currently awaiting effective solution include, above all, the analytical description and numerical modelling of a non-linear environment. These two subdomains are complemented with another task element, namely the design of inhomogeneous, locally periodic structures, which enable us to target acoustic waves into a beam and to create nonlinear components, such as acoustic diodes. Further, the discussed research discipline may comprise a number of potential application subregions, for example, contactless material testing. Within the doctoral thesis, the student will characterize and analyze amplitude modulated acoustic waves of final amplitudes, and they will also provide an analysis of parametrically excited acoustic fields. In the wider context, one of the central aims of the thesis is to employ inhomogeneous periodic structures, methods for input signal processing, and carrier wave modulation to deepen the present knowledge of nonlinear acoustic interactions in liquids.

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

16. Vizualization of quantum and classical turbulent flows of superfluid and gaseous helium by a novel optical method via laser-induced fluorescence of long-living molecular excimers He2*

    Turbulent flows are found almost everywhere in Nature (think of air travel, flow of air around cars, explosions of supernovae, dynamics of quantum vortices in superfluid helium at temperatures close to absolute zero…). One important feature is the enhancement of heat transport in a layer of fluid. To give an illustration of the magnitude - In an atmospheric boundary layer of 1 km height, the turbulent heat transfer increases by at least 5 orders of magnitude compared to the one by molecular diffusion without turbulent air flow. Detailed understanding of this, has an obvious value for understanding Earth’s climate or important technological applications such as processes in cooling blankets in nuclear engineering or the storage of renewable energy in liquid metal batteries. Turbulent heat transfer can be modelled and studied in laboratory conditions, however the highest intensity turbulence experiments (approaching the conditions relevant e.g. in our planetary atmosphere), as the Rayleigh Benard convection (RBC) experiments in cryogenic helium gas done in our laboratory at the Institute of Scientific Instruments in Brno nowadays measure only temperature fluctuations and lack a suitable visualization technique, allowing to measure the flows velocity field. In collaboration with the group of prof. W. Guo at National High-Magnetic Field Laboratory in Florida, who apply a novel and groundbreaking method using laser-induced fluorescence (LIF) of long-living metastable excimers of helium-4 in the regime of superfluid quantum turbulence, we plan to develop an apparatus for visualization of classical turbulent heat transfer by RBC in gas. The work on the PhD student will involve measurements and large data analysis of the experiments in Florida and/or design of the novel apparatus to be built at ISI Brno. The student can also get involved in designing the electronics and instrumentation for data harvesting in upgrades of the ISI experimental RBC apparatus.

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

1. round (applications submitted from 01.04.2022 to 15.05.2022)

1. General solutions to weakly delayed linear differential systems

   The aim will be to derive explicit formulas for general solutions to weakly delayed linear differential systems, to show if its reduction to linear systems of ordinary differential 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 and recently published results. During study a visit to Bialystok University, Poland, where similar problems are studied, is planned.

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

2. Solutions to weakly delayed linear difference systems in the case of zero eigenvalues

   The aim will be to derive explicit formulas for general solutions to weakly delayed linear differential systems in the case of presence of zero eigenvalues of the matrix of linear nondelayed term and its utilization to characterize properties of solutions. 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 and 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. During study a visit to Bialystok University, Poland, where similar problems are studied, is planned.

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