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.

3. round (applications submitted from 01.12.2024 to 15.12.2024)

1. 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.

2. 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.

3. 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.

4. Low level magnetic measurements

   Theme explores two key areas. The first is focused on continuing research into a comprehensive system of measurement methods and metrology for measuring low-level magnetic respectfully strongly disturbed environment in a narrow frequency band f = 0.1-30Hz. It is advisable to focus on methods of achieving the results of S / W <0.05 a signal reconstruction. The proposed methods are used for evaluation of small changes in magnetic fields. The second area of research continues to change human behavior and the overall response of the human body, its properties, and reactions to changes in the magnetic field. As a tool, the procedure is both deterministic and stochastic, with the latest mathematical tools and non-destructive measurement methods.

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

5. 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.

6. Methodology for measuring air ions and charge

   The aim of the dissertation will be an interdisciplinary comparison of air ions with other related quantities and their effect on human organisms. In the field of studying atmospheric electricity, one can look for a correlation with earthquakes and the research of phenomena arising during thunderstorms. Furthermore, the research will also focus on closed spaces, where it is necessary to achieve maximum sensitivity with minimum volumetric air flow. Especially for speleotherapy caves, where the correct methodology for measuring air ions and their mobility will be developed. Nowadays, current atmospheric pollution will be correlated with the concentration of light air ions, which can be used as a possible indicator of chemical pollution. The effect of cigarette smoke and plants on airborne ions will be investigated. Similarly, research will also be conducted in the experimental forest.

   Tutor: Roubal Zdeněk, Ing., Ph.D.

7. Methods for measuring weak magnetic fields in high disturbance environments with applications in defectoscopy and on drones

   t is often necessary to measure the weak magnetic field of a useful signal in an environment with unwanted interference from mains power, switching power supplies. A typical example is the magnetic impedance tomography (MIT) method. Another possibility is magnetic field magnetisation by drone in an urban area. Using the MIT method it is possible to non-destructively reconstruct the conductivity of the object under investigation and find possible faults, cracks. There are also many other methods of determining material properties using accurate mapping of the magnetic field over the specimen. Another use is the search for mines, either by methods of measuring magnetic anomalies or by the method of eddy currents. The PhD thesis will use analogue and digital methods suitable for noise and interference suppression and to obtain the best possible results for subsequent reconstruction or processing. In the case of drones, stabilization in space must be appropriately addressed.

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

8. Models of the structure of matter

   The work is focused on theoretical derivation of numerical models based on quantum mechanical models of materials and in combination with the stochastic, both deterministic and non-deterministic approach to formulate the determination of uncertainty for ordinary differential equations nanoelementární simple deerministic numerical model of the system, periodic system. Research continues on modifications so vytovřeného model based on numerical finite element, finite volume, boundary element method for static and dynamic models formulated using partial differential equations. The aim is to propose a numerical model as a powerful tool for the analysis and characterization of both periodic and nonperiodic structure and its geometry on the atomic and subatomic level verification on a single verifiable example, to examine the characteristics of the resulting numerical model and compared with the requirements for models for electrical discharge dynamics and evaluate the specified parameters.

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

9. Nuclear quadrupole resonance techniques for material detection

   The thesis is focused on the development of techniques for detection of various materials (especially N and Cl based) using nuclear quadrupole resonance. Currently, this method seems to be very promising for the detection and classification of explosives, medicament and drugs. Problems of excitation of cores and subsequent scanning of resonating signal with the possibility of tuning is a relatively complex task both in terms of signal path requirements and in terms of excitation circuit design. Due to the low level of the resonating signal and the short relaxation, it is necessary to solve a number of technical problems. The issue is largely interdisciplinary.

   Tutor: Steinbauer Miloslav, doc. Ing., Ph.D.

10. Numerical models of stochastic problems

    In the modelling process, there are unsolved problems in the area of large multi-parameter problems with explicit description of the minimum parameters . Approaches for solving such models are well known. With appropriate formulation and construction of the method, they become powerful tools in the scientific approach to solving basic and applied research. The aim of the PhD study is to describe and formulate approaches and models for solving large-scale periodic systems with a degree of nonperiodicity, verify the properties of the models in experiments. To perform targeted testing on nanomaterial models, for example not only on graphene structures, surface atomic layers e.g. with the application of plasmas.

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

11. 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.

12. Special methods of measurement of magnetic properties of materials

    The aim of the dissertation thesis will be the design of new and significant improvement of existing methods enabling to determine its material properties for material samples. The focus will be on the measurement of anisotropic magnetization characteristics with the necessary support of numerical methods. For example, new metallic materials in 3D printers exhibit significant anisotropy. Another area will be the measurement of materials with low magnetic susceptibility. Different methods give different results, so the aim will be to compare and unify the results. This topic is particularly important for image quality in NMR tomography for dental implants. A special area is the measurement of magnetic liquids. The force methods will also require optimization using FEM.

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

13. 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.

14. Tuned nanostructure

    One of the current areas of research are working on sophisticated nano-structures. The work is focused on design, modelling and experiments with tuned nanostructures in the region f=10-500THz, also for electron beam frequencies.There are three goals. The first one is the field of numerical modeling of structures. Based on the real properties of nanomaterials to create a numerical model and analyze the structure. The second area focuses on the design methods and methodologies of verification of the results by experiments, measurement and verification of assumptions expected from theoretical model. Modeling using finite element method, finite volume (such as ANSYS, ANSOFT, MAXWELL etc.) to propose a model of behavior dynamics of matter. The third area of ​​research is focused in the field of technology. This is expected to focus research on technology for implementation of the proposed structures and their feasibility in the experimental part of the topic. Results will be used for research of special tuned periodic structures. Topics can be solved in isolation, is not a precondition for any one candidate. The topic is part of the grant announced by CZ.

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

15. Use of plasma nanotechnologies for the design of new lithium-ion battery electrode materials

    Thesis is focused on the research, description, modeling and experimental verification of plasma nanotechnology allowing to modify the functional properties of the surface of an electrode system materials of an lithium-ion accumulators, including 3D micro and nanoporous structures thanks to the excellent conformation of processes. Found technology will also be applicable for material structuring design and pore and nanotubes at the material boundaries. This research will focus among other things on the possibilities of the design and creating multilayered systems. The aim of this work is to propose nanostructure of new material types for lithium-ion accumulator electrodes by means of evaluation of numerical analyzes and experimental realization / verification of the proposed structures using a combination of steps utilizing the potential of modern nanotechnologies, including plasma processes. The work is a part of the grant project with the planned financial support of the doctoral student.

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

2. round (applications submitted from 01.07.2024 to 31.07.2024)

1. Analytical and numerical solving fractional dynamical systems with emphasis on analysis of fractional transfer functions

   The aim of the dissertation thesis is a proposal of a numerical semi-analytical method which will be based 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.

2. 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.

3. Fractional order systems and their applications in electrical engineering

   "Fractional calculus" is the theory of integrals and derivatives of arbitrary order, which unify and generalize the notion of integer order differentiation and n-fold integration. This generalized process is called "differintegration". Systems that can be described by differential equations of fractional order have many applications in electrical engineering. The doctoral thesis should contain both theory and applications and should move forward frontiers in both directions. Detailed topic of the thesis will be specified according to experience and preferences of the selected candidate. Preferred candidates should already have had some experience with fractional derivatives and integrals.

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

4. Mathematical modelling and simulation of biological processes in physical education

   Physical education is a discipline on the boundary between medicine and sports that provides a variety of applications in everyday life. The aim of the dissertation thesis is to design and analyse a mathematical model that corresponds to a dynamical system linking the health and the physical activity of a human being. The doctoral thesis should consist of theoretical and application part and should contain simulations and data analysis. Detailed topic of the thesis will be specified according to experience and preferences of the selected candidate. Preferred candidates should already have some experience with mathematical models of dynamical systems.

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

5. Modern image analysis methods for medical applications

   The aim of the dissertation is to increase scientific knowledge in the field of modern methods of image analysis. The PhD student will work closely with St. Anne's University Hospital (Neurosurgery Clinic). Taking into account the specific characteristics of MRI images and other imaging modalities, methods of image preprocessing, segmentation and classification will be developed. The use of artificial intelligence and machine learning methods for tissue differentiation, standardization of diagnostics, etc. is assumed.

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

1. round (applications submitted from 01.04.2024 to 30.04.2024)

1. 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.