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study programme
Faculty: FEECAbbreviation: DPA-TEEAcad. year: 2024/2025
Type of study programme: Doctoral
Study programme code: P0714D060006
Degree awarded: Ph.D.
Language of instruction: English
Tuition Fees: 2500 EUR/academic year for EU students, 2500 EUR/academic year for non-EU students
Accreditation: 28.5.2019 - 27.5.2029
Mode of study
Full-time study
Standard study length
4 years
Programme supervisor
doc. Ing. Petr Drexler, Ph.D.
Doctoral Board
Chairman :doc. Ing. Petr Drexler, Ph.D.Councillor internal :doc. Ing. Jan Mikulka, Ph.D.doc. RNDr. Dana Hliněná, Ph.D.prof. Ing. Lubomír Brančík, CSc.doc. Ing. et Ing. Vilém Neděla, Ph.D., DSc.doc. RNDr. Martin Kovár, Ph.D.Councillor external :prof. Ing. Jan Macháč, DrSc.prof. RNDr. Ondřej Kalenda, Ph.D.prof. RNDr. Martin Knor, Ph.D.
Fields of education
Study aims
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.
Graduate profile
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.
Profession characteristics
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
Fulfilment criteria
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.
Study plan creation
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.
Issued topics of Doctoral Study Program
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.
The aim of the work is to create or optimize new advanced methods of surveying the Earth's surface. The research will focus on different types of sensors, one of the variants will be the sensing of the magnetic field in order to find different objects such as military mines.
Tutor: Marcoň Petr, doc. Ing., Ph.D.
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.
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.
This topic deals with the development of algorithms and techniques for the autonomous control of unmanned aircraft in particular. The research will focus, among other things, on how airplanes make decisions, plan their route and react to unexpected situations.
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.
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.
"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.
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.
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.
The goal of the study is to propose a solution for processing images captured by a multispectral camera in order to obtain the nutritional values of plants and also to estimate the optimal harvest time based on the established nutritional parameters. We will work with various algorithms including ML AI.
As part of the dissertation, research will be carried out in the field of brain tumor diagnostics. It will focus on different types of images captured by a magnetic resonance tomography. Furthermore, for imaging brain tissue containing pathologies such as glioblastoma, metastasis or abscess. The research carried out will consist in the design of brain pathology classification methods using artificial intelligence.
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.
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.
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.
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.
The topic focuses on identifying and addressing the security threats associated with drones. The research will be focused on the protection of unmanned systems against attacks and the security of their communication.
The aim of the project is to carry out research in the field of navigation of unmanned systems with a focus on the movement of the aircraft using images. Study the possibilities of controlling unmanned aircraft using image data and the possible fusion of data from other sensors. Design UAV movement methods without satellite data, optimize and evaluate the obtained results.
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.