Course detail

Stochastic Mechanics

FSI-RSOAcad. year: 2020/2021

Statistical techniques play indispensable roles in the fields of engineering disciplines, as well as in meteorology, biology and medicine. In this course we discuss the structure of probability space, characteristics of random data, probability function, correlation and spectral density functions, system identification and response, and basic engineering applications of correlation and spectral analysis.

Learning outcomes of the course unit

Students can solve simple stochastic problems after the course. Students will have basic knowledge for following studies this field.


Basic terms of mathematical statistics and probabilistic, basic theory of mechanics, theory of dynamic systems and theory of technical systems.


Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

Kratochvíl, C. a kol.: Stochastická mechanika, I. Část, studijní podpory FSI, Ústav mechaniky, mechatroniky a biomechanika, 2004
Bolotin, V.V.: Použití metod teorie pravděpodobnosti a teorie spolehlivosti při navrhování konstrukcí. SNTL - nakladatelství technické literatury, Praha, 1978. (299 s)
Bendat, J., Piersol, A.: Engineering applications of correlation and spectral analysis, New York, Wiley-Interscience, 1980. 315 p
Kropáč, O.: Náhodné jevy v mechanických soustavách, SNTL Praha, 1987
Sun, J.: Stochastic Dynamics and Control, Elsevier, 2006

Planned learning activities and teaching methods

The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.

Assesment methods and criteria linked to learning outcomes

Exam is written. Students get ahead topics. Oral exam will be in case irresolution.

Language of instruction


Work placements

Not applicable.


The aim of course is insight into stochastic mechanic meaning in engineering and integration to modeling of technical systems. It demand: make clear of knowledge of mathematical statistics and probabilistic theory, basic features of steady and unsteady phenomena, basic features of steady random processes algebra, basic features of modeling possibilities of operative and random processes, knowledge of basic method of dynamic systems responses solving.

Specification of controlled education, way of implementation and compensation for absences

Attendance at practical training is obligatory. Accreditation requirements are attendance on the practice and good results from all courses. Teacher defines concrete requirements in first practice.

Classification of course in study plans

  • Programme M2A-P Master's

    branch M-IMB , 2. year of study, summer semester, 5 credits, compulsory
    branch M-MET , 2. year of study, summer semester, 5 credits, compulsory

Type of course unit



26 hours, optionally

Teacher / Lecturer


Stochastic mechanics in engineering
Basic terms of mathematical statistics and probability
Analysis of the process in the technical systems
Basic theory of dynamic systems
Stationary and non-stationary processes, deterministic chaos
Basic features of stationary process, algebra of stationary processes
Models of non-stationary processes and their phenomena
Correlation and spectral analysis in engineering
Solving of simple stochastic problems in the time and frequency domain

Computer-assisted exercise

13 hours, compulsory

Teacher / Lecturer


Basic problems of probability theory
Calculation of stationary processes characteristics
Calculation of statistical characteristics for simple static problems
Calculation of response characteristics for dynamic system- passage of random signal.
Mechanical system responses - multiple inputs and multiple outputs