228-0313/02 – Probability computations in civil engineering (PV)

Gurantor departmentDepartment of Structural MechanicsCredits5
Subject guarantorprof. Ing. Martin Krejsa, Ph.D.Subject version guarantorprof. Ing. Martin Krejsa, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Study languageEnglish
Year of introduction2019/2020Year of cancellation
Intended for the facultiesFASTIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
KON09 doc. Ing. Petr Konečný, Ph.D.
KRE13 prof. Ing. Martin Krejsa, Ph.D.
LED0036 Tuan Duc Le
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Part-time Credit and Examination 17+0

Subject aims expressed by acquired skills and competences

The aim of the course Probabilistic Calculations in Civil Engineering is to deepen knowledge in the field of probability theory and mathematical statistics and their application in solving selected problems in construction using computer technology and available software.

Teaching methods



In this subject Probability computations in civil engineering, students learn theoretical background and practical information about probabilistic assessment of load-carrying structures. For that purpose, they should master the probability and structure reliability theories. The key feature of the probabilistic method is that it is possible to express variability of input quantities in a stochastic (probabilistic) form, for instance, by histograms. Unlike the applicable standards and procedures which are based on deterministic expression of input quantities (using a single value – a constant), the probabilistic methods provide more precise reliability assessment and improved safety for those who use the buildings and structures.

Compulsory literature:

1. Robert E. Melchers, Andre T. Beck, Structural Reliability Analysis and Prediction (3rd Edition), 528 pages, 2018, ISBN-13: 978-1119265993, ISBN-10: 1119265991. 2. TeReCo: Probabilistic Assessment of Structures using Monte Carlo Simulation, Background, Exercises and Software. Textbook and CD-ROM. ÚTAM AV ČR, Praha 2003. 2nd edition. ISBN 80-86246-19-1.

Recommended literature:

1. Anthony J. Hayter, Probability and Statistics for Engineers and Scientists (4th Edition), 864 pages, 2012, ISBN-13: 978-1111827045, ISBN-10: 1111827044. 2. O. Ditlevsen and H.O. Madsen: Structural Reliability Methods, Technical University of Denmark, 2005.

Way of continuous check of knowledge in the course of semester

Written and oral exam.


Other requirements

Ability to partial self-study.


Subject has no prerequisities.


Subject has no co-requisities.

Subject syllabus:

1. Introduction to the course: Probability calculations in civil engineering, examples of selected calculations. 2. Introduction to probability theory and mathematical statistics: Basic concepts and principles of the theory of probability theory and mathematical statistics, random phenomenon, probability of random phenomenon, statistical moments. 3. Probabilistic expression of random variables: Random variable, nonparametric (empirical) probability distribution, histogram. 4. Monte Carlo method: Inclusion of the Monte Carlo method into a list of probability methods, Monte Carlo history, Buffon\'s needle, the first systematic use of the Monte Carlo method. Law of large numbers, generators (pseudo) of random numbers. Numerical integration with the Monte Carlo method. An illustrative example of elemental calculation using the Monte Carlo method. 5. Simulation Based Reliability Assessment (SBRA): Insertion of the SBRA method into the overview of probability methods, SBRA simulation method, probability computation by SBRA (random quantities, computational model, reliability function analysis), illustrative examples of probability calculations by SBRA. 6. Parametric probability distribution of a continuous random variable: Overview of important continuous probability distribution, Gaussian probability distribution, logarithmic-normal probability distribution, coefficient of determination. 7. Statistical dependence of input random variables: Correlation and correlation coefficient, correlation matrix. Double and triple histogram. 8. Stratified and Advanced Simulation Methods: Incorporating stratified and advanced simulation methods into a list of probability methods. Latin Hypercube Sampling - LHS, the principle of the method and its application. Method of Importance sampling. 9. Approximation methods: FORM and SORM methods. Response surface method. 10. Direct Optimized Probabilistic Computation - DOProC I.: Incorporation of the Direct Optimized Probability Computation Method into the overview of probability methods, substance of the method, basic computational algorithm, DOProC method application in ProbCalc programming system, demonstration of calculation. 11. Direct Optimized Probabilistic Computation - DOProC II.: Optimization techniques in DOProC method, theoretical principles of individual optimization techniques, examples of calculation using individual optimization procedures, recommended optimization techniques utilization in probability calculations by DOProC method. 12. Direct Optimized Probabilistic Computation - DOProC III.: Demonstrations of application software using the DOProC method. 13. Reliability and safety of building structures: Probabilistic approach to assessment of reliability and safety of building structures, calculation of probability of failure: load effect, resistance of the structure, computational model, reliability function, reliability index, target probability. Design working life of a structure. 14. Sample examples of selected probability tasks.

Conditions for subject completion

Full-time form (validity from: 2019/2020 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 35  18
        Examination Examination 65  30
Mandatory attendence parzicipation: 70%

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Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2021/2022 (N0732A260004) Civil Engineering - Building Structures P English Ostrava 1 Compulsory study plan
2021/2022 (N0732A260004) Civil Engineering - Building Structures K English Ostrava 1 Compulsory study plan
2020/2021 (N0732A260004) Civil Engineering - Building Structures K English Ostrava 1 Compulsory study plan
2020/2021 (N0732A260004) Civil Engineering - Building Structures P English Ostrava 1 Compulsory study plan
2019/2020 (N0732A260004) Civil Engineering - Building Structures P English Ostrava 1 Compulsory study plan
2019/2020 (N0732A260004) Civil Engineering - Building Structures K English Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner