Gurantor department | Department of Structural Mechanics | Credits | 4 |

Subject guarantor | prof. Ing. Martin Krejsa, Ph.D. | Subject version guarantor | prof. Ing. Martin Krejsa, Ph.D. |

Study level | undergraduate or graduate | Requirement | Optional |

Year | 1 | Semester | summer |

Study language | Czech | ||

Year of introduction | 2013/2014 | Year of cancellation | 2020/2021 |

Intended for the faculties | FAST | Intended for study types | Follow-up Master |

Instruction secured by | |||
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Login | Name | Tuitor | Teacher giving lectures |

KON09 | doc. Ing. Petr Konečný, Ph.D. | ||

KRE13 | prof. Ing. Martin Krejsa, Ph.D. | ||

MIC60 | Ing. Vladimíra Michalcová, Ph.D. |

Extent of instruction for forms of study | ||
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Form of study | Way of compl. | Extent |

Full-time | Credit and Examination | 2+2 |

Part-time | Examination | 16+0 |

The aim of the course Probabilistic Methods 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.

Lectures

Tutorials

Project work

In this subject, students learn theoretical background and practical information about probabilistic calculations of civil engineering structures. For that purpose, they should master the probability and mathematical statistics 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 or probabilistic distribution.

1. Melchers, R.E.: Structural Reliability Analysis and Prediction}. Second edition, John Wiley & Sons Ltd., England, 1999. (437 s) ISBN 0-471-98324-1.
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.
3. O. Ditlevsen and H.O. Madsen: Structural Reliability Methods, Technical University of Denmark, 2005.

1. FReET (Feasible Reliability Engineering Tool) - http://www.freet.cz/
2. Simulation Based Reliability Assessment – SBRA - http://www.sbra-anthill.com/

At least 70% attendance at the exercises. Absence, up to a maximum of 30%, must be excused and the apology must be accepted by the teacher (the teacher decides to recognize the reason for the excuse).
Tasks assigned on the exercises must be hand in within the dates set by the teacher.

Subject has no prerequisities.

Subject has no co-requisities.

1. Probabilistic Methods in Civil Engineering: Introduction to the theory of probability and mathematical statistics, background standards for structural design (Eurocodes) in connection with the assessment of structural reliability, uncertainty in the design and assessment of structures, limit states.
2. Probabilistic representation of random variables: Basic concepts of probability theory. Random event, the probability of random event. Conditional probability. Random variable (discrete and continuous). frequency and distribution functions, basic probability distributions of random variables, random variables. Approximation limited probability distribution, histograms and their design based on measured data.
3. Monte Carlo simulation method: Incorporating Monte Carlo methods to overview probabilistic methods, history of Monte Carlo, Buffon needle, the first systematic use of Monte Carlo. The law of large numbers, generators (pseudo) random numbers. Numerical integration by Monte Carlo. The demonstration elementary calculation method.
4. Simulation Based Reliability Assessment Method (SBRA): The inclusion of the SBRA method to overview probabilistic methods, principles simulation methods SBRA, reliability assessment method SBRA (random variables, computer model, the analysis of the reliability function) demonstration of probabilistic calculations by SBRA. Computing stochastic model with random variables, concepts, structural resistance and load effect, the reliability function, reliability condition, limit states and their application in the stochastic model, the calculation of the failure probability, the probability of the design.
5. Parametric probability distribution of a continuous random variable: Overview of important continuous probability distribution, normal (Gaussian) probability distribution, lognormal probability distribution. The programming tool Histana: approximation of parametric probability distribution of the trimmed histogram creation of parametric probability distributions entering the statistical moments - parameters or processing of measured values - the raw data. Choosing an appropriate parametric distribution using the coefficient of tightness or residual sum of squares.
6. Stratified and advanced simulation methods: The inclusion of stratified and advanced simulation methods to overview probabilistic methods. Latin Hypercube Sampling Method - LHS, Principle, application of the program FREET: Assignment of random input variables, enter the statistical dependence input values, calculation simulation, computational model definition, analysis of the results of the simulation calculation, calculation examples. Main characteristics of other types of simulation methods. Importance Sampling Method.
7. Numerical method Direct Optimalized Probabilistic Solution-POPV: The inclusion of the Direct Optimized Probabilistic Method to overview probabilistic methods, Principle, basic computing algorithm, application of POPV programming system ProbCalc, examples of calculation.
8. Direct Optimalized Probabilistic Solution-POPV: Optimization techniques in the method POPV, theoretical principles of individual optimization techniques, examples of the calculation using different optimization procedures, recommended the use of optimization techniques in probabilistic calculation method POPV.
9. Direct Optimalized Probabilistic Solution-POPV: Examples of application software, using the methods POPV: stand-alone system for the design of the anchor reinforcement of mines, software for the calculation of the probability of fatigue crack spreading.
10. Reliability and safety of building structures: The probabilistic approach for assessing the reliability and safety of the construction of supporting structures, the calculation of the probability of failure: the effect of load resistance of the structure, computer model, the reliability function, failure rate, an indicator of confidence: design failure probability, reliability index. The design life of the structure.
11. Introduction to Risk Engineering.

Task name | Type of task | Max. number of points
(act. for subtasks) | Min. number of points |
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Examination | Examination | 100 | 51 |

Show history

Academic year | Programme | Field of study | Spec. | Zaměření | Form | Study language | Tut. centre | Year | W | S | Type of duty | |
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2018/2019 | (N3607) Civil Engineering | (3607T040) Building Environment | (01) Building Services | K | Czech | Ostrava | 1 | Optional | study plan | |||

2018/2019 | (N3607) Civil Engineering | (3607T040) Building Environment | (01) Building Services | P | Czech | Ostrava | 1 | Optional | study plan | |||

2018/2019 | (N3607) Civil Engineering | (3607T040) Building Environment | (02) Building Physics | P | Czech | Ostrava | 1 | Optional | study plan | |||

2017/2018 | (N3607) Civil Engineering | (3607T040) Building Environment | (01) Building Services | P | Czech | Ostrava | 1 | Optional | study plan | |||

2017/2018 | (N3607) Civil Engineering | (3607T040) Building Environment | (02) Building Physics | P | Czech | Ostrava | 1 | Optional | study plan | |||

2017/2018 | (N3607) Civil Engineering | (3607T040) Building Environment | (01) Building Services | K | Czech | Ostrava | 1 | Optional | study plan | |||

2016/2017 | (N3607) Civil Engineering | (3607T040) Building Environment | (02) Building Physics | P | Czech | Ostrava | 1 | Optional | study plan | |||

2016/2017 | (N3607) Civil Engineering | (3607T040) Building Environment | (01) Building Services | P | Czech | Ostrava | 1 | Optional | study plan | |||

2016/2017 | (N3607) Civil Engineering | (3607T040) Building Environment | (01) Building Services | K | Czech | Ostrava | 1 | Optional | study plan | |||

2015/2016 | (N3607) Civil Engineering | (3607T040) Building Environment | (01) Building Services | P | Czech | Ostrava | 1 | Optional | study plan | |||

2015/2016 | (N3607) Civil Engineering | (3607T040) Building Environment | (02) Building Physics | P | Czech | Ostrava | 1 | Optional | study plan | |||

2015/2016 | (N3607) Civil Engineering | (3607T040) Building Environment | (01) Building Services | K | Czech | Ostrava | 1 | Optional | study plan | |||

2014/2015 | (N3607) Civil Engineering | (3607T040) Building Environment | (01) Building Services | P | Czech | Ostrava | 1 | Optional | study plan | |||

2014/2015 | (N3607) Civil Engineering | (3607T040) Building Environment | (02) Building Physics | P | Czech | Ostrava | 1 | Optional | study plan | |||

2014/2015 | (N3607) Civil Engineering | (3607T040) Building Environment | (01) Building Services | K | Czech | Ostrava | 1 | Optional | study plan | |||

2014/2015 | (N3607) Civil Engineering | (3607T040) Building Environment | (02) Building Physics | K | Czech | Ostrava | 1 | Optional | study plan | |||

2013/2014 | (N3607) Civil Engineering | (3607T040) Building Environment | (01) Building Services | P | Czech | Ostrava | 1 | Optional | study plan | |||

2013/2014 | (N3607) Civil Engineering | (3607T040) Building Environment | (02) Building Physics | P | Czech | Ostrava | 1 | Optional | study plan | |||

2013/2014 | (N3607) Civil Engineering | (3607T040) Building Environment | (01) Building Services | K | Czech | Ostrava | 1 | Optional | study plan | |||

2013/2014 | (N3607) Civil Engineering | (3607T040) Building Environment | (02) Building Physics | K | Czech | Ostrava | 1 | Optional | study plan |

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