Course detail

# Theory of Reliability

FAST-CD006Acad. year: 2022/2023

Introduction of reliability theory, reliability background of standards for structural design (Eurocodes), Structural resistance and load action as two independent random variables, limit state and philosophy of design by standards, theoretical failure probability, reliability conditions, reliability reserve, reliability index, numerical simulation method Monte Carlo, Latin Hypercube Sampling, Importace Sampling, basic methods for failure probability analysis of structures designed by standards for design, basic methods for statistics, sensitivity and probabilistic analysis application to steel structures design. Introduction into risk engineering.

Language of instruction

Czech

Number of ECTS credits

4

Mode of study

Not applicable.

Department

Institute of Structural Mechanics (STM)

Learning outcomes of the course unit

Student will learn basic knowledge from reliability theory: creation of stochastic model, reliability condition, numerical simulation methods of Monte Carlo type, limit states, risk engineering.

Prerequisites

Knowledge from Elasticity and plasticity, Structural mechanic, Probability and statistics.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Not applicable.

Course curriculum

1.Introduction of reliability theory, reliability background of standards for structural design (Eurocodes), structural resistance and load action as two independent random variables, reliability condition, reserve of reliability.
2.Limit state and philosophy of design by standards.
3.Reliability standards: theoretical failure probability, reliability index.
4.Aproximační metody FORM a SORM.
5.Numerical simulation method Monte Carlo in applications.
6.Computation model, model uncertainty, grosses errors.
7.Numerical simulation methods Latine Hypercube Sampling, Importace Sampling in applications.
8.Random process and random fields – Stochastic finite element methods and these applications.
9.Probabilistic optimization, problems of live-time of structures, use of statistics and sensitivity analysis for design of structures and verification and calibration of standards design procedures.
10.Imperfections analysis and this influence to failure of steel structures.
l1.Unbalanced of the failure probability of the structures designed by standards, option of input variability modelling.
12.Introduction of Risk engineering.
13.Reliability software - replenishment, conclusion and recapitulate.

Work placements

Not applicable.

Aims

Students will get basic knowledge from reliability theory: creation of stochastic model, reliability condition, numerical simulation methods of Monte Carlo type, limit states, risk engineering.

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

Extent and forms are specified by guarantor’s regulation updated for every academic year.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Not applicable.

Recommended reading

Not applicable.

Classification of course in study plans

• Programme N-P-E-SI (N) Master's

branch S , 1. year of study, summer semester, compulsory

• Programme N-K-C-SI (N) Master's

branch S , 1. year of study, summer semester, compulsory

• Programme N-P-C-SI (N) Master's

branch S , 1. year of study, summer semester, compulsory

#### Type of course unit

Lecture

26 hours, optionally

Teacher / Lecturer

Syllabus

1.Introduction of reliability theory, reliability background of standards for structural design (Eurocodes), structural resistance and load action as two independent random variables, reliability condition, reserve of reliability. 2.Limit state and philosophy of design by standards. 3.Reliability standards: theoretical failure probability, reliability index. 4.Aproximační metody FORM a SORM. 5.Numerical simulation method Monte Carlo in applications. 6.Computation model, model uncertainty, grosses errors. 7.Numerical simulation methods Latine Hypercube Sampling, Importace Sampling in applications. 8.Random process and random fields – Stochastic finite element methods and these applications. 9.Probabilistic optimization, problems of live-time of structures, use of statistics and sensitivity analysis for design of structures and verification and calibration of standards design procedures. 10.Imperfections analysis and this influence to failure of steel structures. l1.Unbalanced of the failure probability of the structures designed by standards, option of input variability modelling. 12.Introduction of Risk engineering. 13.Reliability software - replenishment, conclusion and recapitulate.

Exercise

13 hours, compulsory

Teacher / Lecturer

Syllabus

1. Recapitulation of probability and statistics using simple examples. 2. Examples on usage of Cornell reliability index. 3. Simple example to learn Monte Carlo simulation method using Excel. 4. Calculations of failure probability via Latin Hypercube Sampling in Excel. 5. Introduction to individual semestral project. 6. - 7. Work on individual semestral projects.