Course detail

Theory of Reliability

FAST-NDB020Acad. year: 2024/2025

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

Mode of study

Not applicable.

Guarantor

prof. Ing. Drahomír Novák, DrSc.

Department

Institute of Structural Mechanics (STM)

Entry knowledge

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

Rules for evaluation and completion of the course

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

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.
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.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Not applicable.

Recommended reading

Not applicable.

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

prof. Ing. Drahomír Novák, DrSc.

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.
  • 11. 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 hod., compulsory

Teacher / Lecturer

prof. Ing. Drahomír Novák, DrSc.

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.