Probabilistic Mechanics and Reliability

Code:

PRODEM077

Acronym:

MPF

Keywords
Classification	Keyword
OFICIAL	Mechanical Engineering

Instance: 2023/2024 - 1S

Active?	Yes
Responsible unit:	Mathematics Section
Course/CS Responsible:	Doctoral Program in Mechanical Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
PRODEM	0	Syllabus since 2009/10	1	-	6	28	162

Teaching language

Suitable for English-speaking students

Objectives

SPECIFIC AIMS:
The main objectives are to understand probability and stocahstic processes concepts, and its application to Mechanical Engineering problems with particular emphasis on uncertainty modeling and on mechanical systems reliability.

Learning outcomes and competences

LEARNING OUTCOMES:

At the end of lecture period the students should be able to perform the following aspects:
1 – understand the general concepts on stochastic processes;
2 – evaluate and analyse the uncertainty propagation on response of mechanical systems;
3 – evaluate the reliability of mechanical systems;
4 – consider the uncertainty into robust design of mechanical systems.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Knowledge of Mathematics and Statistics.

Program

I –Probability theory: conditional probabilities; random variables and most important distributions.
II - General concepts on stochastic processes. Markov processes. Random walk. Poisson process. Gaussian processes. Brownian motion. White noise process.
III - Simulation of random systems with one or several random variables: generation of random numbers; Monte Carlo method.
IV - Uncertainty analysis of mechanical systems: sensitivity index; equations for the uncertainties propagation.
V - Reliability of mechanical systems: “limit state function”; first and second order methods for reliability analysis.
VI - Applications: structural reliability; reliability of technologic processes; robust design of mechanical systems.

Mandatory literature

Grimmett, Geoffrey R.; Probability and Random Processes. ISBN: 0-19-857222-0
Ayyub, Bilal M.; Probability, statistics, & reliability for engineers. ISBN: 0-8493-2690-7
Melchers, Robert E.; Structural reliability analysis and prediction. ISBN: 0-471-98771-9
Kleiber, Michael; The stochastic finite element method. ISBN: 0-471-93626-X

Complementary Bibliography

Sergio E. Serrano; Engineering uncertainty and risk analysis, HydroScience Inc., 2001. ISBN: 0-9655643-8-X

Teaching methods and learning activities

The course will consist of oral expositions of the program, complemented by the resolution of application problems.

keywords

Physical sciences > Mathematics > Applied mathematics > Engineering mathematics

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Designation	Weight (%)
Teste	60,00
Trabalho escrito	40,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Estudo autónomo	70,00
Trabalho de investigação	30,00
Total:	100,00

Eligibility for exams

To attain frequency, the student must not exceed the absence limit allowed in Article 4 of the General Evaluation Rules of FEUP.

Calculation formula of final grade

Written examination and one individual work.

Examinations or Special Assignments

Research work with report. 

Internship work/project

N/A

 

Special assessment (TE, DA, ...)

Written examination.

Classification improvement

Classification improvement will be exclusively the result of the written exam according to General Evaluation Rules of FEUP.

Observations

N/A