Please note! Course description is confirmed for two academic years (1.8.2018-31.7.2020), which means that in general, e.g. Learning outcomes, assessment methods and key content stays unchanged. However, via course syllabus, it is possible to specify or change the course execution in each realization of the course, such as how the contact sessions are organized, assessment methods weighted or materials used.


The aim of the course is to introduce the student to theoretical treatment random (stochastic) processes such as loads due to wave and wind on structures. After the course the student knows basics of probability concepts and how these are applied in mechanics; knows the random variables and how various probability distributions are connected; can apply time-domain measurements and convert them to frequency domain to define load spectrum in (spectral analysis) and can estimate the probability of exceedance of certain load from the load spectrum (extreme values). In addition the student can define the response (e.g. stress) for linear system (transfer function).

Credits: 5

Schedule: 08.09.2020 - 20.10.2020

Teacher in charge (valid 01.08.2020-31.07.2022): Jani Romanoff

Teacher in charge (applies in this implementation): Jani Romanoff

Contact information for the course (valid 11.08.2020-21.12.2112):

CEFR level (applies in this implementation):

Language of instruction and studies (valid 01.08.2020-31.07.2022):

Teaching language: English

Languages of study attainment: English


  • Valid 01.08.2020-31.07.2022:

    General description of random variables and their properties and continuous and discrete probability distributions. Introduction to random vibrations. Fourier-transformation of for random vibrations. Single degree of freedom system in frequency domain. Gaussian signal in time domain. Random vibrations of beams and strings. Peak and extreme value statistics. 

  • Applies in this implementation:

    1. Design process for random environment

    2. Refreshing probability and statistics

    3. Steady state process

    4. Spectral representation

    5. Environmental loads

    6. Response spectrum

    7. Numerical methods for random variables and processes

    8. Spectral moments

    9. Statistics for short and long term loads and responses

Assessment Methods and Criteria
  • Valid 01.08.2020-31.07.2022:

    The course utilizes problem-based-learning concept. The aim of the course is to identify, categorize, analyse and synthesize the random loads for selected engineering application. Tis goal is acchieved through 5 steps which include the identification of the problem, characterization of the environment, analysing the response for random exitation, definition of the short and long term responses and statistics (fatigue and ultimate limit states). Each week we define a subtask to be solved, lectures will be given and we conclude the week on question hour where students can ask questions related to their projects. Each week the student groups (3-5 persons) return a written report showing in the form of living document that build the course report in steps. The weekly submissions will be graded from 1-5.

    The weekly submissions will contribute up to 40% of the course grade, while the final summaririzing submission gives 10%. The remaining 50% of the grade is defined by the final exam or learning diary. The grading is based 50% on technical contents, 20% on using techical aids, 15% on reporting and 15% on reflection previous studies.  

  • Applies in this implementation:

    The assessment is done in two steps. In first step initial evaluation is carried out along with the proposals for improvement. In the second step the revised submission is graded. This will be part of the entire course evaluation. 

  • Valid 01.08.2020-31.07.2022:

    Lectures: 20h (2 x 2h/week, 10 sessions)

    Instructed exercises: 5 (1 x 1h/week, 5 sessions)

    Home assignments: 50 (5 x 10hours/week)

    Studying materials: 50 (5 x 10hours/week)

    Preparing for exams: 10 hours

  • Applies in this implementation:

    The work load details are based on the experiences from previous years. 


Study Material
  • Valid 01.08.2020-31.07.2022:

    Lecture notes

    Selected articles

    J.J.H. Brouwers, Stochastic Processes in Mechanical Engineering , Eindhoven University of Technology

    Naess, A. and Moan, T. Stochastic Dynamics of Marine Structures , Cambridge University Press 


  • Valid 01.08.2020-31.07.2022:

    B.Sc. studies

SDG: Sustainable Development Goals

    7 Affordable and Clean Energy

    8 Decent Work and Economic Growth

    11 Sustainable Cities and Communities

    13 Climate Action

    14 Life Below Water

    15 Life on Land



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