Topic outline

  • General

    The aim of the course is to introduce the student to theoretical treatment random (stochastic) processes such as loads due to wave, wind and road on structures. We aim to give the student the basic knowledge of probability concepts and how these are applied in mechanics when random excitation and response to this is to be assessed. For this we need to give information of the random variables and how various probability distributions are connected. Then we need to learn to use the tools to apply time-domain measurements and convert them to frequency domain and to define load spectrum in (spectral analysis). These methods are used to estimate the probability of exceedance of certain load from the load spectrum (extreme values, or long term cumulative fatigue loading). 

    The course utilizes problem-based-learning concept. The aim of the course is to identify, categorize, analyze and synthesize the random loads for selected engineering application, that means:

    1. Identification of the problem from the mission,

    2. Characterization of the environment through spectra and probability distributions,

    3. Analyzing the response for random excitation by using linearity assumption in the process,

    4. Definition of the short and long term responses and related statistics (for fatigue and ultimate limit states).

    Each week:

    The students get acquainted with lecture material and send questions related to that prior the lecture·

    We define a subtask to be solved

    Lectures will be given

    We conclude the week on question hour where students can ask questions related to their projects

    Student group completes the weekly assignment and reads the next weeks materials

    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 50% of the course grade; see Assignments -section for the detailed instructions. The remaining 50% of the grade is defined by the final exam. 

    Lectures on-line (use the zoom event in the end of this page to join) 

    Week 1: Mission and probability basics

    Tuesday, September 8th 2020, 08:00-10:00, Design process as a whole

    Wednesday, September 9th 2020, 12:00-14:00, Statistics and probability concepts

    Weeks 2: Stationary process

    Tuesday, September 15th 2020, 08:00-10:00, Stationary response of single frequency

    Wednesday, September 16th 2020, 12:00-14:00, Stationary response of multiple frequencies

    Weeks 3: Spectral treatment of environment

    Tuesday, September 22nd 2020, 08:00-10:00, Environmental spectrum

    Wednesday, September 23rd 2020, 12:00-14:00, Response spectrum

    Week 4: Numerical methods

    Tuesday, September 29th 2020, 08:00-10:00, Numerical methods 

    Week 5: Probability from spectra

    Tuesday, October 6th 2020, 08:00-10:00, Spectral moments

    Wednesday, October 7th 2020, 12:00-14:00, Short- and long-term statistics

    Week 6: Polishing the course assignments and preparing for exam

    Week 7: Exam, Tuesday, October 20th 2020, 09:00-12:00, Teams