# Theory of Random Vibration

(
Morikawa Hitoshi
)

Mon 5-6Session

Credits Lecture:2 Exercise:0 Experiment:0 / code:92008

Update syllabus：2006/12/20

Update lecture notes : 2006/12/20

Access Index :

Fall Semester

- Outline of lecture
- This course discusses the basic theory of probability and stochastic process with some applications to the earthquake engineering.

The grading policy is based on a project and its presentation.

Topics include introduction to the probability and stochastic process, basic idea of time-frequency analysis, and application to the earthquake engineering. - Purpose of lecture
- To understand the basics of probability theory, stationary and non-stationary stochastic processes, and time-frequency analysis. Furtermore, as an application of the theory of stationary stochastic process, the students may understand how to estimate the phase velocity of microseisms obtained from an array observation.
- Plan of lecture
- 1. Basics of probability theory

2. Stationary stochastic process

3. Spatial auto-correlation (SPAC) method to estimate the phase velocity of microtremors

4. Introduction to Time-frequency analysis

4.1 Spectrogram

4.2 Wigner distribution

4.3 Hilbert-Huang transform and Hilbert spectrum

7. Project

8. Presentation - Textbook and reference
- Choen, ""Time-Frequency Analysis,"" Prentice Hall, 1995
- Related and/or prerequisite courses
- basics of mathematics
- Evaluation
- Project and its presentation
- Supplement
- [Office Hours]

After the class (15:00-17:00, Monday)