2016 | Stochastic Systems - TOKYO TECH OCW

2016　Stochastic Systems

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Academic unit or major: Graduate major in Systems and Control Engineering

Instructor(s): Kimura Koji

Class Format: Lecture

Media-enhanced courses

Day/Period(Room No.): Fri5-6(W934)

Group: -

Course number: SCE.A401

Credits: 1

Academic year: 2016

Offered quarter: 1Q

Syllabus updated: 2016/4/27

Lecture notes updated: -

Language used: English

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Syllabus

Course description and aims

Excitations such as earthquakes, wind loads and sea waves are influenced by many uncertain factors. Their wave forms fluctuate randomly over time and identical waveforms cannot be observed. This course focuses on considering how to approach these kinds of problems. The course also presents the probabilistic viewpoints and methods, and the basic concepts for introducing them to the problems of system dynamics.

Student learning outcomes

By the end of this course, the students will be able to:
1) Understand the basic concepts of stochastic systems
2) Have a probabilistic viewpoint to random or uncertain phenomena
3) Learn the methods of stochastic response analysis

Keywords

Probabilistic Viewpoint, Stochastic Systems, Random Vibration, Correlation Function, Power Spectrum, Stochastic Response Analysis

Competencies that will be developed

✔ Specialist skills

Intercultural skills

Communication skills

Critical thinking skills

Practical and/or problem-solving skills

Class flow

At the beginning of each class, the points of the previous class are reviewed. Towards the end of class, the subjects planned on that day will be explained and discussed.

Course schedule/Required learning

	Course schedule	Required learning
Class 1	Stochastic Systems 　－Probabilistic viewpoint, Random phenomena, Uncertain phenomena, Random vibration	Various kinds of random or uncertain phenomena
Class 2	Probability Theory 　－Sample space and probability, Random variables, Probability distribution function	Understanding of random variables
Class 3	Probability Theory 　－Characteristic function,　Independence and correlation Stochastic Processes 　－Sample function, Probability distribution function, Mean and correation function	From probability theory to stochastic prosesses
Class 4	Stochastic Processes 　－Stationary process, Ergodicity, Autocorrelation function and power spectrum	Correlation function and spectrum
Class 5	Random Vibration 　－Single DOF systems, Stationary responses	Stationary random vibration analysis
Class 6	Stochastic Response Analysis 　－Mean square response, Moment equations, Nonstationary responses	Derivation of moment equations
Class 7	Higher Order Moments, Reliability 　－Non-Gaussianity, Level crossing problem	Concept of higher order moments
Class 8	Stochastic Systems 　－Stochastic systems in various research fields	Stochastic systems in various research fields

Textbook(s)

None required

Reference books, course materials, etc.

None required

Assessment criteria and methods

1) Students will be assessed on their understanding of the basic theory and its application associated with stochastic system.
2) Students’ course scores are based on exercise problems and course report.

Related courses

SCE.I202 ： Random Signal Processing
SCE.M303 ： Theory of Vibration

Prerequisites (i.e., required knowledge, skills, courses, etc.)

No prerequisites are necessary, but enrollment in the related courses is desirable.

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