2017 Stochastic Systems

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Academic unit or major
Graduate major in Systems and Control Engineering
Kimura Koji 
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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


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


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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