Textbook: None
Instructor: Goodarz Ahmadi (CAMP 267, 268-2322)
Office Hours: Monday and Wednesday 12:30 – 3:30 p.m.
Prerequisites: MA212, MA 330, Graduate Standing.

Course Learning Objectives

  • To provide the students with a fundamental understanding of probabilistic methods in engineering.
  • To familiarize the students with the stochastic processes.
  • To provide the students with the essential mathematical tools for handling random processes.
  • To familiarize the students with the stochastic simulation techniques.
  • To familiarize the students with the applications of probabilistic and stochastic methods in modern engineering problems.

Course Learning Outcomes

Objective 1

  • Students will be able to evaluate the statistical properties of random variables and can handle probabilistic transformations.

Objective 2

  • Students will become familiar with stationary and non-stationary stochastic processes, including Poisson, Winer, and white noise processes.
  • Students will be able to analyze linear stochastic differential equations with the use of spectral and correlation techniques.

Objective 3

  • Students will become familiar with Markov processes and the Langevin equation.
  • Students will be able to formulate the Fokker-Planck equation for linear and nonlinear stochastic differential equations.
  • Students will be able to analyze nonlinear stochastic differential equations with the use of perturbation and equivalent linearization techniques.
  • Students will become familiar with the concept of stochastic stability.

Objective 4

  • Students will perform stochastic simulations in their respective fields of interest.
  • Students will become familiar with the applications of stochastic processes in engineering, including random vibrations, turbulence, and related topics.

Course Outline

I. REVIEWS

II. INTRODUCTION TO THE THEORY OF PROBABILITY

III. RANDOM PROCESSES

IV. STOCHASTIC DIFFERENTIAL EQUATIONS

V. MARKOV PROCESSES

VI. NONLINEAR SYSTEM ANALYSIS

VII. RANDOM SYSTEMS

  • Stochastic Differential Equations with Random Coefficients
  • Stochastic Stability

VIII. APPLICATIONS

  • Random Vibrations
  • Vehicles on Rough Roads
  • Reliability
  • Linear Stochastic Estimation
  • Neural Networks, Machine Learning, and Big Data
  • Earthquake Response of Structures
  • Turbulent Fluid Flow
  • Dispersion and Diffusion Processes

Evaluation Methods

  • Homework 10%
  • Exam-1 25% – November 3, 2023, CAMP 178, 3:00-4:20 pm
  • Final Exam 40% – Final Exam Week
  • Projects 25% – Due December 1, 2023

Course Description

  • ME 529 Stochastic Process for Engineers R-3, C-3.
  • Prerequisites: Math 222 or equivalent.

Review of the theory of probability. Stochastic processes. Stationary and non-stationary processes. Time averaging and ergodicity. Correlation and power spectrum. Langevin’s equation and Markov processes. Poisson and Gaussian processes. Response of linear systems. Approximate methods for the analysis of nonlinear stochastic equations. Introduction to stochastic stability. Mean square and almost sure stability analysis. Random vibrations, turbulence, and other applications to engineering problems.

Exam & Homework Policies

Exam Policy

Exams will be open books with one book allowed.

Homework Policy

Homework will be collected as assigned. Homework will be graded and returned to the students.