Credits: 3

### Description

Prerequisite: MATH206 and ENME392.
Restriction: Permission of ENGR-Mechanical Engineering department.
Review of probabilistic distributions, introduction to pseudo-random number generation, and algorithms to produce probability distributions using Monte Carlo simulation via Matlab and other approaches to best design probabilistic engineering problems.

### Semesters Offered

Spring 2019, Spring 2020, Spring 2021

### Learning Objectives

• Develop an ability to solve basic probability problems using known distributions (e.g., normal, Poisson, Bernoulli, etc.)
• Understand how pseudo-random numbers are generated as well as maximizing the period until these numbers are repeated
• Develop an ability to simulate both discrete and continuous probability distributions using several well-known approaches such as:
• Inverse transformation method
• Central limit theorem (for normal distribution)
• Acceptance-Rejection method
• Explore queueing theory models and discrete-event simulation
• Understand the tradeoffs between increasing the number of simulation iterations and the variance of the simulated output  Develop an ability to apply several variance-reduction methods such as:
• Antithetic variables
• Control variates
• Understand and be able to apply Bayes theorem in engineering problems
• Be able to apply simulation methods to analyze two case studies in engineering
• Enhance a working knowledge of Matlab geared to solving Monte Carlo simulation problems

### Topics Covered

• Week 1:  Introduction, motivation for simulation, review of Matlab
• Week 2:  Probability review, Bernoulli & binonmial distribtions
• Week 3:  Uniform and triangular distributions, pseudo-random number generation
• Week 4:  Exponential and geometric distributions , normal distribution, lognormal distribution
• Week 5:  Generating discrete and continuous distributions for random variables
• Week 6:  Generating discrete and continuous distributions for random variables
• Week 7:  Normal distribution and Central Limit Theorem with relevance to simulation, in-class exam #1
• Week 8:  Specialized approaches for generating normal random variables
• Week 9:  Background on wind power and the Weibull distribution for wind speeds, Betz’ law for wind power, discussion of case study 1 on renewable energy
• Week 10:  Poisson distribution and Bayes theorem, goodness-of-fit measures
• Week 11:  Case study 1 final presentations, report of results, case study 2 overview, variance reduction techniques
• Week 12:  Variance reduction techniques, discrete event simulation and queueing disciplines
• Week 13:  Open class to discuss case study 2, in-class exam #2
• Week 14:  Case Study 2 final presentations, report of results, review for final exam
• Week 15: Final exam (in-class exam)

### Learning Outcomes

• an ability to apply knowledge of mathematics, science, and engineering
• an ability to design and conduct experiments, as well as to analyze and interpret data
• an ability to design a system, component, or process to meet desired needs within realistic constraints such as economic, environmental, social, political, ethical, health and safety, manufacturability, and sustainability
• an ability to function on multi-disciplinary teams
• an ability to identify, formulate, and solve engineering problems
• an ability to communicate effectively
• the broad education necessary to understand the impact of engineering solutions in a global, economic, environmental, and societal context
• a recognition of the need for, and an ability to engage in life-long learning
• a knowledge of contemporary issues
• an ability to use the techniques, skills, and modern engineering tools necessary for engineering practice

#### Instructor

Gabriel, Steven A.

#### Textbook

Simulation, Sheldon M. Ross, Fifth Edition, Academic Press, San Diego, 2013

#### Class/Laboratory Schedule

• Two 75 minute lectures each week
Last Updated By
Steven A. Gabriel, June 2017