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SE 5102: Uncertainty Analysis, Robust Design, and Optimization, Spring 2021

Course Instructor: Prof. Matthew D. Stuber, PhD

Email: matthew.stuber@uconn.edu (response within 24 hours)

Use the email subject preamble “S21 SE5102”

Availability: Thu 5-7PM or by appointment.

Catalog Description. 3 credits. Provides students with a thorough understanding of

mathematical optimization and uncertainty analysis for the robust design of cyberphysical

systems. Topics include optimization theory and practice, uncertainty modeling, sensitivity

analysis, and formal and classical model-based robust design methodologies.

Recommended Preparation: Background in numerical analysis and comfort with a

programming language (MATLAB).

Intended Audience. The course is designed for all graduate students in systems engineering.

Course Delivery Method. The course will be offered online, asynchronously, in small,

recorded modules according to the course schedule and syllabus. Direct and live

communication with the instructor will be available each week, according to the class schedule,

for discussion, questions, examples, and quizzes. Attendance at live sessions is strongly

recommended, and you should notify the instructor in advance if you cannot attend. Live

sessions will be conducted via WebEx.

WebEx Address: https://uconn-cmr.webex.com/meet/stuber

Course Materials Required course materials should be obtained before the first day of class. All required reading

materials are provided digitally via HuskyCT. Required software can be downloaded from

https://software.uconn.edu and installed on your machine (recommended) or accessed

remotely using the UConn AnyWare system at https://software.uconn.edu/uconn-software-

online/ .

1. MathWorks® MATLAB™ Software Package

2. MiniTab® Software Package

3. Design for Six Sigma, Yang and El-Haik, McGraw-Hill, New York, 2003. (eBook, online)

4. Nonlinear Regression Modeling for Engineering Applications, Rhinehart, Wiley, New

Jersey, 2016. (eBook, online)

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Course Objectives. This course is designed to provide students with the foundations of

model-based methods for uncertainty analysis and robust design of process systems. Students

will develop skills in the areas of numerical analysis and optimization, uncertainty analysis in

design, sensitivity analysis in design, and robust design. Topics include modeling of

uncertainties, sensitivity analysis, robust design methodologies, and critical parameter

management. Anticipated Student Outcomes. By the end of SE 5102, a student will be able to:

(1) Apply optimization theory, methods, and software appropriate for your system.

(2) Predict effects of uncertainty using model-based uncertainty analysis.

(3) Formalize mathematically complex problems of robust design in systems engineering.

(4) Adapt model-based design approaches for an industry-relevant system.

(5) Analyze performance and safety of physical systems under uncertainty.

(6) Communicate rigorously mathematical findings.

Background Information Required on the Following Subjects:

(1) Thermodynamic cycles such as chillers or cabin air conditioning systems

(2) Mathematical modeling of physical systems

(3) Modelica, MATLAB and FMI tools for simulation of thermodynamic systems

Minimum Technical Skills To be successful in this course, you will need the following technical skills:

Use electronic mail with attachments.

Save files in commonly used word processing program formats.

Copy and paste text, graphics or hyperlinks.

Work within two or more browser windows simultaneously.

Open and access PDF files.

Course Organization. The course is organized into five learning modules:

(1) Numerical Analysis and Optimization

(2) Uncertainty Analysis and Quantification

(3) Sensitivity Analysis in Design

(4) Robust Design

(5) Flexibility Analysis

Course Outline. The structuring of these five learning modules into 14 lectures of a one

semester course, along with the topics and references, is described in the following. An

example system model, such as a chiller or cabin air conditioner from earlier pre-requisite

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courses, must be attained by each student team for use in this course as a project, and coded in

MATLAB.

-------------------------Module 1: Numerical Analysis and Optimization -------------------------

Lecture 1: Course Introduction – Jan. 21 Live Session

• Course layout

• Grading

Lecture 2: Optimization Preliminaries – Jan. 28 Live Session

• Introduction to notation

• Standardized formulation concepts

• Intro to Theory

Lecture 3: Optimization – Feb. 4 Live Session

• Convex Analysis

• Unconstrained Programming

Lecture 4: Optimization – Feb. 11 Live Session

• Constrained Programming

• Optimization-based design

---------------------------------Module 2: Uncertainty Analysis-----------------------------------

Lecture 5: Introduction to Uncertainty Analysis – Feb. 18 Live Session

• Types of uncertainty

• Accounting for Uncertainty in Design

• Propagation of Uncertainty

Lecture 6: Uncertainty Quantification – Feb. 25 Live Session

• Modeling Uncertainty

• Estimation of uncertainty distributions

• Operating conditions

• Margin analysis at operating points

Lecture 7: Model Validation and Parameter Estimation – Mar. 4 Live Session

• Estimation of uncertain parameters in modeling

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--------------------------------Module 3: Sensitivity Analysis---------------------------------------

Lecture 8: Introduction to Sensitivity Analysis – Mar. 11 Live Session

• Full Factorial experimentation. Partial factorial designs.

• Linear and quadratic term regression and ANOVA.

• MiniTab implementation of full factorial experiments.

Lecture 9: Sensitivity Analysis in Systems Designs – Mar. 18 Live Session

• Local Sensitivity Analysis

• Global Sensitivity Analysis

• Marginal costs

------------------------------------Module 4: Robust Design------------------------------------------

Lecture 10: Introduction to Robust Design – Mar. 25 Live Session

• Design under uncertainty

• Operations under uncertainty

• Min-max problem formulation

Lecture 11: Formal Robust Design Methodology – Apr. 1 Live Session

• Worst-case design

• Cutting-plane algorithms

• Marginal costs and the price of robustness

Lecture 12: Traditional Probabilistic Methodology – Apr. 8 Live Session

• Taguchi robust design and signal to noise ratios. Traditional factorial experimental

formulation.

• Critical parameter management

---------------------------------------Module 5: Flexibility Analysis--------------------------------

Lecture 13: Introduction to Flexibility in Systems Design and Analysis – Apr. 22 Live

Session

• Problem formulation

• Flexibility analysis metrics

Lecture 14: Course Summary/Final Project Presentations – Apr. 29 Live Session

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Grading. Student grades will be based upon: Homework 70%, Class Participation: 10%, Final

Project Report: 20%. Class participation grades are based on weekly accrual of 1 point for

engaging in the live WebEx session and 1 point for engaging in the HuskyCT discussion board.

Final grades will be assigned based on the following rubric:

Grade Percentage

A 95-100

A- 90-95

B+ 85-90

B 80-85

B- 75-80

C+ 70-75

C 65-70

F <65

Due Dates and Late Policy. All due dates will be identified in blackboard when the work

is posted. Deadlines are based on Eastern Standard Time; if you are in a different time zone,

please adjust your submittal times accordingly. The instructor reserves the right to change

dates accordingly as the semester progresses. All changes will be communicated in an

appropriate manner.

Homework Problem Sets. Homework problem sets will be posted on HuskyCT. Homework

assignment due dates/times will be given with the assignment. NO late homework will be

accepted as the homework will often be discussed in class. Each problem will be graded on a

scale of 0-100 with 80% being allocated to the problem solutions, and 20% being allocated to

the formatting (e.g., clarity, conciseness, organization, comments and discussion of code

(where appropriate), etc.). For problem sets with a design project component, around 40% of

the total points will be allocated to the design project problem.

Project, Presentations, and Project Report. A project is to be developed individually (or

possibly by groups, depending on enrollment) which is expected to evolve during the entirety

of the track. The project that is to be executed in this course refers mainly to the design project

identification, challenge quantification, significance, and relevance to the model-based design

philosophy (with respect to the robust design topics), and plan of attack. The final deliverable

(presentation and report) should identify all the aforementioned elements in a quantifiable

manner and strategy for solution. The final report should be 10 pages or less and adhere to

formal technical writing guidelines and mathematical rigor.

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Attendance. Students should make every effort to attend the live sessions and to talk with

students in the HuskyCT discussion board to get help and assistance from others. It is

extremely difficult to follow the class if sessions are missed.

Absences. Students involved in official University activities that conflict with class time must

inform the instructor in writing prior to the anticipated absence and take the initiative to make

up missed work in a timely fashion. In addition, students who will miss class for a religious

observance must “inform their instructor in writing within the first three weeks of the semester,

and prior to the anticipated absence, and should take the initiative to work out with the

instructor a schedule for making up missed work.”

Student Conduct. As a member of the University of Connecticut student community, you are

held to certain standards and academic policies. In addition, there are numerous resources

available to help you succeed in your academic work. Review these important standards,

policies, and resources, which include:

The Student Code

o Academic Integrity

o Resources on Avoiding Cheating and Plagiarism

Copyrighted Materials

Credit Hours and Workload

Netiquette and Communication

Adding or Dropping a Course

Academic Calendar

Policy Against Discrimination, Harassment, and Inappropriate Romantic

Relationships

Sexual Assault Reporting Policy

The University is committed to maintaining an environment free of discrimination or discriminatory

harassment directed toward any person or group within its community – students, employees, or visitors.

Academic and professional excellence can flourish only when each member of our community is assured

an atmosphere of mutual respect. All members of the University community are responsible for the

maintenance of an academic and work environment in which people are free to learn and work without

fear of discrimination or discriminatory harassment. In addition, inappropriate amorous relationships

can undermine the University's mission when those in positions of authority abuse or appear to abuse

their authority. To that end, and in accordance with federal and state law, the University prohibits

discrimination and discriminatory harassment, as well as inappropriate amorous relationships, and such

behavior will be met with appropriate disciplinary action, up to and including dismissal from the

University. Additionally, to protect the campus community, all non-confidential University employees

(including faculty) are required to report sexual assaults,

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intimate partner violence, and/or stalking involving a student that they witness or are told about to the

Office of Institutional Equity (OIE). Please be aware that while the information you provide will remain

private, it will not be confidential and will be shared with University officials who can help. An exception

to this reporting exists if students disclose information as a part of coursework submitted to an instructor

in connection with a course assignment. Even in the absence of such obligation, all Employees are

encouraged to contact OIE if they become aware of information that suggests a safety risk to the

University community or any member thereof. The University takes all reports with the utmost

seriousness. More information, including resources and reporting options, is available at

equity.uconn.edu and titleix.uconn.edu. https://community.uconn.edu/the-student-code-preamble/. Students are responsible for

adherence to the University of Connecticut student code of conduct. Pay attention to the

section on Student Academic Misconduct, “Academic misconduct is dishonest or unethical

academic behavior that includes, but is not limited, to misrepresenting mastery in an academic

area (e.g., cheating), intentionally or knowingly failing to properly credit information, research

or ideas to their rightful originators or representing such information, research or ideas as your

own (e.g., plagiarism).” Examples of academic misconduct in this class include but are not

limited to: copying solutions from the solutions manual, using solutions from students who

have taken this course in previous years, copying your friend’s homework, looking at another

student’s paper during an exam, lying to the professor or TA, and incorrectly filling out the

student workbook. Academic misconduct is treated very seriously with a zero-tolerance policy.

Students are advised to review UConn's academic misconduct FAQ:

https://community.uconn.edu/academic-misconduct/.

Any student caught deliberately or unwittingly violating the academic integrity policy will

receive an “F” for the course.

Adding or Dropping a Course. If you should decide to add or drop a course, there are

official procedures to follow:

● Matriculated students should add or drop a course through the Student

Administration System.

● Non-degree students should refer to Non-Degree Add/Drop Information located on

the registrar’s website.

You must officially drop a course to avoid receiving an "F" on your permanent transcript.

Simply discontinuing class or informing the instructor you want to drop does not constitute

an official drop of the course. For more information, refer to the online Graduate Catalog

Academic Calendar. The University's Academic Calendar contains important semester dates.

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Students with Disabilities. The University of Connecticut is committed to protecting the

rights of individuals with disabilities and assuring that the learning environment is

accessible. If you anticipate or experience physical or academic barriers based on disability or

pregnancy, please let me know immediately so that we can discuss options. Students who

require accommodations should contact the Center for Students with Disabilities, Wilbur Cross

Building Room 204, (860) 486-2020 or http://csd.uconn.edu/.

Blackboard measures and evaluates accessibility using two sets of standards: the WCAG 2.0

standards issued by the World Wide Web Consortium (W3C) and Section 508 of the

Rehabilitation Act issued in the United States federal government.” (Retrieved March 24, 2013

from Blackboard's website)

Software/Technical Requirements Students will need to have regular access to a computer (e.g., to complete homework, access

software or UConn AnyWhere computing resources) and communication equipment to

participate in the live WebEx sessions (e.g., telephone, microphone for PC, etc.).

The software/technical requirements for this course include:

HuskyCT/Blackboard (HuskyCT/ Blackboard Accessibility Statement, HuskyCT/ Black-

board Privacy Policy)

MiniTab (free to UConn students through software.uconn.edu) (MiniTab Accessibility

Statement, MiniTab Privacy Policy)

MATLAB (free to UConn students through software.uconn.edu) (MATLAB

Accessibility Statement, MATLAB Privacy Policy)

Adobe Acrobat Reader (Adobe Reader Accessibility Statement, Adobe Reader Privacy

Policy)

Google Apps (Google Apps Accessibility, Google for Education Privacy Policy)

Microsoft Office (free to UConn students through software.uconn.edu) (Microsoft

Accessibility Statement, Microsoft Privacy Statement)

Dedicated access to high-speed internet with a minimum speed of 1.5 Mbps (4 Mbps or

higher is recommended).

WebCam and microphone

For information on managing your privacy at the University of Connecticut, visit the

University's Privacy page.

NOTE: This course has NOT been designed for use with mobile devices.

Help. Technical and Academic Help provides a guide to technical and academic assistance.

This course is facilitated in an online format using the learning management platform,

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HuskyCT. If you have difficulty accessing HuskyCT, you have access to the in person/live

person support options available during regular business hours through the Help Center. You

also have 24x7 Course Support including access to live chat, phone, and support documents.

Copyright. Copyrighted materials within the course are only for the use of students enrolled

in the course for purposes associated with this course and may not be retained or further

disseminated.

Course Schedule* Date1 Topic Module Details

Jan. 19-Jan. 21 Course Introduction Homework 1, Due Jan. 29

Jan. 21-Jan. 28 Intro to Optimization 1 Homework 2, Due Feb. 5

Jan. 28-Feb. 4 Convex Analysis & Unconstrained Programming 1 Homework 3, Due Feb. 12

Feb. 4-Feb. 11 Constrained Programming & Optimal Design 1 Homework 4, Due Feb. 19

Feb. 11-Feb. 18 Uncertainty in Design 2 Homework 5, Due Feb. 26

Feb. 18-Feb. 25 Uncertainty Analysis 2 Homework 6, Due Mar. 5

Feb. 25-Mar. 4 Model Validation & Parameter Estimation 2 Homework 7, Due Mar. 12

Mar. 4-Mar. 11 Design of Experiments 3 Homework 8, Due Mar. 19

Mar. 11-Mar. 18 Sensitivity Analysis & Marginal Costs 3 Homework 9, Due Mar. 26

Mar. 18-Mar. 25 Design & Operations Under Uncertainty 4 Homework 10, Due Apr. 2

Mar. 25-Apr. 1 Formal Robust Design 4 Homework 11, Due Apr. 9

Apr. 1-Apr. 8 Probabilistic Robust Design 4 Homework 12, Due. Apr. 23

Apr. 8-Apr. 22 Flexibility Analysis 5 Work on Final

Apr. 29 Course Summary/Final Project Presentations

* Schedule is tentative and may change 1 First Date indicates release of lecture modules

Instructor’s Contact Information:

Matthew Stuber: matthew.stuber@uconn.edu Phone: (860)486-3689

Office Hours: Live Sessions Thursday, 5-7PM ET

Helpful Links:

Virtual Computer Lab at UConn: https://software.uconn.edu/uconn-software-online/

Course Material: https://lms.uconn.edu

Institute for Advanced Systems Engineering: http://www.utc-iase.uconn.edu/