Course Syllabus

AOE 6984 Reliability-Based Design Optimization

Instructor Information

Prof. Canfield, 214 Randolph Hall, 231-5981,
  • Class hours: 10:10AM - 11:00AM MWF, RANDolph 222
  • Office hours: 2:30PM - 4:00PM MWF, RANDolph 214 (or by appointment)

Catalog Description

Analyze the uncertainties associated with mechanical and structural design. Methods to model various uncertainties in a design using probabilistic analysis tools. Computation of safety index and structural reliability using efficient techniques for implicit functions.
 (3H, 3C)

AOE 4084, 5064, or 5734, or ECE 5734, or ISE 5406, or MATH 5486, or ME 5584, or equivalent. 

Required Course Textbook

Choi, Seung-Kyum; Grandhi, Ramana; and Canfield, Robert A., Reliability-Based Structural Design, Springer-Verlag, London, ISBN 978-1-84628-445-8, 2007

Online text:
VT Library digital text:

Supplemental Reference

Holdar, Achintya; and Mahadevan, Sankaran, Probability, Reliability and Statistical Methods in Engineering Design, John Wiley & Sons, New York, ISBN 0-471-33119-3, 2000

Course Objectives

Having successfully completed this course, a student will be able to:
  • Describe need to assess uncertainties in loads, geometry, materials, manufacturing processes, and operational environment when designing structures.
  • Identify reliability assessment techniques that may provide guidance for robust designs.
  • Recommend how further analysis, testing, or quality control may increase safety and efficiency of a structural design.
  • Discuss the use of common concepts from statistics, such as probability distributions, cumulative distribution functions, joint density and distribution functions, and measures of central tendency, dispersion, and correlation, as applied to structural design.
  • Select appropriate probability distributions for particular types of uncertainty, including Gaussian, Log-normal, gamma, extreme value, Weibull, and exponential distributions.
  • Fit curves to data using least-squares regression.
  • Distinguish between random variables and random fields.
  • Numerically approximate probability of failure using Monte Carlo simulation, importance sampling, and Latin hypercube sampling.
  • Numerically calculate reliability using first-order and second-order reliability methods.
  • Construct stochastic expansions for probabilistic analysis, including polynomial chaos expansion, Karhunen-Loeve transform, and spectral stochastic finite element method
  • Formulate and solve reliability-based structural optimization problems.

Course Schedule (Syllabus)

Administration & Review
Uncertainty & Reliability
Probability Distributions
Random Fields & Regression
Structural Reliability & Sampling Methods
Stochastic Finite Element Method
First- and Second-Order Reliability Method
Structural Reliability Applications
Midterm Test & Project Presentations
Reliability-Based Structural Optimization
Polynomial Chaos Expansion
Karhunen-Love Transform
Probabilistic Analysis Examples
Stochastic Optimization
Final Project Presentations

Administrative dates and information for this class are provided by the Office of the Registrar: 

Spring 2016 Calendar

Grading Policy

Homework & Class Participation 35%
 In-Class Test 1 20%
 In-Class Test 2 20%
 Final Project 25%

Tests will be graded on a standard numeric scale. If the mean is below a B, then scaled T-scores* may be used to determine letter grade for the test. 

Grading Scale
 A  >= 93
 A–  >= 90
 B+  >= 87
 B  >= 83
 B–  >= 80
 C+  >= 77
 C  >= 73
 C–  >= 70
 D+  >= 67
 D  >= 63
 D–  >= 60
 F  >= 0

Each homework problem and the final project will be graded on the following letter grade scale. The homework letter grades will be converted to a numeric score, according the the test grading scale, incorporating class participation.

Homework and Project Grades
A Correct Answer and Method
B Correct Method
C Nice Try
D No Clue
F No Attempt

Students are encouraged to discuss homework problems with one another and may compare approach and results, but they are expected to turn in their own, individual work. Do not share computer code. Submit only assignments that are your own work.

The final project grade will be based on midterm and final class presentations and a final written report, equally weighted.

*The article "Testing Memo 6: What kind of Grades Should be Averaged?" explains T-scores.

Honor System

Students shall work independently on tests, exams, and projects and submit only their own work. Students are permitted to discuss homework problems in groups, but they are expected to turn in their own, individual work. Computer programming code may not be shared, copied, or distributed among students before an assignment is due.

Student and instructor behavior in this class is governed by the Virginia Tech Honor Code and its core values:

  • Mutual Trust
  • Intellectual Honesty
  • Honesty and Integrity promote quest for Truth
All assignments submitted shall be considered graded work and shall be completed on an individual basis, unless otherwise stated. While discussing assignments and getting help outside of class is both authorized and encouraged, copying solutions from any source is considered a violation, as is sharing or re-use of an unauthorized (i.e., not provided or authorized by the instructor) computer file in full or in part. Honesty in your academic work will develop into professional integrity. The faculty and students of Virginia Tech will not tolerate academic dishonesty. It is your responsibility to seek clarification if there is a question about how the Honor Code applies to a given assignment.

Attendance and Classroom Behavior

Virginia Tech has a class attendance policy. Class meetings are an integral part of most courses and are the central component of many. Students and faculty are expected to attend class at all regularly scheduled times, except for cancellations announced on a university wide basis by the appropriate authority. When students cannot attend a class, it is their responsibility, as soon as possible, to consult with the course instructor about missed work or tests.

Students are expected to respect one another and the instructors in and outside the classroom. Computers may be used in the classroom only for viewing material for this course or for taking notes. Accessing audio, images, or videos during class may be distracting to other students and is strictly prohibited. Cell phone use is prohibited, except as a student response system.

Policy for Making Up Assignments

Requests to make up for a missed test or assignment must be made by notifying the instructor in advance of the scheduled due date. Requests due to absences shall be documented through the the Dean of Students, who can verify your absence and notify all of your instructors at once. In case of absences for health reasons, Schiffert Health Center medical staff can verify that you have been given medical treatment. For family or personal emergencies, students should consult with Dean of Students Office, who will notify the Associate Dean of Academic Affairs for Engineering. Circumstances out of the student's control, such as illness, a death in the family, or making a presentation at a professional conference, shall normally be considered an excused absence that justifies the request. Circumstances within the student's control are normally considered an unexcused absence for which a make-up request may be denied.

Unscheduled or undocumented requests will be granted or denied at the discretion of the instructor. The make-up test may be an oral exam.

Students may not discuss with other students a test being made up in between the time the student and the class take the test.

Students with Special Needs

Reasonable and appropriate academic accommodations will be made for students who provide documentation of disability and request for such accommodation.

Please inform the instructor and teaching assistant within the first two weeks of class of potential conflicts that may arise due to participation in religious or ethnic holiday events.

Emergency Preparedness

Final Project (Exam)

The final project report will be due on May 9, 2016.

Course Summary:

Date Details