Introduction to Non-Deterministic Approaches

In This Section

Introduction to Non-Deterministic Approaches


This course is offered as an introduction to methods and techniques used for modeling uncertainty. Fundamentals of probability and statistics are covered briefly to lay the groundwork, followed by overviews of each of the major branches of uncertainty assessment used to support component and system level life cycle activities, including: design, analysis, optimization, fabrication, testing, maintenance, qualification, and certification. Branches of Non-Deterministic Approaches (NDA) to be covered include: Fast Probability Methods (e.g., FORM, SORM, Advanced Mean Value, etc.), simulation methods such as Monte Carlo and Importance Sampling, surrogate methods such as Response Surface, as well as more advanced topics such as system reliability, time-dependent reliability, probabilistic finite element analysis, and reliability-based design. An overview of emerging non-probabilistic methods for performing uncertainty analysis will also be presented.

Key Topics:

  • Uncertainty and its role in engineering design and analysis
  • Fundamentals of probability and statistics including distribution selection
  • Classical and modern structural reliability including simulation methods
  • Surrogate models such as Response Surface and Kriging
  • Reliability-based design and optimization
  • Non-probabilistic methods

Who Should Attend:

This course is intended primarily for both engineers and managers involved with uncertainty modeling who are interested in learning about the far reaching capabilities of Non-Deterministic Approaches as taught from a broad perspective. Those individuals who will be attending the Annual Non-Deterministic Approaches Conference will benefit greatly from the layout of the course as it will provide a coherent overview of current and previous activity in Non-Deterministic Approaches.

Course Information:

Type of Course: Instructor-Led Short Course
Course Level: Fundamentals

Course scheduling available in the following formats:

  • Course at Conference
  • On-site Course
  • Stand-alone/Public Course

Course Length: 2 days
AIAA CEU's available: yes


Course Outline:

I. Probability & Statistics Fundamentals
A. Theory of Random Variables & Probability Distributions
B. Statistical Estimation & Distribution Identification


II. Classical Structural Reliability
A. Limit State Formulation
B. Probability Input Space Transformations
C. Second Moment Methods
D. Partial Safety Factor Method

III. Simulation Theory
A. Monte Carlo
B. Variance Reduction

IV. Fast Probability Methods
A. FORM/SORM & Advanced Mean Value
B. Advanced Importance and Latin Hypercube Sampling

V. Surrogate Models
A. Design of Experiments Fundamentals & Response Surface Methodology

VI. Reliability-Based Design and Optimization

VII. Time Dependent Reliability  

A. Degradation Failure Modes (Fatigue, Creep, Corrosion, Crack Growth)

VIII. Random Fields  

A. Probabilistic Finite Element Analysis

IX. System Reliability
A. Fault Tree Analysis & Reliability Block Diagrams
B. Markov Chains

X. Hybrid Methods
A. Genetic Algorithms & Simulated Annealing
B. Petri Nets

XI. Non-Probabilistic Methods
A. Interval and Possibility Theory
B. Fuzzy Sets & Neural Networks


Course Materials:

Since course notes will not be distributed onsite, AIAA and your course instructor are highly recommending that you bring your computer with the course notes already downloaded to the course.

Once you have registered for the course, these course notes are available about two weeks prior to the course event, and are available to you in perpetuity.



Course Instructor:

This course is organized and taught by TBD distinguished subject matter experts from the AIAA Non-Deterministic Approaches Technical Committee.

The instructors include:

Ben H. Thacker – Director, Materials Engineering Department, Southwest Research Institute in San Antonio, Texas (Ph.D. Civil Engineering, University of Texas at Austin, P.E., M. AIAA). Dr. Thacker’s areas of interest include computational mechanics, structural reliability, and computer methods development. He has been heavily involved in the development and application of probabilistic methods for over 16 years and has applied probabilistic methods to geo-mechanics, biomechanics, and other transient non-linear problems. He is an active member of the AIAA Structures Technical Committee and the ASME Standards Committee on Verification and Validation. Dr. Thacker has instructed at the “Probabilistic Analysis and Design: Computational Methods and Applications” annual short course at the Southwest Research Institute for over 20 years.

Michael P. Enright – Principal Engineer, Materials Engineering Department, Southwest Research Institute in San Antonio, Texas (Ph.D. Structural Engineering, University of Colorado at Boulder). Dr. Enright’s focus is on reliability-based life prediction of deteriorating structural and mechanical systems. His technical interests concentrate on probabilistic fatigue and fracture, and time-dependent system reliability. He is an active member of AIAA Non-Deterministic Approaches Committee and Structure Committee, and ASME Structures and Dynamics Committee. Dr. Enright has instructed at the “Probabilistic Analysis and Design: Computational Methods and Applications” annual short course at the Southwest Research Institute.

Sankaran Mahadevan – Professor of Civil & Environmental Engineering, Professor of Mechanical Engineering, Vanderbilt University (Ph.D Civil, Georgia Institute of Technology, 1988, M. AIAA). Professor Sankaran Mahadevan has over 18 years of research and teaching experience in risk and reliability engineering methods. His research contributions cover both basic and applied research topics. In basic research, he has made strong contributions to analytical and simulation-based reliability methods, reliability-based optimization, and model validation under uncertainty. He has applied these methods to civil structures, composite materials, automotive quality, aging aircraft, aging electronics, engines, and railroad wheels. His research has been funded by NASA, NSF, U.S. Army Research Office, U.S. Air Force, U.S. Army Corps of Engineers, Federal Highway Administration, General Motors, DaimlerChrysler, Union Pacific, and Sandia, Idaho and Oak Ridge National Laboratories. His research is documented in more than 200 technical publications, including 60 peer-reviewed journal articles.

Ramana V. Grandhi – Distinguished Professor, Dept. of Mechanical and Materials Engineering, Wright State University in Dayton, OH (Ph.D. Mechanical Engineering, Virginia Polytechnic Institute and State University, 1984). Dr. Grandhi’s expertise is in the fields of uncertainty quantification and multidisciplinary design and optimization, and he has been awarded numerous research contracts with the US Navy, US Air Force, NASA, and many industrial sponsors. He has nearly thirty years’ experience in the field of mechanical and materials engineering. He is a past General Chairman of the AIAA/NASA/USAF/ISSMO Multidisciplinary Analysis and Optimization Conference, and he was named an AIAA Fellow in May, 2005.