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Introduction to Probabilistic Engineering Analysis

Introduction to Probabilistic Engineering Analysis

Introduction to Probabilistic Engineering Analysis

This course explores the role of uncertainty quantification in decision-making and model verification/validation within engineering contexts. It introduces the Cumulative and Probability Density Functions and different distribution models used to express uncertainties. The course covers the formulation of the response function, a critical tool in distinguishing between failure and safe regions in design space. Also covered is the Monte Carlo simulation, a method used to estimate the probability of failure in systems, along with discussions of alternatives like the Latin Hypercube Sampling.

T​he course is based on the session at the NAFEMS World Congress 2023, with the videos coming from the live session that was held at the event.


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Course Outline

1. Why uncertainty matters in engineering simulation

12 minutes

2. Random variables and limit states

19 minutes

3. Select probabilistic methods

22 minutes

4. Application example - Tensile strength

5 minutes

5. Application example - Longitudinal ship strength

5 minutes

6. Application example - Aircraft lever

7 minutes

​7. Outlook

C​ourse length

a​pp. 70 minutes


C​ourse Authors

David Riha

David Riha is a Staff Engineer in the Materials Engineering Department at Southwest Research Institute in San Antonio, Texas, USA. He has over 30 years of experience in probabilistic analysis and design, uncertainty quantification, model verification and validation. He is the lead developer of the NESSUS probabilistic analysis software. He applies this experience to applied reliability, uncertainty quantification, and model validation problems for aerospace, automotive, biomedical, petroleum, and defence industries. Currently he is leading efforts in integrated computation materials engineering (ICME) related to aerospace composite part manufacturing and fitness for service of aging infrastructures. He has a B.S. in aerospace engineering from the University of Texas at Austin and M.S. in mechanical engineering from the University of Texas at San Antonio.

A​lexander Karl

Alexander Karl holds a Master's and a PhD in Aerospace Technology from the University of Stuttgart. His career, which has been steadily advancing over the past 21 years, is rooted at Rolls-Royce. Alexander began his journey specialising in thermo-mechanical analysis but evolved his expertise over the past 18 years. His focus has been steered towards multi-disciplinary optimisation, Robust Design using Design for Six Sigma principles, and Systems Engineering. A major part of his work involves the practical application of these tools and methods to meet real-life engineering challenges. Beyond his work at Rolls-Royce, Alexander contributes actively to the larger professional community. He's an engaged member of NAFEMS and ERCOFTAC, championing the wider use of these advanced optimisation methods and processes.


Uncertainty, Verification & Validation, Systems Engineering, Numerical Methods, Monte Carlo, Latin Hypercube, Stochastics / Probabilistic, Uncertainty Quantification, Monte Carlo, Latin Hypercube Sampling, Structural, Simulation Governance, Digital Engineering