Probablistic Methods in Engineering

Winter 2009 L.M. Lye

ENGINEERING 9411 PROBABLISTIC METHODS IN ENGINEERING

Introduction:

Uncertainties are unavoidable in the design and planning of engineering systems. Therefore, the tools of engineering analysis should include methods and concepts of evaluating the significance of uncertainty on system performance and design. In this regard the principles of probability and statistics offer the mathematical basis for modelling uncertainty and the analysis of its effects on engineering design. This course is thus mainly concerned with the practical applications and relevance of probability and statistical concepts to engineering. Probabilistic modelling, statistical inference and analysis using modern computer intensive methods will be emphasized.

Summary description:

Concept of risk, utility, and uncertainty in engineering; Review of probability theory; Probability distributions; Empirical determination of probability models; Parameter estimation techniques; Introduction to monte carlo simulation and computer intensive techniques; First order and advanced first order uncertainty analysis; Applications in risk and reliability analysis of engineering systems.

Course Outline:

0. Concept of risk and uncertainty in engineering design and analysis. What is meant by probabilistic modelling, statistical analysis, and statistical modelling. Probability as a basis for decisions.

1. Review of probability theory; random variables, and distribution of a random variable; Normal distribution and other discrete and continuous probability distributions.

2. Introduction of Monte Carlo simulation; using Monte Carlo methods to solve probability problems.

3. Means, variances, covariances of random variables; function of random variables; function of random variables using Monte Carlo methods; approximations of means and variances of multi-dimensional random variables; generating multivariates by Monte Carlo.

4. First order uncertainty and reliability analysis: Mean FOSM and Advanced FOSM methods.

5. Other methods of uncertainty analysis: Fuzzy and interval arithmetic, RSM, etc. Winter 2009 L.M. Lye

6. Empirical determination of probabilistic models; probability plotting, transformations, and goodness of fit tests.

7. Methods of parameter estimation: mle, moments, L-moments, Bayesian; concept of bias, variance, and mean square error; use of Monte Carlo methods in statistical studies; bootstrapping and jackknifing methods.

8. Risk and Reliability Analysis of Engineering Systems and other selected topics.

Grading Scheme:

Assignments 25% Journal Reviews 10% Project 20% Final examination 45%

Reference Text:

Halder, A and S. Mahadevan (2000): Probability, Reliability and Statistical Methods in Engineering Design, John Wiley and Sons.

Statistical Journals:

Journal of the American Statistical Association; American Statistician; Technometrics.

Engineering Journals:

IEEE Transaction on Reliability; ASCE Journal of Hydraulic Engineering; ASCE Journal of Structural Engineering; Journal of Mechanical Design; Risk Analysis; Probabilistic Engineering Mechanics, and others.

Other Reference Books on Statistics for Engineers:

Ang and Tang (1975): Probability Concepts in Engineering Planning and Design, Volumes 1 and 2. John Wiley and Sons.

Harr, M.E. (1987): Reliability-Based Design in Civil Engineering. McGraw Hill, Inc. ISBN: 0-07-026697-2.

Rao, S.S. (1992): Reliability-Based Design, McGraw Hill, Inc. ISBN: 0-07-051192-6.

Benjamin and Cornell (1971): Probability, Statistics, and Decision for Civil Engineers. McGraw Hill. Winter 2009 L.M. Lye

Soong (1981): Probabilistic Modelling and Analysis in Science and Engineering. John Wiley and Sons.

Myers (1986): Classical and Modern Regression with Applications. Duxbury Press.

McCuen (1985): Statistical Methods for Engineers. Prentice Hall.

Sander and Badoux (1991): Bayesian Methods in Reliability. Kluwer Academic Publishers.

INSTRUCTOR

Dr. Leonard M. Lye holds a first-class honours degree in civil engineering and a PhD specializing in the areas of statistical and stochastic hydrology, design and analysis of experiments, and environmental statistics. He is a professor of civil engineering and a Fellow of the Canadian Society for Civil Engineering. Dr. Lye has over 80 publications in the areas of hydrology and statistics. Many of which have appeared in well-known journals such as IEEE, Journal of Hydrology, ICE, Stochastic Hydrology Hydraulics, Civil Engineering Systems, Water Resources Bulletin, Canadian Journal of Civil Engineering, Journal of Environmental Engineering and Science, Environmental Management, and the Journal of Applied Ecology. In addition to academic research, Dr. Lye is a consultant to several companies in the areas of flood risk analysis, design and analysis of experiments, environmental sampling designs, and statistical analysis for environmental effects monitoring. He also serves as an Associate Editor of the Canadian Water Resources Journal, a reviewer for Water Resources Research, Journal of Hydrology, IEEE Transactions on Reliability, Canadian Journal of Civil Engineering, and others. Dr. Lye is a highly rated and entertaining teacher and has received excellent reviews from participants of this course in the past. He is winner of the Association of Professional Engineers and Geoscientists of Newfoundland award for excellence in teaching for 2001, and is the winner of the President’s Award for Distinguished Teaching in 2003.

Dr. Leonard M. Lye, PhD, PEng Professor and Chair of Civil Engineering Memorial University of Newfoundland [email protected]