CEE 201L. Uncertainty, Design, and Optimization.
Department of Civil and Environmental Engineering
Edmund T. Pratt School of Engineering
Duke University - Box 90287,
Henri P. Gavin, Ph.D., P.E., Professor
Reading for Martin Luther King Day
Assignments (note: due dates are subject to change)
guideline and template for completing assignments
Matlab functions for optimization
These Matlab functions implement methods for minimizing a function of several parameters subject to a set of inequality constraints:
minimize f(x) such that g(x) ≤ 0,
where x is a vector of design variables,
f(x) is a scalar-valued objective function,
and g(x) is a vector of constraints.
- Examples of running constrained minimization codes
- ORSopt.m implements an optimized step-size random search algorithm.
- NMAopt.m implements a Nelder-Mead algorithm.
- SQPopt.m implements a sequential quadratic programming algorithm.
- avg_cov_func.m calculates average and coefficient of variation of a random penalized objective function.
- box_constraint.m determines the box constraint scaling factor a>0 to the perturbation vector r from x
such that: max(x+ar) < +1 and min(x+ar) > -1
- optim_options.m is needed for ORSopt.m, NMAopt.m, and SQPopt.m
- plot_surface.m plots the cost function as a surface over two of the parameter values, ORSopt, NMAopt, or SQPopt
- plot_cvg_hst.m plots the convergence history for the solution computed by ORSopt, NMAopt, or SQPopt
Matlab functions for random variables
These Matlab functions can be used to compute probability distribution
functions and to generate samples of random variables.
The m-file MCS_intro.m illustrates the use of a number of these functions.
A Sucker Is Optimized Every Minute, Virginia Heffernan, New York Times, March 17, 2015.
- Nonlinear Optimization with Engineering Applications, Michael Bartholomew-Biggs, Springer Optimization and Its Applications, vol 19, 2008.
- An Optimized Step Size Random Search (OSSRS), Sheela, B.V., Computer Methods in Applied Mechanics and Engineering, 19 (1979): 99-106.
- Adaptive Step Size Random Search, Schumer, M.A. and Steiglitz, K., IEEE Transactions on Automatic Control, AC-13, No. 3 (1968): 270-276.
- Evaluation of Adaptive Step Size Random Search, White, L.J. and Day, R.G., IEEE Transactions on Automatic Control, AC-16, No. 5 (1971): 475-478.
- Valuation of some Random Search Methods, Ugray, C., Optimization, 10(1) (1979): 57-65
- Introduction to Analyses of Adaptive Stochastic Search Methods for Global Optimization, by Zelda B. Zabinsky, University of Washington
- A General-Purpose Global Optimizer: Implementation and Applications, Pronzato, L., and Walter, E., Mathematics and Computers in Simulation XXVI (1984): 412-422.
- A simplex method for function minimization, J.A. Nelder and R. Mead, Computer Journal, 7(4) (1965): 308-313.
- Nelder-Mead method(Wikipedia)
- Animation of the Nelder-Mead algorithm, Grabitech Solutions AB, Sweden
- Animation of the Nelder-Mead algorithm, Practical Optimization: A Gentle Introduction, by John W. Chinneck, Carleton University.
- Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions by J.C. Lagarias et al., SIAM J. Optim., vol. 9, no 1, pp 112-147.
- Nonlinear Programming, Becerra, Victor M., University of Reading
- Numerical Optimization, Ascher, Uri M., University of British Columbia
- Matlab Optimization Toolbox, The MathWorks.
Sequential quadratic programming, Boggs, P.T., Acta Numerica, (1995): 1-51.
- For Todayâs Graduate, Just One Word: Statistics, Steve Lohr, New York Times,
August 5, 2009.
- Introduction to Randomness and Random Numbers (random.org)
- A Probability Tutorial, West Texas A and M University.
- Bayes' Theorem for the curious and bewildered; an excruciatingly gentle introduction, Eliezer Yudkowsky, The Singularity Institute for Artificial Intelligence
- Introduction to Probability and Statistics, John Walker, Fourmilab, Switzerland.
- Uncertainty in Probabilistic Risk Assessment, A.R. Daneshkhah, University of Sheffield, UK (2004).
- Aleatory and Epistemic Uncertainty Quantification for Engineering Applications, L.P. Swiler, A.A. Giunta, Sandia labs.
- Uncertainty Modeling and Analysis in Civil Engineering, Bilal M. Ayyub, CRC Press, 1997.
- Quantitative Analysis of Variability and Uncertainty in Energy and Environmental Systems H.C. Frey, N.C. State University.
- Engineering Design Reliability, Efstratios Nikolaidis, Dan M. Ghiocel, Suren Singhal, CRC Press, (2004)
- Uncertainty in Structural Engineering, William M. Bulleit, Practice Periodical on Structural Design and Construction, ASCE, 13(1): 24-30. (2008)
- Dealing with Uncertainty: From Health Risk Assessment to Environmental Decision Making,
Louis A. Cox, Jr. and Paolo F. Ricci, Journal of Energy Engineering, ASCE, 118(2): 77-94. (1992)
- Superfund Decision Analysis in the Presence of Uncertainty,
Aaron A. Jennings, Neel Mehta, and Sumeet Mohan, Journal of Environmental Engineering, ASCE, 120(5): 1132-1150. (1994)
Solid Mechanics Review, References, and Software
Prestressed Concrete Beam Design
Water Supply and Treatment System
- RDU Airport Rainfall statistics, WRAL weather
Big Rain Events in the Southeast, Florida Climate Center, Florida State University.
- Real Time Water Supply Status, City of Durham, NC
- Little River Reservoir and Lake Michie Elevations, City of Durham, NC.
- Water Supply and Treatment, City of Durham, NC.
- Annual Water Quality Reports, City of Durham, NC.
- The Story of Drinking Water, City of Durham, NC.
- Falls Lake Data, USGS
- Falls Lake Data, US Army Corps of Engineers
- Charting Our Water Future, McKinsey&Company
- Average Daily Water Use in North Carolina Cities, by week, North Carolina Department of Environment and Natural Resources
- The Future of Water in North Carolina, Strategies for Sustaining Clean and Abundant Water, Conference Report, August 2007.
Comparison of Methods Used to Estimate Lake Evaporation for a Water Budget of Lake Sminole, Southwestern Georgia and Northwestern Florida, by Melinda S. Mosner and Brnet T. Aulenbach
- Evaporatoin Rates, by David Cook, Argonne National Labs
- Rain Water Solutions, Inc., Raleigh, NC
Structural Dynamics and Vibration Response
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© 2001-2015 Henri P. Gavin; updated: 9-27-2001, 12-15-2003, 1-7-2004, 1-6-2005, 1-22-2005, 2-1-2005, 2-14-2005, 1-11-2006, 2-14-2008, 2-28-2008, 3-24-2008, 1-8-2009, 8-7-2009, 1-5-2011, 1-8-2014, 1-7-2015, 1-13-2016