Orientation
- Spring 2025 Syllabus
- first lecture slides
- Students with Superpowers
- Academic Integrity
- Policy for Short-Term Illness Notification
Reading for Martin Luther King Day
- The King Center
- The Martin Luther King Jr. Papers Project at Stanford University
- Letter from a Birmingham Jail, Rev. Dr. Martin Luther King, Jr., April 16, 1963
- Acceptance Speech at the 1964 Nobel Peace Prize Ceremony, Rev. Dr. Martin Luther King, Jr., December 10, 1964 - listen -
Assignments
- 2025-01-15 - Homework 1 - matlab skills
- 2025-01-22 - Homework 2 - Optimization: search methods
- 2025-01-27 - Homework 3 - Optimization: gradient methods
- 2025-02-05 - Homework 4 - Uncertainty: axioms of probability
- 2025-02-12 - Homework 5 - Uncertainty: probability distributions
- 2025-02-19 - Homework 6 - Uncertainty: monte carlo simulation and regression
- 2025-02-26 - Homework 7 - Uncertainty: confidence intervals, quantiles, hypothesis testing
- 2025-03-21 - Homework 8 - Engineering network systems analyses
- 2025-03-24 - Quiz - HW 4 - HW 7
- 2024-04-07 - Project 1.A - Optimize a statically determinate 2D truss for uncertain loads.
- 2024-04-07 - Project 1.B - Optimize power grid energy distribution.
- 2024-04-07 - Project 1.C - Make as much money as possible.
- 2024-04-18 - Project 2.A - Protect a building and its contents from earthquakes.
- 2024-04-18 - Project 2.B - Supply enough clean drinking water.
- 2024-04-18 - Project 2.C - Supply enough clean solar energy.
- 2025-04-21 - Project Presentations - your Project #1 or your Project #2
- 2024-04-30 - Take Home Final
Course Notes
- matlab language skills and debugging
- A Very Brief Introductoin to Numerical Optimization for Constrained Optimization
- The Nelder-Mead Simplex Algorithm in Two Dimensions
- Linear Programming and Lagrange Multipliers
- Linear Programming in Two Dimensions
- Quadratic Programming and Lagrange Multipliers
- Review of Matrix Math
- Constrained Linear Least Squares
- Minimum Total Potential Energy - example
- Minimum Total Potential Energy, Quadratic Programming, and Lagrange Multipliers
- Rules of Probability with Examples
- Probability Distributions with Examples
- Fitting Models to Data - Generalized Linear Least Squares and Error Analysis
- Confidence Intervalss and Hypothesis Testing
- Network System Reliability
- Introductory Example of Uncertainty, Design, and Optimization
- Introduction to Water Supply and Treatment Project
- Plastic Design of a Fixed-Fixed Beam-Column, MP.m
- Simple Oscillators: Free and Forced Response
- Elastic and Inelastic SDOF Structural Dynamics: simulation and visualization's matlab code
matlab functions for optimization
These matlab functions implement methods for minimizing a function of several variables subject to a set of inequality constraints:
minimize f(x) such that g(x) ≤ 0,
where x is a vector of n design variables,
f(x) is a scalar-valued objective function,
and g(x) is a vector of m 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.
- plotCDFci.m plots the empirical CDF from a sample of data along with the confidence interval of the CDF.
- corr_beta_rnd.m generates a sample of correlated beta values.
- corr_logn_rnd.m generates a sample of correlated log normal values.
- MCS_intro.m illustrates the use of a number of these functions.
Outside Reading
Optimization
- 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.
Uncertainty Analysis
- For Today's 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.
- 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
- MecMovies: Review of Solid Mechanics
- MDSolids: Educational Software for Mechanics of Materials from the University of Alberta
- Mechanics of Solids from the University of Sydney
- Examples of Truss Types
- truss_plot.m Plot a truss configuration.
- On-line (Java) Structural Analysis Software from Dr. D.J.Rao
- Beam-bending Java Applet from Virginia-Tech
- On-Line Bridge-Design applet from Johns Hopkins University
- MS-Windows Truss Analysis Software from Method Computing
- Cross section relationships for Wide-Flange Sections
Water Supply and Treatment System
- RDU Airport Rainfall statistics, RDU rainfal data from WRAL
- 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
- Vibration Response Plotter from Dr. D.J.Rao
- Structural Dynamic Vibrations Prof. B.J. Stone, University of Western Australia
- Frequency Response Functions from Dr. C.W.deSilva
- Acoustics and Vibrations Animations, Dr. Dan Russel, Kettering University
- Nonlinear SDOF Structural Dynamics: Experimental Data (2008):
16apr08.zip | 17apr08.zip | 18apr08.zip
Miscellaneous
