probabilistic analysis and optimization · 2020-07-09 · –sensitivity analysis –introduction...
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Probabilistic Analysis and Optimization
• In this last module we will cover:
– Probabilistic analysis via Monte Carlo simulation
– Monte Carlo convergence and error estimation
– Statistical sampling
– Design of experiments
– Sensitivity analysis
– Introduction to design optimization
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Measurable Outcomes
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Today’s Topics
1. Importance of probabilistic analysis in aerospace design
2. Monte Carlo (MC) methods
3. Probability & statistics refresher
4. Turbine blade heat transfer example
5. MC method for uniform distributions
6. MC method for non-uniform distributions
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Design, optimization and decision under uncertainty
FAA Environmental Tools Suite
Aerostructural shape optimization Vehicle system optimization
Aviation environmental policy decision-making
Characterizing, representing and analyzing uncertainty in simulation tools is essential for aerospace systems• To support decision-making (optimization, control, design, policy)• To inform model development
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2. Monte Carlo methods
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3. Probability & statistics refresher
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4. Turbine blade heat transfer example
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Turbine blade heat transfer example
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5. MC method for uniform distributions
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Simulation Challenge
• You are given the model in the file “blade1D.m”– function [Ttbc, Tmh, Tmc, q] = blade1D(hgas, Tgas, ktbc, Ltbc,
km, Lm, hcool, Tcool)
• Write a Monte Carlo simulator
• Run these cases with N=10, 100, 1000:– LTBC ~ U(0.00025,0.00075)
– Other variables deterministic at values given in HW8
Hint: the Matlab function rand returns a uniformly distributed random number on the interval (0,1).
• Generate an output histogram for Tmh and estimate the output mean
• Qualitatively, what evidence is there that your MCS implementation is correct?
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6. MC method for non-uniform distributions
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Triangular distributions
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MIT OpenCourseWarehttp://ocw.mit.edu
16.90 Computational Methods in Aerospace EngineeringSpring 2014
For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
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