EML 6229
Introduction to Random Dynamical Systems
Mrinal KumarAssistant Prof., MAE
http://www.mae.ufl.edu/~mrinalkumar
Syllabus…
Uncertainty: A Fundamental Challenge
✣Nature is far too complex for engineers
✣ Understanding nature: via math:: analysis via observation:: instruments
Bothimperfect!!
✣Outcome: we must live with uncertainty, aka stochasticity
Specifically, we must make decisions while limited by stochastic information!
Uncertainty: Examples
Weather prediction
Hazardous event management Catastrophic event decision making
Apophis collision probability in 2029: 2.7% (2004 estimate)
Understanding turbulence:affordable transportation
2010 Iceland eruption map
due to practical limitations, e.g. ⇾ model not good enough, ⇾ not enough measurements available, ⇾ neglected effects
Characterization of Uncertainty
✣ Given that uncertainty is unavoidable, how do we best capture it in engineering/scientific/financial/economic/sociological systems?
Uncertainty Quantification (UQ)
UncertaintyTypes
Epistemic:
Aleatory: due to fundamental limitations, e.g.⇾ accuracy of instruments⇾ computational limits⇾ nonrepeatability of experiments
Epistemic uncertainty is reducible to aleatory uncertainty in an ideal world
Uncertainty in System Models
System (physics)…. to be modeled
States… entities that identify/characterize/quant
ify the system
Accurate math model(no uncertainty)…but too complex!!
Uncertainty in System Models
A much simpler, reduced order model, but with uncertainty
noise….
Also need: initial conditions: almost always come from measurements
Uncertainty in Measurements
✣ There is always aleatory measurement uncertainty: unavoidable and irreducible
✣ In today’s world, epistemic measurement uncertainty is also dominant (essentially too much information to track, and too few resources)
Example: consider the so-called potentially hazardous asteroids
Uncertainty in Measurements
✣ There is always aleatory measurement uncertainty: unavoidable and irreducible
✣ In today’s world, epistemic measurement uncertainty is also dominant (essentially too much information to track, and too few resources)
Example: or something closer to home: our space debris
View of debris in LEO Expanded view of debris to include HEO
plus….active satellites!!
limited resources….
Uncertainty Propagation
✣ When measurements cannot be made (due to lack of allocation), only way to quantify uncertainty is to propagate (forecast) it through use the best known models
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