# Uncertainty modeling

Title: Uncertainty modeling
Sim standards listserv subscribers:

I'm trying to get my hands around uncertainty modeling for aerodynamic parameters / function tables.

In my experience, we may be required to support (in a future release of DAVE-ML) variations/uncertainties/statistics about individual aerodynamic parameters. So things like constants and function tables will need to have embedded within their description an idea of the statistical variation or uncertainty in the parameter.

I'm thinking about being able to specify this uncertainty in several possible ways:

1) as a possibly asymmetric limit, either multplicative (CL = 0.15 +/- 10%) or additive (CL = 0.15 +0.02/-0.01)

2) as an upper and lower limit function, with tables, corresponding to the breakpoint values:

alpha      0     5     10      15     18     20

CL       0.0   0.01   0.023  0.034  0.044  0.050

upper lim  0.01  0.02   0.031  0.038  0.046  0.062

lower lim -0.01  0.00   0.020  0.030  0.041  0.045

(also for multidimensional functions; the point is, three tables would be required of identical dimensions)

3) as an upper and lower limit function, with a smaller set of breakpoint (or possibly even smaller dimensionality) than the original table

CL table <!--       alpha       -->
Mach   0     5     10    20   24
0.0  0.01  0.02  0.04  0.08 0.09
0.5  0.00  0.01  0.03  0.07 0.08
0.9  0.00  0.01  0.02  0.06 0.08

CL uncertainty *multiplier* vs alpha only
alpha ->   0    15     25
upper lim      0.1   0.1   0.25
lower lim     -0.1  -0.1  -0.30

so here the uncertainty is a function of alpha only, with a different set of breakpoints, even though CL itself is a function of alpha & Mach

The values can be specified as additive, multplicative, or absolute numbers.

The values could represent 1-, 2-, or 3-sigma confidence levels for a Gaussian/normally distributed parameter, or the values could be absolute limits for a uniform distribution.

--Bruce Jackson
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Bruce Jackson mailto:[EMAIL PROTECTED] Dynamics and Control Branch
18C West Taylor Street MS 132             Airborne Systems Competency
NASA Langley Research Center                  Hampton, Virginia 23681
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