! Calibration of Mathematical Models
Math models usually include constants. Calibration is the determination
of the values of the constants. The calibration can be:
For multivariate models there has to be at least two pairs of data unless
the shape of the model is assumed. Fitting to one pair of data is essentially
positioning a fixed shape model somewhere in two dimensional space. Discussion
of fitting two or more dimensional models is given in the second lesson
Theoretical, i.e. the values are deduced by theory
Empirical, i.e. the values are deduced from observing a process
and measuring the inputs and outputs. Suitable measurements are Calibration
DATA. The data are usually matched dependent & independent variable
values. Fitting a random single variable model is essentially the selection
of a mathematical distribution. Some discussion of this process is given
in the lessons listed below.
Given calibration data some form of FITTING procedure can be
used. It may be as simple as hand plotting of the data and hand fitting
a straight or curved line, or as complicated as a non-linear fit using
some criteria such as maximum likelihood or least squares, etc. Computer
packages for statistical analysis include routines for 'fitting equations
STATGRAPHICS, SASS, SPSS are some of the packages. STATGRAPHICS
is compatible with MYSYS as it uses APL as its platform, was marketed by
MANUGUISTICS which also marketed APL*PLUS/PC.
MYSYS includes notes on fitting functions, and the function FIT.
f60 ¦ FIT; Function fit for polynomial and exponential models.
f62 ¦ simplex; Simplex search technique for fitting models of
f216 ¦ lslfit; least squares linear fit of data array.
^ MYNET Links:
End to date, ams 060624
Discussion of Mathematical Models
LESSON on Fitting Random Variable Models
LESSON on Fitting two variable models
APL IDIOM directory
TOPICS included in MYNET
Introductions to various TOPICS included in MYNET
Time Value and Engineering Economy Topics
General List of Transportation Topics
CE3201 Introduction to Transport Engineering Course