Curve Fitting and Parameter Estimation
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Maple has many tools for curve fitting and parameter estimation. Here, for example, we fit a polynomial to data.
data≔1,2.3,2,5,3,4,4,5,5,8:
CurveFitting:-LeastSquaresdata,v,curve=av2+b v+c
2.74000000000000+0.0257142857142819v+0.185714285714286v2
There are tools in the CurveFitting and Statistics package for curve fitting. You can also create your own least-squares error function, and minimize it using the Optimization package.
The precise command and technique depends on the type of curve or model you are fitting. The table below gives a guide to the functionality, with links to worked examples.
Type of Equation or Model
Function
Application
Linear function
CurveFitting:-LinearFit
Fit Head-Flow Rate Data to a Pump Curve
Spline
CurveFitting:-Spline
Black-box procedure with potential multiple regions, conditional statements, etc.
Statistics:-NonlinearFit
N-Channel Enhancement MOSFET Parameter Estimation
Nonlinear function
PV Diode Parameter Estimation
Differential equations
Optimization:-Minimize
Chemical Kinetics Parameter Estimation
Probability Distribution via MLE and moment matching
fsolve
Fitting Wave Height Data to a Probability Distribution
Transfer function
System ID for a Spring Mass Damper
Applications
Optimize a Rankine Cycle
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