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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.

 

data1,2.3,2,5,3,4,4,5,5,8:

CurveFitting:-LeastSquaresdata,v,curve=av2+b v+c

2.74000000000000+0.0257142857142819v+0.185714285714286v2

(1)

 

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

 

Statistics:-NonlinearFit

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

 

Optimization:-Minimize

System ID for a Spring Mass Damper

 

Applications

Optimize a Rankine Cycle

Chemical Kinetics Parameter Estimation

PV Diode Parameter Estimation