Type of model

Model structure

Parameter estimation

Example

Static

Linearly

Linear function

Linear regression

(Least Squares method)

Energy signature of weekly values

Nonlinear

Polynomials

Any nonlinear function

Linear regression

(Least Squares Method)

Iterative process,

Levenberg Marquardt

Pump curve

Dynamic

Linearly

Transfer functions

models (ARMA, ARMAX, etc.)

Linear regression

(least square method),

an iterative procedure

Heat flow through a plane wall

Nonlinear

Neural Networks

(sigmoid, wavelet, radial basis networks)

Damped Gauss-Newton backpropagation

Arbitrary non-linear systems

Polynomials (Wiener /Hammerstein model, Volterra model)

Linear regression

(least squares method)

Linear system with static nonlinearities at the input or output (control element with saturation behavior)