Model Browser User's Guide

Polynomial Splines

These are essential for modeling torque/spark curves. To model responses that are characterized in appearance by a single and well defined stationary point with asymmetrical curvature either side of the local minimum or maximum, we define the following spline class,

where k is the knot location, denotes a regression coefficient,

• ,
  
  ,

where c is the user-specified degree for the left polynomial, h is the user-specified degree for the right polynomial, and the subscripts Low and High denote to the left (below) and right of (above) the knot, respectively.

Note that by excluding terms in

and

we ensure that the first derivative at the knot position is continuous. In addition, by definition the constant must be equal to the value of the fit function at the knot, that is, the value at the stationary point.

For this model class, response features can be chosen as

• Fit constants
  
  
• Knot position
• Value of the fit function at a user-specified delta

• from the knot position
  
  if the datum is defined, otherwise the value is absolute.

• Difference between the value of the fit function at a user-specified delta from the knot position and the value of the fit function at the knot

Polynomial Models

Truncated Power Series Basis (TPSBS) Splines