### Abstract

Experimental fire research often produces large amounts
of data. Effective
methods of
preprocessing the data are needed to filter out
irrelevant scatter and to make
the data analysis
easier.
Curve fitting techniques are often needed to smooth out
scattered experimental
data to permit
the application of analytical formulae which often
involve derivatives of the
data function.
One of the critical features in fitting the data is to
avoid discontinuous
changes in curvature
and slope, in cases where the associated oscillations in
derivatives are
physically
meaningless.
A working piecewise fitting technique based on the
approximation technique of
the finite
element method is presented in association with the
calculation of the
confidence interval for
the fitted function and its first and second derivatives.
The approximation
assumes the fitted
function and its derivatives up to the second order to be
continuous.
The ideas presented below are then materialized into the
creation of a
performing software
package programmed in standard FORTRAN 77. Given a
sufficient set of data
points (pairs)
this software performs the fitting and calculates the
confidence intervals of
the fitted
function,
and its first and second derivatives.

Original language | English |
---|---|

Place of Publication | Espoo |

Publisher | VTT Technical Research Centre of Finland |

Number of pages | 34 |

ISBN (Print) | 951-38-4253-3 |

Publication status | Published - 1993 |

MoE publication type | Not Eligible |

### Publication series

Series | VTT Publications |
---|---|

Number | 135 |

ISSN | 1235-0621 |

### Keywords

- numerical analysis
- approxination
- finite element analysis
- computer programs
- utilization
- experimental data
- estimating
- least squares method
- curve fitting
- calculations
- functions (mathematics)
- confidence limits
- differential calculus
- temperature gradients
- mass flow
- combustion

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## Cite this

Baroudi, D. (1993).

*Piecewise least squares fitting technique using finite interval method with Hermite polynomials*. VTT Technical Research Centre of Finland. VTT Publications, No. 135