Evaluation of generalized polynomial function specification methods

Abstract

The sequential function specification method (SFSM) for solution of the inverse heat conduction problem was introduced by Beck (1968) [1], and described in more detail [2] in 1985. This method assumes a functional form for the unknown heat flux in order to add more (future) data to regularize the problem and facilitate estimation of the next heat flux component. Two basic forms for the unknown heat flux have been well-explored: a constant function (zeroth order polynomial), and a linear function of time (a first order polynomial). Until now, only these two “traditional” forms have been used and higher order polynomial function approximations have not been considered.A generalized polynomial sequential function specification method (SFSM) is developed and evaluated in this paper. For higher order polynomials, the proper balance of past and future time step information is not obvious; the optimal balance is investigated herein. A generalized algorithm is used to define polynomials of any degree and estimate heat fluxes using SFSM with any number of past and future data. Seven heat flux test cases, including three non-polynomial heat flux variations, are used to evaluate the traditional and new methods, and the “optimal” number of future time steps is chosen for each case. The filter coefficient concept [3] provides additional insights into the new SFSM approaches. Filter coefficients are calculated with the optimal number of future time steps and the results are discussed.