Bi-Criteria Smoothing of Data by Savitzky-Golay Filter
Venko G. Vitliemov, Ivelin V. Ivanov, Ivan A. Loukanov · IOSR Journal of Mechanical and Civil Engineering · 2016
An approach for interactive bi-criteria smoothing of experimental data is proposed using the system (S-G) filter of Salvitzky-Golay.An optimization problem is formulated with the controversial criteria: "total absolute error" and "integral smoothness".For the choice of adjusting parameters of the filterthe degree of the approximation of polynomial and the number of the supporting points is used.A Pareto-optimal solution set is determined for this problem.Then subsets of Pareto-optimal solutions are found by employing the -selection method, which are aranged by their extended efficiency.The solution with the highest rank of efficiency is the Salukvadze-optimum of the formulated extremal problem.The proposed approach allows choosing reasonably a variant of (S-G) filter parameters having adequate representation and smoothness.An example of smoothing the measured values of an acceleration of free damped vibrations in the propulsion mechanism of a vibrobot is provided and analyzed.