A numerical method for approximating coefficients in an Euler-Bernoulli beam equation from spectral data is proposed.
The baseline model is considered as a stable model if the estimated mean coefficients quantifiably approximated the coefficients in the baseline model.
For HB method, by substituting approximation ˜y(x) into force equation, expanding the resulting expression into a trigonometric series, then letting the coefficients of the resulting lowest-order harmonic be zero, one can obtain approximate coefficients of approximation ˜y(x) [R.E.
The coefficients can be approximated in by coefficients and the coefficients can be approximated in by functions on (since is see, e.g., [10, Theorem, page 49]), which yields operators and, of order and respectively, in the obvious way.
A comparison of these approximate coefficients is made with the accurate values obtained with the use of multiple precision arithmetic.
Detection and classification of faults are achieved with the help of approximate coefficients based alienation coefficients of current signals, measured from all the buses of system.
The approximate coefficients of voltage and current signals, obtained over a quarter cycle, are fed to artificial neural network to locate the faults precisely, from respective buses.
The proposed algorithm makes use of wavelet transform based approximate coefficients of three-phase voltage and current signals, obtained over a quarter cycle to detect, classify and locate various faults.
Update-first means the approximate coefficients will be obtained firstly during each decomposition-level, and then the approximate coefficients of next decomposition-level will be obtained using the approximate coefficients of the current decomposition level.
