Moving Low-Pass Gauss Filter with Automatically Defined Influence Region for Diffusive Studies

Abstract

b = probe position, m C = heat capacity, kJ= kg C cn = conventional power spectra coefficient d = source parameter, s, Eq. (8b) f = frequency, Hz fc = cutoff frequency, Hz j = time data index, Eq. (5) jo = time data index, Eq. (6) k = thermal conductivity,W= m C kxx = thermal conductivity coefficient in x direction, W= m C kyx = thermal conductivity coefficient in x-y cross direction, kyx kxy, W= m C kyy = thermal conductivity coefficient in y direction, W= m C M = number of data points less one M = kernel function with arguments b; t=u in Eq. (4b) N = number of terms in influence region, Eq. (7d) N = first approximation to N, Eq. (7c) n = number of terms in power spectra nc = cutoff value in power spectra p = derivative order, Eq. (8c) q00 o = dimensional surface heat flux magnitude, W=m, Eq. (8b) q00 x = dimensional heat flux in x direction, W=m 2 rmsg = root-mean-square-error global filter, C, Eq. (10b) rmsl = root-mean-square-error local filter, C, Eq. (10c) rmso = root-mean-square-error original data, C, Eq. (10a) r = variable in Gauss function r1 = asymptotic infinity value T = temperature, C Ttc = thermocouple temperature, C Ttc;j = noisy thermocouple data at time t tj, C, Eq. (9) t = time, s tinfluence = influence time, s tj = discrete time, s tmax = maximum time for experiment, s u = dummy time variable, s x = spatial variable perpendicular to surface, m y = spatial variable parallel to surface, m yo = dummy spatial variable, m = thermal diffusivity, kxx= C or k= C , m=s t = sampling time width, s tmax -width = maximum time width of influence, s tsampling-time-step = sampling time step, s