Extremum Response Surface Method for Casing Radial Deformation Probabilistic Analysis

Abstract

B = linear term coefficient vector bi = element i of B C = quadratic term coefficient matrix cij = jth element in ith row of C D = variance vector of X D = variance function E = mean value function f, Y, H = generic functions h = lining ring thickness i = row index j = column index k = the variable number of variable set r = the number of input variables t = time index tc = gas temperature X = input variable vector X, = variable set Xi = element i of X xmax = maximum variable value in X Yj = jth output response function Yj;max = the extremum of Yj c = heat transfer coefficient 0 = constant term min = the minimum output response of casing radial deformation = expansion coefficient = thermal conductivity = mean vector of X = normal distribution function

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