where $xi={\xi 1i,\xi 2i,\eta 1i,\eta 2i}$^{T} is the *i*th set of sampling crack parameters expressed as a four-dimension variable vector; $rmsl(xi)$ is the *l*th component of the output RMS vector at the assigned measurement points on the cracked plate, $f(xi)$ is a vector of a linear combination of *p* chosen functions, $\beta l$ is a $p\xd71$ vector given by the *l*th column in matrix of regression coefficients, *q* is the number of dimensions of the predicted RMS vector, and $zl(xi)$ denotes a model of Gaussian and stationary stochastic process with a mean of zero and a variance of $\sigma l2$. The covariance matrix between two given samples $xi$ and $xj$ is expressed byDisplay Formula

(8)$Cov[zl(xi),zl(xj)]=\sigma l2R(\theta ,xi,xj)\u2003\u2003\u2003i,j=1,2,...,n\u2003\u2003\u2003l=1,2,...,q$