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However, as a consequence of the first remedial action, new fault patterns are revealed on the new part surfaces. 19 Karhunen-Loève analysis of surfaces from Part #2. surface analysis tool: a Fourier transform analysis of the surface profile reveals a structure which is no longer random in nature (Fig. 18); however, the distinction in frequency components is not clear using the Fourier-based analysis. Remedial actions by designers can only be taken if the information received from the manufacturers is clear and unambiguous.

The eigenvectors are used here to determine the dominant patterns in the monitored signal. The eigenvalues of the covariance matrix are computed using det(S Ϫ ␭I) ϭ 0, where I is the identity matrix; ␭i are the roots of the characteristic polynomial, representing the eigenvalues of the covariance matrix. The eigenvectors ⌽i of the matrix are then computed using (S Ϫ ␭iI) ⌽i ϭ 0. We will show that these eigenvectors are dependent on the deviations of each point of the input vectors from the mean vector.

The changes in each of these fundamental patterns in the signal are detected by plotting the coefficients corresponding to each eigenvector with respect to the input vectors. If the inputs are taken at regular time intervals, the resulting plot will indicate the change in the fundamental eigenvectors with respect to time. The eigenvalues of the covariance matrix corresponding to each eigenvector will indicate the variance of the coefficients for each eigenvector, as well as the significance of the total energy contained in each eigenvector.

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