Appendix B contains more detailed information on the residuals for the 14 data records. Table B1
lists the normalized rms residual. Figure B1 shows the normalized rms residual for the SVD models
of the Time History, Amplitude spectrum, Fourier Transform of the Time History and the DWT.
First, notice that only two curves are visible on the plot. The normalized rms residual for the models
made from the Time History, Fourier Transform of the Time History and the DWT all coincide to
within about 10-13; these three models appear to be the same model. The Time History, Fourier
Transform and DWT can all be transformed into each other. That is, each contains exactly the same
information about the data. The eigenvectors found in the SVD models of these three descriptions of
the data also match each other in the sense than any one can be transformed into another with an
error of only 10-13 in the computational environment. The normalized rms residual for the Amplitude
Spectra differs from and lies below the residual for the other three descriptions. The Amplitude
Spectra contains no phase information, which means it contains less information than the Time
History. The levels of the residuals are approximately constant and low for each of these four
models of the 80% and 100% torque levels except for a small increase for the records 44-53 on the
models made from the Time History, Fourier Transform and DWT. The levels jump up to a higher