T.NO. 207 
Sp2p_2FILTERED 
Fig. 3.18. Spectra of roll, (roll), (roll)*filtered. 
(From Yamanouchi.??) 
heaving. Heaving itself was not measured, but its effect was assumed to be included in 
the vertical acceleration of a representative point and also to be combined in pitching, 
rolling, and relative wave height. Examples of four—input analysis are shown in Figs. 3.21 
and 3.22, in which stress as the output is given on channel 5 and the inputs of rolling on 
channel 1, pitching on channel 2, relative wave height on channel 3, and (roll)? filtered on 
channel 4. Figure 3.21 shows five auto correlations of output and input Rss, Ry;, R22, R33, 
Rag; ten cross correlations of combinations of the one output with four inputs Rs), Rs2, 
R53, R54; R21; Rai, R42, R43; R31, R32; and five auto spectra of stress Sss, rolling $1, pitch- 
ing S22, relative wave height S33, and roll squared. Figure 3.22 shows conditional (partial) 
gains and phase relations as Hop pwr2, Hsp_pwr2, Hsw_ppp2, and Hsp2_ppy in the form 
of absolute values and arguments. The notation follows the convention already explained 
in Section 2.6.5 on partial coherencies. For example, 
Ssp_RWRW) 
H 2 (CO) ere 
SP-RWR2®) ame) 
shows the frequency response of stress to R: rolling, W: relative wave height, and R?: 
squared roll filtered processes under the condition that the effect of pitch has been 
masked. In the same way, multiple and partial cross spectral analysis was tried with stress 
as one output (4), and roll R (1), pitch P (2), and (roll)? filtered R? (3) as three inputs. In 
another one output/three input cases, pitching P was replaced by vertical acceleration A. 
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