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The identification of true weak modes buried in high-level, noisy, measured data from offshore structures is a practical but challenging problem because weak modes are typically eliminated as noise and rarely, yield a discrete time series.
In addition to produce a residual more sensitive to the weak modes, it is possible to detect system order changes due to the fault using the rotated inputs.
The silica aerogel IR spectra show the expected Si-O modes but also two weak modes arising from Si-CH3 groups indicated by the two arrows [28].
The richest variety was found for molar CO H2 ratios between 4 and 10, while at lower ratios the random and the weak modes were absent.
The performance of this blind method is assessed in terms of its capability in extracting weak modes as well as the accuracy of estimated parameters.
A theoretical development proposed in this study extends the traditional modal analysis to reconstructing the discrete time series of weak modes, thereby removing its previous limitations to only frequencies, damping ratios and mode shapes.
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Although a gradually increasing mode size can be observed due to a slightly weak mode confinement, its modal loss can be mitigated at the same time, resulting in extended propagation distances.
The two strong vibrations of 924 and 330 cm-1 and weak mode at 797 cm-1 can be assigned to the W-O stretching vibration of WO4 tetrahedra.
The results show that two dominant frequencies corresponding to the in-line and cross-flow directions can be identified simultaneously even one mode is very weak compared with the other, and the time series of the weak mode could be reconstructed with a rough frequency window.
The results further demonstrated that a large model order is required to estimate all poles and residues of the original noisy signals, and that the row number corresponding to a weak mode of the isolated pole matrix could be easily determined via finite element analysis or engineering experiences.
The C=C double bond stretch in CC is located at ∼0.22 eV and is found to be a very weak mode.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com