Weak-mode identification and time-series reconstruction from high-level noisy measured data of offshore structures

摘要

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. This study proposes a weak-mode identification and time-series reconstruction method for offshore structures when high-level noise is present. 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. Additionally, a second development proposed in this study makes the reconstructed time series not simply a combination of harmonic components from a Fourier transform but rather complex exponentials; the damping of the test structure is thus estimated with a better accuracy. A third theoretical development avoids variations in the results from different original signals by handling multiple signals simultaneously. The proposed approach primarily includes three steps: (1) estimate the poles and corresponding residues of high-level, noisy, measured data by converting high-order difference equations to first-order difference equations; (2) isolate the poles of weak modes by assigning multiple rough-pole windows, and subsequently extract the corresponding residues based on the row number of the isolated pole vector; and (3) identify and reconstruct the time series of the weak modes of interest in the form of complex exponentials. The most primary advantage of the proposed process in engineering applications is that the pole windows can be easily obtained and assigned from the relationship between the frequencies and their poles. Three numerical examples are studied: the first presents "the detailed numerical operation of the proposed method, the second extends the proposed method from managing one signal to managing multiple signals, and the third demonstrates the advantage of the approach compared with traditional methods. The numerical results indicate that the original signals can be decomposed into multiple complex exponentials with representative poles and corresponding residues, and that the new signals representing weak modes could be reconstructed by assigning a range of frequencies in terms of their relations with the poles. To study the performance of the proposed method when applied to offshore structures such as offshore platforms and marine risers, the experimental data from the high mode VIV experiments sponsored by the Norwegian Deepwater Programme (NDP) are used firstly. 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. Then sea-test data of two offshore platforms are used: one was collected from the JZ20-2MUQ offshore platform when it was excited by ice, and the other was collected from the WZ11-4D platform when it was excited by waves. 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.