Abstract
In order to reduce the time and space complexity of operational modal analysis (OMA) for slow linear time-varying (SLTV) structures based on moving window principal component analysis (MWPCA), this paper proposes a new moving window self-iteration principal component extraction (MWSIPCE) method. Different from getting principal components by singular value decomposition (SVD) or eigenvalue decomposition (EVD) in MWPCA algorithm, MWSIPCE just extracts the first-several-orders principal components by self-iteration. Comparing with MWPCA, MWSIPCE has lower time and space complexity. What’s more, this paper explains the reason of modal exchange in some data windows in detail, and gives an illustration to how to set window length L. The OMA results on non-stationary vibration response simulation signal of time-varying cantilever beam under white noise excitation show that this method can well identify the time-varying transient modal parameters (natural frequencies and modal shapes) for SLTV structures and has less time and space consume, the algorithm is also more precise than MWPCA.
Highlights
Modal parameters (Natural frequencies, mode shapes) are essential for dynamics structural damage recognition, health monitoring [1] and independent modal space control [2]
This study proposed a time-varying operational modal analysis (OMA) method based on moving window selfiteration principal component analysis (MWSIPCE)
Theoretical values and FEA values are set as standard, which are calculated under the condition of undamped real modal shape and undamped real modal nature frequency, and moving window principal component analysis (MWPCA)
Summary
Modal parameters (Natural frequencies, mode shapes) are essential for dynamics structural damage recognition, health monitoring [1] and independent modal space control [2]. From 1980s, operational modal analysis (OMA) deals with the estimation of modal parameters from vibration data obtained in operational rather than laboratory conditions [3]. Traditional calculation method of PCA is using matrix decomposing, which includes SVD and EVD [6]. These ways calculate all principal components in one time, that makes the algorithm always has high time-space complexity. In 1969, NIPALS algorithm [7] is firstly proposed, different from traditional method, the algorithm iteratively calculates principal components. In order to reduce the time-space complexity of traditional PCA, this paper proposes a new self-iteration principal components extraction (SIPCE) algorithm which based on NIPALS algorithm
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