Structural damage identification method combining VMD and ARIMA model

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Journal of Vibration and Shock ›› 2025, Vol. 44 ›› Issue (5) : 131-139.

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Structural damage identification method combining VMD and ARIMA model

YAO Xiaojun*1, SUN Shoupeng1, WANG Qiang1, YANG Xiaomei2

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Abstract

To locate the instant and location of abrupt structural damage accurately, this paper proposes a damage identification method based on variational mode decomposition (VMD) and the autoregressive integrated moving average model (ARIMA). Initially, the method accurately selects the initial central frequencies of high-energy modes and the number of modes to be decomposed using the autoregressive model power spectrum. Then, the variational mode decomposition method is applied to decompose the vibration non-stationary signal into several stationary signal components, followed by fitting each order signal component using the ARIMA model to obtain model residuals. The specific time of damage is determined by analyzing the residuals obtained from fitting the signal components with ARIMA. Finally, the structural modal shapes are obtained using principal component analysis (PCA), and a damage index that integrates frequency and modal shape is constructed. Combined with a damage threshold, the location of the damage is pinpointed. Furthermore, the method is analyzed using numerical examples of a ten-degree-of-freedom structure under seismic excitation and the monitoring acceleration data of an actual steel bridge. The results demonstrate that the proposed method can accurately locate the occurrence time and location of structural damage under both stationary and non-stationary excitations.

Key words

damage identification / variational modal decomposition / autoregressive integration moving average model / autoregressive spectrum / model residual

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YAO Xiaojun1, SUN Shoupeng1, WANG Qiang1, YANG Xiaomei2. Structural damage identification method combining VMD and ARIMA model[J]. Journal of Vibration and Shock, 2025, 44(5): 131-139

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