Abstract
From the viewpoint of vibration control, if the amplitude of the main frequencies of the vibration response can be reduced, the vibration energy of the structure is greatly reduced. Modal parameters, including modal shapes, natural frequencies, and damping ratios, can reflect the dynamics of the structure and can be used to control the vibration. This paper integrates the idea of “forgetting factor weighting” into eigenvector recursive principal component analysis, and then proposes an operational modal analysis (OMA) method that uses eigenvector recursive PCA with a forgetting factor (ERPCAWF). The proposed method can identify the transient natural frequencies and transient modal shapes online and realtime using only nonstationary vibration response signals. The identified modal parameters are also suitable for online, real-time health monitoring and fault diagnosis. Finally, the modal identification results from a three-degree-of-freedom weakly damped linear time-varying structure shows that the ERPCAWF-based OMA method can effectively identify transient modal parameters online using only nonstationary response signals. The results also show that the ERPCAWF-based approach is faster, requires less memory space, and achieves higher identification accuracy and greater stability than autocorrelation matrix recursive PCA with a forgetting factor-based OMA.
Highlights
During the production and use of a structure, vibration is inevitable
The scope of application of the proposed eigenvector recursive Principal component analysis (PCA) with a forgetting factor (ERPCAWF)-based operational modal analysis (OMA) for linear time-varying (LTV) structures is as follows: (1) For real modal analysis in the modal coordinates, the vibration response signals of weakly damped mechanical structures can be decomposed into the inner product of the modal shapes matrix and modal responses matrix
(1) For the LTV three-DOF system considered in the simulations, Figure 7 clearly shows that different forgetting factors have an effect on the recognition of the modal shape for ERPCAWF-based
Summary
During the production and use of a structure, vibration is inevitable. Vibration can cause damages to the structure and endanger human health [1]. Guan et al [36] developed an ARPCA with a forgetting factor (ARPCAWF) for OMA, and identified transient modal parameters for a beam with time-varying density by updating the autocorrelation matrix online This method is suitable for both SLTV and fast linear time-varying (FLTV) structures, but suffers from pathological matrix problems and modal exchange, and has high computation times and memory requirements. Integrating the idea of “forgetting factor weighting” and the technology of ERPCA, we propose an ERPCAWF-based OMA method to identify the transient natural frequencies and transient modal shapes of LTV structures using only nonstationary response signals under unmeasured stationary ambient loads This method is suitable for both SLTV and FLTV structures.
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