One microwave propagating mode extraction algorithm is proposed for microwave waveguide using variational mode decomposition (VMD). The reflected signal acquired by the waveguide can be seen as the mixture of the propagating mode and evanescent modes. The propagating mode contains information regarding defects and evanescent modes can be treated as noise. By using VMD, the propagating mode can be extracted. Currently, decomposition models are mostly limited by lacking mathematical theory, backward error correction not being allowed in most methods due to the recursive sifting, or the inability to properly cope with noise. In VMD, the bands have been determined adaptively and the corresponding modes are estimated concurrently. An ensemble of modes are derived, and these modes collectively reproduce the input signal while each is being smoothed after demodulation into the baseband. This proposed model is particularly robust to sampling and noise. The bridge between the physical and mathematical models is demonstrated. A coated steel defect detection experiment is conducted using an X-band open-ended rectangular waveguide to evaluate the efficacy of the VMD method. Two samples are demonstrated. The steel with hole sample has a regular and clear defect, whereas the defect of steel with peening is fuzzy. For both samples, the VMD results can accurately identify the defects.

Active vibration control approaches have been widely applied on improving reliability of robotic systems. For linear vibratory systems, the vibration features can be altered by modifying poles and zeros. To realize the arbitrary assignment of the closed-loop system poles and zeros of a linear vibratory system, in this paper, an active PID input feedback vibration control method is proposed based on the receptance method. The establishment and verification of the proposed method are demonstrated. The assignable poles during feedback control are calculated and attached with importance to expand the application of the integral control. Numerical simulations are conducted to verify the validity of the proposed method in terms of the assignment of closed-loop poles, zeros, and both. The results indicate that the proposed method can be used to realize the active vibration control of closed-loop system and obtain the desired damping ratio, modal frequency, and dynamic response.

Condition monitoring (CM) is widely used in wind turbines (WTs) to reduce operation and maintenance (O&M) costs. Bearings are crucial components in WT and many bearing CM approaches have focused on vibration analysis. Statistical theory and artificial intelligence-based WT bearings evaluation methods require mass data for training, which makes the detection of incipient failures barely possible. In this paper, a WT bearing performance evaluation method is proposed based on the similarity analysis of fuzzy k-principal curves (FKPCs) in manifold space. For a start, 38 features are extracted from bearing vibration signals to constitute high-dimensional feature matrices. The feature matrices for the healthy samples and the samples to be evaluated are then transformed into 3-D space. Afterward, the FKPCs are extracted and the similarities among the curves of samples are calculated based on the Hausdorff distance to evaluate the performance of the bearing. Bearing degradation experiments are investigated to verify the efficiency of the proposed method. The results indicate that the proposed FKPC method can portray the degradation trend of bearings accurately with the capability of detecting incipient failures. The proposed method can be applied in the case of small-size training samples with stable performance. INDEX TERMS Wind farms, condition monitoring, fault diagnosis, prognostics and health management.

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