It is significant for the machinery fault diagnosis to extract the fault information from the multi-component vibration signal. Feature mode decomposition (FMD) which can accurately separate the fault feature has been widely verified and accepted in this field. However, it greatly limited its application that FMD cannot be directly applied under the speed-varying condition (SVC) since its decomposition objective, correlated kurtosis, is only defined in the stationary condition. Motivated by this, a new angle-domain feature mode decomposition (AFMD) is tailored under the speed-varying condition. In this paper, average kurtosis (AK) which inherently highlights the periodic impulses from the angle domain is firstly used as the decomposition objective. Subsequently, a finite impulse response filter bank initialized by the Hanning window is designed to provide a direction for the decomposition. Then, the adaptive filtering decomposition is iteratively performed constrained by the objective AK. Finally, the redundant and mixing modes are removed by the mode dropout strategy with correlation coefficient as its criterion. The simulations and experiments validate the effectiveness of the proposed method AFMD under SVC and its success in extending FMD to the speed-varying condition.

Lamb wave-based damage identification and localization methods hold the potential for nondestructive evaluation and structural health monitoring. Dispersive and multimodal characteristics lead to complicated Lamb wave signals that are challenging to be analyzed. Deep learning architectures could identify damage-related features effectively. Convolutional neural network (CNN) is a promising architecture that has been widely applied in recent years. However, this data-driven approach still lacks a certain degree of physical interpretability and requires a large number of parameters. In this article, an interpretable Lamb wave convolutional sparse coding (LW-CSC) method is proposed for structural damage identification and localization. First, toneburst signals at different center frequencies are considered in the first convolutional layer. The network convolves the waveforms with a set of parametrized functions that implement band-pass filters, which performs more physical interpretability compared to conventional CNN model. Subsequently, the damage features are extracted according to the multi-layer iterative soft thresholding algorithm for multi-layer CSC model, which could realize a deeper network without adding parameters unlike CNN. Finally, Lamb wave-based damage localization is visualized using an imaging algorithm. The experimental results demonstrate that the proposed method not only enables improvement of the classification accuracy but also achieves structural damage localization accurately.

Composite materials are progressively employed in many safety-critical structural applications due to their superior properties. Structural health monitoring techniques based on Lamb waves have been utilized to assess the damages of composite structures. Recently, deep learning algorithms are adopted for damage detection and localization. Identifying valid damage-related features through neural networks is a crucial step in the analysis process. However, most implemented deep learning architectures are still lacking physical interpretability to some extent. In this paper, a dense convolutional sparse coding network (DCSCNet) is presented for Lamb wave-based damage localization in composite structures, providing a possibility to interpret current networks. In DCSCNet, narrowband Hanning windowed toneburst signals are utilized as kernels of the first convolutional layer to learn more meaningful features. Dense connection is theoretically demonstrated in the scope of DCSCNet, which gathers multiple feature maps directly to develop the potential of the network through feature reuse. The multi-layer iterative soft thresholding algorithm with the dense connection is then employed for solving the multi-layer convolutional sparse coding model. Moreover, effective Squeeze-Excitation is introduced as the channel attention module to boost the representational capability of the network. The experimental results demonstrate the high-performance and interpretable characteristics of the proposed DCSCNet, verifying its feasibility and effectiveness in Lamb wave-based damage localization of composite structures.