Low frequency mechanical vibrations are ubiquitous in practical environments, and how to efficiently harvest them with piezoelectric materials remains a challenge. Frequency up-conversion strategies—up-converting low frequency vibrations to high frequency self-oscillations—can improve the power density of piezoelectric materials. This paper mainly introduces a kind of frequency which up-converts piezoelectric energy harvesters based on an internal resonance mechanism, compared with the other mechanisms caused by mechanical impact, mechanical plucking, etc.; the internal resonance-based harvesters can up-convert the frequency under a condition of lower excitation level, less energy loss, and less wideband operation bandwidth. Benefits to practical vibrations also exist in these multi-degree-of-freedom nonlinear dynamic systems. Moreover, the value of the frequency up-conversion factor based on the 1:2:6 internal resonance mechanism can reach as much as six so far, which is also a quite a high frequency up-conversion value.

Accurate and rapid fault diagnosis is paramount to stabilizing proton exchange membrane fuel cells (PEMFC). To achieve this, this study proposes a novel fault diagnosis method that integrates a convolutional neural network (CNN), a bi-directional long short-term memory network (BiLSTM), and a waveform fault attention (WFA) mechanism. In the proposed framework, data are classified into five distinct categories utilizing a hierarchical clustering algorithm. Additionally, data augmentation techniques are implemented to bolster model performance. The introduction of amplitude attention and temporal difference attention, in conjunction with the construction of WFA, enables the accurate extraction of temporal-spatial features, significantly improving the distinguishability of fault diagnosis. Furthermore, feature contribution is evaluated using permutation feature importance (PFI) to identify key features, enhancing the interpretability of the model. Experimental findings verify that the proposed method enables high-precision fault identification, with precision values spanning 97–100% and an average stability of 98.3%, demonstrating robust performance even when the volume of original sample data is limited. This performance markedly surpasses that of extant methodologies. The comprehensive approach augments the accuracy, reliability, and interpretability of PEMFC fault diagnosis, and introduces a novel research paradigm for feature extraction, thereby possessing significant theoretical and practical application value.