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Abstract Direct inverse analysis of faults in machinery systems such as gears using first principle is intrinsically difficult, owing to the multiple time- and length-scales involved in vibration modeling. As such, data-driven approaches have been the mainstream, whereas supervised trainings are deemed effective. Nevertheless, existing techniques often fall short in their ability to generalize from discrete data labels to the continuous spectrum of possible faults, which is further compounded by various uncertainties. This research proposes an interpretability-enhanced deep learning framework that incorporates Bayesian principles, effectively transforming convolutional neural networks (CNNs) into dynamic predictive models and significantly amplifying their generalizability with more accessible insights of the model's reasoning processes. Our approach is distinguished by a novel implementation of Bayesian inference, enabling the navigation of the probabilistic nuances of gear fault severities. By integrating variational inference into the deep learning architecture, we present a methodology that excels in leveraging limited data labels to reveal insights into both observed and unobserved fault conditions. This approach improves the model's capacity for uncertainty estimation and probabilistic generalization. Experimental validation on a lab-scale gear setup demonstrated the framework's superior performance, achieving nearly 100% accuracy in classifying known fault conditions, even in the presence of significant noise, and maintaining 96.15% accuracy when dealing with unseen fault severities. These results underscore the method's capability in discovering implicit relations between known and unseen faults, facilitating extended fault diagnosis, and effectively managing large degrees of measurement uncertainties. 

Abstract Timely and accurate bearing fault detection plays an important role in various industries. Data-driven deep learning methods have recently become a prevailing approach for bearing fault detection. Despite the success of deep learning, fault diagnosis performance is hinged upon the size of labeled data, the acquisition of which oftentimes is expensive in actual practice. Unlabeled data, on the other hand, are inexpensive. To fully utilize a large amount of unlabeled data together with limited labeled data to enhance fault detection performance, in this research, we develop a semi-supervised learning method built upon the autoencoder. In this method, a joint loss is established to account for the effects of both the labeled and unlabeled data, which is subsequently used to direct the backpropagation training. Systematic case studies using the Case Western Reserve University (CWRU) rolling bearing dataset are carried out, in which the effectiveness of this new method is verified by comparing it with other benchmark models. 

Tunable piezoelectric metasurfaces have been proposed as a means of adaptively steering incident elastic waves for various applications in vibration mitigation and control. Bonding piezoelectric material to thin structures introduces electromechanical coupling, enabling structural dynamics to be altered via tunable electric shunts connected across each unit cell. For example, by carefully calibrating the inductive shunts, it is possible to implement the discrete phase shifts necessary for gradient-based waveguiding behaviors. However, experimental validations of localized phase shifting are challenging due to the narrow bandgap of local resonators, resulting in poor transmission of incident waves and high sensitivity to transient noise. These factors, in combination with the difficulties in experimental circuitry synthesis, can lead to significant variability of data acquired within the bandgap operating region. This paper presents a systematic approach for extracting localized phase shifts by taking advantage of the inherent correlation between the incident and transmitted wavefronts. During this procedure, matched filtering greatly reduces noise in the transmitted signal when operating in or near bandgap frequencies. Experimental results demonstrate phase shifts as large as −170° within the locally resonant bandgap, with an average 28% reduction in error relative to a direct time domain measurement of phase, enabling effective comparison of the dispersive behavior with corresponding analytical and finite element models. In addition to demonstrating the tunable waveguide characteristics of a piezoelectric metasurface, this technique can easily be extended to validate localized phase shifting of other elastic waveguiding metasurfaces. 

Abstract Piezoelectric transducers are widely employed in vibration control and energy harvesting. The effective electro-mechanical coupling of a piezoelectric system is related to the inherent capacitance of the piezoelectric transducer. It is known that passive vibration suppression through piezoelectric LC shunt can be enhanced with the integration of negative capacitance which however requires a power supply. This research focuses on the parametric investigation of a self-sustainable negative capacitance where the piezoelectric transducer is concurrently used in both vibration suppression and energy harvesting through LC shunt. The basic idea is to utilize the energy harvesting functionality of the piezoelectric transducer to aid the usage of negative capacitance in terms of power supply. Specifically, the power consumption and circuitry performance with respect to negative capacitance circuit design is analyzed thoroughly. Indeed, the net power generation is the difference between available power in the shunt circuit and the power consumption of the negative capacitance circuit. There exists complex tradeoffs between net power generation and the vibration suppression performance when we use different resistance values in the negative capacitance circuit. It is demonstrated through correlated analytical simulation and experimental study that the proper selection of the resistance values in the negative capacitance circuit can result in vibration suppression enhancement as well as improved net power generation, leading to a self-sustainable negative capacitance scheme.