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Abstract Mode shape information plays the essential role in deciding the spatial pattern of vibratory response of a structure. The uncertainty quantification of mode shape, i.e., predicting mode shape variation when the structure is subjected to uncertainty, can provide guidance for robust design and control. Nevertheless, computational efficiency is a challenging issue. Direct Monte Carlo simulation is unlikely to be feasible especially for a complex structure with a large number of degrees-of-freedom. In this research, we develop a new probabilistic framework built upon the Gaussian process meta-modeling architecture to analyze mode shape variation. To expedite the generation of input data set for meta-model establishment, a multi-level strategy is adopted which can blend a large amount of low-fidelity data acquired from order-reduced analysis with a small amount of high-fidelity data produced by high-dimensional full finite element analysis. To take advantage of the intrinsic relation of spatial distribution of mode shape, a multi-response strategy is incorporated to predict mode shape variation at different locations simultaneously. These yield a multi-level, multi-response Gaussian process that can efficiently and accurately quantify the effect of structural uncertainty to mode shape variation. Comprehensive case studies are carried out for demonstration and validation. 

Condition assessment of machinery components such as gears is important to maintain their normal operations and thus can bring benefit to their life circle management. Data-driven approaches haven been a promising way for such gear condition monitoring and fault diagnosis. In practical situation, gears generally have a variety of fault types, some of which exhibit continuous severities of fault. Vibration data collected oftentimes are limited to reflect all possible fault types. Therefore, there is practical need to utilize the data with a few discrete fault severities in training and then infer fault severities for the general scenario. To achieve this, we develop a fuzzy neural network (FNN) model to classify the continuous severities of gear faults based on the experimental measurement. Principal component analysis (PCA) is integrated with the FNN model to capture the main features of the time-series vibration signals with dimensional reduction for the sake of computational efficiency. Systematic case studies are carried out to validate the effectiveness of proposed methodology. 

Charge-density waves (CDWs) are a ubiquitous form of electron density modulation in cuprate superconductors. Unveiling the nature of quasistatic CDWs and their dynamical excitations is crucial for understanding their origin––similar to the study of antiferromagnetism in cuprates. However, dynamical CDW excitations remain largely unexplored due to the limited availability of suitable experimental probes. Here, using resonant inelastic X-ray scattering, we observe dynamical CDW excitations in Bi2Sr2LaCuO6+δ (Bi2201) superconductors through its interference with the lattice. The distinct anomalies of the bond-buckling and the bond-stretching phonons allow us to draw a clear picture of funnel-shaped dynamical CDW excitations in Bi2201. Our results of the interplay between CDWs and the phonon anomalies shed light on the nature of CDWs in cuprates.