Rolling bearing fault diagnosis based on acoustic-vibration data fusion and mode decomposition combined with the crested porcupine optimization algorithm.

Variational Mode Decomposition (VMD) is extensively utilized in the domain of rotating machinery fault diagnosis. Nevertheless, the reliance on empirical parameter tuning and the limitations inherent in traditional single-signal (either vibration signals or acoustic signals) fault diagnosis methods present substantial challenges. These include incomplete information and high sensitivity to noise.

Partial Wave Amplitude Basis and Selection Rules in Effective Field Theories.

We derive the generalized partial wave expansion for N→M scattering amplitude in terms of spinor helicity variables. The basis amplitudes of the expansion with definite angular momentum j consist of the Poincaré Clebsch-Gordan coefficients. Moreover, we obtain a series of selection rules that restrict the anomalous dimension matrix of effective operators and how effective operators contribute to some 2→N amplitudes at the loop level.