A Multi-Frequency Input-Admittance Model of Locomotive Rectifier Considering PWM Sideband Harmonic Coupling in Electrical Railways

What the math gives to ML

The paper contributes a non-averaged small-signal mechanism: periodic PWM modulation couples a perturbation at frequency \(\omega\) to sidebands \(\omega+k\omega_s\), so a conventional single-frequency admittance can give an incorrect stability prediction above roughly half the switching frequency. Its transferable asset is a finite harmonic-transfer or lifted model whose spectral condition retains these cross-frequency couplings instead of averaging them away. A practical neural-network analogue is an aliasing-aware stability monitor and controller for periodically modulated optimizers, recurrent state-space models, or gated layers, where the predicted instability boundary can be compared directly with the boundary from an averaged Jacobian.