This paper addresses the challenge of estimating multiple highly oscillating amplitudes within the nonlinear chirp signal model. The problem is analogous to the mode detection task with fixed instantaneous frequencies, where the oscillating amplitudes signify mechanical vibrations concealing crucial information for predictive maintenance. Existing methods often focus on single-frequency estimation, employ simple amplitude functions, or impose strong noise assumptions. Furthermore, these methods frequently rely on arbitrarily chosen hyperparameters, leading to sub-optimal generalization for a diverse range of amplitudes. To address these limitations, our approach introduces two estimators, based on Capon filters and negative log-likelihood approaches respectively, that leverage locally stationary assumptions and incorporate hyperparameters estimation. The results demonstrate that, even under challenging conditions, these estimators yield competitive outcomes across various noisy scenarios, mitigating the drawbacks associated with existing methods.