arXiv Machine Learning By Melisa Bozaci, Alice Cicirello

Fast-varying Natural Frequencies and Damping Ratio Identification for Linear Time-Varying System

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The paper presents a physics‑enhanced machine learning method that combines a long short‑term memory network with an Extended Kalman Filter to identify fast‑varying natural frequencies and damping ratios of Linear Time‑Varying systems. Using vibration data and a physics‑based model, the approach is validated on synthetic data from a 2‑blade offshore wind turbine, achieving a maximum RMS error of 0.0012 Hz for the first Fore‑Aft mode. The study also demonstrates robustness to incorrect damping assumptions and improves damping ratio estimation compared to covariance‑driven stochastic subspace identification.

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arXiv Machine Learning
Aug 27

Adaptive Hybrid Subspace Levenberg Marquardt Algorithm with Adequacy Monitor for Large Scale Least Squares Problems

The paper introduces an Adaptive Hybrid Subspace Levenberg–Marquardt (HSLM) algorithm that tackles large‑scale nonlinear least‑squares problems by building a low‑dimensional subspace from gradient, memory, Krylov‑subspace, and randomized curvature data. It employs a deterministic adequacy monitor to adaptively enrich the subspace and decouples step acceptance from damping adjustment, using Armijo backtracking for step length and a ratio of actual to predicted reduction for damping updates. The authors prove global convergence to stationarity and local linear and superlinear convergence, and demonstrate that HSLM matches the convergence of classical and Krylov‑subspace LM while significantly reducing per‑iteration cost, especially as the parameter dimension increases.

By M. Duc Hoang, Timothy J. Lewis