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arXiv2026

NL-FRA: A MATLAB package for nonlinear frequency response analysis

Nonlinear Output Frequency Response Functions (NOFRFs) provide a one-dimensional frequency-domain representation of nonlinear dynamics, enabling direct decomposition of an output spectrum into contributions from different orders of nonlinearity. NL-FRA (NonLinear Frequency Response Analysis) is an open-source MATLAB package implementing a data-driven Least Squares (LS) method for estimating NOFRFs directly from system input-output data. It provides an integrated workflow for NOFRF estimation, validation, and visualisation, together with nonlinear transmissibility analysis. The package supports different types of inputs, i.e. general band-limited, multi-one and harmonic inputs, and includes routines for identifying the frequency ranges over which each nonlinear order contributes to the output. Furthermore, since the LS approach estimates NOFRFs directly from input-output data, it can be applied to experimental measurements or data generated using any suitable dynamic model of the system. The software facilitates interpretable nonlinear frequency-domain analysis for applications including fault diagnosis, condition and structural health monitoring, and biomedical engineering.

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arXiv2026

QABBA: Symbolic Time-Series Compression via Integer-Quantized Aggregation

The expansion of time-series data from sensors and monitoring systems has made compact representations increasingly important. Such representations should retain signal structure while cutting storage, transmission and computation costs. Adaptive Brownian Bridge-based Aggregation (ABBA) addresses this need by converting long numerical series into short symbolic sequences, but reductions in parameter storage and computational precision remain desirable. We propose Quantized ABBA (QABBA), a quantized version of ABBA. By quantizing the symbolic centers, QABBA reduces the parameter footprint and enables integer arithmetic while maintaining high reconstruction quality. We establish several error bounds for the additional approximation introduced by quantization: a dimension-free bound on the excess error of each segment, a time-domain reconstruction-error bound, a stability condition for symbolic assignment, and a rule for allocating bits between segment lengths and increments. The resulting symbolic strings can be passed directly to a pretrained large language model (LLM) without any extra time-series embedding layer. Experiments on the Monash regression archive, UCR Time Series Classification Archive, and UEA Multivariate Time Series Classification Archive demonstrate a practical trade-off among storage, reconstruction accuracy and downstream predictive performance. QABBA therefore provides an error-controlled, low-precision symbolic representation for time-series compression and LLM-based analysis.

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