Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2609.08723

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

Rajintha Gunawardena·Zi-Qiang Lang·Fei He
View original source ↗Read source document ↗Export metadata ↓

Abstract

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.

Explore related subjects

eess.SYcs.SYeess.SP

Keep this discovery

BibTeXRIS

Rajintha Gunawardena, Zi-Qiang Lang, Fei He. 2026-09-08. NL-FRA: A MATLAB package for nonlinear frequency response analysis. https://arxiv.org/abs/2609.08723

Cite the original work for its findings. Save a collection to share your selection of sources.

Discover connections

cs.SY subjecteess.SP subjecteess.SY subject

Connections use source metadata and explicit phrase matches, not verified experimental comparisons.

KEEP EXPLORING

Related papers

arXiv2026

A simple derivation of the Kalman filter

In this lecture note, we present a concise and self-contained derivation of the discrete-time Kalman filter equations that requires only a basic understanding of least squares estimation. The treatment is designed to minimize mathematical overhead while preserving both rigor and generality.

math.OC↗
arXiv2026

Constrained Parameter Update Law for Adaptive Control

In this paper, constrained parameter update laws for adaptive control are developed using barrier constraints. An interpretation of the parameter update law from a constrained optimization problem, in which a regularized Barrier saddle function is formulated to incorporate parameter constraints using inverse and logarithmic barrier functions from interior-point methods. The resulting constrained update law is integrated with an adaptive trajectory tracking controller, enabling online learning of the unknown system model parameters. Forward invariance of the parameter estimate is established and Lyapunov stability of the closed-loop system with the constrained parameter update law is derived. The effectiveness of the proposed constrained adaptive control law is demonstrated through simulations, which validate its ability to maintain parameter estimates within prescribed bounds while ensuring convergence to the true parameter values and achieving steady state tracking performance.

math.OC↗
arXiv2026

Blockage-Aware Multi-RIS Sensing and Optimization for mmWave Smart Radio Environments

Millimeter-wave (mmWave) multi-user MIMO systems are highly vulnerable to blockage, and reconfigurable intelligent surfaces (RIS) have been proposed as a remedy. However, RIS links may themselves be blocked, while most prior works assume ideal RIS availability. We propose an end-to-end blockage-aware multi-RIS weighted sum-rate (WSR) optimization framework. The BS transmits short per-RIS indexed synchronization signals, enabling each user to identify blocked panels through a simple energy detection test. Based on the detected feasible sets, we jointly optimize the BS precoder and RIS phases via a Closed-form Riemannian Phase Alignment (CRPA) algorithm. CRPA provides unit-modulus-preserving closed-form updates, requiring no projection or line search, and ensures monotone ascent. Simulations validate reliable blockage detection and notable WSR and convergence gains over existing baselines.

eess.SY↗