NL-FRA：用于非线性频率响应分析的MATLAB软件包
NL-FRA: A MATLAB package for nonlinear frequency response analysis
AI总结：
NL-FRA是一个开源MATLAB软件包，采用数据驱动最小二乘法直接从输入输出数据估计非线性输出频率响应函数，提供估计、验证、可视化和非线性传递率分析的一体化流程，适用于故障诊断和健康监测。
AI中文摘要：
非线性输出频率响应函数（NOFRFs）为非线性动力学提供了一种一维频域表示，能够将输出频谱直接分解为不同非线性阶次的贡献。NL-FRA（非线性频率响应分析）是一个开源的MATLAB软件包，实现了数据驱动的最小二乘（LS）方法，可直接从系统输入输出数据中估计NOFRFs。该软件包提供了NOFRF估计、验证和可视化的集成工作流程，以及非线性传递率分析。该软件包支持不同类型的输入，即一般带限输入、多一谐波输入和谐波输入，并包含用于识别每个非线性阶次对输出贡献的频率范围的例程。此外，由于LS方法直接从输入输出数据估计NOFRFs，因此它可应用于实验测量或使用任何合适的系统动态模型生成的数据。该软件促进了可解释的非线性频域分析，适用于故障诊断、状态与结构健康监测以及生物医学工程等应用。
英文摘要：
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.
