Bridging nonlinear identification and industrial practice: NFR-ID with standard frequency-domain testing

Frequency-domain testing is widely adopted for the experimental characterization and qualification of engineering structures in industrial practice. However, the use of such data for nonlinear system identification is still limited, as most existing methods either rely on time-domain measurements or require access to full nonlinear frequency responses, including unstable solution branches. This paper extends the nonlinear frequency-response-based identification framework NFR-ID, originally developed for experimental continuation data, to the practically relevant case of stable-only frequency response measurements obtained from stepped-sine or frequency sweep testing. The proposed formulation targets nonlinear dynamics dominated by primary resonances and enables the identification of compact and interpretable nonlinear state-space models using stable and harmonic data only. The approach is formulated as a grey-box identification framework and assumes that the system exhibits periodic steady-state responses with the same period as the excitation. The method exploits a harmonic balance-based input-output relation and formulates a nonlinear least squares problem that can accommodate limited frequency coverage, jump phenomena, and non-uniform data quality through weighting strategies. The approach is validated on one numerical benchmark and on two experimental systems: a cantilever beam with motion limiters and a double-well oscillator. For the former, the raw experimental data are made openly available to support reproducibility. The results show that accurate nonlinear models can be identified using only stable fundamental-harmonic data for systems satisfying the proposed assumptions, while retaining predictive capability. The double-well system demonstrates that additional harmonic information may be required when the selected nonlinearities are not observable from the fundamental component alone. By enabling nonlinear system identification directly from standard frequency-domain tests, this work lowers the barrier for the adoption of advanced nonlinear modeling techniques in industrial structural dynamics.