Physics- and hardware-aware frequency pair selection for deployment-ready nonlinear Lamb wave mixing

Abstract. Nonlinear Lamb wave mixing can reveal early micro-cracks through intermodulation products at f±=fa±fb, yet its deployment is often hindered by the lack of a pre-acquisition rule for selecting tone pairs that are simultaneously phase-coherent and measurable on a given instrument chain. We propose a physics- and hardware-aware ranking score, J(fa,fb), that integrates (i) normalised phase mismatch |Δk|/kmt and the implied interaction length Lint, (ii) a path length term Lpath/Lint, (iii) measured receive-chain sensitivity Grx(f+)/G0, and (iv) a dynamic-range penalty that accounts for two-tone leakage and front-end limits. Embedded in a three-step workflow (dispersion pre-filtering, hardware screening, and top-K ranking), the score shortlists excitation pairs prior to spectral phase inversion (SPI-4) same-spectrum readout. Experiments on an aluminium plate with controlled crack growth (0–12 mm) show that low-J pairs consistently deliver higher mixed-line SNR(f+), concentrate in the low-mismatch basin, and cross a conservative detection threshold after only a few millimetres of extension, whereas higher-J pairs remain near the noise floor. The results demonstrate a transparent and reproducible route from physics and instrument constraints to deployment-ready frequency pair selection for baseline-free nonlinear guided-wave inspection.