Many pulsating star light curves must be interpreted strictly within the framework of a non-linear theory. The detection of non-linear interactions between pulsation modes has increased due to the ultra-precise photometric data provided by space missions. For this reason, it is now possible and essential to continue the effort of building data-driven non-linear pulsation models. The analysis of non-linear stellar light curves has become a fundamental challenge in asteroseismology in the era of space missions. In this article, a diagnostic method is presented. It is based on an observational characterization of the non-linear behavior of high-amplitude delta Scuti (HADS) stars. It diagnoses the nature of non-linear pulsations in δ Sct stars of lower amplitudes. It potentially provides an extra hint for identifying a radial mode and determine its radial order n. Additionally, it could show signatures of moderate to rapid rotation in these stars. Overall, this article shows the capabilities for making asteroseismic inferences from studying combination frequencies in δ Sct stars.