Hard to say without looking at the actual nonlinear model, but note that in general a "linearization" is valid only in a small local neighborhood of the operating point (state and input values) at which the linear model is generated. There is no guarantee that the approximation will hold for other signal profiles or at other points in the operating space.
For data based linearization (i.e., collect small-excitation response of the model at a given operating point and use it for fitting a linear model), you can conduct a series of experiments wherein you change the size/sign of your input signal and initial conditions incrementally and study the change in the resulting model for each profile. This way, you can roughly carve out the size of the operating space region over which a linearization would be valid.
