This paper aims to address the low-accuracy or inapplicable challenges when applying the existing ones to non-equidistant, noisy sequential data. First, a penalized spline smoothing technique is introduced to learn intrinsic functions together with their high-order derivatives from noise data, weakening the effect of temporal distributions and measurement errors. Then, a general formula of functional grey relational degrees is designed to synthesize both static and dynamic relational degrees. Subsequently, we discuss the properties of normality and closeness, decomposed forms, as well as the practical guides. The empirical results on analyzing erosion and wear of gun barrels show that the proposed method accurately identifies the relationship between erosion and wear at different profiles and bullet velocity reduction, and outperforms the competitive models, indicating its reliability and effectiveness.