Feature-Weighted Echo State Network for Dynamic Frequency Offset Modeling of Quartz Crystal Resonators

Quartz crystal resonators are widely used as reference frequency sources in modern electronic systems. However, their frequency often deviates from the nominal value due to the significant change in the ambient temperature. Therefore, it is of great value to develop an accurate dynamic frequency offset model regarding temperature changes. In this article, a novel feature-weighted echo state network (FWESN) method is presented to capture the dynamic frequency-temperature ( f - T ) characteristic of quartz crystal resonators. Different from the traditional echo state network (ESN), which simply takes the temperature measurement signal as a single model input variable, the proposed method mines the feature information hidden in the temperature measurement series to construct the model input vector. Specifically, five dynamic features are designed to substitute for the original temperature signal by investigating the influence mechanism of temperature versus frequency. Furthermore, considering the difference in these features' importance, two feature weighting strategies, including the Pearson's correlation coefficient (PCC)-based and particle swarm optimization (PSO)-based, are proposed to assign the different weights to the five features. Finally, the weighted features are fed into the ESN model to implement the dynamic frequency offset estimation. The application results on the real experiment datasets demonstrate that the presented FWESN method can estimate the frequency offset more precisely than the basic ESN method.