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.

Dynamic Frequency-Temperature Characteristic Modeling for Quartz Crystal Resonator Based on Improved Echo State Network.

Quartz crystal resonators are the key component of various kinds of electronic systems because they provide the reference frequency source of the system running clocks. However, the frequency stability is often affected by the temperature. Therefore, the frequency-temperature ( f-T ) characteristic modeling has been an important research topic in the frequency control field. The classic f-T modeling method omits the system dynamics and may lead to a large frequency compensation error in the case of rapid temperature changing. To deal with this issue, this article proposes a dynamic f-T modeling method based on improved echo state network (ESN), called residual scaled ESN (RSESN). In the proposed method, the residual modeling framework is designed for purposes of good physical understandability and high prediction precision. This framework uses the static polynomial f-T model to depict the approximated data relationship and applies the complicated network model to compensate the detailed dynamic error. To estimate the dynamic errors, one effective dynamic modeling tool, ESN, is introduced to build the dynamic compensation model for f-T characteristic of quartz crystal resonators. For a better fitting performance, the ESN activation limitations are analyzed and the scaled echo states are constructed in the improved ESN model. The modeling and testing results on the real experiment data show that the proposed method can capture the dynamic information effectively and provide better frequency deviation predictions.

Modified Modeling Method of Quartz Crystal Resonator Frequency-Temperature Characteristic With Considering Thermal Hysteresis.

The frequency-temperature ( f - T ) characteristic of quartz crystal resonators is an important topic closely related to the frequency-deviation compensation in the design of cost-effective oscillators. Traditional studies depict the f - T characteristic as a polynomial function (usually a cubic function). However, this omits the thermal hysteresis phenomenon and cannot provide a very accurate frequency compensation. To handle this issue, this article is to propose two modified f - T characteristic modeling methods with considering the thermal hysteresis. First, to reflect the thermal hysteresis property of quartz crystal resonators, a two-directional f - T model is designed by introducing two individual submodels for describing the increasing and decreasing temperature stages, respectively. Furthermore, to integrate the submodels and provide the more accurate frequency-deviation estimation, a holistic f - T characteristic model based on double-hidden layer extreme learning machine (DHL-ELM) is presented. Different from the basic ELM model, two hidden layers, including one deterministic nonlinear mapping and one random nonlinear activation layer, are constructed for a better description of f - T characteristic. To validate our studies, an experiment system is applied to obtain the testing data of the real crystal resonators, and the applications demonstrate the effectiveness of the proposed methods.