石英晶振老化的建模与模型求解

为预测石英晶振的频率老化，提出了一种非线性时变模型。在一阶马尔可夫假设下，利用多层前向神经网络进行迭代逼近求解。对四种晶体的全部或部分实验数据进行了学习和预测试验。结果表明该模型不仅能拟合函数，而且可在存在野值时，根据以往的数据预测目前的频率。与其他线性模型相比，该模型的预测能力更佳，适用于多种类型的晶振老化模式，预测误差小，有很好的抗噪声能力。

The Modeling and Solution of the Frequency Aging for Quartz Crystal Oscillators

A novel nonlinear time-varying model for frequency aging of crystal oscillator was presented for the frequency aging prediction in this paper. The solution was put forward by the iterative approach through multiple-forward network under Markov hypothesis. The learning and prospect experiment was made on the basis of the total or partial frequency data of 4 kinds of crystals. The result was showed that the model could not only fit function, but also predict the present frequency according to the past data when some error data exited. Compared with the previous linear approaches, this model has better ability of prediction and is suitable for various patterns of frequency aging of crystal oscillators, and has small prediction error and good ability to resist noise.