An LSTM-based probabilistic prediction model for clock jitter
基于LSTM的时钟抖动概率预测模型

摘要

针对电力电子化电力系统中时钟抖动实时估计的工程需求，本文构建了一种基于长短期记忆网络（LSTM）的概率预测模型。模型采用双头结构，均值头输出抖动的点估计，方差头用于不确定性量化。在损失函数中引入对数校准项，并采用MSE预训练、弱校准联合训练和方差头单独校准的三阶段递进策略。将白噪声方差作为不可训练的工程先验注入方差头，使噪声引入的固有不确定性与模型估计的认知不确定性得以分离。在仿真数据集上，模型预测均方误差为7.12×10-8 s²，标准化残差标准差为1.105，不同信号频率（1~9 Hz）下方差中位数稳定在4.87×10-8 s²附近。与标准LSTM和卡尔曼滤波的对比实验表明，本文模型在预测精度接近标准LSTM的条件下，额外提供了经校准的方差输出，在平稳、缓慢变化和突变非平稳测试数据上均保持了良好的泛化能力和不确定性量化水平。

Abstract

Driven by the real-time clock jitter estimation demands in power-electronics-dominated power systems, we use the long short-term memory (LSTM) network to develop a probabilistic prediction model that provides conditional jitter estimates and their associated uncertainty simultaneously. The model uses a dual-head architecture, where a mean head predicts the conditional jitter estimate and a variance head quantifies the prediction uncertainty. We introduce a logarithmic calibration term into the loss function and adopt a three-stage training strategy: pre-training with mean squared error, jointly optimizing with a weakly calibrated loss, and fine-tuning of the variance head separately. We further inject the white noise variance into the variance head as a non-trainable engineering prior. On simulated datasets, the model achieves a mean squared error of 7.12×10-8 s2, a normalized residual standard deviation of 1.105, and a stable median variance around 4.87×10-8 s2 across signal frequencies of 1~9 Hz. Comparisons with standard LSTM and a Kalman filter show that the proposed model can maintain point prediction accuracy close to that of the standard LSTM and deliver well-calibrated variance outputs. It shows strong generalization and reliable uncertainty quantification on stationary, slowly varying, and abruptly changing non-stationary test data.