用加权后验高斯过程建模近似周期时间序列，兼顾结构规律与重复差异。
Generative Modeling of Approximately Periodic Time Series by a Posterior-Weighted Gaussian Process
- 通过新型核函数调制后验，分离重复内结构与重复间差异
- 生成轨迹在重复间保持均值一致，同时允许平滑变化
- 适合工业与网络物理系统中周期性但不完全重复的数据
工业与网络物理系统中的离散自动化过程常呈现近似周期行为：相邻重复具有相似轨迹，但在持续时间、振幅和细微动态上存在差异。传统高斯过程建模面临挑战：严格周期模型抑制重复间变异，非周期模型则无法捕捉强结构规律。本文提出一种针对近似周期时间序列的随机生成模型，基于后验受控的高斯过程，通过两阶段构建实现重复内结构与重复间变异的解耦。该模型在各重复间保持相同的均值函数，同时支持重复间的平滑变化。实验表明，该方法可在模拟数据集上生成真实感强的合成轨迹。
原文摘要 · Abstract (English)
Discrete automated processes in industrial and cyber-physical systems often exhibit a repetitive structure in which successive repetitions follow a common trajectory while differing in duration, amplitude, and fine-scale dynamics. Such \emph{approximately periodic} behavior poses a challenge for Gaussian Processes (GP) modeling: strictly periodic models suppress inter-repetition variability, while non-periodic models fail to capture the strong structural regularities required for generation. In this work, we propose a stochastic generative model for approximately periodic time series. The model is based on a GP whose posterior is modulated by a novel kernel. Our approach decouples intra-repetition structure from inter-repetition variability through a two-stage construction which yields a generative distribution with a identical mean function across repetitions, while allowing smooth variation between repetitions. The modeling choices are supported by an implementation in which realistic synthetic trajectories are generated from toy datasets.
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