Abstract: An improved fractal prediction algorithm based on phase space reconstruction sample selection method is proposed.This algorithm chooses the embedding dimension and delay time obtained from the phase space reconstruction as the data samples selection basis，employs the iterative collage theorem and interpolation algorithm to implement the fractal time series forecasting，and sets up the fractal forecasting model of the time series at the same time.The effectiveness of the improved algorithm is checked by using it in L-PLC noise series forecasting.The results show that the prediction accuracy is improved.The improved algorithm optimizes the method of data sample selecting and improves the similarity of data samples，so it is more suitable to the prediction of time series with uncertain statistical self-similarity and uncertain periodicity.

Key words: phase-space reconstruction, fractal prediction, collage theorem, fractal interpolation, low-voltage power line noise sequence

摘要： 提出一种基于相空间重构原理进行样本选取的改进分形预测算法。该算法将时间序列在相空间重构中得到的嵌入维数和时间延迟作为分形预测中数据样本的选择依据，结合分形理论的拼贴定理和插值迭代算法，实现时间序列的分形预测，建立时间序列的分形预测模型。利用此改进算法对低压电力线噪声序列进行预测的结果表明，与现有分形算法相比，改进算法提高了数据样本间的相似度，优化了数据样本的选取，明显提高了预测的精度，适合于对自相似性和周期性不明确的时间序列的预测。

关键词: 相空间重构, 分形预测, 拼贴定理, 分形插值, 低压电力线噪声序列