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摘要: 工业时间序列数据常伴随缺失、漂移等异常情况, 给准确预测带来挑战. 提出一种结合迁移学习的ESN-AR模型以应对这些问题. 具体而言, 将异常数据集作为目标域, 首先采用动态时间规整筛选源域数据. 不同于仅利用源域数据进行参数初始化的传统迁移学习方法, 将源域数据的自回归特征引入ESN储备池. 该储备池统一处理目标域与源域数据的状态更新, 使源域健康的趋势信息能够持续参与目标域的预测过程. 这一设计增强了对趋势信息的关注, 从而提高了模型在数据异常时的预测鲁棒性. 接着, 通过递归最小二乘法在线更新跨域共享的输出权重, 实现知识的有效迁移. 最后, 基于风电场风电功率数据的实验结果表明, 即使在数据漂移、缺失以及低相似度的情况下, 该方法仍能保持优异的预测性能.Abstract: Industrial time-series data are often plagued by anomalies such as missing values and data drift, which pose challenges to accurate prediction. This paper proposes an ESN-AR model integrated with transfer learning to address the above issues. Specifically, the anomalous dataset is regarded as the target domain, and dynamic time warping is firstly adopted to screen source domain data. Different from conventional transfer learning methods that only use source domain data for parameter initialization, the autoregressive features of source domain data are introduced into the ESN reservoir. The reservoir uniformly performs state updating for both source and target domain data, enabling trend information from healthy source domain to continuously participate in the prediction of the target domain. This design strengthens the capture of trend information and improves the prediction robustness of the model under data anomalies. Furthermore, recursive least squares is utilized to online update cross-domain shared output weights, so as to realize effective knowledge transfer. Finally, experimental results based on wind power data of wind farms verify that the proposed method maintains superior prediction performance even under conditions of data drift, missing data and low similarity.
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图 7 目标域数据缺失时的预测效果对比
Fig. 7 Comparison of prediction performance under target domain data missing
图 8 目标域数据漂移时的预测效果对比
Fig. 8 Comparison of prediction performance under target domain data drift
图 9 不同缺失率时各网络预测结果对比
Fig. 9 Comparison of prediction results for various networks at different missing rates
图 10 不同漂移率时各网络预测结果对比
Fig. 10 Comparison of prediction results for various networks at different drift rates
图 11 目标域与源域神经元激活模式一致性分析
Fig. 11 Consistency analysis of neuron activation patterns in target and source domains
图 12 不同DTW距离下TL-ESN-AR模型的预测误差
Fig. 12 DTW distances versus prediction errors of the TL-ESN-AR model
表 1 风电场数据出现缺失现象时的预测结果比较
Table 1 Comparison of prediction results when wind farm data is missing
风电场 ESN ESN-AR TL-ESN-AR 1号风电场 1-3 1.1425e-04 1.1511e-04 1.6103e-05 1号风电场 1-5 4.4842e-04 4.6593e-04 2.0002e-04 6号风电场 6-5 9.4324e-03 1.2453e-02 5.3012e-05 3号风电场 3-4 1.5147e-03 1.9635e-03 9.3847e-05 注: 表中a-b表示目标域为a号风电场, 源域为b号风电场 
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表 2 风电场数据出现漂移现象时的预测结果比较
Table 2 Comparison of prediction results when wind farm data drifts
风电场 ESN ESN-AR TL-ESN-AR 1号风电场 1-3 1.2664e-03 3.9044e-03 2.6416e-04 1号风电场 1-5 1.7357e-02 4.5748e-02 1.2244e-04 6号风电场 6-5 6.8516e-03 1.8574e-02 1.1937e-04 3号风电场 3-4 1.7675e-03 4.9887e-03 2.0831e-04 注: 表中a-b表示目标域为a号风电场, 源域为b号风电场
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表 3 风电功率数据集之间的相似性
Table 3 Similarity between wind power datasets
数据集1 数据集2 1号风电场 2号风电场 3号风电场 4号风电场 5号风电场 6号风电场 7号风电场 1号风电场 – 109.09 115.86 95.16 87.63 96.46 104.46 2号风电场 109.09 – 113.18 106.14 105.53 108.63 110.38 3号风电场 115.86 113.18 – 111.42 111.71 109.63 110.44 4号风电场 95.16 106.14 111.42 – 101.50 74.56 82.55 5号风电场 87.63 105.53 111.71 101.50 – 95.23 102.63 6号风电场 96.46 108.63 109.63 74.56 95.23 – 66.09 7号风电场 104.46 110.38 110.44 82.55 102.63 66.09 –
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表 4 风电功率数据直接补充预测结果
Table 4 Wind power data directly supplements the prediction results
目标域 源域 1号风电场 2号风电场 3号风电场 4号风电场 5号风电场 6号风电场 7号风电场 1号风电场 – 9.9702e-03 9.6227e-03 9.6319e-03 7.6227e-03 7.8785e-03 1.0068e-02 2号风电场 8.0657e-03 – 6.5947e-03 8.3203e-03 6.4981e-03 7.0318e-03 8.8951e-03 3号风电场 1.4342e-03 1.7375e-03 – 1.5804e-03 1.3043e-03 1.1789e-03 1.8551e-03 4号风电场 1.0954e-02 1.3123e-02 1.0478e-02 – 9.2132e-03 8.2412e-03 1.4162e-02 5号风电场 2.0573e-02 1.9652e-02 1.7771e-02 1.9973e-02 – 2.1722e-02 1.9042e-02 6号风电场 9.0944e-03 1.1532e-02 8.8594e-03 1.0266e-02 7.4853e-03 – 1.2552e-02 7号风电场 1.1693e-02 1.3607e-02 1.0857e-02 1.2347e-02 1.0064e-02 9.4542e-03 –
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表 5 风电功率数据TL-ESN-AR预测结果
Table 5 Wind power data TL-ESN-AR prediction results
目标域 源域 1号风电场 2号风电场 3号风电场 4号风电场 5号风电场 6号风电场 7号风电场 1号风电场 – 3.5509e-04 5.3931e-04 4.4268e-04 5.4361e-04 3.7855e-04 6.8189e-04 2号风电场 3.8254e-04 – 4.3993e-04 4.1699e-04 4.2264e-04 5.1217e-04 8.7065e-04 3号风电场 5.7234e-04 4.4412e-04 – 6.9779e-04 5.5516e-04 3.4778e-04 6.9650e-04 4号风电场 5.1178e-04 3.4436e-04 6.4629e-04 – 5.7136e-04 2.2608e-04 5.2098e-04 5号风电场 5.2633e-04 3.8884e-04 5.7675e-04 6.1722e-04 – 5.3740e-04 6.7593e-04 6号风电场 4.2324e-04 4.4037e-04 3.7248e-04 2.3742e-04 5.7685e-04 – 2.6001e-04 7号风电场 7.1959e-04 8.2231e-04 6.3098e-04 4.7455e-04 6.4307e-04 2.4399e-04 –
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