Adaptive Ensemble Modelling Approach Based on Updating Sample Intelligent Identification
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摘要: 选择表征建模对象特性漂移的新样本对软测量模型进行自适应更新，能够降低模型复杂度和运行消耗，提高模型可解释性和预测精度.针对新样本近似线性依靠程度（Approximate linear dependence, ALD）和预测误差（Prediction error, PE）等指标只能片面反映建模对象的漂移程度，领域专家结合具体工业过程需要依据上述指标和自身积累经验进行更新样本的有效识别等问题，本文提出了基于更新样本智能识别算法的自适应集成建模策略.首先，基于历史数据离线建立基于改进随机向量泛函连接网络（Improved random vector functional-link networks, IRVFL）的选择性集成模型；然后，基于集成子模型对新样本进行预测输出后采用在线自适应加权算法（On-line adaptive weighting fusion, OLAWF）对集成子模型权重进行更新，实现在线测量阶段对建模对象特性变化的动态自适应；接着基于领域专家知识构建模糊推理模型对新样本相对ALD（Relative ALD, RALD）值和相对PE（Relative PE, RPE）值进行融合，实现更新样本智能识别，构建新的建模样本库；最后实现集成模型的在线自适应更新.采用合成数据仿真验证了所提算法的合理性和有效性.Abstract: Some new samples can represent concept drift of the modeling plant. Adaptive updating soft sensor model with these new samples can reduce model complexity and running consumption, improve model interpretation and prediction performance. Concept drift embodies on both approximate linear dependence (ALD) and prediction error (PE). In industrial practice, whether to update the old soft measuring models should be decided by the domain experts. Aimmed at these problems, a new online ensemble modeling approach based on updating sample intelligent identification is proposed in this paper. At first, the offline ensemble model based on improved random vector functional-link networks (IRVFL) algorithm is used for online prediction using the new sample. Then, relative ALD (RALD) and relative PE (RPE) values of the new sample are fed into the fuzzy inference model based on domain expert's knowledge, whose output is used to identify whether this new sample is taken to updating the model. At last, the ensemble model is updated with the re-training strategy. Simulation results based on synthetic data show that the proposed method is valid and effective.
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图 2 基于潜变量特征的选择性集成IRVFL离线软测量模型建模策略
Fig. 2 Selective ensemble IRVFL off-line soft sensor model based on latent variable features
图 3 离线模型学习参数与预测误差
Fig. 3 Learning parameters and prediction errors of the off-line model
图 4 测试样本相对于离线模型(建模样本)的RALD值、RPE值及模糊融合值
Fig. 4 RALD, RPE and fuzzy fusion values of the testing samples relative to off-line model (modeling samples)
图 5 $\theta _{{\rm com}}=-1.5$ 时的在线集成模型预测输出
Fig. 5 Prediction output of the online ensemble model with $\theta _{{\rm com}}=-1.5 $
图 6 基于不同更新样本识别方法软测量模型的预测误差
Fig. 6 Prediction errors of the soft sensor models based on different updating sample identification methods
表 1 更新样本模糊推理规则
Table 1 Fuzzy inference rulers of the updating sample
Us RALD NB NM NS Z PS PM PB R NB NB NB NM NM NS NS Z P NM NB NM NM NS NS Z PS E NS NM NM NS NS Z PS PS Z NM NS NS Z PS PS PM PS NS NS Z PS PS PM PM PM NS Z PS PS PM PM PB PB Z PS PS PM PM PB PB 
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表 2 仿真数据的方差贡献率(%)
Table 2 Percent variance contribution of the simulation data(%)
LV 输入数据(X-Block) 输出数据(Y-Block) 潜变量贡献率 累计贡献率 潜变量贡献率 累计贡献率 1 69.79 69.79 66 66 2 28.33 98.11 25.66 91.65 3 1.62 99.73 7.86 99.51 4 0.16 99.89 0.05 99.56 5 0.11 100 0 99.57
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表 3 仿真数据在线更新模型重复20次的统计结果
Table 3 Statistical results of the online updating model with repeated 20 times for the simulation data
更新样本识别方法 统计项 更新样本预设定阈值 –2.5 –2 –1.5 –1 0 1 非更新方法 最大误差 0.1886 0.1885 0.1884 0.1894 0.1887 0.1892 最小误差 0.1875 0.1865 0.187 0.1872 0.1872 0.1871 误差均值 0.1868 0.1876 0.1878 0.1879 0.1878 0.1879 误差方差 0.0004 0.0004 0.0004 0.0005 0.0004 0.0005 基于RALD的更新样本识别方法 最大误差 0.1758 0.1152 0.0989 0.1127 0.1004 0.1767 最小误差 0.0628 0.0794 0.0856 0.085 0.087 0.1658 误差均值 0.119 0.0876 0.0892 0.0886 0.0911 0.1878 误差方差 0.0376 0.0094 0.0044 0.006 0.0033 0.0071 更新次数最多的样本编号 92, 94, 96, 118, 119, 141 99, 100, 106, 98, 100, 103 99, 106, 118, 124 99, 106 99, 123, 149, 154 - 平均更新次数 11 5 2 2 2 0 基于RPE的更新样本识别方法 最大误差 0.058 0.0665 0.0486 0.085 0.1198 0.1701 最小误差 0.0396 0.038 0.0449 0.05 0.0492 0.0494 误差均值 0.044 0.0446 0.0469 0.0642 0.0785 0.0731 误差方差 0.0042 0.007 0.0008 0.012 0.0231 0.0284 更新次数最多的样本编号 91, 92, 93, 118, 124 91, 93, 92, 97, 95 91, 93, 1 91, 93, 8, 1, 119 91, 93, 8, 16, 11 93, 91, 92, 11 平均更新次数 10.3 4.1 2.05 2.6 2.2 1.9 本文方法 最大误差 0.16 0.0953 0.0733 0.0808 0.1082 0.1878 最小误差 0.0967 0.0529 0.0397 0.0395 0.0556 0.1653 误差均值 0.1309 0.0784 0.0429 0.0474 0.0847 0.1804 误差方差 0.0199 0.0116 0.0078 0.0101 0.0117 0.0066 更新次数最多的样本编号 1180 91, 91, 93, 95, 97, 76 91, 92, 93, 97, 124 93, 91, 92 92, 94, 93, 99 – 平均更新次数 180 72.95 3.4 2.55 1.7 0
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