Adaptive soft sensors including widely used locally weighted partial least square (LW‐PLS) have been established for online prediction, fault detection, and process monitoring. Nevertheless, majority of these existing adaptive soft sensors have zero tolerance to missing data, and the presence of missing data is inevitable due to sensor failures, routine maintenance, changes in sensor equipment over time, merging data from different system, and so forth. In the literature, limited studies could be found on the effects of missing data and the existing missing data imputation methods on the predictive performances of adaptive soft sensors. This work reports combined use of different missing data imputation techniques on LW‐PLS and the nonadaptive soft sensor, the partial least square (PLS). Well known trimmed score regression (TSR) and singular value decomposition (SVD) were employed in this study, and thus, the newly integrated TSR‐LW‐PLS and SVD‐LW‐PLS algorithms were proposed. Meanwhile, both existing TSR‐PLS and SVD‐PLS were used, and their results compared with the novel TSR‐LW‐PLS and SVD‐LW‐PLS algorithms. These algorithms were tested and evaluated using two examples having different percentages of missing data ranging from 5% to 40%. Results showed that TSR‐LW‐PLS model was superior compared with SVD‐LW‐PLS, TSR‐PLS, and SVD‐PLS as indicated by more than 100% improvements in prediction accuracy. It was also evident that TSR‐LW‐PLS is able to cope well with up to 20% of missing data.

中文翻译：

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局部加权偏最小二乘建模的缺失数据处理：一项比较研究

已经建立了包括广泛使用的局部加权偏最小二乘（LW-PLS）在内的自适应软传感器，用于在线预测，故障检测和过程监控。尽管如此，大多数这些现有的自适应软传感器对丢失的数据具有零容忍度，并且由于传感器故障，日常维护，传感器设备随时间变化，合并来自不同系统的数据等原因，不可避免会出现丢失的数据。在文献中，关于丢失数据的影响以及现有的丢失数据插补方法对自适应软传感器的预测性能的影响，研究很少。这项工作报告了在LW-PLS和非自适应软传感器偏最小二乘（PLS）上不同缺失数据插补技术的组合使用。在这项研究中使用了众所周知的修剪得分回归（TSR）和奇异值分解（SVD），因此，提出了新集成的TSR-LW-PLS和SVD-LW-PLS算法。同时，现有的TSR-PLS和SVD-PLS均被使用，其结果与新颖的TSR-LW-PLS和SVD-LW-PLS算法进行了比较。这些算法使用两个示例进行了测试和评估，这些示例的丢失数据百分比从5％到40％不等。结果表明，TSR-LW-PLS模型优于SVD-LW-PLS，TSR-PLS和SVD-PLS模型，预测精度提高了100％以上。同样明显的是，TSR-LW-PLS能够很好地应对多达20％的丢失数据。同时使用了现有的TSR-PLS和SVD-PLS，并将它们的结果与新颖的TSR-LW-PLS和SVD-LW-PLS算法进行了比较。这些算法使用两个示例进行了测试和评估，这些示例的丢失数据百分比从5％到40％不等。结果表明，TSR-LW-PLS模型优于SVD-LW-PLS，TSR-PLS和SVD-PLS模型，预测精度提高了100％以上。同样明显的是，TSR-LW-PLS能够很好地应对多达20％的丢失数据。同时使用了现有的TSR-PLS和SVD-PLS，并将它们的结果与新颖的TSR-LW-PLS和SVD-LW-PLS算法进行了比较。这些算法使用两个示例进行了测试和评估，这些示例的丢失数据百分比从5％到40％不等。结果表明，TSR-LW-PLS模型优于SVD-LW-PLS，TSR-PLS和SVD-PLS模型，预测精度提高了100％以上。同样明显的是，TSR-LW-PLS能够很好地应对多达20％的丢失数据。和SVD-PLS，预测精度提高了100％以上。同样明显的是，TSR-LW-PLS能够很好地应对多达20％的丢失数据。和SVD-PLS，预测精度提高了100％以上。同样明显的是，TSR-LW-PLS能够很好地应对多达20％的丢失数据。