Lu Jun, Ding Jinliang, Dai Xuewu, Chai Tianyou
IEEE Trans Neural Netw Learn Syst. 2020 Dec;31(12):5426-5440. doi: 10.1109/TNNLS.2020.2967816. Epub 2020 Nov 30.
Obtaining accurate point prediction of industrial processes' key variables is challenging due to the outliers and noise that are common in industrial data. Hence the prediction intervals (PIs) have been widely adopted to quantify the uncertainty related to the point prediction. In order to improve the prediction accuracy and quantify the level of uncertainty associated with the point prediction, this article estimates the PIs by using ensemble stochastic configuration networks (SCNs) and bootstrap method. The estimated PIs can guarantee both the modeling stability and computational efficiency. To encourage the cooperation among the base SCNs and improve the robustness of the ensemble SCNs when the training data are contaminated with noise and outliers, a simultaneous robust training method of the ensemble SCNs is developed based on the Bayesian ridge regression and M-estimate. Moreover, the hyperparameters of the assumed distributions over noise and output weights of the ensemble SCNs are estimated by the expectation-maximization (EM) algorithm, which can result in the optimal PIs and better prediction accuracy. Finally, the performance of the proposed approach is evaluated on three benchmark data sets and a real-world data set collected from a refinery. The experimental results demonstrate that the proposed approach exhibits better performance in terms of the quality of PIs, prediction accuracy, and robustness.
由于工业数据中常见的异常值和噪声，获取工业过程关键变量的准确点预测具有挑战性。因此，预测区间（PIs）已被广泛采用来量化与点预测相关的不确定性。为了提高预测准确性并量化与点预测相关的不确定性水平，本文使用集成随机配置网络（SCNs）和自助法估计预测区间。估计的预测区间可以保证建模稳定性和计算效率。为了促进基础SCNs之间的合作，并在训练数据受到噪声和异常值污染时提高集成SCNs的鲁棒性，基于贝叶斯岭回归和M估计开发了一种集成SCNs的同步鲁棒训练方法。此外，通过期望最大化（EM）算法估计集成SCNs的噪声和输出权重上假设分布的超参数，这可以产生最优的预测区间和更好的预测准确性。最后，在三个基准数据集和一个从炼油厂收集的实际数据集上评估了所提出方法的性能。实验结果表明，所提出的方法在预测区间质量、预测准确性和鲁棒性方面表现出更好的性能。
