Abstract: The predictive accuracy and generalization performance of soft sensor model are two important indexes of soft measurement modeling. Extreme learning machine algorithm which is based on optimal bounding ellipsoid (OBE-ELM) can overcome the shortcomings of the traditional extreme learning machines, such as low prediction accuracy and unstable prediction results, but the traditional OBE algorithm only minimizes the model error and does not consider the complexity of the model, which leads to over-fitting of the model. Aiming at the above problems, firstly, an optimal bounding ellipsoid algorithm (POBE) with penalty term is proposed for nonlinear systems with unknown but bounded noise, and the penalty term added to the objective function is used to suppress the magnitude of parameter growth and drive the unimportant parameter to zero gradually. Then, POBE is used for the optimization of ELM model parameters. Finally, the experiments were carried out on the channel parameter estimation and the continuous stirred tank reactor data sets to validate the effectiveness of POBE and POBE-ELM respectively.

Key words: Optimal bounding ellipsoid algorithm, over fitting, penalty term, extreme learning machine, soft sensor

摘要： 软测量模型的预测精度和泛化性能是软测量建模的2个重要指标。基于最优定界椭球的极限学习机算法(OBE-ELM)虽然克服了传统极限学习机建模预测精度不高、预测结果不稳定等缺点，但是传统OBE算法仅考虑模型误差最小化，未考虑模型的复杂程度，导致模型易出现过拟合现象。基于上述问题，首先针对噪声未知但有界的非线性系统，提出了一种带惩罚项的椭球定界算法(POBE)，在模型误差中加入惩罚项起到抑制参数增长太大和驱使不重要参数逐渐减小到零的作用，然后将POBE应用到ELM模型参数优化过程中。最后在信道参数估计实验和连续搅拌反应釜数据集上分别验证POBE及POBE-ELM有效性。

关键词: 最优定界椭球算法, 过拟合, 惩罚项, 极限学习机, 软测量