摘要
To obtain an accurate and robust soft sensor model in dealing with the increasingly complex industrial modeling data,an effective heterogeneous ensemble of extreme learning machines(HEELM)is proposed.Specifically,the kernel extreme learning machine(KELM)and four common extreme learning machine(ELM)models that have different internal activations are contained in the HEELM for enriching the diversity of sub-models.The number of hidden layer nodes of the extreme learning machine is determined by the trial and error method,and the optimal parameters of the kernel extreme learning machine model are determined by cross validation.Moreover,to obtain the best output of the ensemble model,least squares regression is applied to aggregate the outputs of all individual models.Two complex data sets of practical industrial processes are used to test the HEELM performance.The simulation results show that the HEELM has a high prediction accuracy.Compared with the individual ELM models,bagging ELM ensemble model,BP and SVM models,the prediction accuracy of the HEELM model is improved by 4.5%to 8.7%,and the HEELM model can obtain better generalization capability.
为了在日益复杂的工业建模数据基础上建立一个准确、稳定的软测量模型,提出了一种有效的异构集成极端学习机(HEELM)软测量模型.采用4种不同激活函数的极端学习机和核极端学习机模型用以丰富集成模型的多样性.极限学习机的隐含层节点数通过试错法确定,并以交叉验证为准则来获得最优的核极限学习机模型参数.为了获得集成模型的最佳输出,采用最小二乘回归方法对所有单个模型的输出进行集成.通过2组复杂的工业过程数据集验证了HEELM模型具有很好的预测精度.与单独ELM模型、bagging ELM集成模型、BP和SVM模型相比,HEELM模型的预测精度提高了4.5%~8.7%,且HEELM模型具有更好的稳定性.
基金
The National Natural Science Foundation of China(No.71471060)
the Natural Science Foundation of Hebei Province(No.E2018502111)
Fundamental Research Funds for the Central Universities(No.2019QN134).
