多分类概率极限学习机及其在剩余使用寿命预测中的应用

Multi-class probabilistic extreme learning machine and its application in remaining useful life prediction

针对多分类极限学习机(extreme learning machine,ELM)缺乏概率输出能力问题,提出一种基于sigmoid后验概率映射和Lagrange成对耦合法的多分类概率ELM(multi-class probabilistic ELM,MPELM)。采用成对耦合法将多分类问题分解成多个二分类问题,利用sigmoid函数将二分类ELM输出映射成概率输出。为融合所有二分类概率输出,推导基于Lagrange乘子法的多分类概率计算公式,最终求解被预测样本分属不同类别的概率。将MPELM用于剩余使用寿命(remaining useful life,RUL)预测,实验结果表明,相比于多分类概率支持向量机(multi-class probabilistic support vector machine,MPSVM),MPELM耗时高于MPSVM,但MPELM所需优化参数少,预测精度高于MPSVM;与基于Hastie成对耦合法的MPELM相比,两者预测精度相近,本文MPELM的测试耗时较少。

To solve the problem that multi-class extreme learning machine （ELM） lacks the ability of prob- abilistic output, a multi-class probabilistic ELM （MPELM） algorithm is presented based on the combination of sigmoid posterior probability mapping and Lagrange pairwise coupling. Firstly, after separating the multi-class problem into the type of two-class problem by pairwise coupling, each two-class ELM output is transformed to the probabilistic output by sigmoid function. Then, the multi-class probabilistic computing expression is de- duced based on the Lagrange multiplier method, which is utilized to fuse all two-class probabilistic outputs. Fi- nally, the probabilistic results of predicted samples belonging to different classes are obtained. The proposed MPELM is applied to remaining useful life （RUL） prognosis. The experiment results show that, compared with multi-class probabilistic support vector machine （MPSVM）, though time consuming of the proposed MPELM is higher than MPSVM, less optimized parameter is required while higher forecasting accuracy is achieved by MPELM. The predicting accuracy of the proposed MPELM is similar to MPELM based on the Hastie pairwise coupling （Hastie- MPELM） algorithm. But test time consuming of the proposed MPELM is less than Hastie-MPELM.