Group reduced kernel extreme learning machine for fault diagnosis of aircraft engine

The original kernel extreme learning machine (KELM) employs all training samples to construct hidden layer, thus avoiding the performance fluctuations caused by the ELM randomly assigning weights. However, excessive nodes will inevitably lead to structural redundancy, which hinders its application in systems with high real-time performance requirements but limited onboard storage and computing capacity. Considering the well interpretability of sparse learning, this study introduces the group sparse structure for KELM to resolve its limitation of structural redundancy. Specifically, the proposed novel method introduces a special norm to reformulate the dual optimization problem of KELM to realize group sparse structure in output weights. As a result, nodes with large weights can be selected as the significant nodes, while nodes with small weights will be regarded as the redundant nodes and neglected directly. In addition, we have also devised an alternating iterative optimization algorithm and deduced the complete proof of convergence to solve the non-smoothness optimization problem in proposed method. Then, the validity and feasibility of the proposed method are verified by extensive experiments on benchmark datasets. More importantly, tests of fault diagnosis for an aircraft engine show that the proposed approach can maintain the competitive recognition performance with much faster testing speed.