A Novel Hybrid Structured Multi-Layer Extreme Learning Machine Network Efficient in Hard Modeling Problems

Modeling problems involving rugged and sharply varying surfaces continue to be challenging because of their highly irregular nonlinear characteristics. The main motivation of this study arose from the observation that existing multi-layer extreme learning machine (ML-ELM) structures exhibit limited modeling capability for surfaces with such irregular characteristics problems. Motivated by this limitation, this paper proposes a hybrid structured multi-layer extreme learning machine architecture named Hyb-ML-ELM for difficult modeling problems involving rugged and sharply varying surfaces. The proposed Hyb-ML-ELM network consists of three layers integrating an RBF-based kernel mapping layer and autoencoder-based learning layers. The RBF-based kernel layer provides local representation capability, while the autoencoder-based layers enable hierarchical feature learning. Together, they address the limited ability of existing ML-ELM structures to capture local variations and complex nonlinear patterns in rugged and sharply varying surfaces. To evaluate the modeling performance of Hyb-ML-ELM, four benchmark modeling problems characterized by rugged and sharply varying surfaces, together with two real-world regression datasets, were employed. In addition, parameter sensitivity, node-number, and final parameter refinement analyses were conducted. Experimental results demonstrated that Hyb-ML-ELM provided improved modeling capability compared with ML-ELM, particularly for difficult modeling problems involving rugged and sharply varying surfaces. While ML-KELM and the IML-ELM variants achieved competitive performance in certain cases, Hyb-ML-ELM demonstrated strong performance across both benchmark and real-world regression experiments. Although the proposed architecture introduces increased computational overhead, the obtained results indicate that Hyb-ML-ELM represents a promising solution for complex system modeling problems.