Improvement of multilayer extreme learning machines and their analysis of performance in system modeling

Extreme Learning Machine (ELM) has been the subject of significant research in the last decade due to its high efficiency and easy implementation in classification and regression applications. Within the scope of our study, existing ELM structures such as classical ELM, Radial Basic Function Extreme Learning Machine (RBF-ELM), Meta Extreme Learning Machine (Meta-ELM) and Multilayer Extreme Learning Machine (ML-ELM), which were developed for regression and classification problems, were examined. In this study, the weak and superior aspects of the aforementioned structures were examined, and the improvement of the structures and new hybrid structures were proposed. The motivation factor in our study is that ELM methods are widely used in classification problems and system modeling has not been studied. In this context, it was aimed to improve and develop a new mixed network structure by working on the modeling of touchstone systems on uneven and/or sharply changing surfaces as well as systems that are dynamically dependent on time, and the desired goal was achieved in our study. Two ELM network structures, which we call Improved Multilayer Extreme Learning Machine (IML-ELM), aiming to increase the system modeling performance of the ML-ELM structure and reduce the computation time, have been developed and the test results and performance advantages are shown on benchmark systems. Their performances on seven different dynamic system modeling applications compared to the ML-ELM structure performance have been examined. In addition, a hybrid network structure, which we call HybRBF-ML-ELM, has been developed by combining multi-layer extreme learning machine and radial basis function networks. Its performance on uneven and/or sharply changing surface problems has been shown in comparison with the test results. It has been observed that IML-ELM developed in dynamic system modeling experiments exhibits up to 70% better modeling performance for both training and test datasets compared to ML-ELM in some cases. For example, when 100 nodes are used for Benchmark Dynamic System (BDS) 7, the average test Root Mean Square Errors (RMSE) results of 0.627977, 0.104272 and 0.092683 are achieved for the ML-ELM, IML-ELM1 and IML-ELM2 structures. Compared to the ML-ELM, the IML-ELM1 structure provided 83% better mean test RMSE results, while the IML-ELM2 structure provided 85% better mean test RMSE results. It has been observed that the HybRBF-ML-ELM structure developed in surface modeling experiments is more successful for each problem than the ML-ELM structureFor example, when both the training and test RMSE results of HybRBF-ML-ELM for the Griewank, Dropwave and Schaffer2 functions are examined, it is seen that approximately 99% better performance is obtained compared to the ML-ELM structure. Considering the average RMSE value in the training data for the peaks function, it was observed that the modeling performance was 76.87% better than the ML-ELM structure.