Intergroup Cascade Broad Learning System With Optimized Parameters for Chaotic Time Series Prediction

Abstract

The prediction of chaotic time series can well describe the physical properties and influencing factors of a sequence of numerical data points in successive order and has played an increasingly crucial role in various scientific and engineering communities. These time series data require the prediction model to have strong dynamic feature representation ability, which often leads to excessive calculation burden. As an emerging and effective learning method, a broad learning system (BLS) can be trained quickly by incremental learning, and the system can be reconstructed without requiring a lengthy retraining process, which has been shown to facilitate superior time-saving performance. However, the historical information of time series data is often ignored, resulting in the lack of dynamic feature representation ability of the original BLS algorithm. In this article, a novel intergroup cascade BLS (ICBLS) method and its variant with optimized parameters, termed MOICBLS, are proposed, which can combine the previous knowledge with current information to determine the output results by constructing a novel intergroup cascade structure for the enhancement nodes. The new algorithms try to retain the time-saving advantage of BLS and greatly enhance the extraction ability of dynamic features of chaotic time series data. In addition, it cannot be ignored that the network structure parameters have an unquestionable impact on the performance of a BLS. In response, two conflicting goals of prediction accuracy and diversity are formulated as multiobjective optimization functions in the training phase to generate the optimized network structure parameters needed by multiple candidate models. The experimental results on two benchmark chaotic time series dataset, the Lorenz system and Rossler system, and a geomagnetic disturbance storm time chaotic time series dataset demonstrate that our proposed algorithms are effective for prediction of chaotic time series, and the prediction accuracy is better than some existing approaches.