A hybrid approach for measuring the vibrational trend of hydroelectric unit with enhanced multi-scale chaotic series analysis and optimized least squares support vector machine

Accurate vibrational trend measuring for hydroelectric unit (HEU) is of great significance for safe and economic operation of unit. For this purpose, a novel hybrid approach based on variational mode decomposition (VMD), singular value decomposition (SVD)-based phase space reconstruction (PSR) and least squares support vector machine (LSSVM) improved with adaptive sine cosine algorithm optimization (ASCA) is proposed. Firstly, the raw vibration signal is preprocessed into several components with different scales by VMD, while the residual of VMD is defined as an additional component. Then, SVD with median filtering is utilized to unearth the dominating characteristic ingredients of each component, with which the chaotic series analysis will be effectively implemented. Moreover, the optimal parameters of PSR for each original component are determined by applying grid search on the corresponding dominating component. Later, LSSVM improved by ASCA are established for all the components, whose inputs and outputs are obtained by performing PSR with the optimal parameters. Finally, the measuring results of vibration trend are deduced by accumulating the prediction values of all the components. Furthermore, five related methods are employed to evaluate the effectiveness of the proposed approach. The results illustrate that: (1) the VMD-based models obtained better evaluation indexes compared with the relevant models through significantly weakening the non-stationarity of the original signal; (2) the proposed SVD-based PSR enhanced efficiency of chaotic system restoration, thus to improve the measuring accuracy effectively; (3) the proposed ASCA optimization algorithm could effectively search the parameters of LSSCVM, which contributes to improving model performance.