As shown in Figure 3, the randomness and volatility of wind make the LS-SVM model not show a good predictive performance, and the prediction results of the modified LSSVM model are satisfactory.
The biggest change of errors between the LSSVM model and LS-SVM with error correction occurred in the wind farm of Spain, MAE and MSE respectively reached 0.
In addition, although a single LSSVM with optimal parameters and reconstructed input data samples may have an excellent prediction performance under certain circumstances, because its kernel function is fixed, it perhaps has some kinds of inherent bias under other cases.
Particle swarm optimization algorithm is used to search the best parameters for LSSVM members to ensure their prediction accuracies.
LSSVM is the least squares form of a standard SVM; it was firstly proposed by Suykens and Vandewalle .
In LSSVM, the regression issue can be expressed as the following optimization problem:
According to the Lagrange function and Karush-Kuhn-Tucker theorem, the LSSVM for nonlinear functions can be given as below:
The GA is then used to optimize the LSSVM, and, finally, the GA-LSSVM is used for classification of the feature parameters.
From Figures 6 and 7, the hybrid GA-LSSVM model obtains a higher detection rate than LSSVM for fault recognition of railway rolling bearings.
Finally, fault samples of IMF energy-torques were used as LSSVM input parameters to realize intelligent fault diagnosis.
Fu, "Parameters selection of LSSVM based on adaptive genetic algorithm for ship rolling prediction," in Proceedings of the 33rd Chinese Control Conference (CCC '14), pp.
Caption: Figure 6: Testing results of the LSSVM without GA.