Interval prediction of track irregularity based on GM(1, 1) model and relevance vector machine

The GM(1, 1) grey model and relevance vector machine (RVM) algorithm were integrated to propose a GM(1, 1)-RVM combination model for the interval prediction of track irregularities to carry out the preventive maintenance work. Considering the oscillation characteristics of the track quality index (TQI), the GM(1, 1) model was improved by smooth optimization of the quadratic-logarithmic composite function and sequence weight optimization. The parameters to be optimized were searched and determined by the particle swarm optimization (PSO) algorithm, and then the predicted point values were calculated. The mapping mode of sample features with the predicted point value as input and the true TQI as output was constructed, and the 5-fold cross-validation was introduced to optimize and train the combined kernel function of the RVM model. The combination prediction model was integrated by the input-output alignment mechanism between the GM(1, 1) model and the RVM model, and the prediction effect of the track irregularity interval was tested by taking two sections of a ballasted railway line as examples. Research results show that compared with the existing prediction models, the mean and variance of the predicted interval can be calculated by the improved GM(1, 1)-RVM combination model to expand the prediction results from single point values to prediction intervals. Compared with the true TQIs, the mean percentage errors of the predicted point results obtained by the improved GM(1, 1)-RVM combination model on the extrapolation range at the two sections are 1.53% and 4.67%, respectively, and they are 0.58% and 0.61% lower than the support vector regression (SVR) model, respectively, and 0.15% and 1.87% lower than the GM(1, 1)-back propagation neural network (BPNN) model, respectively. Under the confidence levels of 90%, 95%, and 99%, the maximum mean prediction interval widths obtained by the improved GM(1, 1)-RVM combination model are 0.324 5, 0.387 9, and 0.510 5 mm, respectively, and the minimum prediction interval coverage rates are 91.67%, 95.83%, and 95.83%, respectively. The prediction interval can cover most of the TQI evolution data on the extrapolation interval. Thus, the random fluctuation in the track irregularity evolution can be controlled by employing the predicted mean and variance to construct the interval boundary, which provides a new idea for the track irregularity prediction. 3 tabs, 5 figs, 30 refs.