Interval prediction of track irregularity based on GM(1, 1) model and relevance vector machine
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摘要: 为开展以预防修为主的养护维修作业，联合GM(1, 1)灰色模型与相关向量机(RVM)算法，提出一种预测轨道不平顺演化区间的GM(1, 1)-RVM组合模型；结合轨道质量指数(TQI)的振荡演变特性，通过二次-对数复合函数平滑优化和序列权重优化改进了GM(1, 1)模型，通过粒子群优化(PSO)算法对待优化参数进行搜索确定，并在此基础上计算点的预测值；构造以点预测值为输入，以TQI实测值为输出的样本特征映射模式，引入5折交叉验证环节优化与训练了RVM模型的组合核函数；通过GM(1, 1)模型与RVM模型间的输入-输出衔接机制集成了组合预测模型，并以某有砟线路中的2个区段为实例检验了轨道不平顺区间的预测效果。研究结果表明：与既有预测模型相比，改进GM(1, 1)-RVM组合模型可得到预测区间的均值和方差，从而将预测结果从单点数值扩充到预测区间；2个区段实例在外推区间上的点预测结果与TQI真实值相比，平均百分比误差分别为1.53%和4.67%，较支持向量回归(SVR)模型分别降低了0.58%和0.61%，较GM(1, 1)-反向传播神经网络(BPNN)模型分别降低了0.15%和1.87%；改进GM(1, 1)-RVM组合模型在90%、95%和99%三种置信度下的最大平均预测区间宽度分别为0.324 5、0.387 9和0.510 5 mm，最低预测区间覆盖率分别为91.67%、95.83%和95.83%，预测区间基本涵盖了外推区间内的TQI演化数据。可见，利用预测的均值和方差构造区间边界可有效把控轨道不平顺演变过程中的随机波动，为轨道不平顺预测提供了一种新思路。Abstract: 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.
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图 1 改进GM(1, 1)-RVM组合模型求解流程
Figure 1. Solving process of improved GM(1, 1)-RVM combination model
表 1 TQI检测数据
Table 1. Detection data of TQI
动检日期 相对时间/d 实测值/mm 动检日期 相对时间/d 实测值/mm 动检日期 相对时间/d 实测值/mm TQI1 TQI2 TQI1 TQI2 TQI1 TQI2 2021-01-07 0 2.65 2.47 2021-05-07 120 2.96 2.56 2021-09-07 243 3.06 3.08 2021-01-21 14 2.55 2.25 2021-05-20 133 2.91 2.54 2021-09-24 260 3.04 3.07 2021-02-01 25 2.63 2.31 2021-06-07 151 2.94 2.54 2021-10-09 275 3.08 3.33 2021-02-21 45 2.55 2.17 2021-06-20 164 2.74 2.5 2021-10-23 289 3.13 3.27 2021-03-01 53 2.37 2.59 2021-07-05 179 2.74 2.81 2021-11-08 305 3.17 3.37 2021-03-15 67 2.51 2.44 2021-07-21 195 2.83 2.87 2021-11-15 312 3.04 3.16 2021-04-06 89 2.84 2.73 2021-08-03 208 2.74 3.13 2021-11-22 319 3.12 3.64 2021-04-18 101 2.99 2.65 2021-08-15 220 3.02 3.15 2021-12-08 335 3.06 3.47 
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