Permafrost subgrade deformation forecast based on phase space reconstruction and partial least squares regression
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摘要: 为了正确预测多年冻土路基变形, 将多年冻土路基变形单变量混沌时间序列进行相空间重构, 依重构空间嵌入维数38在多维空间中定义自变量、因变量和样本数, 利用偏最小二乘法对所构造的自变量进行主成分提取, 建立路基变形预测模型, 借助多种评判指标进行模型精度分析, 并绘制了预测值与实测值散点图。对比分析结果表明所有样本点都集中在散点图对角线附近, 相关系数达0.889 4, 预测值与实测值最大相对误差为9.75%, 说明建立的预测模型合理可信, 利用该预测模型进行多年冻土路基变形预测可行。Abstract: In order to accurately forecast permafrost subgrade deformation, a single variable chaos time series of permafrost subgrade deformation was constructed in multidimensional phase space, some independent variables, function and sample numbers were defined according to embeded 38 dimensions of the space, the main components of independent variables were picked by using partial least squares regression method, a deformation forecast model was constructed, the precision of the model was analyzed by recurring multiplicate evaluation indices, and the comparative figure between forecast values and measure values was plotted.Analysis result shows that all sample points concentrate near the diagonal line of the figure, their correlation index is 0.889 4, their maximum relative error is 9.75%, which indicates that the model is reasonable and credible, can forecast subgrade deformation in permafrost regions.
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图 1 关联维数与嵌入维数的关系曲线
Figure 1. Correlation curve of correlation dimension and embedding dimension
表 1 计算结果
Table 1. Calculation result
n t1 t2 u1 1 1.3611 -0.2650 2.1092 2 0.1195 -0.5051 0.2194 3 0.0155 -0.1672 0.7593 4 0.7539 -1.5961 0.7593 5 0.5757 1.8262 0.7593 6 -3.1605 0.4499 -3.5603 7 -0.0422 2.4845 -0.0506 8 -0.1750 1.8028 1.0293 9 2.9960 3.2630 4.8090 10 -3.9405 -1.8117 -5.9900 11 -0.2059 0.5387 0.4894 12 -0.0820 -2.9473 -0.5851 13 1.4593 -4.9033 -0.5851 14 1.0862 -0.3122 2.1092 15 -3.2377 -1.3539 -3.2903 16 2.6411 -0.4473 2.1092 17 -2.1337 -1.7324 -2.2104 18 1.0695 -1.2313 -0.0506 19 -1.5002 1.1623 -1.1305 20 -1.6382 3.5111 -0.0506 21 0.7788 -0.6139 0.4894 22 0.6907 1.0541 0.4894 23 2.0650 1.3081 2.6492 24 -1.7810 0.5877 -0.5851 25 0.0494 -0.8479 -0.5851 26 1.5876 -2.3886 -0.5851 27 1.3778 -0.0507 1.5693 28 0.4181 1.2514 1.0293 29 -2.4137 1.2406 -1.6704 30 1.8768 -0.9613 1.5693 31 0.3529 0.9405 -0.0506 32 -1.2449 0.5939 -1.6704 33 -0.3411 1.8492 0.4894 34 -0.8902 1.2532 -0.5851 35 1.2227 -1.3645 1.0293 36 0.0972 0.8040 1.0293 37 -2.3028 -2.2597 -3.2903 38 2.4942 -0.1620 1.0293 均值 0.0000 0.0000 0.0000 方差 2.8870 3.0000 3.7960 
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表 2 预测结果
Table 2. Forecast result
时间序列编号 预测值/cm 时间序列编号 预测值/cm 时间序列编号 预测值/cm 1 -0.5332 9 0.5222 17 -0.1168 2 0.4763 10 -0.2067 18 0.2494 3 -0.4522 11 0.7851 19 0.5545 4 0.3624 12 -0.1399 20 -0.0926 5 -0.0077 13 0.2018 21 0.0825 6 -0.1577 14 0.1399 22 0.0994 7 0.6635 15 0.2879 23 -0.2929 8 -0.5587 16 0.1251 24 0.7716
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