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摘要: 应用最大Lyapunov指数预测多年冻土路基变形, 分析冻土路基变形的相空间重构方法和不同延迟时间及嵌入维数对最大Lyapunov指数的影响。发现当延迟时间为1, 嵌入维数为5时, 最大Lyapunov指数趋于稳定, 其值为0.00528。运用该指数, 进行冻土路基变形预测, 比较预测变形量和实测变形量, 得到最大相对误差为0.749%, 最小为0.135%。结果表明最大Lyapunov指数能够较好地反映冻土路基变形的混沌特征, 利用其进行冻土路基变形预测是可行的。
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关键词:
- 路基工程 /
- 多年冻土 /
- 相空间重构 /
- Lyapunov指数 /
- 变形预测
Abstract: The rules of permafrost subgrade deformation were analyzed by maximal Lyapunov exponent method, the phase space reconstruction of subgrade deformation was discussed. It is pointed that various delay time and embedment dimension are two important influence factors on the exponent, when delay time equals 1, embedment dimension equals 5, steady maximal Lyapunov exponent is 0.005 28. Using the exponent value, the maximal relative error of deformation forecast value and measure value is 0.749%, the minimal relative error is 0.135%. The results indicate that maximal Lyapunov exponent ideally reflect the chaos characteristic of subgrade deformation, forecasting subgrade deformation by maximal Lyapunov exponent is feasible. -
表 1 实际观测与预测数据对比
Table 1. Comparison of calculated and measured deformations
时间/d 实测值/mm 预测值/mm 相对误差/% 540 -74.1 -73.9 0.270 555 -78.2 -77.7 0.639 570 -80.0 -79.6 0.500 585 -80.1 -79.5 0.749 600 -75.3 -75.6 0.398 615 -74.0 -74.1 0.135 630 -73.2 -73.4 0.273 645 -73.5 -73.3 0.272 660 -71.3 -71.7 0.561 675 -72.0 -72.1 0.139 690 -72.5 -72.8 0.414 705 -73.5 -74.2 0.52 注: 表中的值为累计变形量。 
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