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Prediction of seepage water level extremum of earth rock dam
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摘要: 渗压水位极值预测是监控土石坝安全的主要途径之一，目前用于渗压水位极值预测方法需给出正确的自变量。渗压水位极值最主要的影响因素是上游水位，当渗压水位极值与上游水位相关性弱时，预测模型准确度低。提出一种仅考虑测值序列、不考虑自变量的渗压水位极值预测及评价方法。该方法基于最大Lyapunov指数建立预测模型，利用马氏链的遍历性和平稳分布对该无自变量模型进行评价。算例表明：对于与自变量相关性弱的渗压水位极值，预测模型的预测效果优于常规方法，误差评估模型评价合理。基于混沌理论和随机过程的预测模型及评价方法能形成一套精度较高、实用性强的序列预测及评价方法，覆盖常规预测方法的弱能力区域，可用于建立自变量不明确的测值序列预测模型。Abstract: Prediction of seepage water level extremum is one of the main means to monitor the safety of the earth rock dam, and dam body seepage water level is an important physical quantity to evaluate the seepage characteristics of the earth rock dam. Currently, the common sense of the extreme value prediction methods is on the prerequisite of giving correct independent variables, when such methods being applied. The most important factor affecting the seepage water level extremum is the upstream water level. When the correlation between the seepage water level extremum and the upstream water level is quite good, the predication accuracy provided by conventional models is quite high; when the correlation between the seepage water level extremum and the upstream water level is weak, the predication accuracy provided by conventional models is low. To resolve this issue, this paper proposes a method of predicting and evaluating the seepage water level extremum, which considers the measured value sequence only and neglects the independent variables. Based on the maximum Lyapunov index, a prediction model is established, and the ergodicity and stationary distribution of Markov chain are applied to evaluate this independent variable model. The example shows that the prediction effect of the prediction model based on maximum Lyapunov index is better than that of conventional methods for seepage water level extremum, which has weak correlation with independent variables, and the error assessment model based on Markov chain provides reasonable evaluation. The prediction model and evaluation method based on chaos theory and stochastic process that is proposed in this paper can form a systematic approach to the sequence prediction as well as evaluation method with high accuracy and strong practicability, covering the weak area of conventional prediction methods. It can be used to establish the prediction model for the measured value sequence with uncertain independent variables.
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图 2 BP网络预测值与实测值的对比
Figure 2. Comparison between predicted value and measured value of BP network
图 3 C-C法重构相空间参数确定
Figure 3. Parameter determination of phase space reconstruction by C-C method
图 4 混沌模型预测值与实测值的对比
Figure 4. Comparison between predicted value and measured value of chaos model
表 1 模型误差序列及其状态
Table 1. Errors of sequence and their states
日期 实测值/
m模型
预测值/m实测值－
模型值/m混沌模型
相对误差/%状态 2008.5 18.49 18.13 0.36 2.00 Ⅱ 2008.6 18.33 17.92 0.41 2.30 Ⅱ 2008.7 19.86 18.35 1.51 8.24 Ⅲ 2008.8 20.46 20.26 0.20 0.99 Ⅱ 2008.9 20.13 19.67 0.46 2.34 Ⅱ 2008.10 19.84 19.25 0.59 3.07 Ⅱ 2008.11 18.72 19.25 −0.53 −2.75 Ⅰ 2008.12 18.03 18.06 −0.03 −0.16 Ⅰ 2009.1 17.50 17.47 0.03 0.19 Ⅱ 2009.2 17.02 17.01 0.01 0.08 Ⅱ 2009.3 16.65 16.53 0.12 0.75 Ⅱ 2009.4 16.64 17.83 −1.19 −6.66 Ⅰ 2009.5 16.87 16.20 0.67 4.16 Ⅱ 2009.6 19.00 16.76 2.24 13.39 Ⅲ 2009.7 19.77 18.35 1.42 7.75 Ⅲ 2009.8 19.88 20.48 −0.60 −2.93 Ⅰ 2009.9 19.58 19.90 −0.32 −1.61 Ⅰ 2009.10 19.03 19.90 −0.87 −4.39 Ⅲ 
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表 2 相对误差分级
Table 2. Relative error classification table
状态 级别 相对误差区间 Ⅰ 偏小 −6.66%~0.06% Ⅱ 偏大 0.06%~4.37% Ⅲ 大 4.37%~13.39%
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