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摘要: 为合理考虑路基沉降预测时诸多影响因素的不确定性与随机性, 提出基于神经网络范例推理的路基沉降预测模型。以同类工程的成功经验为基础, 建立了基于神经网络的沉降范例检索模型, 在范例相似度计算中, 引入归一化效用函数, 通过神经网络的学习, 建立当前沉降范例与沉降源范例之间的相似关系, 最终实现当前沉降范例的沉降预测。对黄土沟壑区湿软路基沉降预测结果表明, 该模型具有较高的预测准确性, 预测值与实测值绝对误差小于10%。Abstract: In view of the randomness and uncertainty of effect factors in subgrade settlement prediction, a prediction model based on case-based reasoning integrated with neural network was presented.In the model, a model for indexing subgrade settlement cases with neural network was set up, the successful experiences of similar engineerings were analyzed, and a new kind of utility function to calculate the similarities of the cases were introduced.The similarity relationship among the settlement cases was established by training neural network, so that the most similar base case to settlement target case was found out.Settlement prediction result of wettest-soft loess subgrade in ravine regions shows that the absalute errors between predicted data and actual ones are less than 10%, and the model has high prediction precision.
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表 1 沉降范例实例及其最终沉降
Table 1. Practical cases and their final settlements
范例 湿软黄土厚度/m 软土压缩模量/MPa 路堤顶面宽度/m 路堤填土高度/m 施工工期/月 竣工时沉降量/cm 最终沉降量/cm CB1 3.2 3.8 28.0 5.79 3.0 17.0 23.0 CB2 5.0 2.6 28.0 3.80 3.0 75.0 92.0 CB3 2.0 1.7 28.0 4.16 3.0 120.0 140.0 CB4 5.7 2.7 28.0 6.18 1.5 161.0 185.2 CB5 3.6 4.8 28.0 7.40 3.5 90.0 119.1 CB6 3.8 4.6 28.0 4.40 1.5 120.0 149.3 CB7 2.5 1.9 28.0 3.70 3.2 84.0 115.0 CB8 4.1 2.4 21.5 5.83 3.0 35.0 63.0 CB9 1.8 2.7 21.5 5.10 2.5 44.0 52.0 CB10 3.2 4.7 21.5 4.30 3.0 20.0 33.0 CB11 2.0 1.6 21.5 2.50 2.4 57.5 84.2 CB12 3.0 1.3 21.5 5.00 3.2 27.0 34.5 CB13 3.2 1.9 21.5 6.10 3.5 25.0 28.5 CB14 4.5 2.9 21.5 7.10 4.0 90.0 107.0 CB15 4.5 3.5 26.0 7.40 2.0 102.0 144.9 CB16 3.4 2.0 26.0 5.80 3.0 31.0 45.0 CB17 3.0 6.9 26.0 4.40 3.0 92.0 108.0 CB18 3.2 4.8 26.0 3.30 2.0 10.0 59.0 CB19 4.2 4.0 26.0 3.10 2.5 25.0 47.0 CB20 5.0 8.3 26.0 3.40 3.3 10.0 49.1 CB21 4.8 6.0 26.0 4.79 2.4 5.0 19.0 CT1 2.9 5.4 24.5 5.17 3.0 38.0 41.7 CT2 2.7 7.5 24.5 6.78 3.4 15.0 20.5 CT3 2.6 6.2 24.5 6.40 2.0 23.0 58.1 CT4 7.0 4.1 24.5 13.24 3.5 81.0 122.4 CT5 4.3 3.8 24.5 9.75 2.0 73.0 88.3 CT6 2.0 6.4 24.5 6.16 3.0 28.0 31.9 CT7 1.3 1.9 24.5 5.58 3.5 42.0 52.7 
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表 2 相似度序列
Table 2. List of similarity
加权聚类方法计算的目标范例与源范例间的相似度 神经网络方法仿真的目标范例与源范例间的相似度 CT1 CT2 CT3 CT4 CT5 CT6 CT7 CT1 CT2 CT3 CT4 CT5 CT6 CT7 CB1 -0.078 8 -0.000 4 -0.016 1 -0.036 2 -0.073 0 -0.065 9 -0.112 0 -0.083 2 -0.000 4 -0.019 7 -0.020 5 -0.016 2 -0.068 1 -0.118 2 CB2 0.047 9 0.131 9 0.110 6 0.090 5 -0.030 1 0.060 8 0.014 8 0.054 7 0.104 9 0.148 5 0.087 5 -0.014 5 0.100 5 0.037 6 CB3 0.133 9 0.217 9 0.196 6 0.176 5 0.139 7 0.146 8 0.100 8 0.144 0 0.237 1 0.179 9 0.116 0 0.142 4 0.155 4 0.099 4 CB4 0.099 0 0.182 9 0.161 7 0.141 5 0.104 8 0.111 9 0.065 8 0.103 1 0.152 1 0.178 0 0.105 3 0.093 7 0.160 3 0.091 4 CB5 0.062 5 0.146 5 0.125 2 0.002 4 0.068 3 0.075 4 0.029 3 0.066 5 0.167 9 0.136 9 0.007 8 0.021 8 0.087 1 0.033 2 CB6 0.106 5 0.190 5 0.169 2 0.149 1 0.112 3 0.119 4 0.073 4 0.132 2 0.130 6 0.162 9 0.121 4 0.138 1 0.148 9 0.094 2 CB7 0.100 1 0.184 0 0.162 8 0.142 6 0.105 9 0.113 0 0.066 9 0.081 9 0.175 7 0.143 4 0.089 1 0.107 6 0.110 4 0.041 4 CB8 -0.068 9 0.015 1 -0.006 2 -0.026 3 -0.063 1 -0.056 0 -0.102 0 -0.055 3 -0.057 4 -0.002 4 -0.020 5 -0.052 2 -0.077 9 -0.093 8 CB9 -0.055 0 0.108 3 0.087 0 0.066 9 0.053 7 0.037 2 0.008 6 -0.080 3 0.130 6 0.089 7 0.023 1 -0.022 6 -0.040 0 0.003 1 CB10 -0.073 1 0.010 8 -0.010 4 -0.030 6 -0.067 3 -0.032 1 -0.106 3 -0.059 1 -0.016 5 -0.007 7 -0.077 6 -0.101 1 -0.033 8 -0.077 1 CB11 0.073 4 0.157 3 0.136 0 0.115 9 0.079 2 0.086 2 0.040 2 0.052 8 0.141 3 0.109 9 0.080 9 -0.054 4 0.083 7 -0.025 9 CB12 -0.083 5 0.005 2 -0.020 9 -0.041 0 -0.077 7 -0.070 7 -0.116 7 -0.060 2 0.004 0 -0.009 2 -0.068 1 -0.083 2 -0.133 0 -0.081 1 CB13 -0.092 4 -0.008 5 -0.029 7 -0.049 9 -0.086 6 -0.079 5 -0.125 6 -0.091 4 -0.005 7 -0.037 3 -0.096 9 -0.107 7 -0.152 9 -0.101 4 CB14 0.041 8 0.125 7 0.104 5 0.084 3 0.047 6 0.054 7 -0.008 9 0.073 7 0.104 2 0.118 9 0.068 9 -0.078 9 0.088 3 -0.005 1 CB15 0.053 2 0.137 1 0.115 8 0.095 7 0.059 0 0.066 0 0.020 0 0.078 1 0.114 3 0.116 1 0.082 3 -0.036 7 0.100 2 0.041 6 CB16 -0.024 3 0.028 9 0.007 6 -0.012 5 -0.049 2 -0.042 2 -0.088 2 -0.018 1 0.013 3 0.003 3 -0.046 8 -0.058 0 -0.072 5 -0.065 9 CB17 0.102 7 0.186 7 0.165 4 0.145 3 0.108 5 0.115 6 0.069 6 0.113 8 0.132 7 0.164 3 0.120 0 0.095 9 0.136 8 0.077 1 CB18 -0.097 7 -0.013 7 -0.035 0 -0.055 1 -0.091 9 -0.084 8 -0.130 8 -0.059 6 -0.051 9 -0.027 8 -0.056 8 -0.070 6 -0.087 4 -0.077 6 CB19 -0.045 0 0.039 0 0.017 7 0.105 1 -0.039 2 -0.060 2 -0.078 2 -0.057 4 0.018 2 0.052 3 -0.136 4 -0.054 6 -0.072 8 -0.042 5 CB20 -0.117 0 -0.033 0 -0.054 3 -0.074 4 -0.111 2 -0.104 1 -0.150 2 -0.094 3 -0.066 3 -0.014 8 -0.076 0 -0.105 0 -0.109 2 -0.167 4 CB21 -0.177 8 -0.093 8 -0.115 1 -0.135 2 -0.172 0 -0.164 9 -0.211 0 -0.145 4 -0.090 2 -0.092 8 -0.133 5 -0.176 0 -0.134 6 -0.200 5
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表 3 最佳源范例及沉降预测结果
Table 3. Best base cases and settlement prediction result
目标范例 最佳源范例 二者相似度 沉降误差 沉降误差百分比/% 序号 沉降/cm 序号 沉降/cm 加权聚类方法 神经网络仿真 CT1 41.7 CB16 45.0 -0.024 3 -0.018 1 -3.3 7.9 CT2 10.5 CB1 13.0 -0.000 4 -0.000 4 -2.5 23.8 CT3 58.1 CB8 63.0 -0.006 2 -0.002 4 -4.9 8.4 CT4 122.4 CB5 119.1 0.002 4 0.007 8 3.3 2.7 CT5 88.3 CB2 92.0 -0.030 1 -0.014 5 -3.7 4.2 CT6 31.9 CB10 33.0 -0.032 1 -0.033 8 -1.1 3.5 CT7 52.7 CB9 52.0 0.008 6 0.003 1 0.7 1.3
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