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Research on Water Demand Forecasting in Handan City Based on GA-BP Neural Network and Normal Interval Estimation
Yu-hang MA, Mei-qin SUO
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Research on Water Demand Forecasting in Handan City Based on GA-BP Neural Network and Normal Interval Estimation
Scientific and accurate water demand prediction results can provide a reasonable basis for urban water supply and demand balance decisions. In this paper， a combined urban water demand forecasting model is proposed by incorporating GA-BP neural networks and normal interval estimation to address the problems of many factors involved in urban water demands， small sample sizes of historical data and fluctuation and uncertainty of water demands. The results show that the relative error of the point prediction results of a single GA-BP neural networks ranges from -6.2% to 5.13%； the relative error of the interval prediction results of the combined prediction model based on GA-BP neural networks and normal interval estimation ranges from -1.01% to 0.004%， which shows that the combined prediction model based on GA-BP neural networks and normal interval estimation is more stable， more accurate and closer to the actual water demand situation in Handan. The combined model can be used as a way to forecast the water demands in Handan.
GA-BP neural networks / normal interval estimation / combined model / interval forecast {{custom_keyword}} /
Tab.1 Eigenvalues and variance contribution of correlation coefficient matrix表1 相关系数矩阵特征值及方差贡献率 |
| 主成分 | 特征值 | 方差贡献/% | 累计贡献/% |
|---|---|---|---|
| 1 | 17.403 | 69.613 | 69.613 |
| 2 | 2.336 | 9.345 | 78.958 |
| 3 | 1.831 | 7.323 | 86.281 |
| 4 | 1.241 | 4.964 | 91.245 |
Tab.2 Extraction of indicators in principal components表2 主成分中指标的提取 |
| 第一主成分 | 第二主成分 | 第三主成分 | 第四主成分 | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 指标 | 特征向量 | 指标 | 特征向量 | 指标 | 特征向量 | 指标 | 特征向量 | |||
| X 4 | 0.238 511 | X 12 | 0.484 787 | X 1 | 0.410 192 | X 1 | 0.526 016 | |||
| X 24 | 0.238 032 | X 14 | 0.334 968 | X 14 | 0.331 849 | |||||
| X 20 | 0.237 313 | |||||||||
| X 19 | 0.235 875 | |||||||||
| X 7 | 0.233 717 | |||||||||
| X 17 | 0.230 601 | |||||||||
| X 6 | 0.230 361 | |||||||||
| X 15 | 0.229 402 | |||||||||
| X 25 | 0.228 204 | |||||||||
| X 21 | 0.226 286 | |||||||||
| X 8 | 0.225 567 | |||||||||
| X 22 | 0.225 088 | |||||||||
| X 16 | 0.222 930 | |||||||||
| X 5 | 0.215 979 | |||||||||
Tab.3 Calculation results of gray correlation coefficients表3 灰色关联系数计算结果 |
| 指标 | 关联系数 | 指标 | 关联系数 | 指标 | 关联系数 | 指标 | 关联系数 | 指标 | 关联系数 |
|---|---|---|---|---|---|---|---|---|---|
| X 11 | 0.951 6 | X 14 | 0.879 7 | X 6 | 0.832 9 | X 8 | 0.782 8 | X 18 | 0.698 1 |
| X 12 | 0.950 5 | X 10 | 0.871 3 | X 21 | 0.824 6 | X 19 | 0.778 2 | X 7 | 0.687 2 |
| X 20 | 0.946 3 | X 3 | 0.860 1 | X 15 | 0.821 0 | X 4 | 0.772 8 | X 22 | 0.651 1 |
| X 1 | 0.934 3 | X 2 | 0.856 3 | X 5 | 0.805 6 | X 25 | 0.771 2 | X 23 | 0.628 5 |
| X 9 | 0.931 4 | X 17 | 0.837 4 | X 24 | 0.785 4 | X 16 | 0.734 2 | X 13 | 0.624 3 |
Fig.3 BP neural network and GA-BP neural network simulation prediction results图3 BP神经网络和GA-BP神经网络模拟预测结果 |
Tab.4 Statistics of simulation prediction results of BP neural network and GA-BP neural network表4 BP神经网络和GA-BP神经网络模拟预测结果统计 (%) |
| 相对误差 | 农业用水 | 工业用水 | 生活用水 | 总用水 | ||||
|---|---|---|---|---|---|---|---|---|
| BP | GA-BP | BP | GA-BP | BP | GA-BP | BP | GA-BP | |
| 训练样本最大相对误差 | 6.59 | 7.64 | 8.96 | 3.50 | 16.22 | 8.85 | 3.17 | 3.29 |
| 检验样本最大相对误差 | 2.37 | 1.85 | 4.76 | 2.38 | 4.12 | 1.87 | 4.69 | 2.84 |
| 训练样本平均相对误差 | 1.22 | 1.79 | 2.00 | 0.78 | 1.69 | 1.62 | 1.24 | 0.85 |
Fig.4 Frequency distribution of GA-BP neural network 2019 total water demand point forecast results图4 GA-BP神经网络2019年总需水量点预测结果频率分布 |
Tab.5 GA-BP neural network 2019 total water demand point forecast results descriptive statistics表5 GA-BP神经网络2019年总需水量点预测结果描述统计 |
| 样本 | 真实值/亿m3 | 模拟值 | |||||
|---|---|---|---|---|---|---|---|
| 最小值/亿m3 | 相对误差/% | 最大值/亿m3 | 相对误差/% | 平均值/亿m3 | 标准差 | ||
| 80 | 19.278 4 | 18.082 4 | -6.2 | 20.266 6 | 5.13 | 19.18 | 0.44 |
Tab.6 Total water demand interval forecast results for 2019 based on GA-BP neural network with normal interval estimation表6 基于GA-BP神经网络与正态区间估计的2019年总需水量区间预测结果 |
| 邯郸市2019年总需水量/亿m3 | 区间预测（95%置信度） | |||
|---|---|---|---|---|
| 下限/亿m3 | 相对误差/% | 上限/亿m3 | 相对误差/% | |
| 19.278 4 | 19.083 4 | －1.01 | 19.279 2 | 0.004 |
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Fig.1 Combined model designFig.2 Basic structure of BP neural network
Tab.1 Eigenvalues and variance contribution of correlation coefficient matrixTab.2 Extraction of indicators in principal componentsTab.3 Calculation results of gray correlation coefficientsFig.3 BP neural network and GA-BP neural network simulation prediction resultsTab.4 Statistics of simulation prediction results of BP neural network and GA-BP neural networkFig.4 Frequency distribution of GA-BP neural network 2019 total water demand point forecast resultsTab.5 GA-BP neural network 2019 total water demand point forecast results descriptive statisticsTab.6 Total water demand interval forecast results for 2019 based on GA-BP neural network with normal interval estimation
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