GPS elevation fitting of BP neural network optimized by genetic simulated annealing algorithm
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摘要: 针对传统BP神经网络收敛速度慢、易陷入局部最优和遗传算法优化BP神经网络(GA-BP)算法过早收敛的问题,提出了遗传模拟退火算法优化BP神经网络(GSA-BP)算法. 在遗传算法(GA)的种群更新中加入模拟退火算法(SA),保留种群的多样性. 用GSA-BP算法对某地区进行高程异常拟合,并与BP算法和GA-BP算法结果进行比较. 结果显示:GSA-BP算法精度可分别提高约51%、25%,速度提高约77%、39%,且能基本满足四等水准测量精度要求. 该方法在GPS高程拟合中具有可行性.
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关键词:
- GPS /
- 高程异常 /
- BP神经网络 /
- 遗传算法(GA) /
- 模拟退火算法(SA)
Abstract: In order to solve the problems of slow convergence speed of traditional BP neural network, easy to fall into local optimum and premature convergence of genetic algorithm optimized BP neural network (GA-BP) algorithm, a genetic simulated annealing algorithm optimized BP neural network (GSA-BP) algorithm was proposed. The simulated annealing algorithm (SA) was added to the genetic algorithm (GA) to keep the diversity of the population. GSA-BP algorithm is used to fit the elevation anomaly in a certain area, and the results are compared with BP algorithm and GA-BP algorithm. The results show that the GSA-BP algorithm can improve the accuracy by 51% and 25%, and the speed by 77% and 39% respectively, and can basically meet the requirements of the fourth grade leveling accuracy. This method proves to be feasible in GPS elevation fitting.-
Key words:
- GPS /
- elevation anomaly /
- BP neural network /
- genetic algorithm (GA) /
- simulated annealing (SA)
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表 1 不同训练集点个数下测试结果对比表
训练集 测试集 测试集中误差/mm 精度提高/% 训练时间/s 速度提高/% BP GA-BP GSA-BP 较BP 较GA-BP BP GA-BP GSA-BP 较BP 较GA-BP A1 B1 69.0 56.9 30.1 56.4 47.1 0.60 0.23 0.14 76.7 39.1 A2 B2 65.8 51.2 28.7 56.4 43.9 0.58 0.26 0.13 77.6 50.0 A3 B3 61.5 44.2 28.0 54.5 36.7 0.63 0.27 0.12 81.0 55.6 A4 B4 62.3 41.9 26.2 58.0 37.5 0.64 0.25 0.15 76.6 40.0 A5 B5 61.7 37.1 25.1 59.3 32.3 0.60 0.23 0.13 78.3 43.5 A6 B6 55.2 36.4 26.0 53.0 28.7 0.54 0.24 0.14 74.1 41.7 A7 B7 53.3 36.8 25.2 52.8 31.7 0.63 0.21 0.17 73.0 19.0 A8 B8 50.4 36.6 25.0 50.5 31.9 0.60 0.18 0.16 73.3 11.1 A9 B9 50.0 35.4 24.7 50.7 30.4 0.54 0.22 0.15 72.2 31.8 A10 B10 47.7 34.1 24.5 48.7 28.3 0.58 0.21 0.10 82.8 52.4 A11 B11 48.3 32.8 25.4 47.3 22.4 0.54 0.20 0.16 70.4 20.0 A12 B12 48.6 31.6 24.9 48.7 21.0 0.63 0.25 0.10 84.1 60.0 A13 B13 47.8 30.4 24.8 48.0 18.2 0.61 0.20 0.11 82.0 45.0 A14 B14 47.4 29.5 24.7 47.8 16.1 0.58 0.18 0.11 81.0 38.9 A15 B15 47.7 28.3 24.4 48.8 13.6 0.62 0.25 0.12 80.6 52.0 A16 B16 47.0 28.3 25.3 46.2 10.7 0.62 0.24 0.11 82.3 54.2 A17 B17 46.6 28.1 25.1 46.1 10.8 0.59 0.18 0.14 76.3 22.2 A18 B18 45.8 28.6 24.2 47.2 15.5 0.63 0.23 0.17 73.0 26.1 A19 B19 44.8 28.3 24.1 46.2 14.8 0.54 0.25 0.16 70.4 36.0 A20 B20 44.7 27.8 23.4 47.7 16.0 0.59 0.27 0.12 79.7 55.6 A21 B21 44.6 25.2 23.2 48.1 8.1 0.55 0.20 0.13 76.4 35.0 表 2 训练结果与四等水准对比表
分布点 最近点
距离/km四等水准
限差/mm高程异常差/mm BP GA-BP GSA-BP G38 1.8 27.0 −0.2 −12.4 −16.6 G4 1.5 24.5 −24.5 19.4 42.8 G63 1.5 24.5 −8.7 18.9 33.7 G117 3.2 35.7 −40.6 9.8 −0.9 G6 2.8 33.5 −48.0 16.2 −5.2 G1 1.8 27.1 15.9 11.9 27.0 G2 2.1 28.9 4.9 12.4 38.3 G24 1.2 21.5 −5.1 −23.3 16.7 G61 1.0 19.5 −27.3 −41.5 −13.4 G22 1.0 19.5 13.0 −11.0 15.7 G23 1.1 20.7 37.6 7.1 51.8 G13 1.1 20.7 −1.8 −32.4 −6.4 G14 1.6 25.5 22.7 −24.0 −20.2 G10 3.9 39.2 159.9 −3.1 −21.2 G69 1.9 27.8 24.3 −18.3 −15.0 G119 3.3 36.3 −87.9 18.4 −9.8 G7 2.6 32.1 47.0 −20.8 −30.6 G16 1.5 24.8 10.7 15.1 −17.8 G15 1.5 24.8 −18.9 37.5 −23.7 G3 2.3 30.1 3.2 109.8 20.6 -
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