Research on wave prediction method based on nonlinear Schrödinger equation
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摘要: 为探索海浪波面信息的实时预报方法,以三阶非线性薛定谔(NLS)方程的逆散射变换求解为基础,通过理论推导,给出了一种由实测波高时历数据计算其NLS方程本征值的方法,进一步实现了对波浪包络时空演变的预报。通过预报结果与实测波列的比对,验证了方法的有效性和准确性。该方法可为船舶或海上平台的大浪预警,以及为大波浪中海上作业寻找窗口期等提供一条新的技术途径。Abstract: In order to study the real-time prediction method of ocean wave information, some theoretical derivation is made based on inverse scattering transformation of cubic Schrödinger equation, and a method to calculate eigenvalues from measured wave height time series is given. Then the calculated eigenvalues are used to predict spatial-temporal evolution of wave envelope. The predictions are then compared with measured time series, the results show the method has good effectiveness and accuracy. This method can provide support for big wave warning of ships or offshore platform, and time windows seeking for offshore operation under heavy sea.
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Key words:
- nonlinear Schrödinger equation /
- inverse scattering transform /
- eigenvalues /
- predict
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表 1
$A = 1,\;T = 10$ s时实际本征值与仿真结果对比Tab. 1 Comparison of real eigenvalues and simulation resultwhen A=1 and T=10 s
实际本征值位置 对应寻优结果 0.000 0+0.949 4i 0.001 1+0.948 7i 0.000 0+0.778 0i –0.000 7+0.776 9i 0.000 0+0.334 3i –0.000 2+0.334 2i 0.761 0+0.000 0i 0.762 1+0.001 8i –0.761 0+0.000 0i –0.761 7–0.003 3i 1.211 4+0.000 0i 1.212 5+0.001 4i –1.211 4+0.000 0i –1.212 2–0.000 5i 1.597 8+0.000 0i 1.600 5+0.000 4i –1.597 8+0.000 0i –1.598 7–0.000 7i 1.958 6+0.000 0i 1.954 0+0.000 4i –1.958 6+0.000 0i –1.960 9–0.000 0i 2.305 8+0.000 0i 2.306 9+0.000 7i –2.305 8+0.000 0i –2.304 9–0.002 3i 2.644 7+0.000 0i 2.644 4+0.000 3i –2.644 7+0.000 0i –2.644 4+0.000 3i 2.978 2+0.000 0i 2.976 1+0.002 7i –2.978 2+0.000 0i –2.980 1–0.000 5i 表 2 实测和预测最大波高对比
Tab. 2 Comparison of measured max wave height and predicted result of each probe
波高传感器与造波板距离/m 实测最大波高/m 预报最大波高/m 相对误差/% 37 0.114 3 0.100 9 11.74 55 0.094 5 0.113 2 19.74 74 0.124 7 0.130 8 4.87 92 0.122 6 0.151 8 23.78 104 0.165 6 0.156 8 15.68 113 0.156 2 0.172 9 10.74 122 0.160 9 0.175 6 9.12 128 0.178 3 0.174 6 2.06 137 0.187 7 0.168 2 10.39 146 0.163 6 0.158 7 2.99 155 0.166 3 0.148 8 10.52 165 0.161 4 0.137 0 15.12 174 0.152 8 0.127 3 16.69 182 0.142 6 0.118 6 16.78 192 0.132 2 0.110 6 16.36 201 0.121 2 0.104 3 13.88 210 0.103 9 0.099 4 4.29 219 0.106 4 0.094 6 11.13 226 0.107 0 0.091 6 14.36 229 0.113 4 0.090 2 20.50 表 3 各波高传感器处实测波列与预测包络对比
Tab. 3 Comparison of measured wave train and predicted envelope of each probe
与造波板距离/m 实测最大波高/m 预报最大波高/m 幅值相对误差/% 时间偏差/s 30 0.065 8 0.065 5 0.48 0.55 35 0.067 7 0.068 6 1.33 0.55 40 0.074 6 0.072 1 3.25 0.68 45 0.077 0 0.076 2 1.11 0.68 60 0.097 1 0.090 6 6.71 1.25 65 0.108 1 0.096 3 10.88 1.25 70 0.104 6 0.101 4 3.10 1.49 75 0.117 6 0.106 5 9.44 1.49 80 0.128 0 0.110 5 13.69 1.49 85 0.121 6 0.112 6 7.39 1.61 -
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