低信噪比下相干多普勒激光雷达风场矢量反演算法
|
摘要
为了能在低信噪比情况下获得高精度矢量风速,采用非线性最优化理论中的序列二次规划(SQP)求解滤波正弦波拟合(FSWF),实现了速度方位显示(VAD)算法中矢量风场的反演。基于模拟数据进行仿真实验,以反演结果的均方根误差作为评价指标,对比直接正弦波拟合(DSWF)和SQP-FSWF两种算法,结果表明在低信噪比条件下SQP-FSWF算法的反演效果优于DSWF算法。在FSWF计算中,基于风场反演结果的时空连续性,对比SQP算法和无约束最优化算法中的拟牛顿法,结果表明,SQP算法在低信噪比下效果更好。开展了激光雷达和探空气球的风场测量对比实验,获取了真实的激光雷达回波信号和同步探空气球数据,以进一步评估算法的可靠性。实验结果显示,SQP-FSWF算法得到的风速反演结果,同作为对比对象的探空气球的测量结果(水平风速、水平风向),两者间的相关系数分别为0.993和0.988,平均误差分别为0.2 m/s和3.28°,均方根误差分别为0.28 m/s和4.62°。对比分析反演结果的时空连续性发现,所提出方法在低信噪比下时空连续性更好,与模拟数据实验结果的效果表现一致。
In this study, the sequential quadratic programming(SQP) in nonlinear optimization theory is used to solve the filtered sine wave fitting(FSWF). Based on the speed azimuth display(VAD) algorithm, high-precision inversion of the vector wind field is achieved at low signal-to-noise ratio(SNR). In the simulation experiment, the root mean square errors of the inversion results are used as the evaluation index, and the direct sine wave fitting(DSWF) algorithm and the SQP-FSWF algorithm are compared. In the FSWF calculation, based on the spatial-temporal continuity of the wind field inversion results, the SQP algorithm and the quasi-Newton method in the unconstrained optimization algorithm are compared. The comparison results show that the inversion effect of SQP-FSWF is better than those of DSWF and the quasi-Newton method at low SNR. To further evaluate the reliability of the proposed algorithm, we perform the wind field measurement contrast experiments based on lidar and synchronous sounding balloon, in which we obtain the real echo signal of lidar and the wind field data of synchronous sounding balloon. The wind speed inversion results simulated by the SQP-FSWF algorithm and the results measured by synchronous sounding balloon as the comparison object are compared. It can be seen that for horizontal wind speed, the correlation coefficient, the average error, the root mean square error are 0.993, 0.2 m/s, 0.28 m/s; for horizontal wind direction, the correlation coefficient, the average error, the root mean square error are 0.988, 3.28°, 4.62°, respectively. Based on the comparison between the spatial-temporal continuity of the wind retrieval results, the proposed method at low SNR is advantageous, which is consistent with the results of the simulated data.
In this study, the sequential quadratic programming(SQP) in nonlinear optimization theory is used to solve the filtered sine wave fitting(FSWF). Based on the speed azimuth display(VAD) algorithm, high-precision inversion of the vector wind field is achieved at low signal-to-noise ratio(SNR). In the simulation experiment, the root mean square errors of the inversion results are used as the evaluation index, and the direct sine wave fitting(DSWF) algorithm and the SQP-FSWF algorithm are compared. In the FSWF calculation, based on the spatial-temporal continuity of the wind field inversion results, the SQP algorithm and the quasi-Newton method in the unconstrained optimization algorithm are compared. The comparison results show that the inversion effect of SQP-FSWF is better than those of DSWF and the quasi-Newton method at low SNR. To further evaluate the reliability of the proposed algorithm, we perform the wind field measurement contrast experiments based on lidar and synchronous sounding balloon, in which we obtain the real echo signal of lidar and the wind field data of synchronous sounding balloon. The wind speed inversion results simulated by the SQP-FSWF algorithm and the results measured by synchronous sounding balloon as the comparison object are compared. It can be seen that for horizontal wind speed, the correlation coefficient, the average error, the root mean square error are 0.993, 0.2 m/s, 0.28 m/s; for horizontal wind direction, the correlation coefficient, the average error, the root mean square error are 0.988, 3.28°, 4.62°, respectively. Based on the comparison between the spatial-temporal continuity of the wind retrieval results, the proposed method at low SNR is advantageous, which is consistent with the results of the simulated data.
引文
[1] Hawley J G, Targ R, Henderson S W, et al. Coherent launch-site atmospheric wind sounder: theory and experiment[J]. Applied Optics, 1993, 32(24): 4557-4568.
[2] Werner C. Fast sector scan and pattern recognition for a CW laser Doppler anemometer[J]. Applied Optics, 1985, 24(21): 3557-3564.
[3] Smalikho I. Techniques of wind vector estimation from data measured with a scanning coherent Doppler lidar[J]. Journal of Atmospheric and Oceanic Technology, 2003, 20(2): 276-291.
[4] Diao W F, Liu J Q, Zhu X P, et al. Study of all-fiber coherent Doppler lidar wind profile nonlinear least square retrieval method and validation experiment[J]. Chinese Journal of Lasers, 2015, 42(9): 0914003. 刁伟峰, 刘继桥, 竹孝鹏, 等. 全光纤相干多普勒激光雷达非线性最小二乘风速反演方法及实验研究[J]. 中国激光, 2015, 42(9): 0914003.
[5] Huang M, Wang Y L, Wang N, et al. Algorithm and simulation of downward velocity azimuth display of airborne wind lidars[J]. Laser Technology, 2012, 36(1): 22-25, 41. 黄敏, 王玉兰, 王娜, 等. 机载测风激光雷达下视VAD反演及算法仿真[J]. 激光技术, 2012, 36(1): 22-25, 41.
[6] Fan Q, Zhu K Y, Zheng J F,et al. Detection performance analysis of all-fiber coherent wind lidar under different weather types[J]. Chinese Journal of Lasers, 2017, 44(2): 0210003. 范琪, 朱克云, 郑佳锋, 等. 不同天气类型下全光纤相干激光测风雷达探测性能分析[J]. 中国激光, 2017, 44(2): 0210003.
[7] Banakh V A, Smalikho I N, Falits A V, et al. Joint radiosonde and Doppler lidar measurements of wind in the atmospheric boundary layer[J]. Atmospheric and Oceanic Optics, 2015, 28(2): 185-191.
[8] Feng C Z, Wu S H, Liu B Y. Research on wind retrieval method of coherent Doppler lidar and experimental verification[J]. Chinese Journal of Lasers, 2018, 45(4): 0410001. 冯长中, 吴松华, 刘秉义. 相干多普勒激光雷达风场反演方法研究与实验印证[J]. 中国激光, 2018, 45(4): 0410001.
[9] Frehlich R G, Yadlowsky M J. Performance of mean-frequency estimators for Doppler radar and lidar[J]. Journal of Atmospheric and Oceanic Technology, 1994, 11(5): 1217-1230.
[10] Banakh V, Smalikho I. Coherent Doppler wind lidars in a turbulent atmosphere[M]. Massachusetts: Artech House, 2013: 93-103.
[11] Yuan Y X, Sun W Y. Optimization theory and methods[M]. Beijing: Science Press, 1997: 528-536. 袁亚湘, 孙文瑜. 最优化理论与方法[M]. 北京: 科学出版社, 1997: 528-536.
[12] Wang Y J, Xiu N H. Nonlinear programming theory and methods[M]. Xi′an: Shaanxi Science And Technology Press, 2008: 197-210. 王宜举, 修乃华. 非线性规划理论与算法[M]. 西安: 陕西科学技术出版社, 2008: 197-210.
[13] Powell M J D. The convergence of variable metric methods for non-linearly constrained optimization calculations[C]//Proceedings of the Special Interest Group on Mathematical Programming Symposium, July 11-13, 1977,Madison. [S.n.: s.l.], 1978: 27-63.
[14] Yu H M, Ren G Y, Liu Y L.The characteristics of wind speed variation at different altitudes of boundary layer in Heilongjiang province[J]. Journal of Natural Resources, 2013, 28(10): 1718-1730. 于宏敏, 任国玉, 刘玉莲. 黑龙江省大气边界层不同高度风速变化[J]. 自然资源学报, 2013, 28(10): 1718-1730.
[15] Liu C, Che D S, Ke Z J. Application of wind profile radar in upper wind analysis[J]. Desert and Oasis Meteorology, 2013, 7(2): 56-60. 刘成, 车达升, 柯宗建. 风廓线雷达在高空风场分析中的应用[J]. 沙漠与绿洲气象, 2013, 7(2): 56-60.
[2] Werner C. Fast sector scan and pattern recognition for a CW laser Doppler anemometer[J]. Applied Optics, 1985, 24(21): 3557-3564.
[3] Smalikho I. Techniques of wind vector estimation from data measured with a scanning coherent Doppler lidar[J]. Journal of Atmospheric and Oceanic Technology, 2003, 20(2): 276-291.
[4] Diao W F, Liu J Q, Zhu X P, et al. Study of all-fiber coherent Doppler lidar wind profile nonlinear least square retrieval method and validation experiment[J]. Chinese Journal of Lasers, 2015, 42(9): 0914003. 刁伟峰, 刘继桥, 竹孝鹏, 等. 全光纤相干多普勒激光雷达非线性最小二乘风速反演方法及实验研究[J]. 中国激光, 2015, 42(9): 0914003.
[5] Huang M, Wang Y L, Wang N, et al. Algorithm and simulation of downward velocity azimuth display of airborne wind lidars[J]. Laser Technology, 2012, 36(1): 22-25, 41. 黄敏, 王玉兰, 王娜, 等. 机载测风激光雷达下视VAD反演及算法仿真[J]. 激光技术, 2012, 36(1): 22-25, 41.
[6] Fan Q, Zhu K Y, Zheng J F,et al. Detection performance analysis of all-fiber coherent wind lidar under different weather types[J]. Chinese Journal of Lasers, 2017, 44(2): 0210003. 范琪, 朱克云, 郑佳锋, 等. 不同天气类型下全光纤相干激光测风雷达探测性能分析[J]. 中国激光, 2017, 44(2): 0210003.
[7] Banakh V A, Smalikho I N, Falits A V, et al. Joint radiosonde and Doppler lidar measurements of wind in the atmospheric boundary layer[J]. Atmospheric and Oceanic Optics, 2015, 28(2): 185-191.
[8] Feng C Z, Wu S H, Liu B Y. Research on wind retrieval method of coherent Doppler lidar and experimental verification[J]. Chinese Journal of Lasers, 2018, 45(4): 0410001. 冯长中, 吴松华, 刘秉义. 相干多普勒激光雷达风场反演方法研究与实验印证[J]. 中国激光, 2018, 45(4): 0410001.
[9] Frehlich R G, Yadlowsky M J. Performance of mean-frequency estimators for Doppler radar and lidar[J]. Journal of Atmospheric and Oceanic Technology, 1994, 11(5): 1217-1230.
[10] Banakh V, Smalikho I. Coherent Doppler wind lidars in a turbulent atmosphere[M]. Massachusetts: Artech House, 2013: 93-103.
[11] Yuan Y X, Sun W Y. Optimization theory and methods[M]. Beijing: Science Press, 1997: 528-536. 袁亚湘, 孙文瑜. 最优化理论与方法[M]. 北京: 科学出版社, 1997: 528-536.
[12] Wang Y J, Xiu N H. Nonlinear programming theory and methods[M]. Xi′an: Shaanxi Science And Technology Press, 2008: 197-210. 王宜举, 修乃华. 非线性规划理论与算法[M]. 西安: 陕西科学技术出版社, 2008: 197-210.
[13] Powell M J D. The convergence of variable metric methods for non-linearly constrained optimization calculations[C]//Proceedings of the Special Interest Group on Mathematical Programming Symposium, July 11-13, 1977,Madison. [S.n.: s.l.], 1978: 27-63.
[14] Yu H M, Ren G Y, Liu Y L.The characteristics of wind speed variation at different altitudes of boundary layer in Heilongjiang province[J]. Journal of Natural Resources, 2013, 28(10): 1718-1730. 于宏敏, 任国玉, 刘玉莲. 黑龙江省大气边界层不同高度风速变化[J]. 自然资源学报, 2013, 28(10): 1718-1730.
[15] Liu C, Che D S, Ke Z J. Application of wind profile radar in upper wind analysis[J]. Desert and Oasis Meteorology, 2013, 7(2): 56-60. 刘成, 车达升, 柯宗建. 风廓线雷达在高空风场分析中的应用[J]. 沙漠与绿洲气象, 2013, 7(2): 56-60.