电大目标雷达散射截面的研究
|
摘要
随着隐身技术和反隐身技术的发展，电大目标雷达散射截面(RCS)的测量和计算方法也在不断发展。在测量方面，由于直接测量电大尺寸的目标所需费用较高，所以越来越多的人开始采用缩比测量方法，通过测量缩比模型的RCS从而得到原型目标的RCS。而研究缩比模型和原型目标的RCS的关系依赖于缩比理论的研究。在电磁计算方面，基于NURBS建模，采用物理光学方法计算的NURBS_PO技术是目前国内外应用较多的一种电磁计算方法。而NURBS_PO技术的关键就是物理光学方法中积分式的求解。
电大目标的RCS研究是一个很实际的工程问题，对于电大目标，无论测量还是计算都是一个难点。因此本文的工作围绕电大目标雷达散射截面(RCS)的研究展开，采用缩比技术减轻测量的负担，采用高频近似算法PO方法减少了计算量。缩比技术可以有效的降低测量的负担与工作量，然而以往缩比理论的研究大多是基于目标位于全空间的情况下的。在实际工程中，目标有时处于半空间中，比如军舰等，因此作者研究了半空间中的缩比模型，并给出了半空间目标RCS缩比因子的计算公式。
本文还采用了常用的电磁计算方法计算目标的RCS：基于三角面元建模的Gordon算法，和基于NURBS建模的驻相法和LUDWIG方法。并且，作者提出了用驻相法和LUDWIG方法结合计算NURBS模型物理光学积分公式。最后，为了提高计算精度，本文考虑了目标的各个面片之间二次散射的作用，推导了PO_PO法计算二次散射的公式。
本文主要研究了电大目标和缩比模型的缩比关系，基于NURBS建模的目标的一次散射场和二次散射场的计算。其中半空间缩比理论，基于NURBS建模的驻相法结合LUDWIG方法计算目标的RCS及基于NURBS建模的PO_PO方法计算NURBS面片的二次散射场均属本文的创新点，每种方法都给出了具体算例来验证方法的有效性。
With the development of stealthy and anti-stealthy technique, the measuring and computational methods for the Radar Cross Section (RCS) of large electric objects are growing. In measurement, because of the cost of measuring a large electric object is very high, so the method measuring the scaling model becomes a hotspot in electromagnetic field. In computation, PO technique has been widely used to get the RCS of large electric objects modeled by NURBS both at home and abroad.
The study of the RCS of large electric objects is a practical and difficult engineering problem. The paper applies the scaling method to reduce the measurement and high frequency approximation to simplify the calculation. The traditional scaling model lies in total space, but in practice, one usually faces some objects in half space, for example, a ship. So the formulas used to calculate the RCS scaling factors of some objects lying in half space are derived in this paper.
The method commonly used for computing the RCS is as follows: the Gordon algorithm for objects described in flat facets; the stationary phase method and the Ludwig algorithm for objects modeled in NURBS. The author presents the method that merges the stationary phase method and the Ludwig algorithm together to calculate the PO integral formula. Finally, to improve the accuracy, the author studies the double reflection between the patches of an object, and derives the formulas in PO_PO.
The scaling method of large electric objects and the single and double reflection of NURBS surfaces are mainly presented in this paper. The scaling method in half space, the method for merging the stationary phase method and the Ludwig algorithm to calculate the RCS of a NURBS surface and the PO_PO method to compute the double reflection of two NURBS surfaces are presented in this paper for the first time. The results shown in this paper proves that the methods are feasible.
电大目标的RCS研究是一个很实际的工程问题，对于电大目标，无论测量还是计算都是一个难点。因此本文的工作围绕电大目标雷达散射截面(RCS)的研究展开，采用缩比技术减轻测量的负担，采用高频近似算法PO方法减少了计算量。缩比技术可以有效的降低测量的负担与工作量，然而以往缩比理论的研究大多是基于目标位于全空间的情况下的。在实际工程中，目标有时处于半空间中，比如军舰等，因此作者研究了半空间中的缩比模型，并给出了半空间目标RCS缩比因子的计算公式。
本文还采用了常用的电磁计算方法计算目标的RCS：基于三角面元建模的Gordon算法，和基于NURBS建模的驻相法和LUDWIG方法。并且，作者提出了用驻相法和LUDWIG方法结合计算NURBS模型物理光学积分公式。最后，为了提高计算精度，本文考虑了目标的各个面片之间二次散射的作用，推导了PO_PO法计算二次散射的公式。
本文主要研究了电大目标和缩比模型的缩比关系，基于NURBS建模的目标的一次散射场和二次散射场的计算。其中半空间缩比理论，基于NURBS建模的驻相法结合LUDWIG方法计算目标的RCS及基于NURBS建模的PO_PO方法计算NURBS面片的二次散射场均属本文的创新点，每种方法都给出了具体算例来验证方法的有效性。
With the development of stealthy and anti-stealthy technique, the measuring and computational methods for the Radar Cross Section (RCS) of large electric objects are growing. In measurement, because of the cost of measuring a large electric object is very high, so the method measuring the scaling model becomes a hotspot in electromagnetic field. In computation, PO technique has been widely used to get the RCS of large electric objects modeled by NURBS both at home and abroad.
The study of the RCS of large electric objects is a practical and difficult engineering problem. The paper applies the scaling method to reduce the measurement and high frequency approximation to simplify the calculation. The traditional scaling model lies in total space, but in practice, one usually faces some objects in half space, for example, a ship. So the formulas used to calculate the RCS scaling factors of some objects lying in half space are derived in this paper.
The method commonly used for computing the RCS is as follows: the Gordon algorithm for objects described in flat facets; the stationary phase method and the Ludwig algorithm for objects modeled in NURBS. The author presents the method that merges the stationary phase method and the Ludwig algorithm together to calculate the PO integral formula. Finally, to improve the accuracy, the author studies the double reflection between the patches of an object, and derives the formulas in PO_PO.
The scaling method of large electric objects and the single and double reflection of NURBS surfaces are mainly presented in this paper. The scaling method in half space, the method for merging the stationary phase method and the Ludwig algorithm to calculate the RCS of a NURBS surface and the PO_PO method to compute the double reflection of two NURBS surfaces are presented in this paper for the first time. The results shown in this paper proves that the methods are feasible.
引文
[1] 阮颍铮．雷达截面与隐身技术[M]．北京：国防工业出版社，2001．
[2] Jin Au Kong著，吴季等译．电磁波理论[M]．北京：电子工业出版社，2003．
[3] William T. Shaw, Andrew J. Dougan. Green's Function Refinement as an Approach to Radar Backscatter: General Theory and Applications to LGA Scattering from the Ocean[J].IEEE Trans. on Antennas and Propagation. 1998(1):57-66.
[4] F. Daout, A. Khenchaf, J. Saillard. The effect of salinity and temperature on the electromagnetic field scattered by sea water[J]. OCEANS '94. 'Oceans Engineering for Today's Technology and Tomorrow's Preservation.'Proceedings.1994,9. vol.1.pp110-115.
[5] 梁昌洪，胡小培．微波工程设计中的缩比理论[J]．微波与卫星通信．1993，1．PP8-11．
[6] 夏应清，杨河林，鲁述，刘武．超电大复杂目标RCS缩比模型预估方法[J]．微波学报．2003，3．pp8-11．
[7] 时振栋．基本散射体RCS分析和综合[J]．应用科学学报．2003，12．pp331-333．
[8] EliBrookner. Aspects of Modem Rada[M]r. MA:ArtechHouseInc. 1988.
[9] Crispin J W Jr, Maffett A L. RCS estimation for simple shape[J]. Proceedings of the IEEE. 1965. pp833-848.
[10] Shi Z D. Effects of variance in the size of the scatter on its RCS[J]. Microwave and Optical Technology Letter. 1993,24(增刊1):6-9.
[11] 刘宏伟，时振栋．隐身目标雷达截面的缩比测量及反演计算[J]．电子科技大学学报．1995，8．pp13-17．
[12] 刘宏伟，时振栋，武哲，陆柱蕙．隐身目标RCS缩比测量的数据处理及反演计算技术[J]．微波学报．1997，3．pp15-19．
[13] 林溪波．激光雷达散射截面和几何缩比关系[J]．飞航导弹，1998，9．pp52-57．
[14] N. N. Youssef. Radar cross section of complex targets[J]. Proc. IEEE. 1989,5.vol. 72. pp. 722-734.
[15] J. Perez and M. F. Catedra. Rcs of Electrically Large Targets Modeled With NURBS Surfaces[J]. Electronics Leters. Vol. 28,N o.12. 1992,9. pp1119-1121.
[16] J. Perez and M. F. Catedra. Application of physical optics to the RCS computation of bodies modeled with NURBS surfaces[J]. IEEE Trans. Antennas Propagat. 1994,10. vol. 42, pp1404-1411.
[17] M.Domingo,F.Rivas, J. Perez and M. F. Catedra. computation of the RCS Of Complex Bodies Modeled Using NURBS surfaces[J]. IEEE Trans. Antennas Propagat.. 1995,9. vol.37, pp.36-46.
[18] 赵淙．NURBS面片上的RCS计算．硕士论文．西安电子科技大学．2000．
[19] 王超．NURBS曲面的RCS算法研究．硕士论文．西北工业大学．2004．
[20] A.C.LUDWIG. Computation of Radiation Patterns Involving Numerical Double Integration[J]. IEEE Trans. on AR 1968,11. pp767-769.
[21] M.L.X.dos santos, N.R.Rabelo.On the LUDWIG Integration Algorithm for Triangular Subregions [J]. Proc.of IEEE. 1986,10.vo174(10), PP1455-1456.
[22] A.C.LUDWIG. Comments on the Accuracy of the "LUDWIG" Integration Algorithm[J]. IEEE Trans. on AP. 1988,4.vo136(4) pp358-360.
[23] 黄纪军，粟毅，马兴义，毛钧杰．基于路德维格积分的目标RCS计算方法[J]．微波学报．2004，3．pp15-18．
[24] J.L.Volakis.XPATCH. A high-frequency electromagnetic-scattering prediction code and environment for complex three-dimensional objects[J]. IEEE Antennas and propagation Magazine 1994. vo136(1).pp65-69.
[25] D.M.Elking, J.M.Roedder, D.D.Car, S.D.Alspach. A review of high-frequency Radar Cross Section analysis capabilities at McDonnell Douglas aerospace[J]. IEEE Antennas and Propagation Magazine. 1995.vo137(5). pp33-43.
[26] E. F. Knott. RCS reduction of dihedral corners[J]. IEEE Trans. Antennas Propagat. 1977,5. vol. AP-25, no. 3. pp406-409.
[27] T. Griesser and C. A. Balanis. Backscatter analysis of dihedral comerreflectors using physical optics and physical theory of diffraction[J]. IEEETrans. Antennas Propagat. 1989,10. vol. AP-35.
[28] 赵维江，龚书喜，刘其中，葛德彪．复杂目次多次散射计算的高频混合方法研究[J]．微波学报．1999．vol15(4)．pp386～390．
[29] F. Saez de Adana, S. Nieves, E. Garcia, I. Gonzalez, O. Gutierrez, and M. F. Catedra. Calculation of the RCS From the Double Reflection Between Planar Facets and Curved Surfaces[J]. IEEE Tram. Antennas Propagat. 2003,9. vol. 51, no.9. pp. 2509-25122.
[30] W. B. Gordon. Far-field approximation to the Kirchoff-Helmholtz representations of scattered field[J]. IEEE Trans. Antennas Propagat. 1975,7.vol.AP-23.pp864-876.
[31] 王萌．高频并行算法的研究与应用．硕士论文．西安电子科技大学．2004．
[32] 施法中．计算机辅助几何设计与非均匀有理B样条[M]．北京，高等教育出版社．2001．
[33] 倪明田，吴良芝．计算机图形学[M]．北京：北京大学出版社，1999，11．
[34] W. B. Gordon.Far-field approximation to the Kirchoff-Helmholtz representations of scattered field[J]. IEEE Trans. Antennas Propagat. 1975,7.vol. AP-23. pp864-876.
[35] 汪茂光．几何绕射理论[M]．西安：西安电子科技大学出版社．1994．
[36] 陈开周．最优化计算方法[M]．西安：西安电子科技大学内部教材．
[2] Jin Au Kong著，吴季等译．电磁波理论[M]．北京：电子工业出版社，2003．
[3] William T. Shaw, Andrew J. Dougan. Green's Function Refinement as an Approach to Radar Backscatter: General Theory and Applications to LGA Scattering from the Ocean[J].IEEE Trans. on Antennas and Propagation. 1998(1):57-66.
[4] F. Daout, A. Khenchaf, J. Saillard. The effect of salinity and temperature on the electromagnetic field scattered by sea water[J]. OCEANS '94. 'Oceans Engineering for Today's Technology and Tomorrow's Preservation.'Proceedings.1994,9. vol.1.pp110-115.
[5] 梁昌洪，胡小培．微波工程设计中的缩比理论[J]．微波与卫星通信．1993，1．PP8-11．
[6] 夏应清，杨河林，鲁述，刘武．超电大复杂目标RCS缩比模型预估方法[J]．微波学报．2003，3．pp8-11．
[7] 时振栋．基本散射体RCS分析和综合[J]．应用科学学报．2003，12．pp331-333．
[8] EliBrookner. Aspects of Modem Rada[M]r. MA:ArtechHouseInc. 1988.
[9] Crispin J W Jr, Maffett A L. RCS estimation for simple shape[J]. Proceedings of the IEEE. 1965. pp833-848.
[10] Shi Z D. Effects of variance in the size of the scatter on its RCS[J]. Microwave and Optical Technology Letter. 1993,24(增刊1):6-9.
[11] 刘宏伟，时振栋．隐身目标雷达截面的缩比测量及反演计算[J]．电子科技大学学报．1995，8．pp13-17．
[12] 刘宏伟，时振栋，武哲，陆柱蕙．隐身目标RCS缩比测量的数据处理及反演计算技术[J]．微波学报．1997，3．pp15-19．
[13] 林溪波．激光雷达散射截面和几何缩比关系[J]．飞航导弹，1998，9．pp52-57．
[14] N. N. Youssef. Radar cross section of complex targets[J]. Proc. IEEE. 1989,5.vol. 72. pp. 722-734.
[15] J. Perez and M. F. Catedra. Rcs of Electrically Large Targets Modeled With NURBS Surfaces[J]. Electronics Leters. Vol. 28,N o.12. 1992,9. pp1119-1121.
[16] J. Perez and M. F. Catedra. Application of physical optics to the RCS computation of bodies modeled with NURBS surfaces[J]. IEEE Trans. Antennas Propagat. 1994,10. vol. 42, pp1404-1411.
[17] M.Domingo,F.Rivas, J. Perez and M. F. Catedra. computation of the RCS Of Complex Bodies Modeled Using NURBS surfaces[J]. IEEE Trans. Antennas Propagat.. 1995,9. vol.37, pp.36-46.
[18] 赵淙．NURBS面片上的RCS计算．硕士论文．西安电子科技大学．2000．
[19] 王超．NURBS曲面的RCS算法研究．硕士论文．西北工业大学．2004．
[20] A.C.LUDWIG. Computation of Radiation Patterns Involving Numerical Double Integration[J]. IEEE Trans. on AR 1968,11. pp767-769.
[21] M.L.X.dos santos, N.R.Rabelo.On the LUDWIG Integration Algorithm for Triangular Subregions [J]. Proc.of IEEE. 1986,10.vo174(10), PP1455-1456.
[22] A.C.LUDWIG. Comments on the Accuracy of the "LUDWIG" Integration Algorithm[J]. IEEE Trans. on AP. 1988,4.vo136(4) pp358-360.
[23] 黄纪军，粟毅，马兴义，毛钧杰．基于路德维格积分的目标RCS计算方法[J]．微波学报．2004，3．pp15-18．
[24] J.L.Volakis.XPATCH. A high-frequency electromagnetic-scattering prediction code and environment for complex three-dimensional objects[J]. IEEE Antennas and propagation Magazine 1994. vo136(1).pp65-69.
[25] D.M.Elking, J.M.Roedder, D.D.Car, S.D.Alspach. A review of high-frequency Radar Cross Section analysis capabilities at McDonnell Douglas aerospace[J]. IEEE Antennas and Propagation Magazine. 1995.vo137(5). pp33-43.
[26] E. F. Knott. RCS reduction of dihedral corners[J]. IEEE Trans. Antennas Propagat. 1977,5. vol. AP-25, no. 3. pp406-409.
[27] T. Griesser and C. A. Balanis. Backscatter analysis of dihedral comerreflectors using physical optics and physical theory of diffraction[J]. IEEETrans. Antennas Propagat. 1989,10. vol. AP-35.
[28] 赵维江，龚书喜，刘其中，葛德彪．复杂目次多次散射计算的高频混合方法研究[J]．微波学报．1999．vol15(4)．pp386～390．
[29] F. Saez de Adana, S. Nieves, E. Garcia, I. Gonzalez, O. Gutierrez, and M. F. Catedra. Calculation of the RCS From the Double Reflection Between Planar Facets and Curved Surfaces[J]. IEEE Tram. Antennas Propagat. 2003,9. vol. 51, no.9. pp. 2509-25122.
[30] W. B. Gordon. Far-field approximation to the Kirchoff-Helmholtz representations of scattered field[J]. IEEE Trans. Antennas Propagat. 1975,7.vol.AP-23.pp864-876.
[31] 王萌．高频并行算法的研究与应用．硕士论文．西安电子科技大学．2004．
[32] 施法中．计算机辅助几何设计与非均匀有理B样条[M]．北京，高等教育出版社．2001．
[33] 倪明田，吴良芝．计算机图形学[M]．北京：北京大学出版社，1999，11．
[34] W. B. Gordon.Far-field approximation to the Kirchoff-Helmholtz representations of scattered field[J]. IEEE Trans. Antennas Propagat. 1975,7.vol. AP-23. pp864-876.
[35] 汪茂光．几何绕射理论[M]．西安：西安电子科技大学出版社．1994．
[36] 陈开周．最优化计算方法[M]．西安：西安电子科技大学内部教材．