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2016-03-01

Worst-Case Tolerance Synthesis for Low-Sidelobe Sparse Linear Arrays Using a Novel Self-Adaptive Hybrid Differential Evolution Algorithm

By Tao Ni, Yong-Chang Jiao, Li Zhang, and Zi-Bin Weng
Progress In Electromagnetics Research B, Vol. 66, 91-105, 2016
doi:10.2528/PIERB16011403

Abstract

A worst-case tolerance synthesis problem for low-sidelobe sparse linear arrays is solved by using a novel self-adaptive hybrid differential evolution (SAHDE) algorithm. First, we establish a worst-case tolerance synthesis model for low-sidelobe sparse linear arrays, in which random position errors are considered and assumed to obey the Gaussian distributions. Through the random sampling, the random model is converted to a deterministic optimization problem. Then, a novel SAHDE algorithm is presented for solving the problem. As a modification to the existing hybrid differential evolution algorithm, a simplified quadratic interpolation (SQI) operator is used to tune the control parameters self-adaptively, establishing the connections between control parameters and the fitness values. In order to determine appropriate control parameter values quickly, a selection operation is also used. Detailed implementation procedure for the SAHDE algorithm is presented, and some numerical results show its effectiveness. Finally, for the deterministic optimization problem, we present a fast way for calculating its fitness values. The SAHDE algorithm is used to obtain optimal nominal element positions. Simulated results illustrate that the worst-case peak sidelobe levels for the sparse linear arrays are improved evidently. The SAHDE algorithm is efficient for solving the worst-case tolerance synthesis problem.

Citation


Tao Ni, Yong-Chang Jiao, Li Zhang, and Zi-Bin Weng, "Worst-Case Tolerance Synthesis for Low-Sidelobe Sparse Linear Arrays Using a Novel Self-Adaptive Hybrid Differential Evolution Algorithm," Progress In Electromagnetics Research B, Vol. 66, 91-105, 2016.
doi:10.2528/PIERB16011403
http://www.jpier.org/PIERB/pier.php?paper=16011403

References


    1. Lo, Y. T. and S. W. Lee, "A study of space-tapered arrays," IEEE Trans. Antennas Propag., Vol. 14, No. 1, 22-30, Jan. 1966.
    doi:10.1109/TAP.1966.1138612

    2. Skolnik, M. I., G. Nemhauser, and J. W. Sherman, "Dynamic programming applied to unequally spaced arrays," IEEE Trans. Antennas Propag., Vol. 12, No. 1, 35-43, Jan. 1964.
    doi:10.1109/TAP.1964.1138163

    3. Kumar, B. P. and G. R. Branner, "Design of unequally for performance improvement," IEEE Trans. Antennas Propag., Vol. 47, No. 3, 511-523, Mar. 1999.
    doi:10.1109/8.768787

    4. Haupt, R. L., "Unit circle representation of aperiodic arrays," IEEE Trans. Antennas Propag., Vol. 43, No. 10, 1152-1155, Oct. 1995.
    doi:10.1109/8.467654

    5. Haupt, R. L., "Thinned arrays using genetic algorithms," IEEE Trans. Antennas Propag., Vol. 42, No. 7, 993-999, Jul. 199.
    doi:10.1109/8.299602

    6. Cheng, K. S., Z. S. He, and C. L. Han, "A modified real GA for the sparse linear array synthesis with multiple constraints," IEEE Trans. Antennas Propag., Vol. 54, No. 7, 2169-2173, Jul. 2006.
    doi:10.1109/TAP.2006.877211

    7. Khodier, M. M. and C. G. Christodoulou, "Linear array geometry synthesis with minimum sidelobe level and null control using particle swarm optimization," IEEE Trans. Antennas Propag., Vol. 53, No. 8, 2674-2679, Aug. 2005.
    doi:10.1109/TAP.2005.851762

    8. Rocca, P., G. Oliveri, and A. Massa, "Differential evolution as applied to electromagnetics," IEEE Antennas and Propagation Magazine, Vol. 53, No. 1, 38-49, 2011.
    doi:10.1109/MAP.2011.5773566

    9. Cen, L., Z. L. Yu, and W. Ser, "Linear aperiodic array synthesis using an improved genetic algorithm," IEEE Trans. Antennas Propag., Vol. 60, No. 2, 895-902, Feb. 2012.
    doi:10.1109/TAP.2011.2173111

    10. Zhang, L., Y. C. Jiao, B. Chen, and F. S. Zhang, "Synthesis of linear aperiodic arrays using a self- adaptive hybrid differential evolution algorithm," IET Microwaves, Antennas & Propag., Vol. 5, No. 12, 1524-1528, Dec. 2011.
    doi:10.1049/iet-map.2010.0429

    11. Goudos, S. K., K. Siakavara, T. Samaras, E. E. Vafiadis, and J. N. Sahalos, "Sparse linear array synthesis with multiple constraints using differential evolution with strategy adaptation," IEEE Antennas and Wire. Propag. Lett., Vol. 10, 670-673, 2011.
    doi:10.1109/LAWP.2011.2161256

    12. Schjaer-Jacobsen, H. and K. Madsen, "Algorithms for worst case tolerance optimization," IEEE Trans. Circuits & Systems, Vol. 26, No. 9, 775-783, Sep. 1979.
    doi:10.1109/TCS.1979.1084700

    13. Schjaer-Jacobsen, H., "Worst-case tolerance optimization of antenna system," IEEE Trans. Antennas Propag., Vol. 28, No. 2, 247-250, Mar. 1980.
    doi:10.1109/TAP.1980.1142296

    14. Jiao, Y. C., Y. H. Qi, and L.-Y. Zhang, "Tolerance optimization design for low sidelobe linear arrays," IEEE Antennas and Propagation Society International Symposium, 736-739, 1993.
    doi:10.1109/APS.1993.385242

    15. Anselmi, N., L. Manica, P. Rocca, and A. Massa, "Tolerance analysis of antenna arrays through interval arithmetic," IEEE Trans. Antennas Propag., Vol. 61, No. 11, 5496-5507, Nov. 2013.
    doi:10.1109/TAP.2013.2276927

    16. Krischuk, V., G. Shilo, and B. Artyushenko, "Tolerable linear antenna array design with genetic algorithm," 9th International Conference onthe Experience of Designing and Applications of CAD Systems in Microelectronics, 167-169, 2007.

    17. Qin, A. K. and P. N. Suganthan, "Self-adaptive dfferential evolution algorithm for numerical optimization," 2005 IEEE Congress on Evolutionary Computation, Vol. 2, 1785-1791, 2005.
    doi:10.1109/CEC.2005.1554904

    18. Brest, J., S. Greiner, B. Boskovic, and \V. Zumer, "Self-adapting control parameters in differential evolution: A comparative study on numerical benchmark problems," IEEE Trans. on Evolutionary Computation, Vol. 10, No. 6, 646-657, Jun. 2006.
    doi:10.1109/TEVC.2006.872133

    19. Ali, M. M., A. Torn, and S. Vitanen, "A numerical comparison of some modified controlled random search algorithms," J. Global Optim., Vol. 11, 377-385, 1997.
    doi:10.1023/A:1008236920512

    20. Jiao, Y. C., C. Dang, Y. Leung, and Y. Hao, "A modification to the new version of the Price's algorithm for continuous global optimization problems," J. Global Optim., Vol. 36, 609-626, 2006.
    doi:10.1007/s10898-006-9030-3

    21. Li, H., Y. C. Jiao, and Y. P. Wang, "Integrating the simplifiedinterpolation into the genetic algorithm for constrained optimization problems," Computational Intelligence and Security, 247-254, Lecture Notes in Artificial Intelligence 3801, Springer-Verlag, Berlin, 2005.

    22. Zhang, L., Y. C. Jiao, H. Li, and F. S. Zhang, "Antenna optimization by hybrid differential evolution," Int. J. RF and Microwave Comput. --- Aided Eng., Vol. 20, 51-55, 2010.

    23. Massa, A., et al., "Planar antenna array control with genetic algorithms and adaptive array theory," IEEE Trans. Antennas Propag., Vol. 52, No. 11, 2919-2924, Nov. 2004.
    doi:10.1109/TAP.2004.837523

    24. Azaro, R., et al., "Design of a prefractal monopolar antenna for 3.4--3.6 GHz Wi-Max band portable devices," IEEE Antennas and Wire. Propag. Lett., Vol. 5, 116-119, 2007.

    25. Carlo, F., D. Massimo, and G. F.Walsh, "Particle-swarm optimization of broadband nanoplasmonic arrays," Optics Letters, Vol. 35, No. 2, 133-135, 2010.
    doi:10.1364/OL.35.000133

    26. Azaro, R., et al., "Optimized design of a multifunction/multiband antenna for automotive rescue systems," IEEE Trans. Antennas Propag., Vol. 54, No. 2, 392-400, Feb. 2006.
    doi:10.1109/TAP.2005.863387

    27. Donelli, M., I. J. Craddock, D. Gibbins, and M. Sarafianou, "A three-dimensional time domain microwave imaging method for breast cancer detection based on an evolutionary algorithm," Progress In Electromagnetics Research M, Vol. 18, 179-195, 2011.
    doi:10.2528/PIERM11040903

    28. Oliveri, G., M. Donelli, and A. Massa, "Linear array thinning exploiting almost difference sets," IEEE Trans. Antennas Propag., Vol. 57, No. 12, 3800-3812, Dec. 2009.
    doi:10.1109/TAP.2009.2027243

    29. Oliveri, G., M. Donelli, and A. Massa, "ADS-based guidelines for thinned planar arrays," IEEE Trans. Antennas Propag., Vol. 58, No. 6, 1935-1948, Jun. 2010.
    doi:10.1109/TAP.2010.2046858

    30. Oliveri, G., "Bayesian compressive sampling for pattern synthesis with maximally sparse non-uniform linear arrays," IEEE Trans. Antennas Propag., Vol. 59, No. 2, 467-481, Feb. 2011.
    doi:10.1109/TAP.2010.2096400

    31. Viani, F., G. Oliveri, and A. Massa, "Compressive sensing pattern matching techniques for synthesizing planar sparse arrays," IEEE Trans. Antennas Propag., Vol. 61, No. 9, 4577-4587, Sep. 2013.
    doi:10.1109/TAP.2013.2267195

    32. Poli, L., P. Rocca, N. Anselmi, and A. Massa, "Dealing with uncertainties on phase weighting of linear antenna arrays by means of interval-based tolerance analysis," IEEE Trans. Antennas Propag., Vol. 63, No. 7, 3229-3234, Jul. 2015.
    doi:10.1109/TAP.2015.2421952

    33. Rocca, P., N. Anselmi, and A. Massa, "Optimal synthesis of robust arrayconfigurations exploiting interval analysis and convex optimization," IEEE Trans. Antennas Propag., Vol. 62, No. 7, 3603-3612, Jul. 2014.
    doi:10.1109/TAP.2014.2318071

    34. Anselmi, N., P. Rocca, M. Salucci, and A. Massa, "Optimization of excitationtolerances for robust beamforming in linear arrays," IET Microwave, Antenna and Propagation, Vol. 10, No. 2, 208-214, 2016.
    doi:10.1049/iet-map.2015.0508