作者：句海洋1, 王新华1, 金浩2, 潘长城2
作者单位：1. 北京工业大学机械工程与应用电子技术学院，北京 100124;
2. 中国船舶重工集团公司第七一四研究所，北京 100101
关键词：非线性信号;模态分解;解调技术;宽带信号;交替方向乘子法
摘要：
在实际问题中，非线性Chirp信号模态分量提取问题一直是信号处理领域的难点之一，因此，该文通过理论分析与仿真验证，提出一种非线性Chirp信号模态分解算法。该算法采用解调技术将宽带信号转换为窄带信号，然后，将分解问题表述为一个解调问题的最优求解过程，进而采用交替方向乘子法和反解调算子联合分析得到全局最优解。通过仿真信号分解结果表明，所提取的分量频率绝对误差不超过0.02 Hz，分量的幅值波动相对误差小于1%；进一步研究该算法在不同信噪比情况下的估计信号的均方根误差（RMSE）和二范数（L2），在信噪比大于12 dB时，误差在可接受范围内，在信噪比大于20 dB时，RMSE和L2趋于稳定下降状态。通过分析不同信噪比下的仿真信号，验证该文所提出算法的正确性，可为非线性Chirp信号的模态分解提供一种新方法，具备一定的应用价值。
Research on mode decomposition algorithm of nonlinear Chirp signal
JU Haiyang1, WANG Xinhua1, JIN Hao2, PAN Changcheng2
1. College of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology, Beijing 100124, China;
2. The 714 Research Institute of CSIC, Beijing 100101, China
Abstract: In practice, the problem of modal component extraction of nonlinear chirp signal is one of the difficulties in the field of signal processing. Therefore, we propose a nonlinear chirp mode decomposition algorithm through theoretical analysis and simulation verification. The algorithm converts a wide-band signal into a narrow-band signal by using a demodulation technique, and then decomposition problem is expressed as an optimal solution process of demodulation problem. Furthermore, global optimal solution is obtained by the joint analysis of alternating direction method of multipliers and backward modulation operator. Decomposition results of nonlinear chirp simulation signals show that the absolute error of extracted component frequency does not exceed 0.02 Hz, and the relative error of component amplitude fluctuation is less than 1%. Root mean square error (RMSE) and 2-norm of estimated signal under different signal-to-noise ratio (SNR) are studied. When SNR is more than 12 dB, the error is within the acceptable range. RMSE and 2-norm tends to decline steadily when SNR is greater than 20 dB. By analyzing the simulation signals under different SNR, the correctness of the proposed algorithm is verified in this paper. It provides a new method for the mode decomposition of nonlinear chirp signal, which has a certain application value.
Keywords: nonlinear signal;mode decomposition;demodulation technology;wide-band signal;alternating direction method of multipliers
2020, 46(10):103-110 收稿日期: 2020-02-02;收到修改稿日期: 2020-04-02
基金项目: 国家重点研发计划项目(2017YFC0805005-1，2018YFC0810401)；北京市教育委员会科研计划项目资助(KZ201810005009)
作者简介: 句海洋(1990-),男,河北衡水市人,博士研究生,研究方向为管道损伤地磁检测、信号与信息处理
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