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基于自适应梯度下降算法的扬声器系统辨识

曹南 赵磊

曹南,赵磊. 基于自适应梯度下降算法的扬声器系统辨识[J]. 计量科学与技术,2024, 68(3): 38-44 doi: 10.12338/j.issn.2096-9015.2023.0346
引用本文: 曹南,赵磊. 基于自适应梯度下降算法的扬声器系统辨识[J]. 计量科学与技术,2024, 68(3): 38-44 doi: 10.12338/j.issn.2096-9015.2023.0346
CAO Nan, ZHAO Lei. Loudspeaker System Identification Based on Adaptive Gradient Descent Algorithm[J]. Metrology Science and Technology, 2024, 68(3): 38-44. doi: 10.12338/j.issn.2096-9015.2023.0346
Citation: CAO Nan, ZHAO Lei. Loudspeaker System Identification Based on Adaptive Gradient Descent Algorithm[J]. Metrology Science and Technology, 2024, 68(3): 38-44. doi: 10.12338/j.issn.2096-9015.2023.0346

基于自适应梯度下降算法的扬声器系统辨识

doi: 10.12338/j.issn.2096-9015.2023.0346
详细信息
    作者简介:

    曹南(1990-),瑞声科技(南京)有限公司工程师,研究方向:扬声器控制算法,邮箱:chinacaonan@126.com

  • 中图分类号: TB95

Loudspeaker System Identification Based on Adaptive Gradient Descent Algorithm

  • 摘要: 扬声器模型参数辨识中,常规的固定步长梯度下降算法耗时较长,且在初始参数误差较大时,参数辨识常常会不稳定。因此,提出了一种在频域中识别扬声器系统参数的变步长梯度下降算法。变步长梯度下降方法监测识别参数辨识的趋势,并自适应地调整相应的学习速率。该自适应方法消除了手动调整学习速率的需要。此外,由于直接计算复杂模型的梯度并不容易,采用了中心差分的方法近似计算模型的梯度。通过建立动圈扬声器模型,设置不同初值和迭代误差结束标准,比较了固定步长方法、最小二乘法和自适应步长方法的收敛性以及辨识效果,并使用微型扬声器进行测试验证。仿真和实验表明,该方法具有更高的效率,对初始误差有更好的普适性和鲁棒性。
  • 图  1  扬声器等效线路图

    Figure  1.  The equivalent circuit of the loudspeaker

    图  2  扬声器系统辨识过程

    Figure  2.  Loudspeaker system identification process

    图  3  初值参数P1拟合结果

    Figure  3.  Fitting results of initial parameter P1

    图  4  自适应梯度下降算法收敛误差

    Figure  4.  Convergence error of the adaptive gradient descent algorithm

    图  5  初值参数P2拟合结果

    Figure  5.  Fitting results of initial parameter P2

    图  6  实验测试系统示意图

    Figure  6.  Schematic diagram of experimental testing system

    图  7  实测阻抗与位移传递函数

    Figure  7.  Measured impedance and displacement transfer functions

    图  8  初值参数T1拟合结果

    Figure  8.  Fitting results of initial parameter T1

    图  9  测试数据自适应梯度下降算法收敛误差

    Figure  9.  Convergence error of adaptive gradient descent algorithm for test data

    图  10  初值参数T2拟合结果

    Figure  10.  Fitting results of initial parameter T2

    表  1  仿真模型参数初值设定

    Table  1.   Initial parameter settings for the simulation model

    Bl/(N/A)Cms/(N/m)Le/(H)Rms/(kg/s)Mms/(kg)
    R10.85e-44.7e-50.11e-4
    P10.62e-36e-50.35e-5
    P20.42e-36e-50.35e-5
    ReR2L2/HCreepfmin/Hz
    R17.40.155e-50.2280
    P16.50.166e-50.15300
    P260.21e-50.1300
    下载: 导出CSV

    表  2  三种方法辨识参数结果

    Table  2.   Identification parameter results using three methods

    原始自适应梯度定步长最小二乘
    Bl/(N/A)0.80.80070.66250.8027
    Cms/(N/m)5e-44.99e-45.82e-45.42e-4
    Le/(H)4.7e-54.70e-56.16e-54.70e-5
    Rms/(kg/s)0.10.10010.22020.1006
    Mms/(kg)1e-41e-48.35e-51e-4
    Re7.47.40066.61737.4009
    R20.150.14880.16110.1494
    L2/H5e-54.99e-52.94e-44.82e-5
    Creep0.20.20040.14800.1896
    fmin/Hz280281.88300102.13
    $ {\xi }_{{Z}_{e}} $/%0.013212.980.0126
    $ {\xi }_{{H}_{x}} $/%0.010121.220.2080
    下载: 导出CSV

    表  3  辨识初值参数设定

    Table  3.   Setting of initial parameters for actual measurement identification

    Bl/(N/A)Cms/(N/m)Le/(H)Rms/(kg/s)Mms/(kg)
    T10.93.33e-45e-50.16e-5
    T20.92.86e-45e-50.16e-5
    ReR2L2/HCreepfmin/Hz
    T170.51.5e-50.12800
    T270.51.5e-50.12800
    下载: 导出CSV

    表  4  实测参数辨识结果

    Table  4.   Identification results of measured parameters

    Bl/(N/A) Cms/(N/m) Le/(H) Rms/(kg/s) Mms/(kg) $ {\xi }_{{Z}_{e}} $/%
    改进方法 1.1813 2.88e-4 6.25e-5 0.1174 1.25e-4 0.7751
    最小二乘 1.1953 2.86e-4 6.12e-5 0.1195 1.32e-4 2.7983
    Re R2 L2/H Creep fmin/Hz $ {\xi }_{{H}_{e}} $/%
    改进方法 7.1960 0.8044 1.24e-5 0.1584 1360 0.6411
    最小二乘 7.2040 0.9035 1.31e-5 0.2070 765 2.8394
    下载: 导出CSV
  • [1] 沈勇. 扬声器系统的理论与应用[J]. 音响技术, 2012(2): 19.
    [2] R Small. Direct Radiator Loudspeaker System Analysis[J]. Audio Eng. Soc, 1972, 20(5): 307-327.
    [3] W Klippel. Green Speaker Design (Part 1: Optimal Use of Transducer Resources) [C]. Dublin, 2019.
    [4] W Klippel. Green Speaker Design (Part 2: Optimal Use of System Resources) [C]. Dublin, 2019.
    [5] 孔晓鹏, 曾新吾, 田章福. 动圈扬声器涡流阻抗建模[J]. 国防科技大学学报, 2014, 36(6): 6. doi: 10.11887/j.cn.201406007
    [6] 夏洁, 沈勇. 单元扬声器支撑系统的蠕变效应[J]. 电声技术, 2011, 35(2): 21-24.
    [7] 刘成, 沈勇. 微型扬声器蠕变效应与小信号参数研究[C]. 2009年浙苏黑鲁津四省一市声学学术会议论文集, 2009
    [8] Klippel W. Adaptive nonlinear control of loudspeaker systems[J]. Journal of the Audio Engineering Society, 1998, 46(11): 939-954.
    [9] Klippel W. Nonlinear Adaptive Controller for Loudspeakers with Current Sensor[J]. Audio Engineering Society Convention, 1999, 5: 9900-9905.
    [10] Klippel, Wolfgang. Adaptive Stabilization of Electrodynamic Transducers[J]. Journal of the Audio Engineering Society: Audio, Acoustics, Applications, 2015, 63(3): 154-160.
    [11] Amrhein W . Method and arrangement for actuating electromechanical transducers: US07/681511[P]. [2023-12-26].
    [12] Klippel W, Seidel U. Fast and Accurate Measurement of the Linear Transducer Parameters [C]. Amsterdam : 110th Audio Engineering Society, 2001.
    [13] Bright A. Active Control of Loudspeakers: An Investigation of Practical Applications[J]. Technical University of Denmark, 2002, 11: 1.
    [14] Bright A. Adaptive iir filters for loudspeaker parameter tracking[J]. Audio Engineering Society, 2007, 9: 32.
    [15] Chen L, Pan K, Zhang Z, et al. Gradient Descent Method With Multiple Adaptive Step Sizes for Identifying Loudspeaker Nonlinearities[J]. Journal of the Audio Engineering Society, 2021, 69(3): 182-190. doi: 10.17743/jaes.2020.0071
    [16] Ruder S . An overview of gradient descent optimization algorithms[J/OL]. Machine Learning . DOI: 10.48550/arXiv.1609.04747.
    [17] Qian N. On the momentum term in gradient descent learning algorithms[J]. Neural Networks, 1999, 12(1): 145-151. doi: 10.1016/S0893-6080(98)00116-6
    [18] Shamir O. Making Gradient Descent Optimal for Strongly Convex Stochastic Optimization[J/OL]. Omnipress. DOI: 10.48550/arXiv.1109.5647.
    [19] Lee J D , Simchowitz M , Jordan M I , et al. Gradient Descent Only Converges to Minimizers[C]. JMLR, 2016.
    [20] Butz M V , Goldberg D E , Lanzi P L . Gradient descent methods in learning classifier systems: improving XCS performance in multistep problems[J/OL]. IEEE Press. DOI: 10.1109/TEVC.2005.850265.
    [21] DUCHI J, HAZAN E, SINGER Y. Adaptive subgradient methods for online learning and stochastic optimization[J]. Journal of Machine Learning Research, 2011, 12(7): 2121-2159.
    [22] ZEILER M D. ADADELTA: an adaptive learning rate method[EB/OL]. [2021-12-22].https://doi.org/10.48550/arXiv.1212.5701.
    [23] TIELEMAN T, HINTON G. RMSProp: divide the gradient by a running average of its recent magnitude[R]. Toronto: University of Toronto, 2012.
    [24] KINGMA D, BA J. Adam: a method for stochastic optimization[C]. San Diego : Proc of the 3rd International Conference on Learning Representations, 2015.
    [25] REDDI S J, KALE S, KUMAR S. On the convergence of Adam and beyond[C]. Vancouver : Proc of the 6th Int Conf for Learning Representations, 2018.
    [26] Shin Y, Jérme Darbon, Karniadakis G E. Accelerating gradient descent and Adam via fractional gradients[J]. Neural Networks, 2023, 161: 185-201. doi: 10.1016/j.neunet.2023.01.002
    [27] 陈立, 田兴, 夏洁, 等. 四阶带通箱的自回归滑动平均模型[J]. 应用声学, 2020, 39(4): 618-624.
    [28] Tian X, Shen Y, Chen L, et al. Identification of Nonlinear Fractional Derivative Loudspeaker Model[J]. Journal of the Audio Engineering Society, 2020, 68(5): 355-363. doi: 10.17743/jaes.2020.0010
    [29] Dodd M , Klippel W , Oclee-Brown J . Voice Coil Impedance as a Function of Frequency and Displacement[J/OL]. Audio Engineering Society Convention. DOI:http://dx. doi.org/.
    [30] 孔晓鹏. 电动扬声器分数阶建模及非线性失真分析[D]. 长沙: 国防科学技术大学, 2015.
    [31] 龚纯, 王正林. 精通Matlab最优化计算 [M]. 第三版. 北京: 电子工业出版社, 2009.
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出版历程
  • 收稿日期:  2023-12-12
  • 录用日期:  2023-12-22
  • 修回日期:  2023-12-26
  • 网络出版日期:  2023-12-28

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