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Loudspeaker System Identification Based on Adaptive Gradient Descent Algorithm
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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。Abstract: In loudspeaker model parameter identification, the conventional fixed-step gradient descent algorithm is time-consuming and often unstable when the initial parameter error is large. Therefore, a variable-step gradient descent algorithm for identifying speaker system parameters in the frequency domain is proposed. The adaptive method monitors the trend of the parameter identification process and adaptively adjusts the corresponding learning rate, eliminating the need for manual adjustment. Additionally, since directly calculating the gradient of a complex model is challenging, a central difference method is employed to approximate the model's gradient. By establishing a dynamic loudspeaker model and setting different initial values and iteration error termination criteria, the convergence and identification performance of the fixed-step method, least squares method, and adaptive-step method are compared. Micro loudspeakers are used for testing and verification. Simulations and experiments demonstrate that the proposed method has higher efficiency and better robustness to initial errors, exhibiting superior adaptability and universality.
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Key words:
- metrology /
- loudspeakers /
- adaptive algorithms /
- gradient descent algorithm /
- Adam algorithm /
- system identification
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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 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
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) R1 0.8 5e-4 4.7e-5 0.1 1e-4 P1 0.6 2e-3 6e-5 0.3 5e-5 P2 0.4 2e-3 6e-5 0.3 5e-5 Re/Ω R2/Ω L2/H Creep fmin/Hz R1 7.4 0.15 5e-5 0.2 280 P1 6.5 0.16 6e-5 0.15 300 P2 6 0.2 1e-5 0.1 300 
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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) 0.8 0.8007 0.6625 0.8027 Cms/(N/m) 5e-4 4.99e-4 5.82e-4 5.42e-4 Le/(H) 4.7e-5 4.70e-5 6.16e-5 4.70e-5 Rms/(kg/s) 0.1 0.1001 0.2202 0.1006 Mms/(kg) 1e-4 1e-4 8.35e-5 1e-4 Re/Ω 7.4 7.4006 6.6173 7.4009 R2/Ω 0.15 0.1488 0.1611 0.1494 L2/H 5e-5 4.99e-5 2.94e-4 4.82e-5 Creep 0.2 0.2004 0.1480 0.1896 fmin/Hz 280 281.88 300 102.13 $ {\xi }_{{Z}_{e}} $/% 0.0132 12.98 0.0126 $ {\xi }_{{H}_{x}} $/% 0.0101 21.22 0.2080
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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) T1 0.9 3.33e-4 5e-5 0.1 6e-5 T2 0.9 2.86e-4 5e-5 0.1 6e-5 Re/Ω R2/Ω L2/H Creep fmin/Hz T1 7 0.5 1.5e-5 0.12 800 T2 7 0.5 1.5e-5 0.12 800
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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/Ω R2/Ω 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
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