In the field of active vibration control (AVC), it is difficult to use the classical filtered-x least mean squares (FxLMS) algorithm to solve the instability problem of active control system caused by the time-varying secondary path when the multiple channel coupling and the secondary path model are complex. Therefore, this paper proposes a new cost function based on the simultaneous perturbation stochastic approximation notch-filtering (SPSAN) algorithm. The proposed algorithm possesses two key characteristics: first, it eliminates the need for secondary path identification, and second, it extends single-channel algorithms to multiple channel ones. The proposed algorithm considers the energy of each harmonic vibration at each controlled point in the case of multi-channel coupling, and based on the goal of minimizing the total energy of the system. The proposed cost function to address the AVC problem in the case of multiple channel coupling. Theoretical analysis shows that compared to the single-channel case, the noise term of the SPSAN algorithm is smaller than that of the conventional cost function, despite the increase in the noise term when estimating the optimal control filter using this cost function. In addition, the multi-channel coupled SPSAN algorithm has smaller static error and faster convergence. Simulation and experimental results show that the proposed multiple channels coupled SPSAN algorithm can estimate the optimal control filters even with time-varying secondary path, and effectively suppresses the vibration of the seawater pump piping system.

中文翻译：

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在主动振动控制中具有改进成本函数的多通道 SPSA 算法


在主动振动控制（AVC）领域，当多通道耦合和次级路径模型复杂时，很难使用经典的滤波x最小均方（FxLMS）算法来解决时变次级路径导致的主动控制系统不稳定问题。因此，本文提出了一种基于同步扰动随机逼近陷波滤波 （SPSAN） 算法的新成本函数。所提出的算法具有两个关键特性：首先，它消除了对辅助路径识别的需求，其次，它将单通道算法扩展到多通道算法。所提出的算法考虑了多通道耦合情况下每个受控点上每个谐波振动的能量，并基于最小化系统总能量的目标。提出的 cost 函数，用于解决多通道耦合情况下的 AVC 问题。理论分析表明，与单通道情况相比，SPSAN 算法的噪声项小于传统代价函数的噪声项，尽管在使用此代价函数估计最优控制滤波器时噪声项增加。此外，多通道耦合 SPSAN 算法具有较小的静态误差和更快的收敛性。仿真和实验结果表明，所提出的多通道耦合SPSAN算法即使在时变次级路径下也能估计出最优控制滤波器，并有效抑制了海水泵管道系统的振动。