Purpose This paper addresses the distributed vibration reduction problem in multichannel active vibration control (AVC) systems, specifically under scenarios involving multitasking and actuator coupling. The objective is to develop an advanced algorithm that enhances the performance and adaptability of AVC systems in the complex environment. Methods A distinctive diffusion Filtered-x Least Mean Square (FxLMS) algorithm is proposed in the sense that it integrates adaptive fusion matrix and the projected gradient method, capable of dynamically adjusting the exchange of nodal information and applicable to asymmetric AVC systems, different from the metropolis method based on time-invariant fusion matrices. Results Firstly, by extending the Banach fixed point theorem, we derive the convergence conditions for the FxLMS algorithm. It is technically challenging to prove the contraction of the nonlinear mappings and conduct the bias analysis with the introduction of the time-varying fusion matrix. Secondly, simulations for a multi-channel AVC system with 147 nodes are conducted. The simulation results show that the proposed algorithm demonstrates the fast convergence speed in the initial stage, reducing MSE by over <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42417_2024_1720_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">$30\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>30</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> within 1000 iterations and achieving a final vibration reduction of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42417_2024_1720_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="43" /> </InlineMediaObject> <EquationSource Format="TEX">$61.8\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>61.8</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation>. Thirdly, an experiment on a vibration isolation platform with a four-actuator setup is conducted. The experimental results indicate that the proposed algorithm achieves an <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42417_2024_1720_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="43" /> </InlineMediaObject> <EquationSource Format="TEX">$85.6\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>85.6</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> reduction in the mean square error (MSE). Conclusion This paper proposes a diffusion FxLMS algorithm that utilizes an adaptive fusion matrix to address the challenges of vibration reduction in multi-task and multi-channel coupling scenarios. The convergence conditions of the algorithm are provided in the performance analysis section. Simulations and experiments verify the effectiveness of the algorithm in addressing multichannel vibration reduction problems.

Diffusion FxLMS Algorithm Based on Adaptive Fusion Matrix for Multichannel Active Vibration Control Systems

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发表日期：

2025年2月22日

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Wei Xiong,
Yi Dong,
Minyue Lu,
Xunjun Ma

摘要

Purpose

This paper addresses the distributed vibration reduction problem in multichannel active vibration control (AVC) systems, specifically under scenarios involving multitasking and actuator coupling. The objective is to develop an advanced algorithm that enhances the performance and adaptability of AVC systems in the complex environment.

Methods

A distinctive diffusion Filtered-x Least Mean Square (FxLMS) algorithm is proposed in the sense that it integrates adaptive fusion matrix and the projected gradient method, capable of dynamically adjusting the exchange of nodal information and applicable to asymmetric AVC systems, different from the metropolis method based on time-invariant fusion matrices.

Results

Firstly, by extending the Banach fixed point theorem, we derive the convergence conditions for the FxLMS algorithm. It is technically challenging to prove the contraction of the nonlinear mappings and conduct the bias analysis with the introduction of the time-varying fusion matrix. Secondly, simulations for a multi-channel AVC system with 147 nodes are conducted. The simulation results show that the proposed algorithm demonstrates the fast convergence speed in the initial stage, reducing MSE by over $30\%$ $30 %$ within 1000 iterations and achieving a final vibration reduction of $61.8\%$ $61.8 %$ . Thirdly, an experiment on a vibration isolation platform with a four-actuator setup is conducted. The experimental results indicate that the proposed algorithm achieves an $85.6\%$ $85.6 %$ reduction in the mean square error (MSE).

Conclusion

This paper proposes a diffusion FxLMS algorithm that utilizes an adaptive fusion matrix to address the challenges of vibration reduction in multi-task and multi-channel coupling scenarios. The convergence conditions of the algorithm are provided in the performance analysis section. Simulations and experiments verify the effectiveness of the algorithm in addressing multichannel vibration reduction problems.