簡易變動步長的適應性演算法於主動噪音控制之發展與應用

Abstract

在真實世界的主動噪音控制應用中， 主要噪音(primary noise)中無法模式化的部份(unmodeled portion)通常不為零， 且誤差感測器也會受到不相關干擾(unrelated disturbance)的影響， 以上二者的出現皆會使主動噪音控制演算法無法收歛到最佳的濾波器參數值， 而形成調整不當(misadjustment)的問題， 進而在主動噪音控制系統中造成較大的殘留誤差，而降低消音性能，這個現象可藉由我們所發展的FxLMS/CE 演算法來清楚說明。消音演算法中，步長的選擇反映了調整不當與調整速度的交換(trade-off)。因此本研究計畫考慮使用變動步長(variable step size)來處理這個問題。目前已經存在一些變動步長的調整方式，有些是複雜而有許多參數要設定，因而不易使用；有些雖較簡單，但缺乏收斂性的確保。依變動步長的調整方式， 我們將其分為兩類： (1) 前饋的調整(feedforwardadjustment)， 其調整方式不為濾波器參數的函數， 即是與濾波器參數無關； (2)回饋的調整(feedback adjustment)， 其調整方式是濾波器參數的函數，即是與濾波器參數有關。依此特性，本計畫擬以二年的時間，逐年來進行研究， 並考慮使用具有置換誤差之FxLMS/CE 演算法， 作為研究探討的基礎。本研究計畫的目的是希望經由理論的探索來建立簡單而細緻的設計程序，以推導出簡單而容易使用的變動步長之調整方式，並希望發展出新的、簡單而容易控制並具有收斂性確保的變動步長消音演算法於真實世界的主動噪音控制應用中。

In real-world active-noise-control (ANC) applications, unmodeled portion of primarynoise can be non-zero in general. Moreover, error sensors can pick up disturbance that isunrelated to the primary noise. Presence of the unmodeled portion of primary noise andunrelated disturbance will keep ANC algorithms from converging to the optimal values offilter coefficients and result in misadjustment in the steady state. The misadjustment canlead to large steady-state residual error in ANC systems and degrade the ANC performancein practical applications. This can be clearly shown in our developed FxLMS/CE algorithmfor ANC. Since the choice of step size in the ANC algorithms reflects a trade-off betweenfast convergence and low steady-state misadjustment, variable step sizes are considered inthis study to deal with the problem caused by the unmodeled portion of primary noise andunrelated disturbance. Currently, there are many ways of adjustment of variable step sizes.Some are complex such that many parameters need to setup and thus are not easy to control.Some are simple but lack of ensured convergence. In terms of the adjustment ways, weclassify variable step sizes into two kinds: (i) feedforward adjustment that is not a functionof filter coefficients, and (ii) feedback adjustment that is a function of filter coefficients.According to this characteristic, a two-year research project is thus proposed to study simplevariable step sizes for ANC applications. The study will be based on the FxLMS/CEalgorithm and will be conducted year by year according to this classification. The object isto establish a simple and elegant design procedure to derive simple variable step sizes and todevelop new variable step sizes ANC algorithms that are simple and very easy to control inreal-world ANC applications.