Secondary Path Modeling Research Articles

Properties of FXLMS-Based Narrowband Active Noise Control With Online Secondary-Path Modeling

Rotating machines such as diesel engines, cutting machines, fans, motors, etc., generate sinusoidal noise signals that may be effectively reduced by narrowband active noise control (ANC) systems. In this paper, a typical filtered-X LMS (FXLMS) based narrowband ANC system equipped with an online secondary-path modeling subsystem is analyzed in detail. First, difference equations governing the dynamics of the FXLMS algorithm for secondary source synthesis and the LMS algorithm for secondary-path estimation are derived in terms of convergence in both mean and mean square. Steady-state expressions for mean-square error (MSE) as well as the residual noise power are then developed in closed form. Extensive simulations are performed to demonstrate the validity of the analytical results.

Designing a new robust on-line secondary path modeling technique for feedforward active noise control systems

Several approaches have been introduced in the literature for active noise control (ANC) systems. Since the filtered-x least-mean-square (FxLMS) algorithm appears to be the best choice as a controller filter, researchers tend to improve performance of ANC systems by enhancing and modifying this algorithm. This paper proposes a new version of the FxLMS algorithm, as a first novelty. In many ANC applications, an on-line secondary path modeling method using white noise as a training signal is required to ensure convergence of the system. As a second novelty, this paper proposes a new approach for on-line secondary path modeling on the basis of a new variable-step-size (VSS) LMS algorithm in feedforward ANC systems. The proposed algorithm is designed so that the noise injection is stopped at the optimum point when the modeling accuracy is sufficient. In this approach, a sudden change in the secondary path during operation makes the algorithm reactivate injection of the white noise to re-adjust the secondary path estimate. Comparative simulation results shown in this paper indicate the effectiveness of the proposed approach in reducing both narrow-band and broad-band noise. In addition, the proposed ANC system is robust against sudden changes of the secondary path model.

A self-tuning feedforward active noise control system

This paper proposes a self-tuning feedforward active noise control (ANC) system with online secondary path modeling. The step-size parameters of the controller and modeling filters have crucial rule on the system performance. In literature, these parameters are adjusted by trial-and-error. In other words, they are manually initialized before system starting, which require performing extensive experiments to ensure the convergence of the system. Hence there is no guarantee that the system could perform well under different situations. In the proposed method, the appropriate values for the step-sizes are obtained automatically. Computer simulation results indicate the effectiveness of the proposed method.

Optimal Variable Step-Size NLMS Algorithms With Auxiliary Noise Power Scheduling for Feedforward Active Noise Control

The paper introduces two improvements in the feedforward active noise control system with online secondary path modeling developed by Akhtar, Abe, and Kawamata: (1) optimal variable step-size parameters are derived for the adaptation algorithms of the secondary path modeling filter and of the control filter and (2) a self-tuning power scheduling for the auxiliary noise is introduced. The proposed power scheduling is chosen so that in every operating condition a specific ratio between the powers at the error microphone of the auxiliary noise and of the residual noise is achieved. It is shown that for the same auxiliary noise conditions the adaptation algorithms equipped with the optimal variable step-size parameters improve the convergence speed of the system and the estimation accuracy of the secondary path and of the optimal control filter. It is also shown that, compared with a fixed power auxiliary noise, the power scheduling of the auxiliary noise is capable to better meet the conflicting requirements of fast convergence speed of the secondary path modeling filter and of low residual noise in steady state conditions.

An efficient online secondary path estimation for feedback active noise control systems

In practical cases for active noise control (ANC), the secondary path has usually a time varying behavior. For these cases, an online secondary path modeling method that uses a white noise as a training signal is required to ensure convergence of the system. The modeling accuracy and the convergence rate are increased when a white noise with a larger variance is used. However, the larger variance increases the residual noise, which decreases performance of the system and additionally causes instability problem to feedback structures. A sudden change in the secondary path leads to divergence of the online secondary path modeling filter. To overcome these problems, this paper proposes a new approach for online secondary path modeling in feedback ANC systems. The proposed algorithm uses the advantages of white noise with larger variance to model the secondary path, but the injection is stopped at the optimum point to increase performance of the algorithm and to prevent the instability effect of the white noise. In this approach, instead of continuous injection of the white noise, a sudden change in secondary path during the operation makes the algorithm to reactivate injection of the white noise to correct the secondary path estimation. In addition, the proposed method models the secondary path without the need of using off-line estimation of the secondary path. Considering the above features increases the convergence rate and modeling accuracy, which results in a high system performance. Computer simulation results shown in this paper indicate effectiveness of the proposed method.

Use of peak filter for online secondary path modeling in a feedforward active ship-noise cancellation system

The injected auxiliary noise used in online secondary path modeling method often disturbs the convergence of control filter and increases the residual sound field energy of the active noise cancellation (ANC) system. To mitigate this problem, an improved online secondary path modeling method is proposed, in which the transfer function of secondary path is reconstructed by a peak filter. The frequency response of new transfer function remains unchanged at the frequency band of the noise to be cancelled; while the other bands are attenuated deeply. With this system the simulation experiment of active ship-radiated noise cancellation is accomplished. The result shows that new system's noise cancellation capability is improved and residual sound field energy (including channel response to injected auxiliary noise) is smaller than conventional system without peak filter because of the simplified transfer function of secondary path and reduced energy disturbance between control filter and modeling filter.

Online secondary path modeling in multichannel active noise control systems using variable step size

In single-channel feedforward active noise control (ANC) systems, additive random noise based methods are often applied to achieve secondary path modeling (SPM) during online operation. This paper investigates the issue of online SPM in multichannel ANC systems. It is shown that the application of existing methods for online SPM in multichannel ANC systems greatly increases the computational complexity. Here we extend our previous work on single-channel variable step-size online SPM to multichannel ANC systems. It is shown that the proposed method has reduced computational complexity as compared with other methods. Computer simulations are carried out that demonstrate the effectiveness of the proposed method.

The Statistical Behavior of Phase Error for Deficient-Order Secondary Path Modeling

When implementing active noise control (ANC) systems, the filtered-x LMS (FXLMS) algorithm is often used, where the secondary path transfer function between the output of the adaptive control filter and the error sensor has to be modeled. To model the secondary path precisely, the secondary path estimation filter should be of sufficient order. However, too large an order increases the computation load of the FXLMS algorithm. In this letter, the relationship between the modeling phase error and the order of the secondary path modeling filter is analyzed.

A simultaneous equation method-based online secondary path modeling algorithm for active noise control

Existing conventional online secondary path modeling algorithms for active noise control system have the characteristic that the operation of the controller and the modeling process of the secondary path are mutually interfered. So this unwanted interference will degrade the noise-reducing performance and even the stability of the system. A new finite impulse response (FIR) filter-based online secondary path identification algorithm is proposed to eliminate the interactive disturbances. Compared with existing algorithms, the proposed method does not need feeding extra noise to the secondary source, and is also different from the overall modeling method using the control output. Instead, the facts that the FIR filters have coefficient vectors equivalent to impulse responses corresponding to the transfer functions of physical systems are utilized, and when the coefficients of the control filter are updated, the filter coefficient vectors are different at different iteration steps because of estimation errors. Furthermore, in the method, the modeling of the secondary path is relatively independent of the active noise control system, and the reference signal is used as the input for the system identification. Therefore, the unwanted disturbances between the operation of the ANC controller and the identification of the secondary path are eliminated completely, and the complexity of ANC system is greatly reduced. Computer simulations show its effectiveness, robustness, and the advantage of low residual noise.

Noise power scheduling in active noise control systems with online secondary path modeling

In active noise control (ANC) systems, the online secondary path modeling (OSPM) methods that use additive random noise are often applied. The additive random noise, however, contributes to the residual noise, and thus deteriorates the noise control performance of ANC systems. This paper proposes a new OSPM method with power scheduling of additive random noise. Here the OSPM filter is adapted using a variable step size (VSS) LMS algorithm already proposed by authors. Furthermore, the additive-random-noise power is scheduled based on the convergence status of an ANC system. Computer simulations demonstrate the effectiveness of the proposed method.

A new variable step size LMS algorithm-based method for improved online secondary path modeling in active noise control systems

This paper proposes a new method for online secondary path modeling in active noise control systems. The existing methods for active noise control systems with online secondary path modeling consist of three adaptive filters. The main feature of the proposed method is that it uses only two adaptive filters. In the proposed method, the modified-FxLMS (MFxLMS) algorithm is used in adapting the noise control filter and a new variable step size (VSS) least mean square (LMS) algorithm is proposed for adaptation of the secondary path modeling filter. This VSS LMS algorithm is different from the normalized-LMS (NLMS) algorithm, where the step size is varied in accordance with the power of the reference signal. Here, on the other hand, the step size is varied in accordance with the power of the disturbance signal in the desired response of the modeling filter. The basic idea of the proposed VSS algorithm stems from the fact that the disturbance signal in the desired response of the modeling filter is decreasing in nature, (ideally) converging to zero. Hence, a small step size is used initially and later its value is increased accordingly. The disturbance signal, however, is not available directly, and we propose an indirect method to track its variations. Computer simulations show that the proposed method gives better performance than the existing methods. This improved performance is achieved at the cost of a slightly increased computational complexity.

Leaky-FXLMS algorithm: stochastic analysis for Gaussian data and secondary path modeling error

This paper presents a stochastic analysis of the leaky filtered-X least-mean-square (LFXLMS) algorithm. The version with leakage of the adaptive algorithm is used in practical implementations aiming to reduce undesirable effects due to numerical errors in finite-precision machines, overload of the secondary source, among others. Based on new analysis assumptions, instead of the ordinary independence theory frequently used in classical LMS analysis, an analytical model for the first and second moments of the adaptive filter weights has been derived. In addition, the proposed theoretical models consider the situation in which the secondary path is imperfectly modeled. Experimental results demonstrate the accuracy of the proposed model as compared with the classical analysis.

Linear independence method for system identification/secondary path modeling for active control

A method for noninvasive system identification/secondary path modeling has been developed for single- and multi-channel filtered-x least-mean-square (LMS)-based active noise control (ANC). The problem of on-line secondary path modeling is recognized as one of linear dependence associated with an underdetermined system, a one-equation/two-unknown problem in which the highly correlated primary source and secondary source contributions to the error signal are not readily distinguishable. The method resolves this uniqueness issue by introducing a second equation with similar unknowns. The critical linear independence of the two equations, hence the proposed designation, is achieved with a single perturbation of the control filter output, thereby rendering the system solvable. This secondary path modeling strategy was implemented using an innovative real-time DSP control architecture and tested on a “transducerless” system devised to investigate behavior of ANC algorithms. Results of narrowband, broadband, and multi-channel tests reveal response estimates that are accurate in both magnitude and phase; bias due to primary noise and other secondary sources is notably absent in the obtained secondary path models. The rapidity with which the system is identified can also contribute to the stability and performance of filtered-x LMS-based controllers.

A new structure for feedforward active noise control systems with improved online secondary path modeling

This paper proposes a new structure for feedforward active noise control (ANC) systems with online secondary path modeling. The proposed method: 1) uses the same error signal for updating the noise control process as used for the secondary path modeling process and 2) incorporates an adaptive filtering with averaging based filtered-reference algorithm in the noise control process. The computer simulations have been conducted with both narrowband and broadband noise signals. It is shown that in the proposed ANC system the residual noise signal and the secondary-path-modeling error can be reduced at a faster convergence rate than the existing methods. This improved performance is achieved at the expense of a slightly increased computational complexity.

On comparison of online secondary path modeling methods with auxiliary noise

In the past few years, many methods were proposed to model the so-called secondary path on line for an active noise control (ANC) system. In these methods, an auxiliary noise is employed to excite the modeling process. Among many factors to affect the performance of these methods, some play important roles. They are: 1) power of auxiliary noise; 2) ability to detect secondary path change; 3) optimal step sizes for adaptive filters used in an ANC system and 4) independence between ANC and secondary path modeling processes. In literature, however, there is lack of analysis to show how these factors affect the performance of the ANC system. Moreover, the aforementioned online secondary path modeling methods have not been systematically evaluated. In this paper, the performance of these methods is evaluated by investigating the above-mentioned factors through both statistical analysis and computer simulations.

Active control of structural vibration with on-line secondary path modeling*

Abstract An active control strategy with on-line secondary path modeling is proposed and applied in active control of helicopter structural vibration. Computer simulations of the secondary path modeling performance demonstrate the superiorities of the active control strategy. A 2-input 4-output active control simulation for a helicopter model is performed and greatreduction of structural vibration is achieved. 2-input 2-output and 2-input4-output experimental studies of structural vibration control for a free-free beam are also carried out in laboratory to simulate a flying helicopter. The experimental results also show better reduction of the structural vibration, which verifies that the proposed method is effective and practical in structural vibration reduction.

A linear independence method for system identification/secondary path modeling for active control

A novel method for noninvasive system identification/secondary path modeling has been developed for single- and multi-channel filtered-x LMS-based active noise control (ANC). The problem of on-line secondary path modeling is recognized as one of linear dependence associated with an underdetermined system, a one-equation/two-unknown problem in which the highly correlated primary source and secondary source contributions to the error signal are not readily distinguishable. The method resolves this uniqueness issue by introducing a second equation with similar unknowns. The critical linear independence of the two equations, hence the proposed designation, is achieved with a single perturbation of the control filter output thereby making the system solvable. This new secondary path modeling strategy was implemented using a novel real-time DSP control architecture and tested on a novel transducer-less system devised to investigate the behavior of ANC algorithms. Results of narrow-band, broadband, and multi-channel tests reveal estimates of exceptional accuracy, in both magnitude and phase; any bias in the secondary path estimate, whether introduced by the primary noise source or other secondary sources in the system, is eliminated using this method. Its quickness as well contributes significantly to the stability and performance of filtered-x LMS-based controllers. [Work supported by ONR.]

The Behavior of the Modified FX-LMS Algorithm With Secondary Path Modeling Errors

In active noise control there has been some research based in the modified filtered-X least mean square (LMS) algorithm (MFX-LMS). When the secondary path is perfectly modeled, this algorithm is able to perfectly eliminate it's effect. It is also easily adapted to allow the use of fast algorithms such as the recursive least square, or algorithms with good tracking performance based on the Kalman filter. This letter presents the results of a frequency domain analysis about the behavior of the MFX-LMS in the presence of secondary path modeling errors and a comparison with the FX-LMS algorithm. Namely, it states that for small values of the secondary path delay both algorithms perform the same, but that the step-size of the FX-LMS algorithm decreases with increasing delay, while the MFX-LMS algorithm is stable for an arbitrary large value for the secondary path delay, as long as the real part of the ratio of the estimated to the actual path is greater than one half (Re{S/spl circ//sub z//S/sub z/}>1/2). This means that for the case of no phase errors the estimated amplitude should be greater than half the real one and for the case of no amplitude errors the phase error should be less than 60/spl deg/. Analytical expressions for the limiting values for the step-size in the presence of modeling errors are given for both algorithms.

A model predictive algorithm for active noise control with online secondary path modelling

A model predictive algorithm for active noise control with online secondary path modelling

A robust online secondary path modeling method with auxiliary noise power scheduling strategy and norm constraint manipulation

In many practical cases for active noise control (ANC), the online secondary path modeling methods that use auxiliary noise are often applied. However, the auxiliary noise contributes to residual noise, and thus deteriorates the noise control performance of ANC systems. Moreover, a sudden and large change in the secondary path leads to easy divergence of the existing online secondary path modeling methods. To mitigate these problems, this paper proposes a new online secondary path modeling method with auxiliary noise power scheduling and adaptive filter norm manipulation. The auxiliary noise power is scheduled based on the convergence status of an ANC system with consideration of the variation of the primary noise. The purpose is to alleviate the increment of the residual noise due to the auxiliary noise. In addition, the norm manipulation is applied to adaptive filters in the ANC system. The objective is to avoid over-updates of adaptive filters due to the sudden large change in the secondary path and thus prevent the ANC system from diverging. Computer simulations show the effectiveness and robustness of the proposed method.