Filtered-x LMS Research Articles

Simplified fast transversal filter algorithms for multichannel active noise control

In recent years, more attention has been paid to the performance of algorithm in active noise control (ANC). Compared with filtered-x LMS (FxLMS) algorithm based on stochastic gradient descent, filtered-x RLS (FXRLS) algorithm has faster convergence speed and better tracking performance at the cost of high computational complexity. In order to reduce the computation, fast transversal filter (FTF) algorithm can be used in ANC system. In this paper, simplified multi-channel FXFTF algorithms are presented, and the convergence speed and noise reduction performance of different multichannel algorithms are simulated and compared, and the numerical stability of the algorithms are analyzed.

A novel adaptive step-size hybrid active noise control system

The conventional hybrid active noise control (HANC) system adopts the standard filtered-x least mean square (FxLMS) algorithm to adapt its control filters. However, the constant step size in the algorithm leads to not only the contradiction between convergence rate and steady-state noise reduction, but inadequate robustness under certain noise circumstances. For performance improvement, a new adaptive step-size method is incorporated into the HANC (ASHANC) system to optimize the adaptation of the filters. It combines the strengths of the variable step-size FxLMS (VSFxLMS) algorithm and the modified normalized FxLMS (MNFxLMS) algorithm. Different step-size adjustment strategies can be obtained by setting specific parameters. Furthermore, to obtain the best performance of the system, we develop a method to determine the involved key parameters on the basis of the improved particle swarm optimization (IPSO) algorithm. The objective function of the IPSO algorithm takes the convergence rate and noise reduction into consideration to search for optimum values. Simulation results demonstrate that the proposed ASHANC system achieves faster convergence rate, better noise reduction, and enhanced robustness than the other investigated systems.

Hybrid feedback PID-FxLMS algorithm for active vibration control of cantilever beam with piezoelectric stack actuator

FxLMS (Filtered-x Least Mean Square) algorithm and PID (Proportional Integral Derivative) controller have been widely used for AVC (Active Vibration Control). Yet, the convergence rate and vibration suppression performance are restricted by each other for both the classical FxLMS algorithm and the traditional PID controller. A hybrid PID-FxLMS algorithm which combines the feedback FxLMS algorithm and PID controller is proposed, and applied to improve the vibration control efficiency of piezoelectric cantilever beam. In order to conveniently install the piezoelectric stack on the beam structures, a new piezoelectric stack actuator is designed and installed at the root of cantilever beam. Meanwhile, a coupled finite element model of the piezoelectric stack actuator and cantilever beam is established in ABAQUS, and the state-space model of the coupled system is obtained. Subsequently, based on the obtained state-space model, an AVC simulation and experimental system is built to verify the effectiveness of the proposed algorithm. Numerical and experimental results show that convergence rate and vibration suppression performance of the hybrid PID-FxLMS algorithm are much better than that of the classical FxLMS algorithm or traditional PID controller alone, while the hybrid controller also has strong adaptability and anti-noise ability.

Nonlinear Neural System for Active Noise Controller to Reduce Narrowband Noise

Noise in a dynamic system is practically unavoidable. Today, such noise is commonly reduced using an active noise control (ANC) system with the filtered-x least mean square (FXLMS) algorithm. However, the performance of the ANC system with FXLMS algorithm is significantly impaired in nonlinear systems. Therefore, this paper develops an efficient nonlinear adaptive feedback neural controller (NAFNC) to eliminate narrowband noise for both linear and nonlinear ANC systems. The proposed controller is implemented to update its coefficients without prior offline training by neural network. Hence, the proposed method has rapid convergence rate as confirmed by simulation results. The proposed work also analyzes the stability and convergence of the proposed algorithm. Simulation results verify the effectiveness of the proposed method.

Narrowband feedback active noise control systems with secondary path modeling using gain-controlled additive random noise

This paper investigates estimation of the secondary path (SP) during the online operation of the filtered-x least mean square (FxLMS) algorithm-based feedback active noise control (FBANC) systems. The proposed method develops upon a previous work where two adaptive filters were used, one for active noise control (ANC) and the other for secondary path modeling (SPM). The proposed method essentially comprises a similar structure as that of the previous method. The objectives here are to suggest modifications to improve upon the slow convergence of SPM filter and the noise reduction (NR) performance in the previous method. The key idea is to employ a gain-controlled modeling signal (generated from the additive random noise signal) mixed with the cancellation signal. The gain-factor for the modeling signal is adjusted such that a large-level modeling signal is used during the transient state of the ANC system. This improves the converge of the SPM filter. As the ANC system converges, the level of the modeling signal is reduced to achieve good NR performance. Besides controlling the level of the modeling, the gain control parameter is employed in adjusting the various other parameters too, viz. fixed step-size, regularization parameter, convergence monitoring parameter, while computing the time-varying normalized step-size for the SPM filter. The simulation results demonstrate that the proposed method (equipped with the proposed modifications) outperforms the previous method and yet with a negligible increase in the computational complexity.

Experimental investigation on the potential of the Feedback Fx-LMS Active Noise Control technology for use in industrial generator sets

Active Noise Control (ANC) has been considered a promising technology for the abatement of acoustic noise from the mid-20th century. Feedback and Feedforward ANC algorithms, based on the destructive interference principle applied to acoustic waves, have been developed for different applications, depending on the spectrum of the noise source. Feedback ANC algorithms make use of a single control microphone to measure an error signal which is then employed by an adaptive filter to estimate the noise source and generate an opposite-phase control signal. The Fx-LMS (Filtered-X Least Mean Square) algorithm is mostly adopted to update the filter. Feedback ANC systems have proven to be effective for the abatement of low-frequency quasi-steady noises; however, different challenges must be overcome to realize an effective and durable system for high-temperature application. This paper aims at experimentally assessing the feasibility of a Feedback Fx-LMS ANC system with off-line Secondary Path estimation to be used in mid-size diesel gensets for the reduction of the exhaust noise. Several solutions are proposed, including the mechanical design, the development of the Fx-LMS algorithm in the LabVIEW FPGA programming language, and the key features required to prevent parts from thermal damage and fouling. The developed prototype was implemented on a 50-kW diesel genset and tested in a semi-anechoic chamber. The noise abatement inside the exhaust pipe and at different measurement points around the machine was evaluated and discussed, showing good potential for improving the acoustic comfort of genset users.

Indoor Acoustic Signals Enhanced Algorithm and Visualization Analysis.

A pure acoustic signal can be easy to realize signal analysis and feature extraction. However, the surrounding noises will affect the content of acoustic signals as well as auditory fatigue to the audience. Therefore, it is vital to overcome the problem of noises that affect the acoustic signal. An indoor acoustic signal enhanced method based on image source (IS) method, filtered-x least mean square (FxLMS) algorithm, and the combination of Delaunay triangulation and fuzzy c-means (FCM) clustering algorithm is proposed. In the first stage of the proposed system, the IS method was used to simulate indoor impulse response. Next, the FxLMS algorithm was used to reduce the acoustic signals with noise. Lastly, the quiet areas are optimized and visualized by combining the Delaunay triangulation and FCM clustering algorithm. The experimental analysis results on the proposed system show that better noise reduction can be achieved than the most widely used least mean square algorithm. Visualization was validated with an intuitive understanding of the indoor sound field distribution and the quiet areas.

Modified Filtered-X Hierarchical LMS Algorithm with Sequential Partial Updates for Active Noise Control

In the field of active noise control (ANC), a popular method is the modified filtered-x LMS algorithm. However, it has two drawbacks: its computational complexity higher than that of the conventional FxLMS, and its convergence rate that could still be improved. Therefore, we propose an adaptive strategy which aims at speeding up the convergence rate of an ANC system dealing with periodic disturbances. This algorithm consists in combining the organization of the filter weights in a hierarchy of subfilters of shorter length and their sequential partial updates (PU). Our contribution is threefold: (1) we provide the theoretical basis of the existence of a frequency-dependent parameter, called gain in step-size. (2) The theoretical upper bound of the step-size is compared with the limit obtained from simulations. (3) Additional experiments show that this strategy results in a fast algorithm with a computational complexity close to that of the conventional FxLMS.

Particle swarm optimization based novel adaptive step-size FxLMS algorithm with reference signal smoothing processor for feedforward active noise control systems

The unimproved filtered-x least mean square (FxLMS) algorithm is not enough to guarantee the convergence rate and stability when outliers appear in the reference signal Xn. To make up for this deficiency, a novel adaptive step-size FxLMS with reference signal smoothing processor (NASFSxLMS) algorithm is proposed to accelerate the convergence rate and weaken the impact of outliers. The reference signal smoothing processor integrates the Moving-Median filter and the Hampel filter to preprocess different types of reference signals. The novel adaptive step-size is developed by normalizing the step-size adjustment factor which takes the Euclidean Norm of Xn and error signal en into consideration. What’s more, different coefficients of the step-size adjustment factor h(n) in the normalization function result in different noise reduction effects. To further ameliorate the noise reduction performance of the proposed algorithm, we combine the NASFSxLMS algorithm with the particle swarm optimization (NASFSxLMS-PSO) algorithm to get the optimal coefficients of h(n). Simulation results demonstrate the faster convergence rate, enhanced stability and higher noise reduction of the proposed algorithms under different types of reference signals.

A Novel Approach for Improved Noise Reduction Performance in Feed-Forward Active Noise Control Systems With (Loudspeaker) Saturation Non-Linearity in the Secondary Path

In active noise control systems, the performance of the most celebrated filtered-x-least mean square (FxLMS) adaptive algorithm is degraded in the presence of non-linearity in the secondary path. In this article, we propose a novel approach to improve the performance of FxLMS algorithm in the presence of saturation type non-linearity in the secondary path. In the proposed method, the weights of the controller are adapted by minimizing a cost function consisting of two terms. The first term is the squared instantaneous residual error while the second term is the weighted square of the difference between input and output of (estimated) saturation non-linearity. Consequently, in case the saturation has occurred, the resultant adaptive algorithm minimizes the residual error while keeping the controller output close to its saturation limit. This avoids unnecessary fluctuation of the (controller) weights due to large variation (or windup) of the controller output after the saturation has occurred. Numerical simulations are provided to verify the superiority of the reported approach as compared to existing methods under different conditions.

Multirate Audio-Integrated Feedback Active Noise Control Systems Using Decimated-Band Adaptive Filters for Reducing Narrowband Noises.

Audio-integrated feedback active noise control (AFANC) systems deliver wideband audio signals and cancel low frequency narrowband noises simultaneously. The conventional AFANC system uses single-rate processing with fullband adaptive active noise control (ANC) filter for generating anti-noise signal and fullband audio cancelation filter for audio-interference cancelation. The conventional system requires a high sampling rate for audio processing. Thus, the fullband adaptive filters require long filter lengths, resulting in high computational complexity and impracticality in real-time system. This paper proposes a multirate AFANC system using decimated-band adaptive filters (DAFs) to decrease the required filter lengths. The decimated-band adaptive ANC filter is updated by the proposed decimated filtered-X least mean square (FXLMS) algorithm, and the decimated-band audio cancelation filter can be obtained by the proposed on-line and off-line decimated secondary-path modeling algorithms. The computational complexity can be decreased significantly in the proposed AFANC system with good enough noise reduction and fast convergence speed, which were verified in the analysis and computer simulations. The proposed AFANC system was implemented for an active headrest system, and the real-time performances were tested in real-time experiments.

Error Signal Differential Term Feedback Enhanced Variable Step Size FxLMS Algorithm for Piezoelectric Active Vibration Control

FxLMS (Filtered-x Least Mean Square) algorithm is widely used in the field of AVC (active vibration control) for its good convergence and strong adaptability. However, the convergence rate and steady-state error are mutually restricted for the fixed step FxLMS algorithm. Increasing step size μ to accelerate the convergence rate will result in larger steady-state error and even cause control divergence. In this paper, a new DVSFxLMS (error signal Differential term feedback Variable Step size FxLMS) algorithm is proposed by establishing nonlinear function between μ and error signal, while using differential term of the error signal as the feedback control function. Subsequently, a DVSFxLMS controller is designed to carry out the AVC simulation and experiments on cantilever beam with PSA (piezoelectric stack actuator). Simulation and experimental results show that the proposed DVSFxLMS algorithm has faster convergence rate and smaller steady-state error than the traditional FxLMS algorithm, which also has strong antinoise ability and adaptive control ability to quickly track the variable external disturbance.

Nonlinear aeroservoelastic analysis of a supersonic aircraft with control fin free-play by component mode synthesis technique

To investigate the nonlinear aeroservoelastic behaviors of a three-dimensional supersonic aircraft with control fin free-play, a modeling method based on the component-mode synthesis technique is utilized. The most distinctive feature of this method is that the structural nonlinearity can be expressed explicitly in the reduced-order aeroservoelastic model. The unsteady aerodynamic model with discrete gust loads is formulated using the supersonic lifting surface theory and the minimum state approximation. The results validate the feasibility of the reduced-order aeroelastic model for gust response analysis. A hybrid adaptive feedback control algorithm is proposed for the gust load alleviation by integrating the positive position feedback (PPF) and the filtered-x least-mean-square (FxLMS) algorithm. The comparative study demonstrates that the designed PPF-FxLMS algorithm has a better control performance for the alleviation of the pitch attitude angle induced by the gust loads, and it remains effective in the post-flutter regime. Moreover, the effects of free-play nonlinearity on the dynamic behaviors of the aeroservoelastic system are also studied, and numerical results show that the presence of free-play can lead to a larger peak value of gust response. The nonlinear vibration of the control fin induces the aircraft pitch attitude to produce stable limit cycle oscillations with high frequency, and variation in the free-play magnitude significantly influences the gust responses of the nonlinear aeroservoelastic system.

Bias‐compensated FX‐LMS algorithm

Active noise control is an expanding field that requires a suitable synthesis of secondary perturbations. Unfortunately, most schemes for noise cancelling do not take into account that the input signal that drives the adaptive filter can be noisy. In this Letter, it is theoretically shown that noise perturbations in the excitation data degrade the performance of the standard filtered-x least mean squares (FX-LMS) algorithm. Furthermore, a method that compensates such an issue is devised, and a first-order stochastic analysis of the resulting algorithm is performed. The results reveal that the proposed scheme outperforms the standard FX-LMS algorithm, even when the variance of the additive noise in the input is not accurately estimated.

Active noise control for centrifugal and axial fans

Fans are widely used in industry for heat dissipation or airflow production. It is achieved by driving a motor of fan to rotate a number of blades. Most industrial fans can be categorized into one of two general types: centrifugal fans and axial fans. However, fan noise is loud when the motor speed is high. This article develops using active noise control (ANC) system to reduce noise from both centrifugal and axial fans. By integrating loudspeakers and microphones, we present multiple-channel feedback ANC structure with the filtered-X least mean square (FXLMS) algorithm to simultaneously reduce noise from the inlet and the outlet of the fans. Several realtime experiments verify that the proposed method and experimental setup not only reduces the narrowband noise but also achieves the global cancellation of the fan noise.

Application of probabilistic assessment for optimal prediction in active noise control algorithms

This study explores a modified active noise control (ANC) system using a Bayesian inference approach as a pre-processing method. The key aspect of low-frequency noise attenuation is investigated with the existing control algorithms, the conventional filtered-x least mean square (FxLMS) algorithm and a new convex structure via an FxLMS/F algorithm (C-FxLMS/F), that combine Bayesian inference with a dynamic linear model (DLM). The combination of a Bayesian approach and a DLM comprises the statistic strategy and a descriptive time series, which is conductive to raw signal pre-processing and concurrently generating a predicted signal as a reference signal. For signal processing, pretreatment enables the determination of the noise characteristics of the operating machine and its feedback to the control system. This is an important input to enable the time domain control algorithm to prevent environmental disturbance and time-delay effects. In addition, the use of active control theory mainly relies on the response time of secondary source generation. The predicted signals based on prior observational information and Bayesian inference afford an alternative to the normal costs of the secondary path, such as those associated with electro-acoustic signal conversion and computation efforts in the control algorithm. In this work, the combination of a Bayesian approach and an FxLMS algorithm is studied via a case study. To explore more applicability, the combination of a C-FxLMS/F algorithm with Bayesian inference is also investigated, and a convergence analysis is presented. The in-situ measurement data obtained from a construction site acoustic apparatus is used for analysis. The simulation results are presented via two illustrative cases. In addition, a comparison for three different signal forms under the effect of Bayesian inference is also discussed. It is found that a Bayesian inference approach based on DLM is workable in the ANC system, and the convergence performance is superior to that of an ANC system without Bayesian inference. This suggests that to implement such a system for signal control, it is better to enhance the final system performance in the time-domain field of ANC algorithms. This pre-processing system based on a characteristic strategy and having a low computational loss is needed not only to reduce the time-delay compromise, but also to prevent the sudden disturbance of the reference signal.

Modelling and active damping of engine torque ripple in a power-split hybrid electric vehicle

Torsional vibrations in the power drivetrain are a serious problem for power-split hybrid electric vehicles (HEVs) since the engine is directly connected to the transmission system. The torque ripple also decreases the performance of such vehicles and passenger comfort. The purpose of this paper is to investigate the vibrational performance induced by the engine ripple torque of a power-split HEV under the control of active damping. First, a detailed dynamic model of a power-split HEV is introduced to analyse the dynamic characteristics of the system. Subsequently, a simplified dynamic model of the transmission is proposed; this model simplifies the dynamic analysis of the transmission and makes active vibration control possible. Then, an active vibration controller based on the filtered-x least mean square (FxLMS) algorithm is applied to deal with the vibration in the power-split HEV. The electric motors of the powertrain are used as active damping actuators. The proposed approach is authenticated with simulations. The simulation results show that in steady-state conditions, by applying the active damping algorithm, over 60% of the fluctuation torque in driveline shafts is reduced at different velocities and driving modes, demonstrating that the proposed strategy is effective.

Design of Variable Auxiliary Noise Influence Ratio for Adaptive Active Vibration Control

Active vibration control (AVC) is an effective way to reduce low-frequency vibration. Accurate secondary path modeling (SPM) is crucial for the implementation of AVC system based on filtered-x least mean square (FXLMS) algorithm. The FXLMS algorithm with online SPM comprises two filters, i.e., an active control filter and an online SPM filter. Mutual interference between them is the key factor that restricts the performance of AVC system with online SPM. This paper designs a novel approach based on variable auxiliary noise influence (ANI) ratio to measure the contrastive relationship of convergence status between the active control filter and the online SPM filter. Based on the proposed variable ANI ratio, the proportion of auxiliary noise component in residual vibration is scheduled. Furthermore, a variable step-size strategy is derived to realize fast and stable online SPM. Comparative simulations with the competing methods are carried out in the case of secondary path sudden change and broadband vibration control. The simulation results indicate that the proposed method gives better performance than the other competing methods.

Active control for vehicle interior noise based on DWT-FxLMS algorithm using a piezoelectric feedback system

A piezoelectric feedback system for active noise control (ANC) of vehicle interior noise is built in this paper. Firstly, a mathematical vibration model of a typical vehicle-used plate with piezoelectric patch is derived for revealing piezoelectric mechanism. An improved filtered-x least mean square (FxLMS) algorithm based on the discrete wavelet transform (DWT), so-called DWT-FxLMS, is presented. Comparisons with the common-used algorithms suggest that, the DWT-FxLMS is superior to the time-domain FxLMS (TD-FxLMS) algorithm in terms of the computational complexity and the convergence speed. The DWT-FxLMS can cope with both the stationary and nonstationary noises, but the frequency-domain FxLMS (FD-FxLMS) algorithm is failed to eliminate the nonstationary noise. Secondly, based on a simplified vehicle cavity model, some numerical simulations are performed for its structural vibration and acoustic characteristics. The top plate with maximum acoustic contribution is selected as a target for active control. The arrangement of piezoelectric sensor and actuator on the top plate is determined following the D-optimization criterion. Finally, the experimental verifications are conducted by using the established piezoelectric feedback system. The results suggest that, after applying ANC, the vibration acceleration of the top plate and the sound pressure level (SPL) at the passenger’s ear sides are attenuated to a certain extent. The proposed method based on the piezoelectric feedback DWT-FxLMS algorithm is effective and feasible for active control of vehicle interior noise, and can be regarded as a promising technique for developing the active noise and/or vibration control systems of other products with enclosed spaces in engineering.

Diagonal-structure adaptive bilinear filters for multichannel active noise control of nonlinear noise processes

To accommodate multichannel nonlinear active noise control, the second-order Volterra filtered-x LMS (VFXLMS) and filtered-s least mean square (FSLMS) algorithms are usually applied in practical noise control systems. These two algorithms are effective in dealing with polynomial nonlinearity. Recently, a simplified bilinear leaky filtered-x least mean square (SBLFXLMS) algorithm is proposed based on a bilinear model in order to further reduce the computational load but it may have performance degradation. In this paper, we propose a novel nonlinear adaptive algorithm named as the diagonal-structure bilinear filtered-x least mean square (DBFXLMS) algorithm for multichannel nonlinear active noise control. In addition, the developed multichannel DBFXLMS algorithm is equipped with a stability control scheme to maintain a stable condition of the adaptive bilinear filter during the adaptive process. The performance of the proposed algorithm is validated through computer simulations and the computational complexity of the developed algorithm is analyzed. Computer simulations demonstrate that the proposed method has an improvement in terms of control performance in comparison with the conventional first-order FSLMS, second-order VFXLMS, and SBLFXLMS algorithms.