Filtered-x LMS Research Articles

Cascading time-frequency domain filtered-x LMS algorithm for active control of uncorrelated disturbances

The presence of uncorrelated disturbances at the error sensor of an active noise control (ANC) system has become very common with increase in the use of industrial machinery such as rotating machines, fans, vehicular motors, etc. The feed-forward ANC system employing filtered-x least mean squares (FXLMS) algorithm to solve this problem has not produced acceptable noise canceling performance. We propose a new cascading time-frequency domain FXLMS algorithm for active control of uncorrelated disturbances in a feed-forward ANC system. In the proposed method, the error signal of the ANC system containing the uncorrelated disturbances is decomposed into various band-limited parts using the discrete wavelet transform (DWT). Dividing the uncorrelated disturbance into various parts enables independent analysis of each part resulting in improved accuracy of error modeling. As a result of this multi-resolution analysis of the error signal, a superior noise canceling performance is achieved. Numerical simulations validate that the proposed algorithm outperforms its counterparts in terms of noise canceling performance and achieves faster adaptive filter convergence as well.

Order Tracking based Least Mean Squares Algorithm

This paper presents a novel least mean squares approach for active control of structural mechanic systems. Order tracking is used to estimate the gradient for a steepest descent approach more precisely than the standard narrow-band filtered-x least mean squares (FxLMS). The derivation for the new order tracking based least mean square (OLMS) algorithm is presented for a single-input single-output system. The update equations of the OLMS are then compared with an FxLMS algorithm, leading to an interpretation that the FxLMS incorporates order tracking properties. Both algorithms are compared in simulations to show their different convergence performances at multiple frequencies. If only one frequency is present, the OLMS shows similar performance. However, in the case of multiple frequencies being present, the OLMS shows a significant performance increase. The presence of multiply frequencies lowers the performance of the FxLMS. This is analogous to the performance of the OLMS with an improper order tracking filter.

Improved adaptive recursive even mirror Fourier nonlinear filter for nonlinear active noise control

In this paper, we analyze the theoretical mechanism for the effectiveness of recursive filters including both linear and nonlinear feedforward and feedback subsections to accurately approximate nonlinear distributions in the active noise control (ANC) system. As a result, we improve the recursive even mirror Fourier nonlinear (REMFN) filter by adding an additional linear section termed REMFNL filter together with its channel reduced form (CRREMFNL) to explore better control performance. As for the linear feedback section introduced, we have studied the bound-input bound-output (BIBO) stability condition for the REMFNL filter and designed a stable control scheme to guarantee the filter satisfying the stability criteria. The performance of the proposed filters equipped with a filtered-x least mean square (FXLMS) algorithm is validated through analyses of computational complexity and simulations of various nonlinearities for nonlinear ANC (NANC) systems. Simulation results demonstrate that the proposed REMFNL and CRREMFNL filters can achieve better performance over the bilinear, recursive second-order Volterra (RSOV), recursive functional link artificial neural network (RFLANN) and standard REMFN filters based on the FXLMS algorithm, which often outperform the conventional Volterra FXLMS (VFXLMS) and filtered-s least mean square (FSLMS) algorithms.

Implementación de un Control Activo de Ruido en Configuración Feedback basado en un Microcontrolador

Este trabajo describe la implementación de un sistema de control activo de ruido sobre la plataforma EDU-CIAA-NXP con hardware reducido y de bajo costo. Se hace una revisión del algoritmo filtered-X LMS en configuraciones feedforward y feedback, y se detalla el diseño de filtros anti-alias y de reconstrucción. Se describe el software que corre sobre la plataforma, y se muestran resultados de ensayos con la configuración feedback. Usando un tono puro como señal perturbadora se logró una atenuación de 30dB, que es adecuada según requerimientos de performance en aplicaciones de control activo de ruido.

Frequency-Domain Filtered-x LMS Algorithms for Active Noise Control: A Review and New Insights

This paper presents a comprehensive overview of the frequency-domain filtered-x least mean-square (FxLMS) algorithms for active noise control (ANC). The direct use of frequency-domain adaptive filters for ANC results in two kinds of delays, i.e., delay in the signal path and delay in the weight adaptation. The effects of the two kinds of delays on the convergence behavior and stability of the adaptive algorithms are analyzed in this paper. The first delay can violate the so-called causality constraint, which is a major concern for broadband ANC, and the second delay can reduce the upper bound of the step size. The modified filter-x scheme has been employed to remove the delay in the weight adaptation, and several delayless filtering approaches have been presented to remove the delay in the signal path. However, state-of-the-art frequency-domain FxLMS algorithms only remove one kind of delay, and some of these algorithms have a very high peak complexity and hence are impractical for real-time systems. This paper thus proposes a new delayless frequency-domain ANC algorithm that completely removes the two kinds of delays and has a low complexity. The performance advantages and limitations of each algorithm are discussed based on an extensive evaluation, and the complexities are evaluated in terms of both the peak and average complexities.

Multi-channel adaptive active vibration control of piezoelectric smart plate with online secondary path modelling using PZT patches

Abstract Reducing the vibration of smart structures based on adaptive active vibration control (AAVC) has been extensively studied in recent years, because it is a light weight and effective method for reducing low-frequency structural vibrations. The multi-channel AAVC methodology based on the filtered-X least mean square (FXLMS) algorithm is widely implemented in active control applications owing to its self-adjustment ability to adapt to dynamically varying structures. In this paper, a new multi-channel FXLMS with online secondary path modelling (SPM) is designed based on the auxiliary random noise technique. Through a defined indirect error signal, the proposed variable step-size (VSS) strategies can ensure that every online SPM filter and every active control filter have their own exclusive step size to update the coefficients. Moreover, the proposed auxiliary noise power scheduling (ANPS) strategy can ensure that the variation rules of auxiliary noise power applied to different secondary paths are different. A complete multi-channel AAVC real-time experimental system based on NI compact RIO is set up to conduct the experimental investigation. A series of AAVC control experiments on a piezoelectric smart cantilever plate with PZT sensors and actuators are conducted to demonstrate the validity and efficiency of the proposed method. The experimental results show that the vibration of the smart cantilever plate could be effectively attenuated with a high convergence rate. The proposed methodology has an important advantage in applications where active vibration control of piezoelectric smart structures is required.

A normalized frequency-domain block filtered-x LMS algorithm for active vehicle interior noise control

Abstract A novel normalized frequency-domain block FxLMS (NFB-FxLMS) algorithm is proposed for active vehicle interior noise control. Different from the time-domain FxLMS (TD-FxLMS) algorithm that processes noise data point by point, the NFB-FxLMS algorithm processes noise data block by block based on the fast Fourier transform (FFT) and the overlap–save method, such that the calculation amount is considerably reduced. In the process, the input signal of a control filter and the filtered input signal are transferred to frequency domain, respectively. Meantime, its convergence performance is improved by normalizing each frequency-domain bin. The interior noise of a high-speed vehicle is recorded and analyzed. The simulations of ANC based on the TD-FxLMS, normalized TD-FxLMS (TD-NFxLMS), basic FB-FxLMS, and NFB-FxLMS algorithms are performed. The results show that the interior noises are suppressed by these four algorithms. But the NFB-FxLMS with greater stability has faster convergence rate and lower steady-state error in the entire frequency band compared with other three algorithms. The higher the vehicle speed, the more obvious the advantages of the NFB-FxLMS. Furthermore, the NFB-FxLMS shows very good effect on nonstationary noise. The NFB-FxLMS algorithm can be directly used in an active interior noise control system of the sample vehicle, which can be extended to other types of vehicle for interior noise control.

Filtered-x least mean square/fourth (FXLMS/F) algorithm for active noise control

The filtered-x least mean square (FXLMS) algorithm is widely used for active noise control (ANC) systems. However, due to the fixed step-size of FXLMS algorithm being used, the FXLMS algorithm results in a compromise between noise reduction performance and convergence speed. Therefore, this paper proposes the filtered-x least mean square/fourth (FXLMS/F) algorithm for ANC systems, which can be viewed as a variable step-size FXLMS (VSS-FXLMS) algorithm. In order to further improve the algorithm performance, the convex combination of the FXLMS/F (C-FXLMS/F) algorithm for ANC systems is presented. Moreover, the computational complexity of the proposed algorithms is analyzed, and a stability condition for the proposed algorithms is provided. Simulation results show that the proposed FXLMS/F and C-FXLMS/F algorithms can achieve better convergence performance as compared to the FXLMS and FXLMF algorithms under various noise input conditions, and the C-FXLMS/F algorithm outperforms the FXLMS/F algorithm.

Design and implementation of multichannel adaptive active vibration control with online secondary path modeling using piezoelectric transducers patches

Adaptive active vibration control (AAVC) is an effective way for reducing structure vibration at low frequency. AAVC methodology is preferred in AVC system due to its self-adjustment ability to adapt to varying dynamics of the structure. The Filtered-X Least Mean Square (FXLMS) algorithm is widely implemented in active control applications. Accurate secondary path models are very crucial for the implementation in multichannel AAVC system based on FXLMS algorithm. The auxiliary random noise technique is often applied to achieve secondary path modeling (SPM) during online operation. This paper proposes a new multichannel AAVC methodology based on online SPM method. The online SPM error is estimated indirectly to reduce the interaction between the AAVC controller and the online SPM filter. A new variable step-size (VSS) strategy for online SPM filter is proposed based on the estimated online SPM error. A simple but effective auxiliary noise power scheduling (ANPS) method is proposed to eliminate the contribution of the auxiliary noise on the residual vibration. A series of multi-channel AAVC experiments on a cantilever epoxy resin plate with PZT sensors and actuators are presented to demonstrate the performance of the proposed methodology. Experiment results indicate that the proposed method provides very good online SPM accuracy, and the vibration of the smart cantilever plate has been effectively attenuated with high convergence rate.

Adaptive vibration suppression of time-varying structures with enhanced FxLMS algorithm

Abstract Filtered-x least mean square (FxLMS) control algorithm has been widely used for adaptive noise and vibration control. Yet, classical FxLMS controller is not applicable for time-varying system since the secondary path identified offline cannot reflect the system characteristics in real-time. In order to overcome this challenge, here online modelling of secondary path is realized by existing signals, i.e. no noise injection. In addition, FxLMS is further enhanced with variable step size that is adaptively adjusted via bang-bang controller. The adaptation of step size is aimed to achieve the balance between control efficiency and system stability. To verify the feasibility of proposed control algorithm, numerical and experimental efforts are undertaken for the buffeting suppression of vertical tail which is a typical time-varying system. Both results demonstrate that the proposed method is able to reduce the vibration response effectively for varied structures under harmonic and random excitations, while the classical FxLMS cannot. This performance improvement indicates that the online modeling of secondary path captures the system characteristics accurately and timely. Moreover, compared with the FxLMS controller with fixed step size, the control efficiency of the proposed method is also strengthened. These multiple enhancements of the performance of FxLMS controller reveal that online modeling and variable step size are favorable for adaptive vibration control of time-varying structures.

All-pass filtered x least mean square algorithm for narrowband active noise control

Active noise control (ANC) is the most popular method for attenuating acoustic primary noise or disturbances by generating controllable secondary sources by which the output noise can be cancelled with the same amplitude but with opposite sign/sense. Most available ANC uses the secondary path modelling including filtered x least mean square (FxLMS) algorithm. The modelling requirement of the secondary path increases the complexity of the system implementation and decreases the control system performance. Recently several new ANC algorithms have been developed; in which there is no requirement for the modelling of the secondary path transfer function. In this regard, the aim of this paper is concerned about a narrowband feedforward ANC system in systems like air intake duct system and its novelty is to introduce all-pass filtered x LMS (APFxLMS) algorithm which do not require an estimation of the secondary path. Here first-order all pass filters with single parameter is used to improve the convergence of the LMS algorithm. The performance evaluation in terms of convergence speed of the proposed algorithm is validated with standard ANC without secondary path modelling. The results also show that the proposed method outperforms other LMS algorithm without secondary path modelling. The proposed narrowband LMS algorithm would benefit in the design of efficient feedforward ANC system that can realize noise control in air intake duct applications.

Functional link artificial neural network filter based on the q-gradient for nonlinear active noise control

As one of the most commonly used nonlinear active noise control (NANC) algorithms, the filtered-s least mean square (FsLMS) algorithm outperforms the conventional filtered-x least mean square (FxLMS) algorithm when the primary path has a quadratic nonlinearity. However, it still suffers from performance degradation under strong interferences. In this paper, two new algorithms, named filtered-s q-least mean p-norm (FsqLMP) and filtered-s q-least mean square (FsqLMS), based on the concept of Jackson's derivative, are proposed. By using new Jackson's derivative method, the proposed algorithms are less sensitive to the interferences in NANC system. Additionally, it is shown that the family of q-least mean square algorithms are special cases of the proposed FsqLMP algorithm. To further improve performance of the FsqLMS algorithm and solve the parameter selection problem, a time varying q scheme is developed. Simulation studies indicate that the proposed algorithms provide superior performance in various noise environments as compared to the existing algorithms.

Performance evaluation of a back-to-back speaker system using a low-cost single board computer as a digital signal processor

A back-to-back speaker system with a user-designed filter results in a low-frequency cardioid-like radiation pattern where a back-facing loudspeaker is used to suppress the radiation in the rear direction. This paper presents an application of a low-cost single board computer as a digital signal processor on a back-to-back speaker system to obtain a cardioid-like radiation pattern in the low-frequency range. The system consists of two loudspeakers and a US$7 Orange Pi Zero PC. The loudspeakers are closely spaced and mounted in a back-to-back arrangement. A cancellation filter, which is identified in advance in an anechoic chamber using the filtered-x least mean square (FxLMS) algorithm, is used in the Orange Pi Zero PC. A buffering technique is used to make the PC act as a real-time-like signal processing unit. The performance evaluation was conducted under two conditions which were offline and online filtering. In offline filtering, sounds with and without cancellation were pre-prepared. On the other hand, in online filtering, the sound was simultaneously filtered and played. This paper also indicates conditions, for which the system exhibits great performance.

A new adaptive blind background calibration of gain and timing mismatch for a two-channel time-interleaved ADC

This study investigates a new adaptive blind calibration structure for the calibration of gain and timing mismatch error, which is applied for a two-channel Time-Interleaved Analog-to-Digital Converter (TI-ADC). This technique calibrates the mismatch error in the output of the converter without any interrupt at the typical performance of the TI-ADC. The output of the time-interleaved ADC is approximated by modeling based on Taylor's series. The effect of gain and timing mismatch in the output is represented by the first order of Taylor's series. By using a Least-Mean Square (LMS) and correlation-based algorithm, the approximate coefficients of the Taylor's series are identified. Input signal and its chopped image or input signal and its chopped and delayed image will be correlated in the proposed algorithm. This algorithm can identify the coefficients blindly. It is simpler than the previous similar techniques. Also, this technique does not have the drawbacks of a technique which uses the Taylor's series approximation and filtered-X LMS algorithm. Simulation results confirm these claims and show that by entering six sinusoidal inputs in the whole bandwidth of the proposed technique, 48.2 dB improvement in Spur Free Dynamic Range (SFDR) is achieved.

Kernel Filtered-x LMS Algorithm for Active Noise Control System with Nonlinear Primary Path

In active noise control (ANC) systems, the primary path may exhibit nonlinear impulse responses. Conventional linear ANC controllers based on a filtered-x least mean square (FxLMS) algorithm exhibit performance degradation when compensating for nonlinear distortions of the primary path. Several nonlinear active noise control algorithms, including Volterra filtered-x least mean square (VFxLMS) and filtered-s least mean square (FsLMS), have been utilized to overcome this nonlinear effect. However, the performance still needs to be improved when the reference noise is mixed with multiple narrowband signals and additional Gaussian white noise. Over the last several years, kernel adaptive filters have exhibited powerful capabilities in multiple signal processing domains. When kernel adaptive filters are introduced into the ANC system, a great challenge is to compensate for the inherent delay caused by the secondary path. Due to the implicit mapping of the kernel method, it is difficult to filter the reference signal in the high-dimensional feature space. In this paper, an approximate method is proposed in which the filtered reference signal is mapped to the high-dimensional feature space. In addition, a kernel filtered-x least mean square (KFxLMS) algorithm is developed for an ANC system with a nonlinear primary path. Simulation experiments demonstrate that the performance of the proposed KFxLMS algorithm is better than that of the FxLMS, VFxLMS, and FsLMS algorithms.

Vibration suppression with electromagnetic hybrid vibration isolators

The design and control of a novel electromagnetic hybrid vibration isolator is presented in this paper. In the proposed hybrid vibration isolator configuration, an electromagnetic actuator and a rubber vibration isolator are configured in a parallel structure with the rubber vibration isolator installed inside the mover of the actuator. The magnetic force of the actuator is linearized by magnetic configuration design. Filtered-x least mean square (FxLMS) control algorithm is implemented for hybrid vibration isolation. Experimental results show that the vibration is suppressed significantly with the proposed hybrid vibration isolator and the FxLMS control algorithm.

Modal filtered-x LMS algorithm for global active noise control in a vibro-acoustic cavity

Abstract This paper proposes an algorithm called as 'Modal filtered-x LMS algorithm' for global active noise control in vibro-acoustic cavities. The proposed algorithm is a formulation of the conventional filtered-x least mean square algorithm in modal domain to reduce acoustic potential energy in a cavity. The formulation leads to a concept of what has been called as 'modal secondary path' in the paper. The active control method makes use of the reference signal filtered using modal secondary paths instead of the reference signal filtered using physical secondary paths as done in the conventional FxLMS algorithm. The method requires knowledge of acoustic modal pressures which in the present paper are estimated using acoustic pressure measurements at a discrete number of points in the cavity. The proposed method allows a modal based control of acoustic potential energy in the cavity. The proposed method also has an advantage that it reduces the computational burden associated with filtering of the reference signal with secondary paths for global control. A numerical study to actively control noise due to structural and acoustic disturbances acting on a car-like cavity is presented. Results of modal based control are compared with maximum reduction that is possible for given disturbances and control sources. It is found that the noise reduction obtained using the modal based approach is close to the maximum possible but at a lower computational cost.

An improved LMS algorithm for active sound-quality control of vehicle interior noise based on auditory masking effect

Abstract Based on the adaptive least mean square (LMS) algorithm commonly used in active noise control (ANC), an improved active sound-quality control (ASQC) method for vehicle interior noise, so-called post-masking LMS (PmLMS) algorithm, is presented in this paper. Aiming at sound loudness index of measured vehicle interior noises, the PmLMS is derived by considering the post-masking effect of human auditory system. Through adjusting the sizes of iteration step in simulations, it is proven that the newly proposed PmLMS has similar properties as those of the LMS. Comparisons of simulation experiment show that, under the same conditions of appropriate iteration step, filter order and target noise signal, the ASQC results from the PmLMS are better than those from the LMS algorithm, which suggests an effective control of vehicle interior noise. In applications, if one may reasonably match the size of iteration step and vehicle running speed, the PmLMS algorithm can be directly used in ASQC system of a vehicle for improving the ride comfort of passengers. The proposed PmLMS algorithm as a promising method may be further extended to the filtered-x LMS (FxLMS) and applied in other ANC fields for sound quality control in engineering.

An adaptive algorithm for nonstationary active sound-profiling

The use of active sound profiling (ASP) in the automobile industry has been under investigation for several years, and the applications have taken advantage of such techniques, balancing amplitudes instead of simply minimizing the sound pressure level (SPL). This paper presents a novel adaptive algorithm to profile nonstationary disturbances such as the noise generated by a gasoline engine. The new algorithm provides profiling capabilities for nonstationary disturbances and stability properties of the system, whilst expending minimum control effort. Mainly assisted through the use of a reshaping signal, necessary phase information is extracted from nonstationary disturbance signals. To deal with changes in sound as the operating conditions of the engine change, the short-time Fourier transform (STFT) filtered-x least mean square (FXLMS) scheme is introduced to improve the convergence rate. The stability properties are based on the command FXLMS approach, which prevents instabilities caused by magnitude errors in the estimated plant model. Moreover, modification of the STFT-FXLMS scheme improves stability and performance when phase error does exist. In this paper, the performance of the proposed algorithm is demonstrated through a series of simulations configured with either simulated noises or noises from a real engine. The results revealed the effectiveness of the proposed algorithm in profiling nonstationary harmonic noise, and enhancement of stability and performance due to the modification of the STFT-FXLMS scheme.

An interactive simulation of the filtered-x least-mean-squares algorithm for active noise control

As part of a graduate acoustics course at Brigham Young University, students learn about principles of active noise control (ANC). One of the concepts covered is how a basic ANC algorithm functions. This presentation describes an interactive simulation of the filtered-x least-mean-squares (FXLMS) algorithm implemented in MATLAB. Available user-selected inputs include sampling frequency, type of signal to be controlled, number of filter coefficients, convergence coefficient, and system model parameters. As outputs, the students are able to observe the different signals, the attenuation, and the filter coefficients. Altering inputs and observing the simulation results motivates classroom discussion and facilitates students' gaining a working understanding of an ANC algorithm.