Filtered-x LMS Research Articles

An active noise control algorithm based on an improved convex combination loop

The conflict between a faster convergence using a Filtered-X Least Mean Square (FXLMS) algorithm and the requirement of a small steady-state error of an adaptive active control (ANC) system which limits its performance in terms of computation efficiency and the control error. The problem can be solved by using two paralleling adaptive filters to form a convex combination loop in the control system. However, the exponential weight function used in the original convex combination loop design can consume a large computer power which has limited its application. As a result, a new weight function is proposed to replace the original exponential function in the original convex combination loop to enhance the convergence rate of the adaptive ANC system. Furthermore, a MRFXLMS algorithm is used to replace the FXLMS algorithm in the ANC system so that it can be used for impulse noise control. The result shows that the proposed algorithm performs well in the control of input impulse noise with different intensity.

An Investigation of Real-Time Active Noise Control for 10 kV Substation Noise Suppression

Substation noise is a crucial factor that influences residents’ quality of life, especially in the densely residential areas. Despite small- and medium-sized transformer facilities having relatively low noise levels, due to their proximity to residential areas, they generate considerable annoyance, rendering them a focal point among environmental noise complaints. The predominant noise emitted by these facilities falls within the medium- and low-frequency spectrum range, and the conventional passive noise reduction techniques exhibit limited efficacy in attenuating such low-frequency noise. This study develops a real-time active noise control (ANC) system based on a digital signal processor, TMS320F28335, and various ANC methods, including Filtered-X Least Mean Squares (FxLMS), Normalized Filter-X Least Mean Squares (FxNLMS), and variable step-size FxLMS (VS-FxLMS), are evaluated for the low-frequency noise reduction. In addition, the substation noises at a residential community are measured, analyzed, and used as noise source together with a series of sinusoidal waves for evaluation of the ANC algorithms. Results show the ANC system are effective in attenuating most low-frequency noises (within 600 Hz) and the average noise reduction for the substation noises has achieved by more than 12 dB.

Implementation of active noise cancelling for sound isolation box

A quiet room is essential for acoustical instrument calibration, such as the sound level meter. A small acoustic chamber can be utilized to create an environment that is free from noise. Commonly, it is built with a passive noise-blocking system using high-density absorber material such as rock wool or glass wool. However, this approach results in a room that is both heavy and costly. This paper proposes a mini acoustic chamber that utilizes an active noise cancelling (ANC) system to block the noise. A filtered-x least mean square (FxLMS) algorithm was implemented for the ANC system. A simulation of the system with the recorded actual noise data was conducted to find the optimum filter parameter. The results show that the ANC system could reduce the noise up to 2 dB for certain types of noises. The sound outside the chamber was recorded and processed offline to tune the filter parameter. Evaluation of the effectiveness of the proposed noise reduction system was performed by measuring the sound inside the chamber.

Reproduction of transport-induced vibration of paintings based on a multi-channel FxLMS controller

Monitoring the vibration of the painting canvas during transport is of great significance to protect paintings from damage. However, limited to the narrow structure of the transport crate, the lack of an inertial reference, and the limitations to attach sensors to the canvas, this is a difficult task. For this reason, based on vibration data measured on the strainer that is easily obtained during transport, this contribution proposes to reproduce these with high accuracy in the laboratory. There, the resulting vibration of the canvas can be conveniently observed in a controlled environment with respect to an inertial reference. A real-time simulation platform based on the multi-channel Filtered-x Least Mean Square (FxLMS) algorithm controls four actuators simultaneously and reproduces the vibration of the strainer obtained from a real transport experiment. The vibration of the canvas is then measured by a laser Doppler vibrometer without contact. The experimental results show that the vibration reproduction system has sufficient reproduction accuracy for the vibration response. Even though some overshoot in the reproduced acceleration can be observed in some cases, the overall reproduction is very good. A long-term reproduction experiment verifies its stable reproducibility. Therefore, the designed vibration reproduction system provides a reference for the unknown canvas response during transport, and further helps art conservators to evaluate the transport process of the painting.

Convergence Analysis of the Phase-Scheduled-Command FXLMS Algorithm with Phase Error

In this paper, a phase-scheduled-command filtered-x least mean square (FXLMS) algorithm with a phase error between the disturbance and command signal is analyzed in detail. The influence of the phase error on the control effort, convergence time constant and performance of convergence is explained for both stationary and nonstationary disturbance signal cases. An estimation ratio, in both stationary and nonstationary disturbance cases, of the pseudo-error MSE convergence performance is also developed and discussed. Simulation results were collected to verify the analysis. The results show that, for both stationary and nonstationary disturbance, the phase error may heavily increase the distance of the optimum vector from the initial value, leading to a large control effort, a large convergence time constant and poor convergence performance. The estimation ratio also has a satisfactory performance for estimating the influence of the phase error.

Predicting the performance and optimizing the control parameters of an active vibration control system by pre-identifying the secondary path

In an active vibration control (AVC) system, the secondary path can generally only be identified when the system has been built. The performance of a typical adaptive feedforward control system using the filtered-x least mean square (FxLMS) algorithm is heavily dependent upon the dynamic characteristics of the secondary path. It would, therefore, be helpful for engineers to have knowledge of this behavior early in the design process. In this paper, pre-identification of the secondary path is proposed, which means its offline identification model can be obtained without installing the AVC equipment. This can save both time and money. In the pre-identification process, the secondary path is split into three parts. The first part includes the actuator and related electrical equipment. The frequency response function of this part can be identified after the hardware has been selected. The second part involves the dynamic behavior of the structure to be controlled, which is identified by impact excitation using a specially developed pneumatic impact harmer. The third part concerns the analogue/digital and digital/analogue converters whose effect on the secondary path is offset by a phase shift corresponding to half the sampling time. In this paper, the pre-identification process of the secondary path components is described, and some experiments are conducted to verify the feasibility of the approach and to demonstrate the significance of the pre-identification results. This mainly involves predicting the control performance and optimizing the parameters of the control system. Combined with the simulation of the control system, the approach proposed can improve the work efficiency of large-scale engineering projects and reduce the cost of testing.

Stability Guaranteed Active Noise Control: Algorithms and Applications

Stability of the controller, robust stability of the active noise control (ANC) system, and limited output power of the hardware control board or actuators are crucial issues for ANC applications. Violation of these requirements results in output saturation, and hence nonlinear distortion by overloading the actuators. As a consequence, noise reduction performance of an ANC system will be dramatically degraded. A novel frequency-weighted leaky filtered-x least-mean-square (FxLMS) algorithm is developed in this article to fulfill these requirements. The proposed algorithm is an improvement of the traditional leaky FxLMS algorithm, where a frequency-weighted matrix is designed to replace the corresponding scalar weight. The frequency-weighted matrix, which is achieved by solving a constrained optimization problem, consists of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\it N$</tex-math> </inline-formula> frequency-weighted factors. By the frequency-weighted factors, the frequency response of the control filter is only suppressed at specific frequencies where the requirements on stability and/or limited output power are violated. Thus, the proposed control algorithm achieves better noise reduction performance than the traditional leaky FxLMS algorithm, which unnecessarily suppresses the control filter at all the frequencies. Simulations and experiments are carried out in a duct ANC system to verify the effectiveness of the proposed algorithm for both the feedforward and feedback ANC systems.

Maximum versoria criterion applied to hybrid active noise control algorithm for the impulsive noise

In the conventional hybrid active noise control (CHANC) algorithm, the filtered-x least mean square (FXLMS) algorithm is used in both feedforward and feedback structures. However, the FXLMS algorithm does not process the reference signal and the error signal before updating the weight vector, which leads to the inadequate robustness of the CHANC algorithm in the impulsive noise environment. To solve this problem, the maximum versoria criterion is incorporated into the HANC (MVC-HANC) algorithm in this paper. Firstly, the MVC-HANC algorithm employs a novel nonlinear function to compress the error signal. Secondly, the proposed algorithm uses the modified sigmoid function to constrain the reference signal. To further improve the noise attenuation performance, the MVC-HANC algorithm uses a novel exponential function to adjust the step-size adaptively. Simulation and experiment results demonstrate that the proposed algorithm has the better attenuation performance than the conventional HANC algorithm.

Identification of Control-Related Signal Path for Semi-Active Vehicle Suspension with Magnetorheological Dampers

This paper presents a method for the identification of control-related signal paths dedicated to a semi-active suspension with MR (magnetorheological) dampers, which are installed in place of standard shock absorbers. The main challenge comes from the fact that the semi-active suspension needs to be simultaneously subjected to road-induced excitation and electric currents supplied to the suspension MR dampers, while a response signal needs to be decomposed into road-related and control-related components. During experiments, the front wheels of an all-terrain vehicle were subjected to sinusoidal vibration excitation at a frequency equal to 12 Hz using a dedicated diagnostic station and specialised mechanical exciters. The harmonic type of road-related excitation allowed for its straightforward filtering from identification signals. Additionally, front suspension MR dampers were controlled using a wideband random signal with a 25 Hz bandwidth, different realisations, and several configurations, which differed in the average values and deviations of control currents. The simultaneous control of the right and left suspension MR dampers made it necessary to decompose the vehicle vibration response, i.e., the front vehicle body acceleration signal, into components related to the forces generated by different MR dampers. Measurement signals used for identification were taken from numerous sensors available in the vehicle, e.g., accelerometers, suspension force and deflection sensors, and sensors of electric currents, which control the instantaneous damping parameters of MR dampers. The final identification was carried out for control-related models evaluated in the frequency domain and revealed several resonances of the vehicle response and their dependence on the configurations of control currents. In addition, the parameters of the vehicle model with MR dampers and the diagnostic station were estimated based on the identification results. The analysis of the simulation results of the implemented vehicle model carried out in the frequency domain showed the influence of the vehicle load on the absolute values and phase shifts of control-related signal paths. The potential future application of the identified models lies in the synthesis and implementation of adaptive suspension control algorithms such as FxLMS (filtered-x least mean square). Adaptive vehicle suspensions are especially preferred for their ability to quickly adapt to varying road conditions and vehicle parameters.

A Robust Adaptive Filter for Diffusion Strategy-based Distributed Active Noise Control

Active noise reduction in the existential of impulsive noise poses a serious challenge in a distributed scenario. The conventional centralized multichannel active noise control (MANC) and diffusion filtered-x least mean square (F-xLMS) based distributed active noise control (DANC) systems exhibit deteriorated performance in the existence of impulse noise and outliers. In this regard, a diffusion least logarithmic hyperbolic cosine function (D-Llncosh) based algorithm for DANC system is developed with the goal of mitigating noise in such an environment. It utilizes natural logarithmic of hyperbolic cosine function integrating the mean square error (MSE) and mean absolute error (MAE) as the cost function depending upon the parameter value. The weight update rule of the introduced D-Llncosh-based DANC system is hereby derived. The convergence analysis of the suggested method is also carried out. The proposed system is validated for various types of impulsive noise under different scenarios. The extensive simulation results assert the efficacy of the posited DANC system in comparison with the existing techniques. The suggested method achieves quicker convergence and approximately a 1–5 dB improvement is the noise reduction for different noise scenarios as evident from the obtained results.

Directional Suppression of Monotone Noises with A Parametric Array Loudspeaker

Monotone noises at high decibels have been identified as a main cause of degradation in people’s mental health. This paper proposes a directional monotone noise reduction method to suppress spatially localized single-frequency noises. The system is designed based on a feedforward active noise control (ANC) structure by implementing filtered-x least mean square (FxLMS) algorithms. Compared with traditional ANC methods, our system employs a parametric array loudspeaker (PAL) as the active noise-canceling source with high audio directivity for directional noise suppression. The system monitors the ambient monotone noise and implements the ANC algorithm in real-time through a software-based platform operating on a generic personal computer (PC). Experimental measurements demonstrate an 8dB reduction of different monotone noises at a 260cm distance from the active source. Compared with traditional ANC methods with a voice coil loudspeaker (VCL) as the noise-canceling source, our PAL-based system achieves similar noise suppression performance with a 5.8 times improvement in the source-to-target distance and 64% reduction in the −3dB audio main lobe beam width. The results prove the advantage of introducing PALs as active-noise-canceling sources for monotone noise suppression with a cost-effective enhancement in operating distances and noise control directivities.

Thermal failure analysis and control algorithm improvement for the active controlled mount with consideration of thermal–magnetic coupling

This paper proposes an improved narrowband filtered-x least mean square(FxLMS) algorithm to overcome the thermal failure problems of the active controlled mount(ACM). Firstly, the temperature-rising model and the thermal demagnetization model of the ACM are respectively developed. Combining these two models with the powertrain mounting system model, an analytical method is established for the thermal–magnetic coupling analysis of the ACM. Then a numerical simulation is carried out to obtain the permanent magnet(PM) temperature and the coil current. The ACM failure problem is discussed according to the working point trajectory. Finally, an improved algorithm is proposed. This algorithm is able to overcome the thermal failure problems by sacrificing part of the vibration isolation performance. The effectiveness of this algorithm is validated by numerical simulations and a comparison with conventional algorithms.

Selection of the convergence step of the Fx-LMS algorithm

The choice of a suitable convergence step that allows the fast convergence of the filtered-x LMS algorithm in practical scenarios is usually carried out by trial and error, since the theoretical developments provide only indicative values. The particularity of the filtered-x structure, which adds a delay between the output of the adaptive filter and the error signal and colors the reference signal, increases the inaccuracy of the theoretical models. Furthermore, the use of band-limited reference signals is beyond the scope of most theoretical studies, which focus on the cases of full-band reference signals, making it difficult to extrapolate these models to band-limited signals. In this paper, we propose a low-cost and meaningful method for selecting the convergence step that is well tuned in most practical cases. It can be used regardless of the type of the reference signal, the system delays, and the nature of the filter required in the filtered-x structure. Numerical simulations are performed to validate the effectiveness of the proposed approach.

A Novel Active Vibration Control Method for Helicopter Fuselages Based on Diffusion Cooperation

Against the background of low-frequency vibration control for a helicopter fuselage in flight, active control of structural response (ACSR) has been employed for vibration control design. With the increase in control positions in the fuselage, more actuators and error sensors are needed to meet the vibration reduction requirements, forming a large-scale multichannel system. This leads to a rapid increase in the computation amount, causing the control performance of the conventional centralized algorithm main processor to become poor under overload operation. To this end, a novel distributed active vibration control algorithm based on the diffusion cooperative strategy was proposed and explored in this research. The diffusion cooperative strategy is widely used in complex wireless sensor network (WSN) systems to efficiently reduce the computation amount during data aggregation. This distributed algorithm utilizes the advantages of the diffusion-cooperative strategy to reduce the computation amount and coupling relationship of the secondary path in a large-scale multichannel system. First, a novel control law was established by introducing the network topology of the diffusion cooperation strategy into the classical filtered-x least mean square (FxLMS) algorithm, forming the diffusion FxLMS (DFxLMS) algorithm. Then, a secondary path trade-off quantization standard based on the complex undirected network connectivity condition was developed. It determined whether a secondary path was discarded or not and formed the topology of a large-scale multichannel system control network. To examine the effectiveness and superiority of the proposed DFxLMS algorithm, a comparative simulation with a scale of 1 × 10 × 10 was carried out for a simplified helicopter fuselage. Numerical results in realistic scenarios showed the ability of the DFxLMS algorithms to achieve good control performance when proper values of these parameters are chosen.

Assessment of stability of distributed FxLMS active noise control systems

This paper addresses the assessment of the stability of distributed active noise control (ANC) systems, which are designed to cancel acoustic noise at given points in space. These systems distribute the control task across several simple acoustic nodes that generate the control signals by filtering a noise reference signal. The coefficients of each node filter are iteratively calculated by the filtered-X LMS algorithm. The nodes remain stable when the adaptive filters computed in each node converge to finite values. However, the acoustic coupling among nodes can cause instability (i.e., divergence). Collaboration among nodes is required to avoid this phenomenon. It is shown that the properties of the system are summarized in a system matrix and that the system remains stable when the real parts of all of the eigenvalues of this system matrix are positive. However, computation of all of the eigenvalues is computationally expensive. In this paper, we propose a fast method for checking the positiveness of the real parts of the system matrix eigenvalues. It is shown that the proposed method is faster than the direct calculation of eigenvalues and it assesses the stability/instability of the ANC systems without any false stability outcomes and more accurately than existing alternatives.

An alternative switching filtered-x LMS algorithm for road impact noise control in vehicle

An adaptive switching FxLMS algorithm is proposed to deal with the problem that the performance of the active control system of interior noise drops sharply when come across road impact. According to the state of the system, the algorithm updates the weight coefficient of the control filter in two different ways. Firstly, the normalization algorithm is adopted to improve the convergence speed. After convergence, the relationship between iteration step size and residual error is established by using deformed Gaussian function. The adverse effects of road impact will be dealt with by a new iteration step. On the premise of increasing a small amount of calculation, it improves the convergence speed of the system and ensures the steady-state performance of the system. Numerical simulation and real vehicle test verify the effectiveness of the proposed algorithm in the face of road impact.

Analysis of Adaptive Algorithms Based on Least Mean Square Applied to Hand Tremor Suppression Control

The increase in life expectancy, according to the World Health Organization, is a fact, and with it rises the incidence of age-related neurodegenerative diseases. The most recurrent symptoms are those associated with tremors resulting from Parkinson’s disease (PD) or essential tremors (ETs). The main alternatives for the treatment of these patients are medication and surgical intervention, which sometimes have restrictions and side effects. Through computer simulations in Matlab software, this work investigates the performance of adaptive algorithms based on least mean squares (LMS) to suppress tremors in upper limbs, especially in the hands. The signals resulting from pathological hand tremors, related to PD, present components at frequencies that vary between 3 Hz and 6 Hz, with the more significant energy present in the fundamental and second harmonics, while physiological hand tremors, referred to ET, vary between 4 Hz and 12 Hz. We simulated and used these signals as reference signals in adaptive algorithms, filtered-x least mean square (Fx-LMS), filtered-x normalized least mean square (Fx-NLMS), and a hybrid Fx-LMS–NLMS purpose. Our results showed that the vibration control provided by the Fx-LMS–LMS algorithm is the most suitable for physiological tremors. For pathological tremors, we used a proposed algorithm with a filtered sinusoidal input signal, Fsinx-LMS, which presented the best results in this specific case.

MIMO Multi-Frequency Active Vibration Control for Aircraft Panel Structure Using Piezoelectric Actuators

Undesirable vibration of aircraft panel structures has a significant impact on the safety of their occupants and the operational reliability of various systems. The traditional time-domain controller based on the parallel multi-frequency filtered-x least mean square (FxLMS) control algorithm is simple and effective. However, the mutual influence of convergence steps and the induced harmonic components will limit its performance. An improved parallel multi-input multi-output multi-frequency FxLMS (MIMOMF-FxLMS) algorithm is proposed, considering the multi-input multi-output (MIMO) control requirement of the aircraft panel structure active vibration control (AVC) system and its inevitable channel coupling phenomenon. The feedback error signal and the control channel model are processed by frequency division in the MIMOMF-FxLMS algorithm, so that the FxLMS algorithm of each control channel runs independently, effectively avoiding mutual interference between convergence steps and the generation of induced harmonic components. Simulation and experimental research on multi-frequency AVC of the panel structure model is performed using a new type of piezoelectric stack actuator. The test results show that the proposed controller reduces the vibration level of each observation point by more than 98%, and the vibration responses of the first two-order frequency component are significantly suppressed, which also has strong adaptability and anti-noise ability.

Experimental tests of a multichannel active noise control system with single and multiple reference signals applied to the cabin of a tractor

A feedforward active noise control system represents a valid solution whenever it is necessary to attenuate a disturbing noise at low frequency. One example of application is the case of tractors, in which the agricultural operators are exposed for several hours per day to loud noise at low frequency, mainly generated by the engine. Generally, the feedforward systems make use of one reference sensor to measure the noise produced by the main source. However, this way of proceeding could be inadequate to describe the disturbing noise, especially when the noise is divided both in structure-borne and air-borne components. In this article, a comparison between the use of a single and multiple reference signals, processed in a multichannel active noise control system applied to the cabin of a motionless tractor, is proposed. In particular, an accelerometer positioned on the turbocharger is used to sense the vibration generated by the engine, while a microphone placed near the engine is used to measure the air-borne noise. The active system implements the filtered-X least mean squares (FXLMS) algorithm to produce the anti-noise signals. The results show that the use of two simultaneously acquired reference signals improves the performance of the active system.

Generalized Hyperbolic Tangent Based Random Fourier Conjugate Gradient Filter for Nonlinear Active Noise Control

The filtered-x least mean square (FxLMS) algorithm has been proposed for an active noise control (ANC) system. However, due to the used mean square error (MSE) criterion, FxLMS suffers from performance degeneration for non-Gaussian noises, dramatically. To address this issue, a novel robust generalized hyperbolic tangent (GHT) criterion is first constructed in this paper. Then, the random Fourier features (RFF) method and the conjugate gradient (CG) method are used to address the nonlinearity existing in ANC and solve the quadratic optimization problem induced by the GHT criterion, respectively. Finally, a novel robust random Fourier conjugate gradient filtered-x generalized hyperbolic tangent (RFCGFxGHT) algorithm is proposed for ANC. The theoretical analyses regarding the convergence and computational complexity of RFCGFxGHT are also derived. Simulation experiments on nonlinear ANC systems corrupted by the synthetic logistic chaotic and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula> -stable noises, as well as real-world functional magnetic resonance imaging (fMRI) and server room noises, are conducted to confirm the effectiveness, robustness, and desirable nonlinear learning ability of the proposed algorithm.