Nonlinear Secondary Path Research Articles

A Secondary Path-Decoupled Active Noise Control Algorithm Based on Deep Learning

Active noise control (ANC) systems are widely used to cancel unwanted noise. However, for high-level noise, the residual error signal cannot be fully eliminated because of the nonlinearity of the secondary path, resulting in the diverging of the adaptive filter. In this letter, we propose a secondary path-decoupled ANC (SPD-ANC) algorithm based on deep learning. Specifically, the secondary path decoupled module consisting of two time-domain convolutional recurrent networks, one for modeling the nonlinear secondary path and the other for modeling the reverse process, is employed to calculate the secondary path-decoupled (SPD) error signal. The control signal is then generated by an adaptive filter that is optimized towards minimizing the SPD error signal. Simulation results indicate that the proposed method outperforms the conventional ANC methods under different conditions.

A Low-Complexity Volterra Filtered-Error LMS Algorithm with a Kronecker Product Decomposition

Nonlinear active control is very important in many practical applications. Many well-known nonlinear active noise control algorithms may suffer from high computational complexity and low convergence speed, especially in the nonlinear secondary path case. Thus, it is still an actively researched topic for reducing complexity and improving the convergence rate. This paper presents a low-complexity Volterra filtered-error least mean square algorithm when taking a decomposable Volterra model into account for active control of nonlinear noise processes, which is referred as DVMFELMS. The computational complexity analysis shows that the proposed DVMFELMS algorithm can significantly reduce the nonlinear active noise control system’s complexity. The simulation results further show that the proposed algorithm can achieve promising performance compared with the Volterra-based FELMS algorithm and other state-of-the-art nonlinear filters, while the decomposable error of the Volterra kernel may be introduced inevitably. Moreover, the proposed DVMFELMS algorithm shows a better convergence rate in the broadband primary noise case due to fewer parameters used in each sub-filter.

Hybrid control of piezoelectric flexible manipulator based on Volterra filtered-xLMS algorithm

To suppress the nonlinear vibration of the flexible manipulator during motion, this article presents a hybrid control strategy based on a servo motor and a piezoelectric actuator. The dynamic model of the piezoelectric flexible manipulator is established first. To realize the trajectory tracking, a proportional derivative control method is used to schedule the control torque. Because the Volterra filter can approximate the nonlinear system model, a Volterra filtered-xLMS algorithm based on a second-order Volterra filter structure is proposed, by which the active nonlinear vibration control of flexible link is realized. Simulation results show that the proposed Volterra filtered-xLMS algorithm can not only make use of the advantages of the classical filtered-xLMS algorithm but also solve the problem of effective modeling of nonlinear secondary path. The proposed hybrid control strategy based on Volterra filtered-xLMS algorithm and proportional derivative control algorithm can improve the position accuracy of joint and effectively suppress the vibration response of the nonlinear flexible link. A piezoelectric flexible manipulator with PZT (lead zirconate titanate) sensor and actuator is designed to demonstrate the validity and efficiency of the proposed method by experiments. Experiment results demonstrate that the attenuation time of vibration response is reduced from 5 s to 1.5 s, the vibration response at the first-order frequency is reduced by 60%, and the proposed methodology has an important advantage in application of active vibration control of piezoelectric flexible manipulator.

Incremental Learning Based Adaptive Filter for Nonlinear Distributed Active Noise Control System

Active control of noise for multi-channel applications is affected by the existence of nonlinear primary and secondary paths. There is a degradation in the performance of linear multi-channel active noise control (LMANC) systems based on minimization of sum of squared errors obtained from multiple sensors in presence of nonlinear primary path (NPP) and nonlinear secondary path (NSP) conditions. The NPP and NSP problems are more prominent and challenging for multi-point noise control applications owing to different locations of silent zones and acoustic coupling between secondary sources and error sensors. In order to surmount this problem, an incremental strategy based nonlinear distributed ANC (NDANC) system is developed in this article. The adaptive exponential functional link network (AE-FLN) is employed as an adaptive control unit at the acoustic sensor nodes (ASNs) for the design of NDANC system. The incremental co-operation scheme is utilized to provide uniform noise cancellation in presence of NPP and NSP conditions. Simulation study is conducted extensively to demonstrate the efficiency of the proposed system for different practical NPP and NSP scenarios. The detailed computational load analysis and subjective evaluation of reduction in perceptual noise levels are performed for different real noise conditions.

Reweighted adaptive bilinear filters for an active noise control system with a nonlinear secondary path

The nonlinearities of active control systems are the main factors that deteriorate noise-reduction performance. To improve the performance of a control system with a nonlinear secondary path, a filtered-x least mean square algorithm using reweighted bilinear filters is proposed in this paper and a generalized filter to model different nonlinear secondary paths is explored. Within the controller of an adaptive feedforward control system, the proposed algorithm uses trigonometric expansions to achieve high-order nonlinearities and combines the cross terms between the controller output, sine and cosine functions of the input with the reference signal. As a result, satisfactory control performance can be achieved with a shorter memory length of the controller compared to certain control algorithms. It is also found that the introduction of a reweighting factor in the weight-updating process can effectively reduce the interference produced by the small coefficients of the control filter and accelerate the convergence rate. The computational complexity of the proposed algorithm is analyzed and its control performance is verified through simulation experiments with different nonlinear secondary paths and input noises. Simulation results show that the proposed algorithm outperforms four other widely accepted algorithms in terms of convergence rate and residual error.

A generalized exponential functional link artificial neural networks filter with channel-reduced diagonal structure for nonlinear active noise control

The nonlinear adaptive exponential functional link artificial neural networks (E-FLANN) filter has been introduced to improve the noise reduction capability of the functional link artificial neural networks (FLANN) in nonlinear active noise control (NANC) system. It, however, suffers from a heavy computational burden at the nonlinear secondary path (NSP) and poor convergence performance in strong nonlinearity systems. To surmount these shortcomings, a computationally efficient generalized E-FLANN filter with the channel-reduced diagonal structure (GE-FLANN-CRD) for NANC system is developed in this paper. Based on introducing the suitable cross-terms and adaptive exponential factor into the trigonometric functional expansions, the nonlinear processing capability of the filter is enhanced in NANC. Also, by applying the filtered-error least mean square (FELMS) algorithm to the GE-FLANN-CRD, it substantially decreases the computational cost to update the exponential factor. Computer simulations demonstrate that the proposed filter-based the NANC system performs better than the FLANN, E-FLANN and Generalized FLANN (GFLANN) filters-based NANC system in the presence of strong nonlinearity.

Sparse Modeling of Nonlinear Secondary Path for Nonlinear Active Noise Control

In many practical active noise control systems, the nonlinear secondary path (NSP) model can offer broader applications than the linear secondary path (LSP) model for the widespread existence of nonlinearities in the secondary path. However, the computational burden often limits the application of the NSP algorithms. In this paper, we apply a sparse Volterra model for the LSP and NSP instead of the complete Volterra model, which may be over parameterized for the nonlinear active noise control (NANC) system. The developed new control algorithms greatly result in reduction of computational complexity. We also provide an analysis of the NANC system to show that the noise at the canceling point could be approximated by the function expansion filters when the secondary path is modeled as the second-order Volterra series. In addition, two new function expansion forms, the even mirror Fourier nonlinear filter with a linear finite-impulse response section and the Chebyshev filter, are explored to process the nonlinearities in the NANC system using the filtered-x least mean square and filtered-error least mean square algorithm structures. The computational complexity analysis and the computer simulations validate that the new control algorithms with a sparse Volterra model for the secondary path can significantly reduce computational load without sacrificing the control performance.

Improved functional link artificial neural network via convex combination for nonlinear active noise control

A method relying on the convex combination of two normalized filtered-s least mean square algorithms (CNFSLMS) is presented for nonlinear active noise control (ANC) systems with a linear secondary path (LSP) and nonlinear secondary path (NSP) in this paper. The proposed CNFSLMS algorithm-based functional link artificial neural network (FLANN) filter, aiming to overcome the compromise between convergence speed and steady state mean square error of the NFSLMS algorithm, offers both fast convergence rate and low steady state error. Furthermore, by replacing the sigmoid function with the modified Versorial function, the modified CNFSLMS (MCNFSLMS) algorithm with low computational complexity is also presented. Experimental results illustrate that the combination scheme can behave as well as the best component and even better. Moreover, the MCNFSLMS algorithm requires less computational complexity than the CNFSLMS while keeping the same filtering performance.

Nonlinear Thf‐Fxlms Algorithm For Active Noise Control With Loudspeaker Nonlinearity

AbstractAdaptive algorithms are prevalently applied in the design of nonlinear active noise control (ANC) systems. The most important nonlinearity in ANC is the saturation effect produced by the electro‐acoustical sensors and transducers. The dominant saturation nonlinearity is in the transducers, which can be represented by a Wiener model. An effective solution to mitigate such nonlinear distortion is to employ the Nonlinear Filtered‐X Least Mean Square (NLFXLMS) algorithm. The controller compensates the nonlinearity using a model of the saturation effect represented by the scaled error function (SEF). However, the NLFXLMS is limited by two practical issues such that the degree of nonlinearity has to be known in advance and the SEF cannot be evaluated in real time. In this work, the NLFXLMS algorithm is modified by incorporating the tangential hyperbolic function (THF) to model the saturation effect of the loudspeaker. The proposed THF‐NLFXLMS algorithm, models the nonlinear secondary path and applies the estimated degree of nonlinearity in the control algorithm design. The results show that the Wiener secondary path, with saturation nonlinearity represented by SEF, can be modelled by THF with a certain degree of accuracy and can yield a reasonable estimate of the degree of nonlinearity. The performance of the proposed algorithm is comparable with the benchmark NLFXLMS and is superior to the conventional FXLMS as well as the second order Volterra algorithm of similar computational complexity with the proposed algorithm.

Active noise control using an adaptive bacterial foraging optimization algorithm

This paper presents an adaptive bacterial foraging optimization (ABFO) algorithm for an active noise control system. The conventional active noise control (ANC) systems often use the gradient-based filtered-X least mean square algorithms to adapt the coefficients of the adaptive controller. Hence, there is a possibility to converge to local minima. In addition, this class of algorithms needs prior identification of the secondary path. The ABFO algorithm helps the ANC system to prevent falling into local minima. The proposed ANC system is also simpler since it does not need any prior information of the secondary path. Moreover, the adaptive strategy of the algorithm results in improved search performance compared with the basic bacterial foraging optimization algorithm, as well as other conventional algorithms. Experimental studies are performed for nonlinear primary path along with linear and nonlinear secondary path. The results show the effectiveness of the proposed ABFO-based ANC system for different kinds of input noise.

Adaptive RSOV filter using the FELMS algorithm for nonlinear active noise control systems

This paper presents a recursive second-order Volterra (RSOV) filter to solve the problems of signal saturation and other nonlinear distortions that occur in nonlinear active noise control systems (NANC) used for actual applications. Since this nonlinear filter based on an infinite impulse response (IIR) filter structure can model higher than second-order and third-order nonlinearities for systems where the nonlinearities are harmonically related, the RSOV filter is more effective in NANC systems with either a linear secondary path (LSP) or a nonlinear secondary path (NSP). Simulation results clearly show that the RSOV adaptive filter using the multichannel structure filtered-error least mean square (FELMS) algorithm can further greatly reduce the computational burdens and is more suitable to eliminate nonlinear distortions in NANC systems than a SOV filter, a bilinear filter and a third-order Volterra (TOV) filter.

Non-linear active noise cancellation using a bacterial foraging optimisation algorithm

This study presents a new scheme for non-linear active noise control (ANC) systems. In the proposed ANC system, a new evolutionary algorithm known as bacterial foraging (BF) is used for optimising the adaptive controller. The proposed ANC system using bacterial foraging optimisation (BFO) has the ability to prevent falling into local minima. Moreover, using the BF algorithm to adapt the ANC filter coefficients removes the need for the preliminary identification of the secondary path. Several computer simulations are developed in order to analyse the performance of the proposed BFO-based ANC system (BFO-ANC). The experiments are carried out in two major groups including a linear and a non-linear secondary path, along with a non-linear primary path. In each group, the effect of different parameters of the BFO algorithm is investigated on the performance and robustness of the proposed ANC system. The authors also compare the results obtained by three ANC systems; the proposed BFO-based ANC, the GA-based ANC and the filtered-X LMS-based ANC. Simulation results demonstrate the effectiveness of the proposed BFO method in noise cancellation performance under several situations.

A novel frequency-domain periodic active noise control algorithm with nonlinear secondary path

Frequency-domain periodic active noise control (FDPANC) algorithm is usually adopted for harmonic noise reduction. However it may fail to converge when the secondary path includes a nonlinear element. In this paper, the convergence behavior of FDPANC algorithm with nonlinear secondary path is analyzed and a sufficient condition for convergence is derived. Unlike the conventional FDPANC algorithm with linear secondary path, this sufficient condition for FDPANC algorithm with nonlinear secondary path is time-varying and depending on the coefficients of the adaptive filter. If system has a steady-solution, the sufficient condition can be satisfied for all iterations by selecting the proper initial values. In this situation, the adaptive filter will convergent to the optimum value and the disturbance signal can be eliminated totally. If system has no steady-solution, the sufficient condition cannot be satisfied for all iterations whatever the initial values are. Based on the sufficient condition for convergence, a modified FDPANC algorithm integrated with convergence detector is also proposed in this paper.

On the BIBO Stability Condition of Adaptive Recursive FLANN Filters With Application to Nonlinear Active Noise Control

In this paper, a bounded-input bounded-output (BIBO) stability condition for the recursive functional link artificial neural network (FLANN) filter, based on trigonometric expansions, is derived. This filter is considered as a member of the class of causal shift-invariant recursive nonlinear filters whose output depends linearly on the filter coefficients. As for all recursive filters, its stability should be granted or, at least, tested. The relevant conclusion we derive from the stability condition is that the recursive FLANN filter is not affected by instabilities whenever the recursive linear part of the filter is stable. This fact is in contrast with the case of recursive polynomial filters where, in general, specific limitations on the input range are required. The recursive FLANN filter is then studied in the framework of a feedforward scheme for nonlinear active noise control. The novelty of our study is due to the simultaneous consideration of a nonlinear secondary path and an acoustical feedback between the loudspeaker and the reference microphone. An output error nonlinearly Filtered-U normalized LMS adaptation algorithm, derived for the elements of the above-mentioned class of nonlinear filters, is then applied to the recursive FLANN filter. Computer simulations show that the recursive FLANN filter, in contrast to other filters, is able to simultaneously deal with the acoustical feedback and the nonlinearity in the secondary path.

Efficient Adaptive Nonlinear Filters for Nonlinear Active Noise Control

In this paper, we treat nonlinear active noise control (NANC) with a linear secondary path (LSP) and with a nonlinear secondary path (NSP) in a unified structure by introducing a new virtual secondary path filter concept and using a general function expansion nonlinear filter. We discover that using the filtered-error structure results in greatly reducing the computational complexity of NANC. As a result, we extend the available filtered-error-based algorithms to solve NANC/LSP problems and, furthermore, develop our adjoint filtered-error-based algorithms for NANC/NSP. This family of algorithms is computationally efficient and possesses a simple structure. We also find that the computational complexity of NANC/NSP can be reduced even more using block-oriented nonlinear models, such as the Wiener, Hammerstein, or linear-nonlinear-linear (LNL) models for the NSP. Finally, we use the statistical properties of the virtual secondary path and the robustness of our proposed methods to further reduce the computational complexity and simplify the implementation structure of NANC/NSP when the NSP satisfies certain conditions. Computational complexity and simulation results are given to confirm the efficiency and effectiveness of all of our proposed methods