Step-size Algorithm Research Articles

Optimal Step Size Technique for Frequency Domain and Partition Block Adaptive Filters for PEM based Acoustic Feedback Cancellation

The adaptive filtering approach has been commonly used to perform acoustic feedback cancellation (AFC) in digital hearing-aids due to its reliable performance and feasibility. Because the loudspeaker and microphone are close together in hearing aids, the corresponding signals are highly correlated, resulting in biased estimation if adaptive filters are used. This problem can be addressed with the help of the decorrelation prefilter by incorporating the Prediction Error Method (PEM) technique into AFC. Frequency-Domain Adaptive Filters (FDAF) are preferable over the time-domain implementation to achieve better performance in terms of convergence and computational complexity. In addition, Partition-Block Frequency-Domain Adaptive Filters (PBFDAF) offers low processing delay. However, because of their fixed step-size, there is a trade-off between initial convergence and steady-state misalignment in the widely used frequency-domain algorithms. While Variable Step-Size (VSS) algorithms can help with this issue, VSS techniques for frequency-domain algorithms have not been extensively studied in the context of PEM-AFC. Hence, in this paper, we presented an Optimal Step-Size (OSS) technique for both the FDAF-PEM_AFC and PBFDAF-PEM_AFC algorithms to simultaneously accomplish fast convergence and minimal steady-state error. A Feedback Path Change Detector (FPCD) was also incorporated into the proposed algorithms to address the problem of convergence in non-stationary feedback paths. The results of simulations show that the proposed algorithms are clearly superior, and they are encouraging.

Задача управления сенсорной сетью на основе рандомизированного и многоагентного подходов и ее приложения

Tracking multiple targets is a classic signal processing problem that occurs in many applications such as air, maritime and traffic control. Autonomous sensor networks serve as desirable platforms for multipurpose tracking due to their redundancy and reconfigurability. However, the network implementation makes it impossible to use the classical centralized approaches to filtering, since each sensor has limited computing power and limited access to the measurements of other sensors. In addition to topological limitations (each sensor can only communicate with several neighboring network nodes), communication between sensors can be limited, for example, due to limited bandwidth of communication channels, delay and data distortion. This article proposes a new algorithm for distributed tracking of multiple targets in a sensor network, which is a combination of the SPSA algorithm and the local voting protocol. The algorithm is consolidated under conditions of unknown but limited noise, the algorithm step size is optimized, and simulation is carried out to confirm the algorithm’s performance. Possible applications for the algorithm are also described.

A family of variable step-size sparsity-aware SSAF algorithms with individual-weighting-factors under model-driven method

Recently, the sparsity-aware sign subband adaptive filter algorithm with individual-weighting-factors (S-IWF-SSAF) was devised. To accomplish performance enhancement, the variable parameter S-IWF-SSAF (VP-S-IWF-SSAF) algorithm was developed through optimizing the step-size and penalty factor, respectively. Different from the optimization scheme, we devise a family of variable step-size strategy S-IWF-SSAF (VSS-S-IWF-SSAF) algorithms based on the transient model of algorithms via minimizing the mean-square deviation (MSD) on each iteration with some reasonable and frequently adopted assumptions and Price's theorem. And in order to enhance the tracking capability, an effective reset mechanism is also incorporated into the proposed algorithms. It is worth mentioning that the presented algorithms could acquire lower computational requirements and exhibit higher steady-state estimation accuracy obviously and acceptable tracking characteristic in comparison to the VP-S-IWF-SSAF algorithm. In addition, the stable step-size range in the mean and mean square sense and steady-state performance are concluded. And the computational requirements are exhibited as well. Monte-Carlo simulations for system identification and adaptive echo cancellation applications certify the proposed algorithms acquire superior performance in contrast to other related algorithms within various system inputs under impulsive interference environments.

Automatic Data Clustering by Hybrid Enhanced Firefly and Particle Swarm Optimization Algorithms

Data clustering is a process of arranging similar data in different groups based on certain characteristics and properties, and each group is considered as a cluster. In the last decades, several nature-inspired optimization algorithms proved to be efficient for several computing problems. Firefly algorithm is one of the nature-inspired metaheuristic optimization algorithms regarded as an optimization tool for many optimization issues in many different areas such as clustering. To overcome the issues of velocity, the firefly algorithm can be integrated with the popular particle swarm optimization algorithm. In this paper, two modified firefly algorithms, namely the crazy firefly algorithm and variable step size firefly algorithm, are hybridized individually with a standard particle swarm optimization algorithm and applied in the domain of clustering. The results obtained by the two planned hybrid algorithms have been compared with the existing hybridized firefly particle swarm optimization algorithm utilizing ten UCI Machine Learning Repository datasets and eight Shape sets for performance evaluation. In addition to this, two clustering validity measures, Compact-separated and David–Bouldin, have been used for analyzing the efficiency of these algorithms. The experimental results show that the two proposed hybrid algorithms outperform the existing hybrid firefly particle swarm optimization algorithm.

Adapting step size algorithms for solving split equilibrium problems with applications to signal recovery

Recent developments in split equilibrium problems (SEPs) have found practical applications in convex optimization problems, information theory, and signal processing. In this paper, we present three novel algorithms with no prior knowledge of the operator norm of a bounded linear operator to approximated solutions for SEPs. Strong convergence results are well presented under appropriate conditions. In addition, we illustrate our main results by providing various numerical examples. Their computational performances are compared with those previously studied in the literature, and the results are presented by showing numerical implementation of the sparse sensor signal recovery problem.

Variable Matrix-Type Step-Size Affine Projection Sign Algorithm for System Identification in the Presence of Impulsive Noise

This paper presents a novel variable matrix-type step-size affine projection sign algorithm (VMSS-APSA) characterized by robustness against impulsive noise. To mathematically derive a matrix-type step size, VMSS-APSA utilizes mean-square deviation (MSD) for the modified version of the original APSA. Accurately establishing the MSD of APSA is impossible. Therefore, the proposed VMSS-APSA derives the upper bound of the MSD using the upper bound of the L1-norm of the measurement noise. The optimal matrix-type step size is calculated at each iteration by minimizing the upper bound of the MSD, thereby improving the filter performance in terms of convergence rate and steady-state estimation error. Because a novel cost function of the proposed VMSS-APSA was designed to maintain a form similar to the original APSA, they have symmetric characteristics. Simulation results demonstrate that the proposed VMSS-APSA improves filter performance in a system-identification scenario in the presence of impulsive noise.

New iterative algorithms with self-adaptive step size for solving split equality fixed point problem and its applications

The purpose of this paper is to propose a new alternative step size algorithm without using projections and without prior knowledge of operator norms to the split equality fixed point problem for a class of quasi-pseudo-contractive mappings. Under appropriate conditions, weak and strong convergence theorems for the presented algorithms are obtained, respectively. Furthermore, the algorithm proposed in this paper is also applied to approximate the solution of the split equality equilibrium and split equality inclusion problems.

Robust Standard Gradient Descent Algorithm for ARX Models Using Aitken Acceleration Technique.

A robust standard gradient descent (SGD) algorithm for ARX models using the Aitken acceleration method is developed. Considering that the SGD algorithm has slow convergence rates and is sensitive to the step size, a robust and accelerative SGD (RA-SGD) algorithm is derived. This algorithm is based on the Aitken acceleration method, and its convergence rate is improved from linear convergence to at least quadratic convergence in general. Furthermore, the RA-SGD algorithm is always convergent with no limitation of the step size. Both the convergence analysis and the simulation examples demonstrate that the presented algorithm is effective.

Music Genre Classification Algorithm Based on Multihead Attention Mechanism

Retrieving music information is indispensable and divided into multiple genres. Music genres can be attributed to set categories, which are the indispensable functions of intelligent music recommendation systems. To improve the effect of music genre classification and model construction, combined with the music genre classification algorithm, this paper combines the multihead attention mechanism to study the music genre classification algorithm model, and it analyzes the key technology of music beamforming. Moreover, this paper has made a detailed description and derivation of the array antenna model, the principle of music beamforming, and the performance evaluation criteria of music adaptive beamforming. In the second half, the nonblind classical LMS algorithm, RLS algorithm, and variable step size LMS algorithm of adaptive beamforming are studied in detail. A music genre classification algorithm model based on the multihead attention mechanism is constructed. It can be seen from the experimental research that the music genre classification algorithm based on the multihead attention mechanism proposed in this paper has obvious advantages compared with the traditional algorithm, and it has a certain role in music genre classification.

A novel channel estimation model for broadband wireless communication system using hybrid heuristic-based invariable step-size zero-attracting NLMS algorithm

A novel channel estimation model for broadband wireless communication system using hybrid heuristic-based invariable step-size zero-attracting NLMS algorithm

Numerical Integration of Stiff Differential Systems Using Non-Fixed Step-Size Strategy

Over the years, researches have shown that fixed (constant) step-size methods have been efficient in integrating a stiff differential system. It has however been observed that for some stiff differential systems, non-fixed (variable) step-size methods are required for efficiency and for accuracy to be attained. This is because such systems have solution components that decay rapidly and/or slowly than others over a given integration interval. In order to curb this challenge, there is a need to propose a method that can vary the step size within a defined integration interval. This challenge motivated the development of Non-Fixed Step-Size Algorithm (NFSSA) using the Lagrange interpolation polynomial as a basis function via integration at selected limits. The NFSSA is capable of integrating highly stiff differential systems in both small and large intervals and is also efficient in terms of economy of computer time. The validation of properties of the proposed algorithm which include order, consistence, zero-stability, convergence, and region of absolute stability were further carried out. The algorithm was then applied to solve some samples mildly and highly stiff differential systems and the results generated were compared with those of some existing methods in terms of the total number of steps taken, number of function evaluation, number of failure/rejected steps, maximum errors, absolute errors, approximate solutions and execution time. The results obtained clearly showed that the NFSSA performed better than the existing ones with which we compared our results including the inbuilt MATLAB stiff solver, ode 15s. The results were also computationally reliable over long intervals and accurate on the abscissae points which they step on.

Variable step-size saturation affine projection algorithm against impulsive noise

This study proposes a variable step-size saturation affine projection algorithm (VSS-sat-APA) robust to impulsive noise. The proposed algorithm is analytically derived from the optimal solution, which minimizes a newly defined ℓ2 cost function of a posteriori output error with weight-estimate variation limited by the step-size threshold. In contrast, the conventional robust VSS APA (RVSS-APA) is geometrically derived from a suboptimal solution, which minimizes an ℓ2 cost function of a posteriori output error with weight-estimate variation limited by the step-size threshold. The proposed algorithm operates as the original APA with the unit step-size when the magnitude of the normalized a priori output error is saturated with the step-size threshold and as a modified APA with the step-size when it is not saturated. This study derives a VSS scheme by analyzing the propagation of the mean square deviation of the weight-error vector when the saturation occurs and when it does not. The simulation results show that the proposed algorithm performs better with a fast convergence rate and small steady-state error compared to the conventional algorithms in both non-impulsive and impulsive noisy environments.

Theoretical and experimental investigation study of discrete time rate‑dependent hysteresis modeling and adaptive vibration control for smart flexible beam with MFC actuators

A new rate‑dependent hysteresis modeling and identification method, and a new adaptive filtering control algorithm is proposed to solve the hysteresis nonlinearity identification problem and adaptive parameter auto-tuning problem for vibration control of smart flexible beam employing MFC actuators. A Hammerstein model is proposed by composing asymmetric Bouc-Wen model and ARX model in series to for secondary path modelling to model the MFC actuator hysteresis and mechanical hysteresis of the flexible beam. To improve the convergence speed and performance for complex parameter identification of the Hammerstein model, an improved Jaya algorithm named hybrid Jaya is proposed which combines the mutation strategy of two kinds of DE algorithms as the individual update method of the proposed hybrid Jaya. To balance the convergence speed and steady-state error for active vibration control performance, a new variable tap-length and step-size FXLMS algorithm named FX-VSSFT-LMS algorithm is proposed and the adaptive parameters are auto-tuned by our proposed Hybrid Jaya algorithm. To verify the proposed Hammerstein model and adaptive filtering algorithm, a cantilever beam experimental platform with MFC actuators is constructed. Hybrid Jaya algorithm and Jaya algorithm were used to identify the Hammerstein model and Bouc-wen model of MFC actuator, and the improved effects of hybrid Jaya algorithm and Hammerstein model were compared and verified. The FX-VSSFT-LMS algorithm is compared with FX-VSSLMS algorithm with variable step size and FX-FTLMS algorithm with variable tap-length on the MFC cantilever beam. The experimental comparison proves that the Hammerstein model identified by the proposed Hybrid Jaya algorithm is effective and the FX-VSSFT-LMS algorithm has better convergence performance than FX-VSSLMS and FX-FTLMS algorithm.

Fast convergent background calibration technique for timing mismatch in M-channel time-interleaved ADCs

This work presents a fully digital background calibration technique of timing mismatch in time-interleaved analog-to-digital converters (TIADCs). The timing mismatch is estimated by the correlation function of adjacent channels’ digital outputs. The proposed estimation method is suitable for an arbitrary number of channels. Compared with the traditional fixed step-size least mean square (LMS) algorithm, a variable step-size iteration algorithm is adopted to ensure accurate estimation parameters and fast convergence speed. A coarse-fine correction structure based on two-order Taylor series is proposed to satisfy the high-precision correction. Simulation results show that the proposed calibration technique increases the signal-to-noise-and-distortion (SNDR) and spurious-free dynamic range (SFDR) from 30.18 and 30.69 dB to 79.69 and 93.94 dB, respectively.

Coupled-generalized nonlinear Schrödinger equations solved by adaptive step-size methods in interaction picture

We extend two adaptive step-size methods for solving two-dimensional or multi-dimensional generalized nonlinear Schrödinger equation (GNLSE): one is the conservation quantity error adaptive step-control method (RK4IP-CQE), and the other is the local error adaptive step-control method (RK4IP-LEM). The methods are developed in the vector form of fourth-order Runge–Kutta iterative scheme in the interaction picture by converting a vector equation in frequency domain. By simulating the supercontinuum generated from the high birefringence photonic crystal fiber, the calculation accuracies and the efficiencies of the two adaptive step-size methods are discussed. The simulation results show that the two methods have the same global average error, while RK4IP-LEM spends more time than RK4IP-CQE. The decrease of huge calculation time is due to the differences in the convergences of the relative photon number error and the approximated local error between these two adaptive step-size algorithms.

A Denoising Method of Micro-Turbine Acoustic Pressure Signal Based on CEEMDAN and Improved Variable Step-Size NLMS Algorithm

The acoustic pressure signal generated by blades is one of the key indicators for condition monitoring and fault diagnosis in the field of turbines. Generally, the working conditions of the turbine are harsh, resulting in a large amount of interference and noise in the measured acoustic pressure signal. Therefore, denoising the acoustic pressure signal is the basis of the subsequent research. In this paper, a denoising method of micro-turbine acoustic pressure signal based on the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) and Variable step-size Normalized Least Mean Square (VSS-NLMS) algorithms is proposed. Firstly, the CEEMDAN algorithm is used to decompose the original signal into multiple intrinsic mode functions (IMFs), based on the cross-correlation coefficient and continuous mean square error (CMSE) criterion; the obtained IMFs are divided into clear IMFs, noise-dominated IMFs, and noise IMFs. Finally, the improved VSS-NLMS algorithm is adopted to denoise the noise-dominated IMFs and combined with the clear IMF for reconstruction to obtain the final denoised signal. Adopting the above principles, the acoustic pressure signals generated by a micro-turbine with different rotation speeds and different states (normal turbine and fractured turbine) are denoised, respectively, and the results are compared with the axial flow fan test (ideal interference-free signal). The results show that the denoising method proposed in this paper has a good denoising effect, and the denoised signal is smooth and the important features are well preserved, which is conducive to the extraction of acoustic pressure signal characteristics.

Optimal Timing Fault Tolerant Control for Switched Stochastic Systems with Switched Drift Fault

In this article, an optimal timing fault tolerant control strategy is addressed for switched stochastic systems with unknown drift fault for each switching point. The proposed controllers in existing optimal timing control schemes are not directly aimed at the switched drift fault system, which affects the optimal control performance. A cost functional with system state information and fault variable is constructed. By solving the optimal switching time criterion, the switched stochastic system can accommodate switching drift fault. The variational technique is presented for the proposed cost function in deriving the gradient formula. Then, the optimal fault tolerant switching time is calculated by combining the Armijo step-size gradient descent algorithm. Finally, the effectiveness of the proposed controller design scheme is proved by the safe trajectory planning for a four wheel drive mobile robot and numerical example.

A Study of Engine Intake Noise Control Based on the Improved Filtered-x Least Mean Square Algorithm

To reduce the intake noise of automobile engines, an active control system model of engine intake noise is established with the Filtered-x least mean square (FxLMS) algorithm. The offline identification method is adopted to identify the secondary path. The engine speed signal is used to construct the reference signal of a sound source to avoid interference of a secondary sound source to the reference signal. A variable-step algorithm is proposed, in which parameters are added to the normalized algorithm instead of the sinusoidal variable-step algorithm to adjust the amplitude range. This algorithm not only has the advantages of fast convergence speed and small steady-state error but also adapts to the characteristics of a time-varying reference signal and easy selection of parameters. In this paper, the noise of automobile engines under the New European Driving Cycle (NEDC) is studied and the proposed algorithm has faster convergence speed compared with the normalization algorithm, better adaptability to the change of the reference signal, and better stability compared with the sinusoidal variable step-size algorithm. The results show that the algorithm proposed can effectively reduce the intake noise of the engine at each speed and the noise reduction effect can reach 23.11 dB at a certain frequency. Meanwhile, the stability of the system is improved.

A Self-Adaptive Step Size Algorithm for Solving Variational Inequalities with the Split Feasibility Problem with Multiple Output Sets Constraints

In this paper, we investigate the problem of solving strongly monotone variational inequality problems over the solution set of the split feasibility problem with multiple output sets in real Hilbert spaces. The strong convergence of the proposed algorithm is proved without knowing any information of the Lipschitz and strongly monotone constants of the mapping. In addition, the implementation of the algorithm does not require the computation or estimation of the norms of the given bounded linear operators. Special cases are considered. Finally, a numerical experiment has been carried out to illustrate the proposed algorithm.

Multi-Terrain Velocity Control of the Spherical Robot by Online Obtaining the Uncertainties in the Dynamics

One controller cannot work on multiple and unknown terrains in the velocity control of the spherical robot, because the dynamic models of the robot vary on different terrains, and unmodeled dynamics and uncertainties exist in estimated dynamic models. Based on the above problem, a new velocity controller for spherical robot is designed. This controller combines a hierarchical sliding mode controller (HSMC), an adaptive RBF neural network (RBFNN) and a variable step-size algorithm. The RBFNN is used to online estimate the uncertainties, and the Lyapunov function is utilized to design the adaptive law for the RBFNN. In order to learn the uncertainties faster, while minimizing overshoot and preventing velocity oscillations, a variable step-size algorithm is proposed. The practical experiments demonstrate that, this controller of the spherical robot achieves velocity tracking on multiple and complex terrains, while eliminating steady-state error, having a good control effect, and maintaining high stability.