A novel variable step size least mean square method for adaptive micro-vibration control

Three recursive methods especially suited for identification of systems with rapidly changing parameters are applied to tracking of the viscoelastic properties of the systemic arterial bed. These methods include two least squares (LS) algorithms with constant or variable forgetting factor (RLS and LSVF) and a LS algorithm incorporating both a constant forgetting factor and covariance modification (CFCM). The methods are presented in a unified framework and their sensitivity with respect to the design variables is investigated using noisy data from computer simulations. All analysed methods have shown themselves to be able to satisfactory track rapid changes in peripheral resistance. The LSVF method, which offers slightly better performances than the classical RLS, may be preferred when calculation efficiency is the prime requirement. The CFCM algorithm, although maintaining reasonable simplicity, shows the best tracking ability also on varying of the noise sequence.

This paper presents a method of recursive least squares (RLS) using variable forgetting factor for estimating harmonic load model. In order to evaluate harmonic contributions between supply system and consumers, the harmonic equivalent models of supply system and consumers are needed. The parameters of harmonic load model can be estimated using a recursive least squares algorithm. The parameter estimation performance of RLS is depending on various factors such as forgetting factor, data characteristics and white noise. Even though it is very important to determine an appropriate forgetting factor corresponding to measured data, previous studies have used a constant forgetting factor. In this paper, we proposed an effective RLS parameter estimation with variable forgetting factor and carried out a comparative analysis of the estimation performance between constant and variable forgetting factors. To verify the performance of the proposed method, voltage and current are measured at PCC(Point of Common Coupling) of PSCAD test system and harmonic load parameters are estimated using the proposed RLS.

The present study considers the application of recursive least squares (RLS) method with variable forgetting factor (VF) and directional forgetting factor (DF) in dynamic modelling of a flexible plate structure. Recursive least squares with fixed forgetting factor is used to update parameter changes suitable for stationary environments. However for dynamic environments, VF is needed to include fast tracking capability. The performance of the algorithm is compared with that of standard RLS using operations based on one-step-ahead prediction. The performance of each algorithm is assessed in terms of mean square of output error and frequency domain response of the model in characterizing the plate system. Correlation tests are also carried out to validate the model. Simulation results show that the new algorithm can outperform the fixed forgetting factor algorithm in parametric modelling of the flexible structure.

Channel estimation in wireless communication system using various supervised learning algorithms traditionally involves two very popular algorithms namely Least Mean Square (LMS) and Recursive Least Square (RLS). The concept of variable step size adaptive algorithms came into picture later on to achieve a trade-off between convergence speed and mathematical complexity of these two algorithms (LMS and RLS). The family of variable step size least mean square (VSSLMS) algorithms consists of various members depending on their separate step size adaptation rule. In this paper, a new modified variable step size algorithm is proposed employing a simple mathematical adaptation strategy- the “reward-punishment” rule. The performance of the newly developed algorithm is analyzed in estimating an unknown time varying Rayleigh faded channel and compared with the performance of existing algorithms. The computer simulation shows that the “reward-punishment based variable step size least mean square” algorithm exhibits faster convergence rate compared to LMS and other competitors from VSSLMS family of algorithms and consequently acts as better trade-off between LMS and RLS algorithm. The mathematical complexity measured in terms of CPU time usage also indicates betterment over existing VSSLMS algorithms.

Step size control for efficient discrete element simulation

In this study, we employ the active noise control (ANC) method to eliminate the low-frequency part of the noise generated by the rotation of the axial fan in heating, ventilation, and air-conditioning (HVAC) pipelines. Because the traditional variable step size least mean square (VSS-LMS) algorithm has poor tracking performance, we propose a variable step size filtered-X least mean square (FXLMS) algorithm based on the arctangent function to improve the adaptive filtering method of the convergence speed and noise cancellation effect. The step size of the proposed algorithm can be adjusted according to the error. When the error signal is significant, a larger step can be obtained, and when the error is small, the step size smoothness of the algorithm can be optimized. Compared with the traditional VSS-LMS algorithm, the convergence speed of the proposed algorithm is increased by 29%, the noise reduction effect is enhanced by 19%, and the mean square error (MSE) is reduced by 23% (0.0084). In addition, we developed a hardware experimental platform based on noise characteristics. In the noise reduction test using a GB/T 5836.2-06 standard PVC pipeline, the system reduced the noise by 12–17 dB.

A new adaptive algorithm is proposed for implementation of channel estimation for Orthogonal Frequency Division Multiplexing-Interleave Division Multiple Access (OFDM-IDMA)-based wireless communication systems. This is named the variable forgetting factor modified recursive least mean square (VFF-MRLS) algorithm. The modification imposed is based on the enforcement of a constraint on the a posteriori error of the conventional RLS algorithm. The variable step size is obtained by following a time average procedure which is based on the correlation of two consecutive a priori estimation errors. Computer simulation is carried out to establish the performance of the proposed channel estimator. Comparative associated computational complexity of the proposed estimator and others are documented in this paper. From the results obtained, the proposed VFF-MRLS-based estimator shows improved performance over its counterparts but with high computational complexity.

CDMA system is a promising multiple access technique which extremely increases the channel capacity and supports multiple-access and multimedia transmission.However, the performance of CDMA system degrades in presence of multipath and dense multiple-access environment .Usually an adaptive filter is utilized to compensate the effect of multipath and multiple-access interference and signal fading over the channel.This paper provides a variable step size algorithm to accelerate convergence of the adaptive filter.The optimum performance is achieved by governing the rate of convergence and the amount of steady state excess mean square error (MSE).The performance is optimized in this paper by two main methods mainly: variable step size parameters and gradient adaptively regularization parameter.The first method is implemented through variable step size least mean square algorithm VSSLMS, modified variable step size MVSS algorithm and variable step size affine projection algorithm VS-APA.On the other hand, the second method is implemented using generalized normalized gradient descent algorithm GNGD and generalized square-error-regularized LMS algorithm GSER-LMS.This paper concerns with comparative study of the five mentioned adaptive algorithms, (VSSLMS -MVSS -VS-APA -GNGD -GSER-LMS), to overcome the multipath and multiple-access problems of CDMA systems.The mentioned algorithms had the advantages of fast convergence and low steady state MSE, these advantages candidate the mention algorithms to improve the bit error rate (BER) performance of the CDMA system, in the presence of multipath and multiple-access environment.The results indicate that the proposed algorithm provides faster convergence compared with the fixed step size and fixed regularization parameters algorithms.

In this paper, a new control mechanism for the variable forgetting factor (VFF) of the recursive least square (RLS) adaptive algorithm is presented. The control algorithm is basically a gradient-based method of which the gradient is derived from an improved mean square error analysis of RLS. The new mean square error analysis exploits the correlation of the inverse of the correlation matrix with itself that yields improved theoretical results, especially in the transient and steady-state mean square error. It is shown that the theoretical analysis is close to simulation results for different forgetting factors and different model orders. The analysis yields a dynamic equation of mean square error that can be used to derive a dynamic equation of the gradient of mean square error to control the forgetting factor. The dynamic equation can produce a positive gradient when the error is large and a negative gradient when the error is in the steady state. Compared with other variable forgetting factor algorithms, the new control algorithm gives fast tracking and small mean square model error for different signal-to-noise ratios (SNRs).

In many practical applications, the impulse responses of the unknown system are sparse. However, the standard Least Mean Square (LMS) algorithm does not make full use of the sparsity, and the general sparse LMS algorithms increase steady-state error because of giving much large attraction to the small factor. In order to improve the performance of sparse system identification, we propose a new algorithm which introduces a variable step size method into the Reweighted Zero-Attracting LMS (RZALMS) algorithm. The improved algorithm, whose step size adjustment is controlled by the instantaneous error, is called Variable step size RZALMS (V-RZALMS). The variable step size leads to yielding smaller steady-state error on the premise of higher convergent speed. Moreover, the sparser the system is, the better the V-RZALMS performs. Three different experiments are implemented to validate the effectiveness of our new algorithm.

ARX model is an autoregressive model with exogenous terms. Because of its simplicity and easy parameterization, the ARX model has been widely used in various applications. However, most reports on ARX identification are about Gaussian noise or white noise environment. In many practical industrial applications, impulse noise widely exists. For systems contaminated by this noise, the performance of the mean square error algorithm will deteriorate. To get more accurate results, a variable step size stochastic information gradient algorithm is proposed. The algorithm is based on the Renyi square error entropy and introduces a fourth‐order statistic of the error–kurtosis–into the variable step size, which not only effectively suppresses the impulse noise, but also accelerates the convergence speed. At the same time, a simple method of determining the maximum step size is given. The computational cost and the convergence are also analyzed. Numerical experiments and case study show that for the ARX model disturbed by impulse noise, the proposed algorithm can obtain high‐precision parameter estimates with fast convergence speed.

Nowadays, the electrocardiogram (ECG) signal is widely used to detect cardiovascular diseases. Several studies are conducted on noise removal of ECG signal based on the adaptive filter with least-mean Square (LMS) algorithm. In this paper, for improving the traditional LMS method, the evolutionary algorithms are used to select the variable optimal step size of LMS, causing the least error between the main and filtered ECG signals. The proposed Adaptive Noise Cancellation System (ANC) includes Wavelet Transform and IIR-Notch filter to reduce the baseline Wander and Power Line Interference noises. Afterward, an additive white noise generator unit is employed to evaluate the performance of the three adaptive models involving GA-LMS, PSO-LMS, and GA-PSO-LMS algorithms in terms of Signal to Noise Ratio (SNR) and Mean Square Error (MSE). Eventually, to evaluate the performance of the proposed models in terms of the MSE and SNR criteria, we conduct comprehensive experiments on the ECG records of the MIT -BIH database. The obtained results of variable step size, GA-LMS, PSO-LMS, and hybrid GA-PSO-LMS, demonstrate more efficiency in filtered signal compared to constant step size LMS. Besides, in most cases, the Hybrid GA-PSO-LMS method has superiority over two other proposed methods concerning the SNR and MSE criteria.

An adaptive optimization algorithm using a dynamic identification scheme with a bilevel forgetting factor (BFF) has been developed. The simulation results show superiority of this method to other methods when applied to maximize the cellular productivity of a continuous culture of baker's yeast, Saccharomyces cerievisiae. Within the limited ranges of tuning parameters tested the BFF algorithm is found to be superior in terms of initial optimization speed and accuracy and reoptimization speed and accuracy when there is an external change and long term stability (removal of "blowing up" phenomena). Algorithms tested include those based on a constant forgetting factor, an adaptive variable forgetting factor (VFF) and moving window (MW) identification.

The main aim of this paper is to present an efficient method to cancel the noise in the ECG signal, due to various sources, by applying adaptive filtering techniques. The adaptive filter essentially reduces the mean-squared error between a primary input, which is the noisy ECG, and a reference input, which is either noise that is correlated in some way with the noise in the primary input or a signal that is correlated only with ECG in the primary input. The Least Mean Square (LMS) algorithm is familiar and simple to use for cancellation of noises. However, the low convergence rate and low signal to noise ratio are the limitations for this LMS algorithm. To enhance the performance of LMS algorithm, in this paper, we present an efficient variable step size LMS algorithms which will provide fast convergence at early stages and less misadjustment in later stages. Different kinds of variable step size algorithms are used to eliminate artifacts in ECG by considering the noises such as power line interference and baseline wander. The simulation results shows that the performance of the variable step size LMS algorithm is superior to the conventional LMS algorithm, while for sign based, the sign regressor variable step size LMS algorithm is equally efficient as that of variable step size LMS with additional advantage of less computational complexity.

Numerous various step size normalized least mean square (VSS-NLMS)Algorithms have been derived to solve the problem of fast convergence rate and low mean square error.Here we find out the ways to control the step size. A normalized subband adaptive filter algorithm uses a fixed and variable step size, which is chosen as a trade-off between the steady-state error and the convergence rate. A variable step size for normalized subband adaptive filter is derived by minimizing the mean-square deviation between the optimal weight vector and the estimated weight vector at each instant of time. The variable step size is presented in terms of error variance. Therefore, we verify thedifferent algorithmseither they are capable of tracking in stationary and non-stationary environments. The results show good tracking ability and low misalignment of the algorithm in system identification. Parameters are tracking, steady state errors, and misalignment, environment, step size.