Fourth Algorithm Research Articles

Hybrid VSS–LMS–LMF based adaptive control of SPV‐DSTATCOM system under distorted grid conditions

This study presents a solar photovoltaic distribution static compensator (SPV-DSTATCOM) system feeding a non-linear load connected at point of common coupling. A hybrid variable step size–least mean square–least mean fourth (VSS–LMS–LMF) algorithm is proposed for the control of voltage source converter, which acts as DSTATCOM. A weighing factor is used so that LMS and LMF work simultaneously, and a varying step-size helps in obtaining an adaptable system. The proposed control shows high convergence rate and low value of mean square error. The SPV array uses perturb and observe technique for maximum power extraction. The transition of SPV-DSTATCOM to DSTATCOM and vice-versa is also studied. In SPV-DSTATCOM mode, the SPV feeds power to the load and the grid, resolving the power quality issues of the system, whereas in DSTATCOM mode, the grid feeds power to the load at unity power factor. The system is first simulated in MATLAB environment and then these results are experimentally verified on the developed prototype in the laboratory. The system is studied for both power factor correction and zero voltage regulation modes and under distorted grid conditions. The obtained results adhere to an IEEE-519 standard.

Unified Lambert Tool for Massively Parallel Applications in Space Situational Awareness

This paper introduces a parallel-compiled tool that combines several of our recently developed methods for solving the perturbed Lambert problem using modified Chebyshev-Picard iteration. This tool (unified Lambert tool) consists of four individual algorithms, each of which is unique and better suited for solving a particular type of orbit transfer. The first is a Keplerian Lambert solver, which is used to provide a good initial guess (warm start) for solving the perturbed problem. It is also used to determine the appropriate algorithm to call for solving the perturbed problem. The arc length or true anomaly angle spanned by the transfer trajectory is the parameter that governs the automated selection of the appropriate perturbed algorithm, and is based on the respective algorithm convergence characteristics. The second algorithm solves the perturbed Lambert problem using the modified Chebyshev-Picard iteration two-point boundary value solver. This algorithm does not require a Newton-like shooting method and is the most efficient of the perturbed solvers presented herein, however the domain of convergence is limited to about a third of an orbit and is dependent on eccentricity. The third algorithm extends the domain of convergence of the modified Chebyshev-Picard iteration two-point boundary value solver to about 90% of an orbit, through regularization with the Kustaanheimo-Stiefel transformation. This is the second most efficient of the perturbed set of algorithms. The fourth algorithm uses the method of particular solutions and the modified Chebyshev-Picard iteration initial value solver for solving multiple revolution perturbed transfers. This method does require “shooting” but differs from Newton-like shooting methods in that it does not require propagation of a state transition matrix. The unified Lambert tool makes use of the General Mission Analysis Tool and we use it to compute thousands of perturbed Lambert trajectories in parallel on the Space Situational Awareness computer cluster at the LASR Lab, Texas A&M University. We demonstrate the power of our tool by solving a highly parallel example problem, that is the generation of extremal field maps for optimal spacecraft rendezvous (and eventual orbit debris removal). In addition we demonstrate the need for including perturbative effects in simulations for satellite tracking or data association. The unified Lambert tool is ideal for but not limited to space situational awareness applications.

On Some Separated Algorithms for Separable Nonlinear Least Squares Problems.

For a class of nonlinear least squares problems, it is usually very beneficial to separate the variables into a linear and a nonlinear part and take full advantage of reliable linear least squares techniques. Consequently, the original problem is turned into a reduced problem which involves only nonlinear parameters. We consider in this paper four separated algorithms for such problems. The first one is the variable projection (VP) algorithm with full Jacobian matrix of Golub and Pereyra. The second and third ones are VP algorithms with simplified Jacobian matrices proposed by Kaufman and Ruano et al. respectively. The fourth one only uses the gradient of the reduced problem. Monte Carlo experiments are conducted to compare the performance of these four algorithms. From the results of the experiments, we find that: 1) the simplified Jacobian proposed by Ruano et al. is not a good choice for the VP algorithm; moreover, it may render the algorithm hard to converge; 2) the fourth algorithm perform moderately among these four algorithms; 3) the VP algorithm with the full Jacobian matrix perform more stable than that of the VP algorithm with Kuafman's simplified one; and 4) the combination of VP algorithm and Levenberg-Marquardt method is more effective than the combination of VP algorithm and Gauss-Newton method.

Compressive Sensing Signal Reconstruction Using L0-Norm Normalized Least Mean Fourth Algorithms

Stochastic gradient-based adaptive algorithm has recently attracted considerable attention as one of the best candidates for solving compressive sensing (CS) problems due to its two obvious advantages: low complexity and robust performance. In this paper, in order to further improve the reconstruction accuracy for CS problems under Gaussian background noise, two novel sparse fourth-order error criterion adaptive algorithms, i.e., the $${\ell }_{{0}}$$ -norm normalized least mean fourth ( $${\ell }_{{0}}$$ -NLMF) algorithm and the $${\ell }_{{0}}$$ -norm exponentially forgetting window NLMF ( $${\ell }_{{0}}$$ -EFWNLMF) algorithm, are proposed. In addition, to extend the obtained results to non-Gaussian noise environment, the variants of the above two algorithms, i.e., the sign $${\ell }_{{0}}$$ -NLMF ( $${\ell }_{{0}}$$ -SNLMF) algorithm and the sign $${\ell }_{{0}}$$ -EFWNLMF ( $${\ell }_{{0}}$$ -EFWSNLMF) algorithm, are presented which can effectively mitigate certain impulsive noises. Numerical simulations are also given to demonstrate the evident performance improvement and extensive stability of the proposed algorithms.

Effects of Oil-Based Nanofluid on a Stretching Surface with Variable Suction and Thermal Conductivity

The combined effect of suction and thermal conductivity on the boundary layer flow of oil–based nanofluid over a porous stretching surface has been investigated. Similarity techniques were employed in transforming the governing partial differential equations into a coupled third order ordinary differential equations. The higher third order ordinary differential equations were then reduced into a system of first order ordinary differential equations and solved numerically using the fourth order Runge-Kutta algorithm with a shooting method. The results were presented in tabular and graphically forms for various controlling parameters. It was found that increasing the thermal conductivities of the base fluid (oil) and nanoparticle size (CuO) of the nanofluid did not affect the velocity boundary layer thickness but depreciates with suction and permeability. The suction parameter and thermal conductivity of the base fluid also made the thermal boundary layer thinner.

Performance analysis of diffusion least mean fourth algorithm over network

The diffusion least mean fourth (DLMF) algorithm was initially presented for distributed estimate over network with the sub-Gaussian node noise, which can obtain better performance than diffusion least mean square (DLMS) algorithm. Unfortunately, due to the higher order moment of the weight error in the DLMF algorithm and complexity of the network, it is difficult to analyze the mean square performance of the DLMF algorithm. In this paper, the stochastic behaviors including mean behavior and mean square behavior are investigated when the input signals of all nodes are Gaussian processes and the background noises have symmetric probability density functions. The analytical models of the mean weight error and the mean square deviation (MSD) are derived by using a novel manner, which can accurately predict the algorithm behavior. The simulations are carried out to verify the validity of the analysis and compare the performance of DLMF algorithm with that of the DLMS algorithm under different background noise distributions.

Graph-based loop extraction for automatic analysis of a water pipe distribution network and comparison with EPANET

This study introduces a new approach for automatic water pipe distribution network analysis by four integrated algorithms using graph theory, which are algorithms of minimal loop extraction, automatic initialization, automatic updating of initial discharges, and automatic pressure calculation at nodes. Object-oriented concepts have been used to design the algorithms for efficient data handling. The present integrated approach reduces the dependency of different processes involved in the analysis. The nested breadth first search traversal is used in the first algorithm to extract the loops without subdividing the graphical network. The initialization of pipes in loops is performed by satisfying the continuity equation at nodes in the second algorithm. The initialization, in the loop, is done in such a way that the adjacent loop will carry the residual discharge. Friction in the pipes is calculated iteratively for all flow types. Updating of discharge in pipes is according to the simultaneous loop flow adjustment method in the third algorithm. Initial discharges in the pipes of the loop in network are updated by corrective discharge in the loop according to the direction. The algorithm of nodal pressure calculation is done in the fourth algorithm, which is based on the energy equation in terms of pressure on the reference node. The results obtained by the proposed work are matched with EPANET software, in which the graphical display of the network is more user friendly and has the desired accuracy.

Least mean square fourth based microgrid state estimation algorithm using the internet of things technology.

This paper proposes an innovative internet of things (IoT) based communication framework for monitoring microgrid under the condition of packet dropouts in measurements. First of all, the microgrid incorporating the renewable distributed energy resources is represented by a state-space model. The IoT embedded wireless sensor network is adopted to sense the system states. Afterwards, the information is transmitted to the energy management system using the communication network. Finally, the least mean square fourth algorithm is explored for estimating the system states. The effectiveness of the developed approach is verified through numerical simulations.

Bias-Compensated Normalized Least-Mean Fourth Algorithm for Noisy Input

This paper proposes a bias-compensated normalized least-mean fourth (NLMF) algorithm to compensate for the bias caused by noisy input. In the proposed algorithm, we add a bias-compensation vector to the conventional NLMF algorithm, and the bias-compensation vector is then derived based on the unbiasedness criterion. Simulation results in system identification context show that the proposed algorithm provides lower steady-state misalignment as compared to the conventional NLMF algorithm.

A Stable Normalized Least Mean Fourth Algorithm With Improved Transient and Tracking Behaviors

The stability problems of the least mean fourth (LMF) algorithm put a limitation on its tracking capability. The paper investigates the possibility of solving this problem via stabilization of the algorithm. The analysis is done for a Markov plant. It is found that the available stable normalized LMF (NLMF) algorithm has a tracking limitation for high signal-to-noise ratio. The paper presents a new stable NLMF algorithm that is free of this limitation. Mean-square stability of the algorithm is proved. Expressions are derived for the minimum steady-state mean square deviation (MSD) and the corresponding convergence time. The new algorithm outperforms the available stable NLMF algorithm in both the transient and steady states. The new algorithm is also compared with the NLMS algorithm when the adaptation parameter of each algorithm is set to the value that minimizes its steady-state MSD. For large initial MSD, the algorithm outperforms the NLMS algorithm, even for Gaussian noise. For small initial MSD, the algorithm outperforms the NLMS algorithm for sub-Gaussian noise, while the situation is opposite for Gaussian noise. Analytical results are supported by simulations.

Stochastic analysis of the Least Mean Kurtosis algorithm for Gaussian inputs

The Least Mean Kurtosis (LMK) algorithm was initially proposed as an adaptive algorithm that is robust to the observation noise distribution. Good performances of this algorithm have been shown for non-Gaussian additive measurement noise. However, the complexity of the algorithm imposes difficulties for the development of a reasonably complete theoretical stochastic model for its behavior. The purpose of this paper is to contribute to the development of such a model. We study the stochastic behavior of Least Mean Kurtosis (LMK) algorithm for Gaussian inputs and for additive noises with even probability density functions. Deterministic recursions are derived for the adaptive weight error covariance matrix in a very novel manner, leading to a recursive model for the excess mean square error (EMSE) behavior that is shown to be accurate for Gaussian, uniform and binary noise distributions. The analysis results are then used to compare the performances of LMK with the least mean squares (LMS) and least mean fourth (LMF) algorithms under different circumstances.

Clutter attenuation‐stable normalised least‐mean fourth for PBR

The stable normalised least-mean fourth (SNLMF) algorithm is developed in the passive bistatic radar (PBR) system to realise the interference cancellation. The larger power of the reference signal may lead to the poor convergence rate. By replacing the reference signal vector with the instantaneous echo signal, the concept of the clutter attenuation (CA) is introduced in the SNLMF algorithm, and the CA-SNLMF algorithm is proposed to provide a fast convergence. The real measured data collected from the PBR system demonstrate that the proposed CA-SNLMF algorithm has a faster convergence speed and better cancellation performance than the SNLMF algorithm.

Stochastic behavior of the nonnegative least mean fourth algorithm for stationary Gaussian inputs and slow learning

Some system identification problems impose nonnegativity constraints on the parameters to be estimated due to inherent physical characteristics of the unknown system. The nonnegative least-mean-square (NNLMS) algorithm and its variants allow one to address this problem in an online manner. A nonnegative least mean fourth (NNLMF) algorithm has been recently proposed to improve the performance of these algorithms in cases where the measurement noise is not Gaussian. This paper provides a first theoretical analysis of the stochastic behavior of the NNLMF algorithm for stationary Gaussian inputs and slow learning. Simulation results illustrate the accuracy of the proposed analysis.

음향 통신 채널 추정기를 이용한 대수학적 스텝크기 least mean fourth 알고리즘

ABSTRACT: The least-mean fourth (LMF) algorithm is well known for its fast convergence and low steady-state error especially in non-Gaussian noise environments. Recently, there has been increasing interest in the least mean square (LMS) algorithms with variable step size. It is because the variable step-size LMS algorithms have shown to outperform the conventional fixed step-size LMS in the various situations. In this paper, a variable step-size LMF algorithm is proposed, which adopts an algebraic optimal step size as a variable step size. It is expected that the proposed algorithm also outperforms the conventional fixed step-size LMF. The superiority of the proposed algorithm is confirmed by the simulations in the time invariant and time variant channels.Keywords: Acoustic communication, Channel estimation, LMF, Algebraic optimal step-sizePACS numbers: 43.60.Dh, 43.60.Mn†Corresponding author: Jun-Seok Lim (jslim@sejong.ac.kr) Department of Electrical Engineering, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul 05006, Republic of Korea(Tel: 82-2-3408-3299, Fax: 82-2-3408-4329)

Efficient local search algorithms for job-shop scheduling problems

To solve job-shop scheduling problems, this paper develops four local search algorithms based on an input parameter of controlling the maximum allowable delay times of all machines. The use of this parameter in different values can change the size in numbers of the algorithm's solution space. The first proposed algorithm fixes the mentioned parameter's value and generates only forward schedules. The second algorithm reduces the parameter value iteratively and generates only forward schedules. The third algorithm reduces the parameter value iteratively; in addition, each operation-based permutation generated by this algorithm is transformed into both forward and backward schedules simultaneously. The fourth algorithm in the first-half iterations reduces the parameter value iteratively as well as generating only forward schedules; after that, this algorithm in the second-half iterations increases the parameter value iteratively as well as generating only backward schedules.

Variable step-size diffusion least mean fourth algorithm for distributed estimation

The diffusion LMS (DLMS) is one of the most popular online distributed estimation algorithms, due to its simplicity and ease of implementation. However, it may suffer from large steady-state misalignment in some strong, non-Gaussian noise environments. To address this problem, this paper introduces a diffusion least mean fourth (DLMF) algorithm by using the mean-fourth error cost function in a diffusion strategy. Moreover, a variable step-size (VSS) method is developed to further reduce the steady-state misalignment of the DLMF. Simulation results show that the DLMF outperforms the DLMS with uniform or binary noise, and that the VSS-DLMF has a superior steady-state performance as compared to the DLMF.

Radix-2 Division Algorithms with an Over-Redundant Digit Set

This paper presents a derivation of four radix-2 division algorithms by digit recurrence. Each division algorithm selects a quotient digit from the over-redundant digit set {−2, −1, 0, 1, 2}, and the selection of each quotient digit depends only on the two most-significant digits of the partial remainder in a redundant representation. Two algorithms use a two’s complement representation for the partial remainder and carry-save additions, and the other two algorithms use a binary signed-digit representation for the partial remainder and carry-free additions. Three algorithms are novel. The fourth algorithm has been presented before. Results from the synthesized netlists show that two of our fastest algorithms achieve an improvement of 10 percent in latency per iteration over a standard radix-2 SRT algorithm at the cost of 36 percent more power and 50 percent more area.

Fast stable normalised least‐mean fourth algorithm

A fast stable normalised least-mean fourth (FSNLMF) algorithm is proposed. The major drawback of the stable normalised least-mean fourth (SNLMF) algorithm is its poor convergence rate, especially in the presence of high signal-to-noise ratios (SNRs). Considering the effect of high SNRs, a corresponding constant is introduced in SNLMF algorithm to offer a fast convergence. Simulations on system identifications demonstrate that the proposed FSNLMF algorithm achieves a faster convergence speed than the SNLMF algorithm.

State Space Least Mean Fourth Algorithm for Dynamic State Estimation in Power Systems

Power system dynamic state estimation (DSE) has always been a critical problem in studying power systems. One of the essential parts of power systems are synchronous machines. In this work, we dealt with the problem of DSE of a synchronous machine by introducing a novel state space-based least mean fourth (SSLMF) algorithm. The rationale behind the proposed algorithm is the fact that a power system may encounter non-Gaussian disturbances/state errors and the least mean fourth algorithm is proven to be better in such environments. Moreover, we have also introduced a normalized version of the proposed algorithm, namely state space normalized least mean fourth (SSNLMF) algorithm to deal with the stability issue under Gaussian disturbances. Another motivation for developing the SSLMF algorithm is its simplicity as compared to other model-based nonlinear filtering algorithms such as Kalman filter, extended Kalman filter (EKF). Moreover, we also investigate the performance of the recently introduced state space least mean square (SSLMS). Performance of the SSLMF and the SSLMS is compared with existing EKF in both Gaussian and non-Gaussian noise environments. Extensive simulation results are presented which show superiority of the proposed algorithms, and hence, it verifies our rationale behind the work.

Large-depth hydrogeological detection in the North China-type coalfield through short-offset grounded-wire TEM

The North China-type coalfield is the most important coalfield in China. With the development of Chinese economy, shallow coal resources (<600 m) have been exhausted and large-depth detection is being conducted. Water-inrush is disastrous for coal mining. However, large-depth (600–1200 m) detection of water-filled zones in the North China-type coalfield is a difficult geophysical task due to its low-resistivity coverage. The traditional loop-source transient electromagnetic method (TEM) cannot realize large-depth detection. On the other hand, high-resolution detection of LOTEM is limited by the problem of recording points and large volume effect. To explore the large-depth targets with high-resolution, Short-offset grounded TEM (SOTEM) was applied in the North China-type coalfield. SOTEM is one branch of grounded-wire TEM. The response of SOTEM is calculated using superposing-dipole method rather than the direct-dipole approximation, which is used in the calculation of the response of LOTEM. This paper analyzes the comparison of the resolution and detection depth between SOTEM and loop-source TEM at first. Compared to the loop-source TEM with frequently used parameters, the detection depth of SOTEM with the usual setup parameters is about twice of magnitude, and the resolution capability of SOTEM at large depth is higher than that of loop-source TEM. Then, the resolution capability and detection depth between LOTEM and SOTEM are analyzed. For the grounded-wire TEM, offsets are strictly related to the detection depth. So, the detection depth of LOTEM with larger receiver–transmitter offset will be greater. However, at the depth of 600–1200 m, the resolution capability to conductive targets of SOTEM is higher than that of LOTEM. At last, SOTEM with a 1000-m long source and 1000–2000 m offset is applied to the 1200 m-depth exploration of water-filled zones in the North China-type coalfield. The induced voltage is observed and transformed into magnetic field. Then, the data is inverted using the least mean fourth algorithm. The distribution of water on the top and bottom surface of the large-depth No. 4 coal seam is given, and is verified by the drilling result.