Recursive Least-squares Technique Research Articles

Novel hybrid arithmetic optimization algorithm-recursive least square approach for power system harmonic estimation

Abstract Accurate harmonic estimation is essential for effective power quality assessment, designing appropriate harmonic filters, and ensuring the reliable operation of electrical equipment. This article proposes a novel hybrid harmonic estimation technique combining recursive least square (RLS) and arithmetic optimization algorithm (AOA) for accurate estimation of harmonics, inter-harmonics and sub-harmonics. AOA is a new meta-heuristic method based on distribution behaviour of main arithmetic operators such as addition, subtraction, multiplication and division. RLS is used for estimation of amplitude of harmonics, whereas phase is estimated by AOA. The performance of AOA–RLS is investigated in detail for estimation of power system signals using two set of test signals buried with noise. The proposed AOA–RLS is proved to be efficient for estimating both phase and amplitude parameters under different signal to noise ratio (SNR) conditions with an estimation of error of E−3. The efficacy of AOA–RLS technique is demonstrated by comparing with competitive existing techniques. The performance of AOA–RLS also verified in experimental studies.

Insulation Detection of Electric Vehicles by Using FPGA-Based Recursive-Least-Squares Algorithm

The principal reason for why electric vehicles are required to serve as an alternative to the more widespread gasoline and petroleum-based vehicles used in modern times is due to the use of an environmentally conscious means of transportation or to circumvent the tumultuous economic dealings of the compressed natural gas and petroleum industries. There is a growing daily need for large, high-voltage e-mobilities, mostly driven by anticipated advancements in electric vehicle technology. Consequently, all of the various components of these vehicles must be able to be accommodated within a limited and compact space. The battery is an essential component in e-mobility. The insulation, health monitoring, and problem diagnostics of lithium-ion (Li-ion) batteries are of utmost importance in ensuring these vehicles’ safety and efficient functioning. Real-time and fast insulation detection techniques are required to ensure safety in high-voltage (HV) vehicles and to avoid insulation failure. This paper used the Recursive-Least-Squares (RLS) algorithm because it is computationally efficient for building the insulation detection system. Based on the RLS technique, we proposed field programmable gate array (FPGA)-based algorithms and implemented them using VHDL coding. The FPGA is very fast at detection, and the error is lower. We validated the FPGA results with MATLAB simulation results from the existing literature, and the errors are much less when using FPGAs. An experimental hardware platform was also created to validate the proposed FPGA technique with various motor and resistive loadings on electric vehicles (EVs).

Implementation of Real-time Parameter Estimation in Labview and Dsp

This paper presents the results of real time aircraft parameter estimation technology in an aircraft real time simulator. The equation error Recursive Least Squares (RLS) method is used for performing the parameter estimation. The RLS technique is successfully adapted for on-line parameter estimation by a novel methodology that will work when measurements of state derivatives are not available. Subsequently, the algorithm is implemented in Lab VIEW and in digital signal processor (DSP) hardware to demonstrate its suitability for further implementation at flight test centers and for on-board parameter estimation for aircraft.

A Co-Estimation Framework for State of Charge and Parameters of Lithium-Ion Battery With Robustness to Aging and Usage Conditions

Aging and usage conditions affect the battery parameters such as capacity and changes in the open-circuit voltage and internal resistance dependencies on the state of charge. This paper proposes an on-board strategy for the simultaneous estimation of these parameters and their robust evaluation during the battery life. The proposed co-estimation framework consists of a set of interconnected subsystems grounded on the integration of recursive least-squares techniques and a Luenberger-like observer which are independently designed by relying on moving averages of voltage and current measurements. Each subsystem is separately activated through logic variables which select the operating conditions proper for the estimation purposes and allows tracking of model parameters variations. The effectiveness of the solution is shown over experiments with a cylindrical LG M50T INR21700 Li-ion cell with NMC cathode and graphite/silicon anode.

A Recursive Least-Squares with a Time-Varying Regularization Parameter

Recursive least-squares (RLS) algorithms are widely used in many applications, such as real-time signal processing, control and communications. In some applications, regularization of the least-squares provides robustness and enhances performance. Interestingly, updating the regularization parameter as processing data continuously in time is a desirable strategy to improve performance in applications such as beamforming. While many of the presented works in the literature assume non-time-varying regularized RLS (RRLS) techniques, this paper deals with a time-varying RRLS as the parameter varies during the update. The paper proposes a novel and efficient technique that uses an approximate recursive formula, assuming a slight variation in the regularization parameter to provide a low-complexity update method. Simulation results illustrate the feasibility of the derived formula and the superiority of the time-varying RRLS strategy over the fixed one.

Static Baseline Estimation Using NavIC Pseudoranges: A Long-Term Study

We assess the estimation accuracy for two static baselines (350 m and 8 km) with NavIC L5 double-differenced (DD) pseudoranges using weighted and recursive least-square techniques for a day. Additionally, we analyze the 350-m baseline for a span of 9 months. The mean of the 3D residual sum-of-squares (RSS) error for the 350-m baseline using least-square error is 2.72 m with 1σ of 2.08 m for the 24-h duration. With the recursive technique, the mean and 1σ of the 3D RSS error reduce to 46 and 24 cm, respectively. For an 8-km baseline, the 3D RSS error mean and the standard deviation are 2.71 m and 1.72 m, respectively. Compared to NavIC’s baseline estimation accuracy, the 3D RSS error mean using GPS L1 DD pseudoranges for the 350-m and 8-km baselines are 1.13 m (1σ = 0.64 m) and 1.63 m (1σ = 0.78 m).

Trajectory Tracking Control of Autonomous Ground Vehicles Using Adaptive Learning MPC.

In this work, an adaptive learning model predictive control (ALMPC) scheme is proposed for the trajectory tracking of perturbed autonomous ground vehicles (AGVs) subject to input constraints. In order to estimate the unknown system parameter, we propose a set-membership-based parameter estimator based on the recursive least-squares (RLS) technique with the ensured nonincreasing estimation error. Then, the estimated system parameter is employed in MPC to improve the prediction accuracy. In the proposed ALMPC scheme, a robustness constraint is introduced into the MPC optimization to handle parametric and additive uncertainties. For the designed robustness constraint, its shape is decided off-line based on the invariant set, whereas its shrinkage rate is updated online according to the estimated upper bound of the estimation error, leading to further reduced conservatism and slightly increased computational complexity compared with the robust MPC methods. Furthermore, it is theoretically shown that the proposed ALMPC algorithm is recursively feasible under some derived conditions, and the closed-loop system is input-to-state stable (ISS). Finally, a numerical example and comparison study are conducted to illustrate the efficacy of the proposed method.

Real-Time Tracking of Structural Stiffness Reduction with Unknown Inputs, Using Self-Adaptive Recursive Least-Square and Curvature-Change Techniques

In this paper, a new computationally efficient algorithm is developed for online and real-time identification of time, location, and severity of abrupt changes in structural stiffness as well as the unknown inputs such as earthquake signal. The proposed algorithm consists of three stages and is based on self-adaptive recursive least-square (RLS) and curvature-change approaches. In stage 1 (intact structure), a simple compact RLS is hired to estimate the unknown parameters and input of the structure such as stiffness and earthquake. Once the damage has occurred, its time and location are identified in stage 2, using two robust damage indices which are based on the structural jerk response and the error between measured and estimated responses of structure from RLS. Finally, the damage severity as well as the unknown excitations are identified in the third stage (damaged structure), using a self-adaptive multiple-forgetting-factor RLS. The method is validated through numerical and experimental case studies including linear and nonlinear buildings, a truss structure, and a three-story steel frame with different excitations and damage scenarios. Results show that the proposed algorithm can effectively identify the time-varying structural stiffness as well as unknown excitations with high computational efficiency, even when the measured data is contaminated with different levels of noise. In addition, as no optimization method is used here, it can be applied to real-time applications with computational efficiency.

Recursive Least-Squares Temporal Difference With Gradient Correction.

Since the late 1980s, temporal difference (TD) learning has dominated the research area of policy evaluation algorithms. However, the demand for the avoidance of TD defects, such as low data-efficiency and divergence in off-policy learning, has inspired the studies of a large number of novel TD-based approaches. Gradient-based and least-squares-based algorithms comprise the major part of these new approaches. This paper aims to combine advantages of these two categories to derive an efficient policy evaluation algorithm with O ( n 2 ) per-time-step runtime complexity. The least-squares-based framework is adopted, and the gradient correction is used to improve convergence performance. This paper begins with the revision of a previous O ( n 3 ) batch algorithm, least-squares TD with a gradient correction (LS-TDC) to regularize the parameter vector. Based on the recursive least-squares technique, an O ( n 2 ) counterpart of LS-TDC called RC is proposed. To increase data efficiency, we generalize RC with eligibility traces. An off-policy extension is also proposed based on importance sampling. In addition, the convergence analysis for RC as well as LS-TDC is given. The empirical results in both on-policy and off-policy benchmarks show that RC has a higher estimation accuracy than that of RLSTD and a significantly lower runtime complexity than that of LSTDC.

Tire-Road Friction Coefficient Estimation under Constant Vehicle Speed Control

Abstract Tire-road friction coefficient (TRFC) is of critical importance for advanced vehicle control systems and autonomous vehicle applications. This paper presents a sequential tire longitudinal stiffness and TRFC estimation method for road vehicles by separate control of the front and rear wheels, for which only standard Kalman filter (KF) and recursive least squares (RLS) techniques are required. While braking torque is actively applied to rear wheels, the proportional-integral-derivative (PID) speed controller dictates the corresponding driving torque to front wheels to compensate the decrease of the vehicle longitudinal speed. Tire force of rear tires are estimated based on the KF, both longitudinal stiffness and TRFC of rear tires are identified using RLS technique. The proposed method has simple structure and the potential of estimating the parameters without severely affecting the vehicle’s desired longitudinal speed. Simulation results from vehicle dynamics software CarSim and Matlab/Simulink validate the effectiveness of the proposed method.

Online Estimation of the Electrochemical Impedance Spectrum and Remaining Useful Life of Lithium-Ion Batteries

An electrochemical impedance spectrum (EIS) is considered to be one of the key indicators to monitor the health status of lithium-ion batteries. Experimental procedures to measure the EIS of a battery are offline and require manual intervention. So, in order to monitor the state of health of a battery in real time, online methods for EIS estimation would be very useful. This paper presents an approach for estimation of the EIS of lithium-ion batteries based on a fractional-order equivalent circuit model (FOECM) which can be implemented online. First, the parameters of the fractional-order model are determined using recursive least-squares technique in conjunction with a fractional-order state variable filter based on current and voltage measurements. The parameters obtained are then used to generate the estimated EIS of the battery under different aging conditions. Thereafter, a regression model is obtained based on the estimated EIS spectrum which can represent the degradation trend of the battery in terms of its internal resistance growth. Finally, the obtained regression model is used in the particle filtering framework to predict the remaining useful life (RUL) of the battery quite satisfactorily as compared to the RUL obtained based on the measured EIS data. Moreover, in order to justify the proposed RUL estimation method based on FOECM, comparative analyses with respect to other FOECM-based regression models and an integer order model have also been carried out.

Improvement in Power Quality using Hybrid Power Filters based on RLS Algorithm

In industrial and utility power system it has been observed that harmonics build a major role in reducing the quality of power. These harmonics are caused because of increasingly utilize of nonlinear loads connected to the power system. In this context, active power filters play a very significant role for improvement in power quality. Moreover, at transmission ground, there is a high requirement to control reactive power and voltage stability. Conventionally, passive and active filters (shunt and series filters) were used for the development of power quality. But, they suffered from the issues like resonance, fixed compensation, and other PQ problems. Therefore, to minimize these issues, a hybrid combination of filters using passive and active filters is designed. In this paper, a comparative study of two hybrid model of HAPF is done based on current control techniques like d-q and p-q theory under different operating conditions. These results are again compared with a new estimation technique proposed in this paper well known called as recursive least square (RLS) harmonic estimation technique. The amplitude and phase angle of both the fundamental and harmonic currents are estimated with the proposed RLS technique. At the point of common coupling (PCC) the signal which is composed with harmonics is estimated with and without HAPF. Finally, it is analysed from the observation that the load current and supply current is improved significantly with a decrease of total harmonic distortion (THD) under different operating scenarios.

Particle Swarm Optimization-Based Multivariable Generalized Predictive Control for an Overhead Crane

The transient and residual vibrations in flexible underactuated mechatronic systems adversely affect the effectiveness and accuracy of performed tasks and movements. Moreover, in the case of crane operation the transient underactuated payload swing may present a safety hazard. In this paper, a novel control approach based on a multivariable model predictive control and a particle swarm optimizer is proposed for limiting the transient and residual swing of a payload transferred by an overhead crane. A control scheme is developed based on a discrete-time model approximating the decoupled dynamic of an actuated cart and an underactuated pendulum identified on-line using a recursive least-squares technique with parameters projection. A particle swarm optimizer is applied to determine the optimal sequence of control increments in the presence of constraints on input and output variables. The control scheme was successfully tested on a laboratory scaled overhead crane for different constraints and operating conditions. The experiments proved the feasibility and robustness of the proposed method.

Piecewise affine regression via recursive multiple least squares and multicategory discrimination

In nonlinear regression choosing an adequate model structure is often a challenging problem. While simple models (such as linear functions) may not be able to capture the underlying relationship among the variables, over-parametrized models described by a large set of nonlinear basis functions tend to overfit the training data, leading to poor generalization on unseen data. Piecewise-affine (PWA) models can describe nonlinear and possible discontinuous relationships while maintaining simple local affine regressor-to-output mappings, with extreme flexibility when the polyhedral partitioning of the regressor space is learned from data rather than fixed a priori. In this paper, we propose a novel and numerically very efficient two-stage approach for PWA regression based on a combined use of (i) recursive multi-model least-squares techniques for clustering and fitting linear functions to data, and (ii) linear multi-category discrimination, either offline (batch) via a Newton-like algorithm for computing a solution of unconstrained optimization problems with objective functions having a piecewise smooth gradient, or online (recursive) via averaged stochastic gradient descent.

Real-Time Power System Phasors and Harmonics Estimation Using a New Decoupled Recursive-Least-Squares Technique for DSP Implementation

This paper presents the mathematical basis to restructure the recursive-least-squares (RLS) technique for real-time implementations on digital signal processors (DSPs). The proposed decoupled RLS (DRLS) technique is adapted for real-time estimation of phasors and harmonics. The comparison between the proposed technique and the conventional RLS one shows considerable improvement in terms of reducing the turnaround time on two different off-the-shelf research and development DSP platforms. The DRLS technique also shows better computational efficiency than the adaptive linear combiner (ADALINE) and recursive discrete Fourier transform (RDFT) technique sin direct estimation of amplitude and phase angle when implemented on DSPs. The DRLS technique performance is also superior to that of the ADALINE and RDFT techniques under the presence of noise, subharmonics, and frequency variations. The performance of the proposed technique has been evaluated by simulations using MATLAB-Simulink and through real-time experiments. Selected results presented in this paper confirm the DSP turnaround time improvementand satisfactory performance of the proposed technique.

A Direct Method of Adaptive FIR Input Shaping for Motion Control With Zero Residual Vibration

In this paper, we describe a method of adaptive feedforward control that can achieve zero residual vibration in rest-to-rest motion of a vibratory system. When a finite impulse response filter is used to preshape a command input, zero residual vibration is achieved for any input signal if the impulse response of the filter satisfies a condition of orthogonality with respect to the impulse response of the system under control. An equivalent condition involving sets of measured I/O data is derived that forms the basis of a direct method of adaptively tuning filter coefficients during motion. The approach requires no prior model of the system and can be applied to multimode and multiinput systems under arbitrary and nonrepetitive motions. Versions of the algorithm employing recursive least-squares techniques are developed and analyzed. As a special case of the general adaptation problem, tuning of impulse-based shapers with fixed impulse timings can also be achieved. An experimental implementation on a two-link rigid-flexible manipulator is presented. The method is thereby shown to be realizable and effective for real-world motion control problems.

Recursive Algorithms for Bias and Gain Nonuniformity Correction in Infrared Videos

Infrared focal-plane array (IRFPA) detectors suffer from fixed-pattern noise (FPN) that degrades image quality, which is also known as spatial nonuniformity. FPN is still a serious problem, despite recent advances in IRFPA technology. This paper proposes new scene-based correction algorithms for continuous compensation of bias and gain nonuniformity in FPA sensors. The proposed schemes use recursive least-square and affine projection techniques that jointly compensate for both the bias and gain of each image pixel, presenting rapid convergence and robustness to noise. The synthetic and real IRFPA videos experimentally show that the proposed solutions are competitive with the state-of-the-art in FPN reduction, by presenting recovered images with higher fidelity.

회귀 최소 자승법을 이용한 고조파 발생원 추정 연구

A technique to allocate responsibilities among the interested parties in electric power system with harmonic voltage distortion at the point of common coupling (PCC) has been presented. The recursive least-squares technique has been used to estimate the parameters of the Thevenin equivalent load model. The validity of the technique has been verified using a simulation which considered the voltage waveform distortion at the PCC between the utility and two industrial consumers. With the estimated data from the measured voltage and current waveform at the PCC, the individual contributions to the distortion of voltage waveform at an interested harmonic frequency have been calculated and could provide a flexible solution to identify the source of harmonic pollution in distribution systems.

An Adaptive Feedforward Compensation for Stability Enhancement in Droop-Controlled Inverter-Based Microgrids

This paper proposes an adaptive feedforward compensation that alters the dynamic coupling between a distributed-resource unit and the host microgrid, so that the robustness of the system stability to droop coefficients and network dynamic uncertainties is enhanced. The proposed feedforward strategy preserves the steady-state effect that the conventional droop mechanism exhibits and, therefore, does not compromise the steady-state power sharing regime of the microgrid or the voltage/frequency regulation. The feedforward compensation is adaptive as it is modified periodically according to the system steady-state operating point which, in turn, is estimated through an online recursive least-square estimation technique. This paper presents a discrete-time mathematical model and analytical framework for the proposed feedforward compensation. The effectiveness of the proposed control is demonstrated through time-domain simulation studies, in the PSCAD/EMTDC software environment, conducted on a detailed switched model of a sample two-unit microgrid.

Evaluation of Recursive Least Squares algorithm for parameter estimation in aircraft real time applications

This paper presents results of evaluation of Recursive Least Squares (RLS) algorithm for real time applications in flight control and testing. The RLS proposed here is based on the equation error principle and can start with zero values of the unknown parameters. The technique makes use of only forgetting factor and a stabilizing parameter to achieve better convergence characteristics. In the present study, the RLS technique is applied for parameter estimation in the context of (i) reconfigurable/restructurable control, (ii) estimation of aircraft short period and Dutch roll characteristics in the absence of calibrated air data, and (iii) online stability (gain and phase) margin estimation.