Recursive Least-squares Method Research Articles

Real-time estimation of the ship manoeuvrable range in wind

A real-time identification procedure is applied to the estimation of hydrodynamic derivatives of ship manoeuvring equations. In the procedure, not only the ship motion data but also the wind data are used for making up a CARX (Continuous Auto Regressive eXogenous) model. The main advantage of the procedure is that the coefficients of the model directly correspond to the hydrodynamic derivatives. The identification algorithm consists of the IIR (Infinite Impulse Response) digital filters and RLS (Recursive Least Square) method. To discuss the reliability of the identified coefficients, the procedure is applied to a full-scale ship's data and the results are compared to the hydrodynamic derivatives provided by the shipbuilding company. Moreover, a simple navigation support system is proposed using the identified hydrodynamic derivatives. The system can indicate the ship manoeuvrable range under wind conditions and its usefulness is shown.

On-Line Parameter Identification of a Squirrel Cage Induction Motor

Based on the principle of coordinate transformation, a mathematical model of induction motors in the three-phase stationary coordinate system was transformed to that in the synchronous rotating coordinate system. For motors with low-speed rotors, the multi-variable, high-order, strong-coupling and nonlinear equation of motors was further transformed to a linear equation. However, it was found difficult to solve the deduced linear equation through the method of least squares due to its high singularity. The steady-state stator resistance could be predetermined by temperature revision on the stator resistant in the motor nameplate. Identification of four motor parameters (Ls,M, Rr, Lr) was followed by the recursive least-squares method. Simulations of motor parameter estimation were carried out in Simulink of Matlab. The recursive least-squares method was used to deal with the measured data. The results demonstrate that the real-time electrical parameters (Ls, σ, Tr) can be accurately predicted. Given the assumption of Ls = Lr in the classical motor theory, the other three electrical parameters (M, Rr, Lr) can also be identified. The identification of these parameters is of great importance for the analysis, control and fault diagnosis of induction motors.

고조파 부하 모델 추정을 위한 순환 최소 자승법 적용 연구

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.

Identification of continuous-time hybrid “Box–Jenkins” systems with multiple unknown time delays using two-stage parameter estimation algorithm

PurposeThis study/paper aims to present a separable identification algorithm for a multiple input single output (MISO) continuous time (CT) hybrid “Box–Jenkins”.Design/methodology/approachThis paper proposes an optimal method for the identification of MISO CT hybrid “Box–Jenkins” systems with unknown time delays by using the two-stage recursive least-square (TS-RLS) identification algorithm.FindingsThe effectiveness of the proposed scheme is shown with application to a simulation example.Originality/valueA two-stage recursive least-square identification method is developed for multiple input single output continuous time hybrid “Box–Jenkins” system with multiple unknown time delays from sampled data. The proposed technique allows the division of the global CT hybrid “Box–Jenkins” system into two fictitious subsystems: the first one contains the parameters of the system model, including the multiple unknown time delays, and the second contains the parameters of the noise model. Then the TS-RLS identification algorithm can be applied easily to estimate all the parameters of the studied system.

Maximum likelihood-based recursive least-squares estimation for multivariable systems using the data filtering technique

ABSTRACTFor multivariable equation-error systems with an autoregressive moving average noise, this paper applies the decomposition technique to transform a multivariable model into several identification sub-models based on the number of the system outputs, and derives a data filtering and maximum likelihood-based recursive least-squares algorithm to reduce the computation complexity and improve the parameter estimation accuracy. A multivariable recursive generalised extended least-squares method and a filtering-based recursive extended least-squares method are presented to show the effectiveness of the proposed algorithm. The simulation results indicate that the proposed method is effective and can produce more accurate parameter estimates than the compared methods.

Removal of ECG Artifacts From EEG Using an Effective Recursive Least Square Notch Filter

Electroencephalogram (EEG) is a common tool for medical diagnosis, cognitive research, and managing neurological disorders. However, EEG is usually contaminated with various artifacts, making it difficult to interpret EEG data. In this study, a recursive least square (RLS) notch filter was developed to effectively suppress electrocardiogram (ECG) artifacts from EEG recordings. ECG artifacts were estimated and modeled using the instantaneous frequency of the cardiac cycle. Then it was adaptively estimated using a RLS filter and directly subtracted from contaminated EEG data. Based on the validation measures of improvement of normalized power spectrum (INPS), mean square error (MSE) and information quantity (IQ), the performance of ECG artifacts suppression was compared among the proposed RLS approach, independent component analysis (ICA) and blind deconvolution method under information maximization (Infomax) on simulated and animal experimental data. Simulation data demonstrated that INPS of RLS method (19.75(18.37,20.95) dB) was significantly higher than that of ICA (4.35(3.35,5.41) dB) and Infomax (5.76(4.60,6.88) dB). Meanwhile, MSE of RLS method (0.20(0.08,0.53) μV 2 ) was considerably lower than that of ICA (5.59(2.35,19.79) μV 2 ) and Infomax (3.21(1.01,10.69) μV 2 ). Animal experimental data showed that INPS was 1.76(0.42,9.40) dB for RLS method, which was dramatically higher than that of ICA (0.02(0.00,0.14) dB) and Infomax (0.57(0.08,2.45) dB). The calculated IQ for RLS method (0.331(0.021,0.584)) was relatively lower than that of raw EEG (0.350(0.070,0.586)), ICA (0.350(0.069,0.581)) and Infomax (0.341(0.050,0.585)). The RLS notch filter can effectively eliminate ECG artifacts from EEG and preserve the majority of EEG information with little loss.

Steering Controller Design for Smart Autonomous Surface Vessel Based on CSF L2 Gain Robust Strategy

During the mission at sea, the yaw motion of the smart autonomous surface vessel (SASV) is always subject to the external disturbances. These issues make the design of a robust controller for steering autopilot system a quite challenging task. This paper focuses on the utilization of closed-loop shaping filter (CSF) to improve the SASV steering L2 gain robust control scheme. First, the mathematical model of the SASV is proposed and the parameters of the SASV model are obtained by the recursive least squares method (RLSM) based on the SASV turning test. Then the CSF L2 gain nonlinear robust controller design for SASV steering autopilot is described, and the stability and robustness of the proposed controller are proved based on the Lyapunov synthesis. Finally, the strong robustness and superior control performance are demonstrated through the practical SASV experiments. At the same time, the concise controller structure and definite physical meaning of SASV controller parameters are also concluded.

Experiment on impedance adaptation of under-actuated gripper using tactile array under unknown environment

Theexperiment on impedance adaptation to achieve stable grasp for an under-actuated gripper grasping different unknown objects with tactile array is conducted Under-actuated gripper has a wildly application in the field of space robot and industrial robot because of its better shape-adaptation. However it is difficult to achieve stable grasp owning to the uncertain properties of environment. Acontrol strategy of adaptive matching the impedance parameters is proposedto achieve stable grasp. Firstly, the unknown objects are described as linear systems with unknown dynamics, and the parameters of the object are identified with the recursive least-squares (RLS) method through tactile sensor array. Then a desired impedance model is obtained by defining a cost function that includes the contact force, velocity and displacement errors, and the critical impedance parameters are found to minimize it. Finally, an experiment is presented and shows that the proposed impedance model can guarantee the stable grasp for various unknown objects.

Синтез нейронной сети для реализации рекуррентного метода наименьших квадратов

Синтез нейронной сети для реализации рекуррентного метода наименьших квадратов

Model based insulation fault diagnosis for lithium-ion battery pack in electric vehicles

The condition monitoring and fault diagnosis of the lithium-ion battery system are crucial issues for electric vehicles. The shocks, blows, twists, and vibrations during the electric vehicle driving process may cause the insulation fault. In order to ensure the safety of the drivers and passengers, a real-time monitor to detect the insulation state between the high voltage and ground is required. However, the conventional battery management system only provides very simple and coarse-grained measurements to detect the insulation resistance. In this work, a model-based insulation fault diagnosis method is proposed. Firstly, the equivalent circuit model for insulation fault diagnosis is established using a high-fidelity cell model. Then, the recursive least-squares method is employed to identify the model parameters. Considering the system nonlinear properties, measurement noise and unknown disturbance, the Kalman filter based state observer is designed for joint estimation of both the battery voltage and state-of-charge using the identified battery model. Finally, the positive and negative virtual insulation resistance are quantitatively assessed based on the prediction results of the state observer. Experiments under different loading profiles are performed to verify the proposed method.

An echo state network algorithm based on recursive least square for electrocardiogram denoising

Electrocardiogram (ECG) is easily submerged in noise of the complex environment during remote medical treatment, and this affects the intelligent diagnosis of cardiovascular diseases. Considering this situation, this paper proposes an echo state network (ESN) denoising algorithm based on recursive least square (RLS) for ECG signals. The algorithm trains the ESN through the RLS method, and can automatically learn the deep nonlinear and differentiated characteristics in the noisy ECG data, and then the network can use these characteristic to separate out clear ECG signals automatically. In the experiment, the proposed method is compared with the wavelet transform with subband dependent threshold and the S-transform method by evaluating the signal-to-noise ratio and root mean square error. Experimental results show that the denoising accuracy is better and the low frequency component of the signal is well preserved. This method can effectively filter out complex noise and effectively preserve the effective information of ECG signals, which lays a foundation for the recognition of ECG signal feature waveform and the intelligent diagnosis of cardiovascular disease.

A new information-weighted recursive algorithm for time-varying systems: application to UAV system identification

ABSTRACTThis paper presents a new recursive identification method which can efficiently estimate time-varying parameters in discrete time systems and has significant advantages over standard recursive least-squares (RLS) method. This new information-weighted recursive algorithm for time-varying systems has three novel features, discounting of inaccurate estimates through weighting by the Information matrix, using the reuse of past data in computing current parameter estimates, a new tuneable damping factor parameter and a precisely designed compensation term to neutralise the estimation error caused by time-varying coefficients. A rigorous proof of convergence is also provided. Simulations show that the new algorithm significantly outperforms standard RLS, exhibiting better tracking performance and faster convergence. Flight tests on a T-REX 800 helicopter Unmanned Aerial Vehicle platform show that it gives system parameter estimates that are accurate enough and converge quickly enough that flight controllers can be designed in real-time based on the online identified model.

State Estimation of Vehicle’s Dynamic Stability Based on the Nonlinear Kalman Filter

An accurate estimation of a vehicle’s state of motion is the basis of dynamic stability control. Two different nonlinear Kalman filters are adopted for the estimation of the vehicle’s lateral/rollover stability state. First, the overall structure of the state estimation with four inputs and four outputs is introduced. After determining tire-cornering stiffness using a recursive least-squares (RLS) method, the equations of state and of observation for the nonlinear Kalman filter are established based on a vehicle model with four degrees of freedom including planar and rollover dynamics. Then, the specific steps of real-time state estimation using the extended Kalman filter (EKF) and unscented Kalman filter (UKF) are both given. In a co-simulation, we find that the RLS algorithm estimates tire-cornering stiffness accurately and quickly, and the UKF improves the effect of state estimation compared with EKF. In addition, the UKF is verified against data from vehicle tests. The results show the proposed method is reliable and practical in estimating vehicle states.

Adaptive positive position feedback control with a feedforward compensator of a magnetostrictive beam for vibration suppression

In this paper, a Fe–Ga alloy magnetostrictive beam is designed as an actuator to restrain the vibration of a supported mass. Dynamic modeling of the system based on the transfer matrix method of multibody system is first shown, and then a hybrid controller is developed to achieve vibration control. The proposed vibration controller combines a multi-mode adaptive positive position feedback (APPF) with a feedforward compensator. In the APPF control, an adaptive natural frequency estimator based on the recursive least-square method is developed to be used. In the feedforward compensator, the hysteresis of the magnetostrictive beam is linearized based on a Bouc–Wen model. The further remarkable vibration suppression capability of the proposed hybrid controller is demonstrated experimentally and compared with the positive position feedback controller. Experiment results show that the proposed controller is applicable to the magnetostrictive beam for improving vibration control effectiveness.

Recursive identification of multiple-input single-output fractional-order Hammerstein model with time delay

This paper deals with identification of the continuous-time Hammerstein systems with time delay using Genetic Algorithm (GA) combined with the Recursive Least-Squares (RLS) method. This model consists of the Radial Basis Function Neural Network (RBFNN) as its nonlinear static part and fractional order transfer function as its dynamic linear part. The fractional orders are identified by GA with an innovative strategy called Modified Genetic Algorithm (MGA). The main innovative idea is the selection and transferring the best characteristics or properties to the next generation. On the other hand, the centers and widths and the weighting parameters of the RBFNN and the transfer function coefficients of the linear dynamic part are updated by the RLS method. Simulation results are applied to illustrate the proposed method accuracy.

Superpixel based recursive least-squares method for lossless compression of hyperspectral images

Filtering based compression methods have become a popular research topic in lossless compression of hyperspectral images. Recursive least squares (RLS) based prediction methods provide better decorrelation performance among the filtering based methods. In this paper, two superpixel segmentation based RLS methods, namely SuperRLS and B-SuperRLS, are investigated for lossless compression of hyperspectral images. The proposed methods present a novel parallelization approach for RLS based prediction method. In the first step of SuperRLS, superpixel segmentation is applied to hyperspectral image. Afterwards, hyperspectral image is partitioned into multiple small regions according to the superpixel boundaries. Each region is predicted with RLS method in parallel, and prediction residuals are encoded via arithmetic encoder. Additionally, superpixel based prediction approach provides region of interest compression capability. B-SuperRLS, which is bimodal version of SuperRLS, evaluates both spectral and spatio-spectral correlations for prediction. The performance of the proposed methods are exhaustively analysed in terms of superpixel number, input vector length and number of parallel nodes, used in the prediction. Experimental results show that the proposed parallel architecture dramatically reduces the computation time, and achieves lower bit-rate performances among the state-of-the-art methods.

Fault detection and location in a microgrid using mathematical morphology and recursive least square methods

The concept of microgrids has been proposed as an economical, reliable, and efficient way to integrate a large number of distributed energy resources (DERs) into distribution networks. To ensure the safe operation of a microgrid fast and accurate fault detection and location are crucial. This paper proposes fault detection and location in a microgrid using mathematical morphology (MM) and recursive least-square (RLS) methods. The proposed method first applies dilation and erosion median filter (DEMF) on a current signal to detect and classify the faults in microgrids. Then, the RLS method estimates the fault location using a differential equation derived from an equivalent model of the microgrid. The performance of the proposed method is evaluated on a medium voltage microgrid test system through simulations using MATLAB/SIMULINK. The simulation results depict that the proposed method provides faster fault detection and accurate fault location.

Impedance Identification Using Tactile Sensing and Its Adaptation for an Underactuated Gripper Manipulation

Underactuated gripper has a broad application in the field of space robot and industrial robot because of its better shape-adaptation. However, because of the underactuated characteristics, it is a great challenge to accurately obtain the displacement of the contact point between the finger and grasped object, which makes it difficult to control the gripper grasp stably, especially the environmental parameters are unknown. This paper develops the identification of the unknown environmental parameters using a tactile array sensor based on the recursive leastsquares (RLS) method. The unknown environments are described as linear systems with unknown dynamics, and the environmental parameters are identified using the measured contact force and the derived displacement of the contact point which is obtained through the underactuated gripper dynamics. Meanwhile, an impedance adaptive control is presented to match the variability of the environment parameters, and the desired impedance model is imposed to the underactuated gripper to achieve stable grasp. A cost function that measures the contact force, velocity and displacement error is defined, and the critical impedance parameters are found to minimize it. At last, a co-simulation of ADAMS and MATLAB for an underactuated gripper grasp is implemented to show the feasibility of environmental parameters identification and its adaptive method.

Prognostics and Health Management of Bearings Based on Logarithmic Linear Recursive Least-Squares and Recursive Maximum Likelihood Estimation

Prognostics and health management allows us to predict the remaining useful life (RUL) of machinery, which is important in reducing maintenance costs and downtime, and even preventing casualties. Bearing faults account for a large proportion of machine faults. To predict the RUL of bearings, health indicators that represent the degeneration state are extracted based on the Hilbert–Huang transform and selected according to Spearman's coefficient. A model-based particle filter method is then used to track the degradation state. The unknown parameters in the nonlinear system are updated by a new method of logarithmic linear recursive least squares. A recursive maximum likelihood estimation algorithm is introduced to learn the noise in the system, and an innovative parameter fusion technique based on normalized partial derivative weights is used. Finally, the RUL of the bearings is predicted. The proposed method is validated using data from the test platform PRONOSTIA.

Correlation analysis-based error compensation recursive least-square identification method for the Hammerstein model

ABSTRACTIn this paper, the correlation analysis based error compensation recursive least-square (RLS) identification method is proposed for the Hammerstein model. Firstly, the covariance matrix between input and output data points of the Hammerstein model is derived by using separable signal to realize that the unmeasurable internal variable is replaced by the covariance matrix of input. Thus, the correlation analysis method can be accordingly used to estimate parameters of the linear part, which results in the identification problem of the nonlinear part separated from the linear part. In addition, a correction term is added to least-square estimation to compensate error caused by output noise, further the error compensation-based RLS method is obtained for the observed data from the Hammerstein model. As a result, the least-square identification method, which generates error in the presence of noise distribution, can be compensated. Finally, simulation experiments are conducted to illustrate the performance of the proposed identification method.