Variable Forgetting Factor RLS Research Articles

Combing dynamic parameter identification and singular value decomposition adaptive unscented Kalman filter for predictive state of charge of lithium-ion batteries

The development of a secure battery management system (BMS) for electric vehicles depends heavily on the correct assessment of the online state-of-charge (SOC) of Li-ion batteries. The ternary lithium battery is used as the research object in this paper, and a second-order RC equivalent circuit model is developed to characterize the dynamic operating characteristics of the battery. In order to solve the problem that the adaptive unscented Kalman filter (AUKF) algorithm is easy to fail SOC estimation because the error covariance matrix is not positively definite due to the incomplete accuracy of the equivalent circuit model, a corresponding solution is proposed. Considering the poor real-time battery SOC estimate caused by the battery model’s fixed parameters, therefore we propose the Variable Forgetting Factor Recursive Least Squares (VFFRLS) algorithm for joint estimation of Li-battery SOC and the Singular Value Decomposition-AUKF (SVD-AUKF) algorithm. The SVD-AUKF algorithm can accurately estimate the SOC of the battery when the error covariance is negative. The algorithm can be adaptively adjusted in both the parameter identification and SOC estimation stages, which can effectively solve the problem of poor estimation accuracy caused by fixed parameters. According to experiments, under two separate dynamic operating situations, the joint estimation algorithm’s error is less than 2%, and its stability has also been greatly enhanced. At the same time, when the initial SOC value is set incorrectly, the convergence time of the algorithm proposed in this paper can reach within 2.1 seconds for BBDST and DST conditions, which can be well adapted to complex working conditions.

An Adaptive Hammerstein Model for FES-Induced Torque Prediction Based on Variable Forgetting Factor Recursive Least Squares Algorithm.

Modeling the muscle response to functional electrical stimulation (FES) is an important step during model-based FES control system design. The Hammerstein structure is widely used in simulating this nonlinear biomechanical response. However, a fixed relationship cannot cope well with the time-varying property of muscles and muscle fatigue. In this paper, we proposed an adaptive Hammerstein model to predict ankle joint torque induced by electrical stimulation, which used variable forgetting factor recursive least squares (VFFRLS) method to update the model parameters. To validate the proposed model, ten healthy individuals were recruited for short-duration FES experiments, ten for long-duration FES experiments, and three stroke patients for both. The isometric ankle dorsiflexion torque induced by FES was measured, and then the test performance of the fixed-parameter Hammerstein model, the adaptive Hammerstein model based on fixed forgetting factor recursive least squares (FFFRLS) and the adaptive Hammerstein model based on VFFRLS was compared. The goodness of fit, root mean square error, peak error and success rate were applied to evaluate the accuracy and stability of the model. The results indicate a significant improvement in both the accuracy and stability of the proposed adaptive model compared to the fixed-parameter model and the adaptive model based on FFFRLS. The proposed adaptive model enhances the ability of the model to cope with muscle changes.

State of charge estimation for lithium-ion battery based on improved online parameters identification and adaptive square root unscented Kalman filter

Accurate state of charge estimation is crucial for the safe and efficient operation of lithium-ion batteries. The Kalman filtering algorithm has been widely used in state-of-charge (SOC) estimation. To solve the problem of filter divergence and sensitivity to noise, the joint SOC estimation method is proposed to achieve accurate and robust estimation of SOC, which is composed of improved variable forgetting factor recursive least square (VFFRLS) and adaptive square root unscented Kalman filter (ASRUKF). The improved VFFRLS method uses the mean square value of the multi-step voltage residual instead of the traditional one-step voltage residual to correct the forgetting factor, and the ASRUKF improves the accuracy and stability of estimation by introducing the square root method and the adaptive method. Estimations under three typical working conditions are quantitatively studied, the experimental results show that the proposed method has good accuracy and stability. The maximum mean absolute error (MAE) is 0.0061, and the corresponding root mean square error (RMSE) is 0.0090. Furthermore, the experimental verification after adding offset errors to measured data shows that the proposed method can still track the reference SOC with satisfactory accuracy in the range of voltage offset error less than ±0.5 % and current offset error less than ±3 %, both for the constant offset error and the random error, and the SOC error is less than 2.5 %.

High-Precision Harmonic Current Extraction for PMSM Based on Multiple Reference Frames Considering Speed Harmonics

Based on Multiple reference frames (MRF), this paper investigates high-precision harmonic current extraction for permanent magnet synchronous motor (PMSM), while taking the disturbance of speed harmonics into account. Firstly, the extraction error in MRF caused by speed harmonics is deduced and analyzed, showing that the error is non-ignorable and detrimental. Secondly, a novel preprocessing of fundamental current reconstruction and elimination in MRF is proposed, which effectively suppresses the extraction error. Thirdly, a variable forgetting factor recursive least squares (VFF-RLS) algorithm is proposed for the fundamental current amplitude identification, which guarantees fast and accurate preprocessing. Furthermore, the above method parallelly resolves the conflict between rapid extracting and low steady-state fluctuation in MRF, which significantly enhances harmonic current extraction performance. The superiority and accuracy of the proposed algorithms are proved by experiments. <fn fn-type="other" id="fn3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <p/></fn>

An Adaptive Peak Power Prediction Method for Power Lithium-Ion Batteries Considering Temperature and Aging Effects

The battery power state (SOP) is the basic indicator for the Battery management system (BMS) of the battery energy storage system (BESS) to formulate control strategies. Although there have been many studies on state estimation of lithium-ion batteries (LIBs), aging and temperature variation are seldom considered in peak power prediction during the whole life of the battery. To fill this gap, this paper aims to propose an adaptive peak power prediction method for power lithium-ion batteries considering temperature and aging is proposed. First, the Thevenin equivalent circuit model is used to jointly estimate the state of charge (SOC) and SOP of the lithium-ion power battery, and the variable forgetting factor recursive least squares (VFF-RLS) algorithm and extended Kalman filter (EKF) are utilized to identify the battery parameters online. Then, multiple constraint parameters including current, voltage, and SOC were derived, considering the dependence of the polarization resistance of the battery on the battery current. Finally, the verification experiment was carried out with LiFePO4 battery. The experimental results under FUDS operating conditions show that the maximum SOC estimation error is 1.94%. And the power prediction errors at 20%, 50%, and 70% SOC were 5.0%, 8.1% and 4.5%, respectively. Our further work will focus on the joint estimation of battery state to further improve the accuracy.

Chatter detection for micro milling considering environment noises without the requirement of dominant frequency

Existing chatter detection methods were mainly developed for conventional milling processes, and did not consider the influences of environment noises. Thus, they are not suitable for micro milling, in which the widely used small cutting parameters easily lead to the occurrence of non-negligible noises. This article proposes a new variable forgetting factor recursive least-squares (VFF-RLS) algorithm to filter out the chatter-independent component, which is composed of environment noises and periodic components, for the signals sampled from the micro milling process. It is theoretically found that with the aid of VFF-RLS algorithm, there is almost nothing in the filtered signal for stable cuts, while chatter components will be dominant in the filtered signal for unstable cuts. This important finding confirms that some features can be easily extracted from the filtered signal to directly reflect the stable or unstable machining states without the requirement to measure the system’s dominant frequency, which is necessary for some existing methods to obtain the frequency band where chatter vibrations appear. Subsequently, a streaming feature selection considering feature interaction (SFS-FI) method is established to select optimal features and remove irrelevant and redundant features. Then, a chatter detection model is developed based on the selected features. Finally, a series of micro milling tests with various axial depths of cut and spindle speeds prove that the proposed model can accurately identify the cutting state, even for slight chatter and stable cuts with small little depths of cut, which are more easily disturbed by environment noises. Results confirm that the detection accuracy is larger than 99 %, and this fact means that the proposed method is effective and practical for detecting chatter occurring in micro milling processes.

A Novel Digital Predistortion Identification Algorithm Based on Variable Forgetting Factor Recursive Least Square Method

The transmitting signal of wireless communication system is impaired by the nonlinearity of RF power amplifier (PA) which leads to signal distortion and spectrum spillover, by which the signal transmission quality is affected. Digital predistortion (DPD) is an efficient and economical way to correct the nonlinear effects of power amplifiers. The recursive least square (RLS) recognition algorithm is commonly used to extract the correction coefficients of the DPD model, and the accuracy of the extraction directly affects the system performance. In this paper, a new variable forgetting factor identification algorithm (new variable forgetting factor recursive least square, NVFFRLS) is proposed for recursive least square (RLS) identification algorithm. The 64-QAM signal is combined with a memory polynomial (MP) predistortion model for predistortion system simulation. The experimental results show that, compared with the RLS identification algorithm and two kinds of variable forgetting factor RLS identification algorithms, the algorithm has smaller estimation error, faster convergence, and better tracking capability, stability, and adaptability; the predistortion system based on NVFFRLS identification algorithm can compensate the nonlinear memory effects of power amplifier more effectively.

Analysis and Estimation of Internal Temperature Characteristics of Lithium-Ion Batteries in Electric Vehicles

To avoid thermal runaway in battery packs, it is necessary to estimate the internal temperature. Herein, the relationship between measurable electrical parameters and adjustable electrochemical parameters is first studied. Then, adjustable electrochemical parameters at different temperatures are rapidly calibrated. Based on this, an electrochemical-thermal coupling model is proposed. Second, the internal temperature field distribution is analyzed by the coupling model. It is found that the gradient of the radial temperature distribution is greater than that in the axial direction. Third, a radial thermodynamic reduced-order model is developed. The thermal parameters are calculated by the combination of the direct method and Variable Forgetting Factor Recursive Least Square (VFFRLS) algorithm. Finally, an internal temperature estimator based on the Kalman Filter algorithm is produced. Results show that the maximum estimated error is only 1.57 K under different working conditions. Furthermore, the results also validate the feasibility of thermal parameters obtained algorithm.

Lithium-ion battery health estimation with real-world data for electric vehicles

Complex environments and variable working conditions lead to irreversible attenuation of battery pack capacity in electric vehicles (EVs). Online capacity estimation is of great significance for battery pack management and maintenance. This work proposes a state-of-health (SOH) attenuation model considering driving mileage and seasonal temperature for battery health estimation. Firstly, a variable forgetting factor recursive least square (VFFRLS) algorithm is proposed for battery model parameter identification. It adaptively adjusts the forgetting factor according to current fluctuations. Then, an extended Kalman-particle filter (EPF) algorithm is proposed for online capacity estimation. In addition, a battery pack SOH attenuation model is constructed considering seasonal temperature and driving mileage. Finally, the performance of the proposed model and algorithm is verified with nine months of actual vehicle data. The experimental results show that the proposed parameter identification and capacity estimation algorithm can accurately estimate the model parameters and capacity. The average capacity of the battery module decreases with the total mileage. The compensation of monthly driving mileage and ambient temperature factors effectively improves the accuracy of SOH model.

Intelligent Vehicle Trajectory Tracking Control Based on VFF-RLS Road Friction Coefficient Estimation

This paper proposes an autonomous vehicle trajectory tracking system that fully considers road friction. When an intelligent vehicle drives at high speed on roads with different friction coefficients, the difficulty of its trajectory tracking control lies in the fast and accurate identification of road friction coefficients. Therefore, an improved strategy is designed based on traditional recursive least squares (RLS), which is utilized for accurate identification of the friction coefficient. First, the tire force and slip rate required for the estimation of the road friction coefficient by constructing the vehicle dynamics model and tire effective model are calculated. In this paper, a variable forgetting factor recursive least squares (VFF-RLS) method is proposed for the construction of the friction coefficient estimator. Second, the identified results are output to the model predictive controller (MPC) constructed in this paper as a way to improve tire slip angle constraints, to realize the trajectory tracking of the intelligent vehicle. Finally, the joint simulation test results of Carsim and Matlab/Simulink show that the trajectory tracking system based on the VFF-RLS friction coefficient estimator has outstanding tracking performance.

An Online Parameter Identification Method for Non-Solid Aluminum Electrolytic Capacitors

Aluminum electrolytic capacitors are the most commonly used components in circuit systems but are the weakest part of the systems. To make better use of this kind of components, it is crucial to monitor their status and parameter variations more accurately. This brief puts forward a prototype to test the frequency-dependent characteristics of the capacitors, both the capacitor voltage and current are acquired by using the prototype, while a variable forgetting factor recursive least square (VFF-RLS) method based scheme is applied to identify the capacitance (C) and the equivalent series resistance (ESR). Experiments are present by using the proposed scheme and the results of which are compared with the LCR meter measurement results. The extensive comparison results show that the relative error between experimental results and measurements are less than 5.03% which are acceptable compared with some other existing schemes and indicate that the proposed scheme is effective for the online parameter identification of Aluminum electrolytic capacitors.

An Adaptive Tracking-Extended Kalman Filter for SOC Estimation of Batteries with Model Uncertainty and Sensor Error

Accurate state of charge (SOC) plays a vital role in battery management systems (BMSs). Among several developed SOC estimation methods, the extended Kalman filter (EKF) has been extensively applied. However, EKF cannot achieve valid estimation when the model accuracy is inadequate, the noise covariance matrix is uncertain, and the sensor has large errors. This paper makes two contributions to overcome these drawbacks: (1) A variable forgetting factor recursive least squares (VFFRLS) is proposed to accomplish parameters identification. This method updates the forgetting factor according to the innovation sequence, which accuracy is superior to the forgetting factor recursive least squares (FFRLS); (2) an adaptive tracking EKF (ATEKF) is proposed to estimate the SOC of the battery. In ATEKF, the error covariance matrix is adaptively corrected according to the innovation sequence and correction factor. The value of the correction factor is related to the actual error. Proposed algorithms are validated with a publicly available dataset from the University of Maryland. The experimental results indicate that the identification error of VFFRLS can be reduced from 0.05% to 0.018%. Additionally, ATEKF has better accuracy and robustness than EKF when having large sensor errors and uncertainty of the error covariance matrix, in which case it can reduce SOC estimation error from 1.09% to 0.15%.

Parameter Identification of Lithium-ion Battery Equivalent Circuit Model Based on Limited Memory Recursive Least Squares Algorithm with Variable Forgetting Factor

Equivalent circuit method is the most widely used methodology in dynamic modeling of lithium-ion battery. An equivalent circuit with second-order RC network is used to model lithium-ion battery, and a limited memory recursive least square with variable forgetting factor (VFF-LMRLS) is proposed to identify the model parameters in this paper. Firstly, based on the current and voltage data measured from the battery cyclic discharging experiment, the VFF-LMRLS algorithm is used to identify the time-varying parameters of equivalent circuit model. Then, the model verification system is constructed by taking the average value of the identification results in the stable stage as the component parameter value of the equivalent circuit. Finally, through the comparative experiment and analysis with the variable forgetting factor RLS (VFFRLS), it is verified that the terminal voltage error of the proposed method is smaller, indicating that the identified model parameters are closer to the actual parameters.

A novel fuzzy adaptive cubature Kalman filtering method for the state of charge and state of energy co-estimation of lithium-ion batteries

The state of charge (SOC) and state of energy (SOE) are the key indices of the battery management system (BMS) of lithium-ion batteries. Based on the second-order resistor-capacitor equivalent circuit model and online parameter identification using variable forgetting factor recursive least square (VFF-RLS), a fuzzy adaptive controller is proposed to improve the convergence speed of the cubature Kalman filter (CKF) for the SOC estimation. Then, the estimated SOC with another fuzzy adaptive controller to correct the estimation and improve the accuracy of the SOE estimation of lithium-ion batteries. The feasibility of the proposed algorithm is verified using two different initial values and working conditions. The verification results show that under simple working conditions, the convergence time of the proposed algorithm for the estimated SOC is 15 s, and the maximum SOE estimation error is 0.0193. Under complex working conditions, the convergence speed of the SOC estimation is increased by 52.17%, and the maximum error of SOE estimation is 0.0463, which is 24.59% less than that of the SOE estimation by the traditional CKF algorithm. The proposed algorithm significantly improves the convergence speed of SOC estimation and the accuracy of SOE estimation, providing a reference for the radical application of lithium-ion batteries.

State of Charge Dual Estimation of a Li-ion Battery Based on Variable Forgetting Factor Recursive Least Square and Multi-Innovation Unscented Kalman Filter Algorithm

Battery management is the key technical link for electric vehicles. A good battery management system can realize the balanced charge and discharge of batteries, reducing the capacity degradation and the loss of health caused by battery overcharge and discharge, which all depend on the real-time and accurate estimation of the battery’s state of charge (SOC). However, the battery’s SOC has highly complex nonlinear time-varying characteristics related to the complex chemical and physical state and dynamic environmental conditions, which are difficult to measure directly, and this has become a difficulty in design and research. According to the characteristics of ternary lithium-ion batteries of electric vehicles, a battery SOC dual estimation algorithm based on the Variable Forgetting Factor Recursive Least Square (VFFRLS) and Multi-Innovation Unscented Kalman Filter (MIUKF) is proposed in this paper. The VFFRLS algorithm is used to estimate battery model parameters, and the MIUKF algorithm is used to estimate the battery’s SOC in real time. The two algorithms are coupled to update battery model parameters and estimate the SOC. The experiment results show that the algorithm has high accuracy and stability.

State of charge estimation for electric vehicle lithium-ion batteries based on model parameter adaptation

Accurate state of charge (SOC) estimation is the basis of the battery management system in electric vehicles. In order to reduce the influence of time-varying model parameters on SOC estimation accuracy for lithium-ion batteries under complex operating conditions, this paper proposes an improved method for online model parameter identification using variable forgetting factor recursive least squares (VFFRLS), which is based on the sliding window time-varying forgetting factor theory. The VFFRLS was used for online parameter identification at the macroscopic timescale, and extended Kalman filter (EKF) was used for estimating the battery SOC at the microscopic timescale. The accuracy of parameter identification was verified using pulsed discharging and urban dynamometer driving schedule (UDDS) tests, and recursive least squares (RLS) was used to identify the parameters of lithium-ion batteries under UDDS test and estimate the SOC of lithium-ion batteries in combination with EKF, and the experimental results verify the accuracy and robustness of VFFRLS-EKF.

Adaptive Notch Filter for Piezo-Actuated Nanopositioning System via Position and Online Estimate Dual-Mode.

Due to the excellent advantages of high speed, high precision, and driving force, piezoelectric actuators nanopositioning systems have been widely used in various micro/nanomachining fields. However, the inherent resonance dynamic of the nanopositioning system generated by the flexure-hinge greatly deteriorates the positioning performance and limits the closed-loop bandwidth. Even worse, the notch filter for eliminating the effect of resonance does not work due to the varying resonant frequency resulting from the external disturbance or mass load. To this end, an adaptive notch filter for piezo-actuated nanopositioning system via position and online estimate dual-mode (POEDM) has been proposed in this paper, which can estimate the varying resonant frequency in real-time and suppress the resonance to improve the closed-loop bandwidth. First, a novel variable forgetting factor recursive least squares (VFF-RLS) algorithm for estimating resonant frequency online is presented, which is robust to the noise and provides the performances of both fast tracking and stability. Then, a POEDM method is proposed to achieve the online identification of the resonant frequency in the presence of noise and disturbance. Finally, a series of validation simulations are carried out, and the results indicate that, the frequency of input signal and the bandwidth have been achieved up to 12.5% and 87.5% of the first resonant frequency, respectively.

A Novel Adaptive Multi-time Scale Joint Online Estimation Method for SOC and SOH of Lithiumion Batteries

The state of charge (SOC) and state of health (SOH) are essential indicators for estimating the performance of lithium-ion batteries. In most of the existing methods to estimate SOC and SOH through step-by-step calculation may bring obstacles to real-time prediction of battery performance. To adapt the complex and dynamic situation of the batteries and estimate SOC and SOH in an accurate and fast manner, a novel multi-time scale joint online estimation method is proposed. In order to quickly identify the battery model and estimate the battery state, SOC and SOH are evaluated on a multi time scale framework based on extended Kalman filter (EKF). To improve the accuracy of the equivalent circuit model (ECM), a variable forgetting factor recursive least square (VFFRLS) method is introduced to identify the internal parameters in the battery model. A fuzzy variable time scale EKF (FVEKF) is proposed to estimate SOC and SOH online, where the fuzzy inference engine change the time scale to increase the convergence speed especially in complex stress conditions. Database from the University of Maryland is adopted to testify the effectiveness and efficiency of the algorithm. The results demonstrate that the method has better estimation accuracy and efficiency comparing to traditional joint estimation method, and meet the requirements of real-time estimation.

Absolute finite differences based variable forgetting factor RLS algorithm

Adaptive signal processing requires an efficient non-stationarity detector. Most of the known non-stationarity detection algorithms are based on residual statistics. The study proposes a novel non-stationarity detection algorithm based on finite differences analysis of the processed signal. It also includes a suitable procedure for the forgetting factor design in the adaptation process. The performance of the proposed algorithm is experimentally compared with other known algorithms with regard to slow changes in signal stationarity as well as the influence of free coefficient selection on the quality of estimation. The developed algorithm exhibits the ability to effectively track both slow and abrupt changes in signal stationarity, with a small steady-state error. The coefficients that need to be set during the application of this algorithm are given intuitive physical meaning. Simulations show good resistance to low signal-to-noise ratio and abrupt changes in noise variance. The results also demonstrate estimation performance relative to the water level signal from a thermal power plant steam separator.

A Novel Method for Online Extraction of Small-Angle Scattering Pulse Signals from Particles Based on Variable Forgetting Factor RLS Algorithm.

The small-angle optical particle counter (OPC) can detect particles with strong light absorption. At the same time, it can ignore the properties of the detected particles and detect the particle size singly and more accurately. Reasonably improving the resolution of the low pulse signal of fine particles is key to improving the detection accuracy of the small-angle OPC. In this paper, a new adaptive filtering method for the small-angle scattering signals of particles is proposed based on the recursive least squares (RLS) algorithm. By analyzing the characteristics of the small-angle scattering signals, a variable forgetting factor (VFF) strategy is introduced to optimize the forgetting factor in the traditional RLS algorithm. It can distinguish the scattering signal from the stray light signal and dynamically adapt to the change in pulse amplitude according to different light absorptions and different particle sizes. To verify the filtering effect, small-angle scattering pulse extraction experiments were carried out in a simulated smoke box with different particle properties. The experiments show that the proposed VFF-RLS algorithm can effectively suppress system stray light and background noise. When the particle detection signal appears, the algorithm has fast convergence and tracking speed and highlights the particle pulse signal well. Compared with that of the traditional scattering pulse extraction method, the resolution of the processed scattering pulse signal of particles is greatly improved, and the extraction of weak particle scattering pulses at a small angle has a greater advantage. Finally, the effect of filter order in the algorithm on the results of extracting scattering pulses is discussed.