Forgetting Factor Recursive Least Squares Research Articles

A simulation-driven prediction model for state of charge estimation of electric vehicle lithium battery

Accurately predicting the state of charge (SOC) of lithium-ion batteries in electric vehicles is crucial for ensuring their stable operation. However, the component values related to SOC in the circuit typically require estimation through parameter identification. This paper proposes a three-stage method for estimating the SOC of lithium batteries in electric vehicles. Firstly, the parameters of the constructed second-order RC circuit are identified using the Forgetting Factor Recursive Least Squares (FFRLS) method. Secondly, an innovative approach is employed to construct a battery simulation model using modal-data fusion method. Finally, the predicted values of the simulation model are corrected using the unscented Kalman filter (UKF). Validation through datasets demonstrates the high precision of this method in parameter identification. Moreover, in the comparison of SOC prediction corrections with Particle Filter (PF), Extended Kalman Filter (EKF), and the proposed UKF on simulated prediction data and experimental test data. The proposed method achieves the lowest root mean square error (RMSE) of 0.0025 for simulation prediction data and 0.0186 for experimental test data. It also maintained its error within 5 % on actual data.

State of charge estimation of electrical vehicle battery by Using Box Particle Filter Signal Tracking Method

ABSTRACT This paper concentrates on the effective study of the online state of charge (SoC) estimation of lithium-ion batteries used in electric vehicles (EVs). Box Particle filters (BPF) are commonly used in the estimation of multivariate systems under noisy environments. In this study, a Joint-estimator is proposed which uses the forgetting factor recursive least square (FF-RLS) method for the 1-RC battery model online parameter estimation and the lithium-ion battery SoC is estimated using battery terminal voltage signal tracking with (BPF). The implemented method is compared with a Sequential Importance Resampling Particle Filter (SIR-PF) which shows that the proposed BPF has reduced the number of particles and computational time and maintained the efficiency comparable to the SIR-PF. The BPF performance is further evaluated at assorted voltage signal tracking accuracy, the number of boxes and the initial dimension of the boxes. The BPF method requires less number of boxes as compared to the SIR-PF with compatible efficiency. Therefore, BPF can be used as an alternative to the complex algorithms used in the SoC estimation in battery management systems (BMS) of electric vehicles.

Joint Estimation of SOC and SOH for Lithium-Ion Batteries Based on Dual Adaptive Central Difference H-Infinity Filter

The accurate estimation of the state-of-charge (SOC) and state-of-health (SOH) of lithium-ion batteries is crucial for the safe and reliable operation of battery systems. In order to overcome the practical problems of low accuracy, slow convergence and insufficient robustness in the existing joint estimation algorithms of SOC and SOH, a Dual Adaptive Central Difference H-Infinity Filter algorithm is proposed. Firstly, the Forgetting Factor Recursive Least Squares (FFRLS) algorithm is employed for parameter identification, and an inner loop with multiple updates of the parameter estimation vector is added to improve the accuracy of parameter identification. Secondly, the capacity is selected as the characterization of SOH, and the open circuit voltage and capacity are used as the state variables for capacity estimation to improve its convergence speed. Meanwhile, considering the interaction between SOC and SOH, the state space equations of SOC and SOH estimation are established. Moreover, the proposed algorithm introduces a robust discrete H-infinity filter equation to improve the measurement update on the basis of the central differential Kalman filter with good accuracy, and combines the Sage–Husa adaptive filter to achieve the joint estimation of SOC and SOH. Finally, under Urban Dynamometer Driving Schedule (UDDS) and Highway Fuel Economy Test (HWFET) conditions, the SOC estimation errors are 0.5% and 0.63%, and the SOH maximum estimation errors are 0.73% and 0.86%, indicating that the proposed algorithm has higher accuracy compared to the traditional algorithm. The experimental results at different initial values of capacity and SOC demonstrate that the proposed algorithm showcases enhanced convergence speed and robustness.

Adaptive coordinated control strategy for improving shift quality under different operating conditions

In order to improve the shift quality of vehicles under different operating conditions (such as road resistance coefficient and throttle opening), this paper proposes an adaptive coordinated control strategy. This strategy utilizes a Forgetting Factor Recursive Least Squares (FFRLS) to achieve online identification of the road resistance coefficient. Based on the changes in throttle pedal opening and road resistance coefficient during the vehicle’s shifting process, the strategy adaptively adjusts the coordinated control parameter (fuel cut-off time) to achieve optimal control of vehicle shifting under different operating conditions. To evaluate the shift quality, shift jerk, friction work, torque peak, and shift time are used as performance indicators. Based on a constructed simulation model of the powertrain system, the influence of different operating conditions on the performance indicators is analyzed, and the effect of coordinated control parameters on improving shift quality under different operating conditions is compared. Corresponding fuzzy rules are then established to achieve adaptive adjustment of the coordinated control parameters through fuzzy control, ensuring effective improvement of shift quality for vehicles under different operating conditions.

A battery internal short circuit fault diagnosis method based on incremental capacity curves

The safe operation of battery energy storage systems (BESSs) has become one of the research priorities in this industry. And it is usually threated by various faults caused by design flaws, environmental conditions, and operating conditions et al. Among these faults, the internal short circuit (ISC) faults pose a significant threat to the safety of BESSs. Relevant studies focus on ISC fault diagnosis itself and ignore the impact of battery aging within the pack on fault diagnosis. To solve this problem, this paper proposes an ISC fault diagnosis method based on incremental capacity (IC) curves. And a qualitative differentiation between ISC batteries and aging ones is first achieved by leveraging the characteristic variations of IC curves. Then, an equivalent circuit model is constructed for ISC batteries. Further, a joint estimation of ISC resistance and SOC of the faulty battery is performed by combining Extended Kalman Filtering (EKF) and Forgetting Factor Recursive Least Squares (FFRLS). Finally, an experimental platform is established to verify the proposed method. Results show the proposed method can effectively differentiate between ISC batteries and aging batteries. Moreover, the estimation errors of SOC are less than 0.26% and the estimation accuracy of ISC resistance is more than 99.42%.

Robust state of charge estimation for lithium-ion batteries in variable temperatures using truncated singular value decomposition Cubature Kalman Filter algorithm

Advanced battery management systems play a significant role in the safe and efficient use of battery energy storage systems. While the accurate and reliable estimation of state of charge (SOC) is essential for improving the utilization efficiency of batteries and extending their service life. However, the working environment of battery energy storage systems is highly complex, and temperature changes can often affect the accuracy of modeling and estimation. The traditional methods of SOC estimation often ignore the changes in temperature of the whole system, thus resulting in the cumulative errors in SOC estimation. To address this problem, an improved method is proposed in this paper to estimate the SOC of lithium-ion batteries. It requires the use of Cubature Kalman Filter (CKF) algorithm that is based on Truncated Singular Value Decomposition (TSVD). Additionally, the Forgetting Factor Recursive Least Squares (FFRLS) method is used to determine the parameters of the Thevenin equivalent model for lithium batteries. This algorithm is then validated through simulation analysis and comparison with the experimental data obtained under cyclic operating conditions at a temperature of 5 ℃, 25 ℃, and 40 ℃, respectively. The results demonstrate that the proposed TSVD-CKF algorithm is accurate in reflecting the impact of ambient temperature on the model parameters and is applicable to SOC estimation in a wide range of temperatures, showing a strong robustness.

Selective Memory Recursive Least Squares: Recast Forgetting Into Memory in RBF Neural Network-Based Real-Time Learning.

In radial basis function neural network (RBFNN)-based real-time learning tasks, forgetting mechanisms are widely used such that the neural network can keep its sensitivity to new data. However, with forgetting mechanisms, some useful knowledge will get lost simply because they are learned a long time ago, which we refer to as the passive knowledge forgetting phenomenon. To address this problem, this article proposes a real-time training method named selective memory recursive least squares (SMRLS) in which the classical forgetting mechanisms are recast into a memory mechanism. Different from the forgetting mechanism, which mainly evaluates the importance of samples according to the time when samples are collected, the memory mechanism evaluates the importance of samples through both temporal and spatial distribution of samples. With SMRLS, the input space of the RBFNN is evenly divided into a finite number of partitions, and a synthesized objective function is developed using synthesized samples from each partition. In addition to the current approximation error, the neural network also updates its weights according to the recorded data from the partition being visited. Compared with classical training methods including the forgetting factor recursive least squares (FFRLS) and stochastic gradient descent (SGD) methods, SMRLS achieves improved learning speed and generalization capability, which are demonstrated by corresponding simulation results.

A hybrid on-line approach for predicting the energy consumption of electric buses based on vehicle dynamics and system identification

Energy consumption modeling for electric vehicles is conducive to achieving eco-driving optimization and alleviating driver ‘range anxiety’. However, it remains challenging due to the complexity of influencing factors. In this study, we propose a novel hybrid cumulative energy consumption (CEC) prediction approach by a combination of vehicle dynamics and the forgetting factor recursive least squares (FFRLS) to achieve real-time online forecasting accurately. The approach is developed with real-world data collected from over 983,000 frames across six electric buses in Guangzhou, China. To enhance the accuracy and practical application of the approach, we divide the data into segments as a unit of calculation for CEC. Subsequently, we constructed the model in three working conditions based on the vehicle longitudinal dynamics, and determined the parameters to be estimated for the model. With the help of the online learning capabilities of FFRLS algorithm, the estimated parameters can be constantly adjusted and updated according to the state of the buses. The results demonstrate that the mean absolute percentage error (MAPE) of the proposed method is 7.05 %. This performance surpasses that of existing relevant studies, indicating that the model provides a more accurate method for eco-driving and city-scale electric bus operation systems.

A novel genetic marginalized particle filter method for state of charge and state of energy estimation adaptive to multi-temperature conditions of lithium-ion batteries

Power lithium-ion batteries are widely used in various fields, the battery management system (BMS) is the main object of battery energy management and safety monitoring, so the accurate collaboration of state of charge (SoC) and state of energy (SoE) is estimated to be essential for the BMS system. In this work, a novel genetic marginal particle filter (GMPF) algorithm to estimate SoC and SoE accurately. The forgetting factor recursive least square (FFRLS) algorithm is used to identify the second-order Thevenin equivalent model parameter, and the genetic algorithm is used to improve the re-sampling process of the traditional particle filtering (PF) algorithm, according to the Rao-Blackwell theory in statistical science, the marginalization of part of the linear state variables during the calculation of particle filtering, the distribution of the post-test is similar to a single Gaussian distribution. The GMPF algorithm is verified under the conditions of the hybrid pulse power characteristic (HPPC) and the Beijing bus dynamic stress test (BBDST) with 15 °C, 25 °C, and 35 °C respectively, and experimental results show that the improved GMPF algorithm can effectively realize the collaborative estimation of the SoC and SoE of power lithium-ion batteries. The mean absolute error of SoC and SoE estimation is always less than 1.56 %, the root-mean-square error is always less than 1.58 %. And the GMPF algorithm is suitable for temperature environments of 15 °C to 35 °C.

State of Charge Estimation of Lithium-Ion Batteries Based on Vector Forgetting Factor Recursive Least Square and Improved Adaptive Cubature Kalman Filter

Accurate online parameter identification and state of charge (SOC) estimation are both very crucial for ensuring the operating safety of lithium-ion batteries and usually the former is a base of the latter. To achieve accurate and stable SOC estimation results, this paper proposes a model-based method, which incorporates a vector forgetting factor least square (VFFLS) algorithm and an improved adaptive cubature Kalman filter (IACKF). Firstly, considering it is difficult for the traditional forgetting factor recursive least square (FFRLS) algorithm to balance the accuracy, convergence, and stability for multiple parameters with different time-varying periods, an improved VFFLS method is employed to determine the multiple parameters of the first-order RC battery model online. It supersedes the single forgetting factor in the FFRLS with multiple forgetting factors in a vector form for improving adaptive capability to multiple time-varying parameters. Secondly, aiming at the fact that the standard cubature Kalman filter (CKF) cannot operate properly when the error covariance matrix is non-positive definite, which is caused by disturbance, initial error, and the limit of the computer word length, the UR decomposition rather than the Cholesky decomposition is applied, thus improving the algorithm stability. In addition, an adaptive update strategy is added to the CKF to enhance accuracy and convergence speed. Finally, comparative experiments with different operating patterns, positive and non-positive definite error covariance matrices, and temperatures are carried out. Experimental results showed that the proposed method can estimate the SOC accurately and stably.

Hydrostatic pressure adaptive dual-polarized model for state of charge estimation of lithium-ion batteries

Pressure-tolerated lithium-ion batteries have been used in autonomous underwater vehicle (AUV), due to their ability to withstand pressure directly and save structural parts that protect itself. As an important component of the battery, state of charge (SOC) is critical for evaluating the reliable operation of AUV batteries. The influence of hydrostatic pressure is not considered in typical SOC estimation process, which leads to a large deviation of terminal voltage estimation, and finally the accurate estimation of SOC cannot be realized. In this paper, a dual-polarized equivalent circuit model dependent on hydrostatic pressure is established, which fully considers the influence of pressure on the internal characteristic parameters of the battery. The characteristic parameters in the equivalent circuit model are measured at hydrostatic pressure and identified by forgetting factor recursive least squares (FFRLS). Compared with the blank model without considering hydrostatic pressure, the proposed model can capture voltage and SOC, which can contribute to the estimation accuracy of terminal voltage in a wide pressure range. The typical algorithms of unscented Kalman filter (UKF), cubature Kalman filter (CKF) and adaptive cubature Kalman filter (ACKF) are used to estimate the SOC based on the two models (OCV-SOC-Pressure and OCV-SOC) at different hydrostatic pressures. The results show that the accuracy of the SOC estimation algorithm under different hydrostatic pressure environments is improved, which is attributed to the compensation correction of the original OCV-SOC model. The root mean square error (RMSE) value of the ACKF algorithm based on the hydrostatic pressure adaptive multivariate regression model is 0.94 %, which significantly improves the SOC estimation effectiveness of the OCV-SOC model without considering the pressure factor (RMSE is 7.36 %) at the hydrostatic pressure of 60 MPa. At the preset different SOC initial values, the three algorithms based on the hydrostatic pressure adaptive multivariate regression model can achieve fast convergence, and ACKF shows the best environmental adaptability.

Research on a High-Precision State-of-Charge Estimation Method Based on Forgetting Factor Recursive Least Squares and Adaptive Extended Kalman Filter Applied to LiFePO4 Battery

The state-of-charge (SOC) estimation accuracy is closely associated with the estimation method and the battery parameter identification performance. The battery parameter identification method based on forgetting factor recursive least squares (FFRLS) has the advantages of high parameter identification accuracy and fast dynamic response speed. On this basis, the performance of two SOC estimation methods, the extended Kalman filter (EKF) and adaptive extended Kalman filter (AEKF) are compared and studied. The results show that AEKF has better steady-state and dynamic SOC estimation performance, but the estimation accuracy and dynamic response performance are still not objective. To further improve the performance of SOC estimation, a joint SOC estimation method based on FFRLS-AEKF is proposed, and the SOC estimation experimental results with FFRLS-AEKF and AEKF are conducted. The experimental results show that the proposed joint SOC estimation method based on FFRLS-AEKF has a better steady-state and dynamic performance of SOC estimation. The maximum absolute error of the proposed algorithm is 4.97%. As the battery working time increases, the SOC estimation accuracy continues to converge to the true value, and the average absolute error is reduced to 2.5%. The proposed method and theoretical analysis are proven to be correct and feasible.

Online Broadband Impedance Identification for Lithium-Ion Batteries Based on a Nonlinear Equivalent Circuit Model

Models play a crucial role in explaining internal processes, estimating states, and managing lithium-ion batteries. Electrochemical models can effectively illustrate the battery’s mechanism; however, their complexity renders them unsuitable for onboard use in electric vehicles. On the other hand, equivalent circuit models (ECMs) utilize a simple set of circuit elements to simulate voltage–current characteristics. This approach is less complex and easier to implement. However, most ECMs do not currently account for the nonlinear impact of operating conditions on battery impedance, making it difficult to obtain accurate wideband impedance characteristics of the battery when used in online applications. This article delves into the intrinsic mechanism of batteries and discusses the influence of nonstationary conditions on impedance. An ECM designed for non-steady state conditions is presented. Online adaptive adjustment of model parameters is achieved using the forgetting factor recursive least squares (FFRLS) algorithm and varied parameters approach (VPA) algorithm. Experimental results demonstrate the impressive performance of the model and parameter identification method, enabling the accurate acquisition of online impedance.

Online parameters identification and state of charge estimation for lithium-ion batteries based on improved central difference particle filter

Accurate SOC is of great significance to alleviate the endurance anxiety of electric vehicle drivers. To improve the accuracy of SOC estimation, a method of combining FFRLS and GPR for parameter identification and an improved particle filter for lithium battery SOC estimation are proposed. The proposed collaborative parameter identification method uses the forgetting factor recursive least squares (FFRLS) to identify the parameters in the middle and high SOC region. In the low SOC region, the parameters identified by the FFRLS are used as the training data of Gaussian process regression (GPR) for model parameter prediction to improve the parameter identification accuracy in the low SOC region; in the SOC estimation stage, the central difference Kalman filter is used to generate the importance density function to overcome the particle degradation, and the step size h of the central difference is calculated suboptimal to further improve the prediction accuracy. Finally, the proposed method is compared with other methods under different working conditions and different temperatures, and the effectiveness and adaptability of the proposed method are verified.

A Novel Fusion Method for State-of-Charge Estimation of Lithium-Ion Batteries Based on Improved Genetic Algorithm BP and Adaptive Extended Kalman Filter

The lithium-ion battery is the power source of an electric vehicle, so it is of great significance to estimate the state of charge (SOC) of lithium-ion batteries accurately to ensure vehicle safety. To improve the accuracy of the parameters of the equivalent circuit model for batteries, a second-order RC model for ternary Li-ion batteries is established, and the model parameters are identified online based on the forgetting factor recursive least squares (FFRLS) estimator. To improve the accuracy of SOC estimation, a novel fusion method, IGA-BP-AEKF, is proposed. Firstly, an adaptive extended Kalman filter (AEKF) is used to predict the SOC. Then, an optimization method for BP neural networks (BPNNs) based on an improved genetic algorithm (IGA) is proposed, in which pertinent parameters affecting AEKF estimation are utilized for BPNN training. Furthermore, a method with evaluation error compensation for AEKF based on such a trained BPNN is proposed to enhance SOC evaluation precision. The excellent accuracy and stability of the suggested method are confirmed by the experimental data under FUDS working conditions, which indicates that the proposed IGA-BP-EKF algorithm is superior, with the highest error of 0.0119, MAE of 0.0083, and RMSE of 0.0088.

Robustness Enhanced Predictive Control for Dual Three Phase PMSM with Duty Ratio Modulation and Parameter-Free Solution

The classical model predictive control not only relies on the motor model but also is sensitive to the system parameters. To improve the robustness of the model predictive control system, this article proposes a parameter-free predictive control for a dual three-phase PMSM with duty ratio modulation. First, the free-model theory is employed to reconstruct the prediction model of the motor, of which no parameters are needed. So, the problem of parameter mismatch between the motor and the inverter can be handled, and enhance the robustness of the system as well. Moreover, the ultra-local model is optimized with the forgetting factor recursive least-squares algorithm to improve the identification accuracy of the estimated value. Finally, the deadbeat duty ratio modulation solution is introduced to further improve operational performance while ensuring the robustness of the system. Simulation and experiment verify the feasibility and effectiveness of the proposed algorithm.

A Hybridization Grey Wolf Optimizer to Identify Parameters of Helical Hydraulic Rotary Actuator

Based on the grey wolf optimizer (GWO) and differential evolution (DE), a hybridization algorithm (H-GWO) is proposed to avoid the local optimum, improve the diversity of the population, and compromise the exploration and exploitation appropriately. The mutation and crossover principles of the DE algorithm are introduced into the GWO algorithm, and the opposition-based optimization learning technology is combined to update the GWO population to increase the population diversity. The algorithm is then benchmarked against nine typical test functions and compared with other state-of-the-art meta-heuristic algorithms such as particle swarm optimization (PSO), GWO, and DE. The results show that the proposed H-GWO algorithm can provide very competitive results. On this basis, the forgetting factor recursive least squares (FFRLS) method and the proposed H-GWO algorithm are combined to establish a parameter identification algorithm to identify parameters of the helical hydraulic rotary actuator (HHRA) with nonlinearity and uncertainty questions. In addition, the proposed method is verified by practical identification experiments. After comparison with the least squares (LS), recursive least squares (RLS), FFRLS, PSO, and GWO results, it can be concluded that the proposed method (H-GWO) has higher identification 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.

Parameter Identification Model and Capacity Analysis of Retired Power Battery

The accuracy and connection mode of the equivalent model of retired power battery cells will affect the size of the combined capacity. To this end, this article analyzes series-parallel combination capacity of retired power batteries. First, because an accurate single equivalent circuit model of retired power batteries is necessary for the capacity analysis of the combination, the forgetting factor recursive least squares (FFRLS) algorithm is used to identify the parameters of the model, and the second-order RC equivalent circuit is selected as the single equivalent circuit model of retired power battery. Then the equivalent circuit model is used as the basis, respectively constructing first-parallel-before-series and first-series-before-parallel power battery combination, and fully and unequally arranged the retired power batteries under the two assemblies. Finally, the capacity and distribution characteristics of the two combinations under different arrangements are verified by simulation. The results show that no matter how the arrangement is changed, the maximum capacity of the first-parallel-before-series retired power battery combination is always better than the first-series-before-parallel combination, and the distribution position of the single retired battery in both combinations under the maximum combination capacity is obtained.