Forgetting Factor Recursive Research Articles

The novel methods of insulation detection based on Adaptive Levenberg–Marquardt algorithm and Third-Order Variable Forgetting Factor Recursive Least Squares-Decouple algorithm

Electric vehicles (EVs) are central to the future of automotive development, with high-voltage insulation performance critical for operational safety. Existing insulation detection methods face challenges such as limited scope, low accuracy, poor interference resistance, and slow response. This study introduces two insulation detection models based on the unbalanced bridge method and low-frequency signal injection, analyzing their theoretical effectiveness and confirming superior detection capability in the unbalanced bridge method. Furthermore, to address feedback voltage waveform issues in this method, an adaptive Levenberg–Marquardt (ALM) algorithm is proposed to prevent the divergence typically seen in traditional approaches. Additionally, a decoupling algorithm utilizing a Third-order Variable Forgetting Factor Recursive Least Squares (TVFF-Decouple) simplifies algorithm complexity significantly while enabling anomaly detection. Finally, AEKF and SRCKF algorithms were used for observation, identifying an optimal combination that reduces noise interference effectively. Simulations and bench tests demonstrate that the proposed methods swiftly and accurately detect positive and negative insulation resistances and equivalent Y capacitance under various conditions.

A novel hybrid electrochemical equivalent circuit model for online battery management systems

Accurate battery modeling and parameter identification play pivotal roles in ensuring safety and reliability across the entire battery life cycle. Equivalent circuit models (ECM) are convenient but do not represent physical characteristics well; in contrast, electrochemical models with strong physical meaning are hard to parameterizing in an online setting. To address these challenges, this paper introduces a novel hybrid electrochemical Equivalent Circuit Model (eECM), which integrates electrochemical processes into an ECM, representing slow-dynamic internal processes with a simplified representation of solid- and liquid-phase diffusion; fast-dynamics are represented by ECM terms. The model is supported by an Adaptive Extended Kalman Filter (AEKF) to manage battery state changes and mitigate noise. To enhance parameter identification, a Fisher information matrix-enhanced Variable Forgetting Factor Recursive Least Squares (Fisher-VFFRLS) approach is employed, guided by the Cramér–Rao bound for identifying the most sensitive data points directly from the discharge cycle. Electrochemical parameters are determined via post-charging rest via a Genetic Algorithm (GA). The proposed methodology is validated on three dynamic cycles—DST, US06, and FUDS-demonstrates the effectiveness of the proposed eECM and parameter identification strategy, with maximum Root Mean Square Error (RMSE) for terminal voltage and State of Charge (SoC) estimation below 0.0076 and 0.0122, respectively.

Identification of MIMO Nonlinear Gaussian Time-Varying System Based on Multi-Dimensional Taylor Network Multi-Level Approximation

Aiming at the problems of identification difficulties and low identification accuracy in modelling and identification of multiple-input multiple-output (MIMO) nonlinear Gaussian time-varying systems, this paper proposes an identification scheme based on the step-by-step approximation of multidimensional Taylor network (MTN). The aim of this paper is to improve the modelling of complex nonlinear systems so as to improve the prediction performance and control effect of the system. Different from the traditional multidimensional Taylor network identification method, this method adopts an order-by-order approximation strategy, which seeks its parameters sequentially from the lower order to the higher order, and continuously optimises the parameter weights during the parameter seeking process. Firstly, the nonlinear function model is approximated as a polynomial form by the order-by-order Taylor expansion, and then the weight parameters of each order of the Taylor expansion are calculated and updated step by step by using the algorithm based on the Variable Forgetting Factor Recursive Least Squares (VFF-RLS) method. Through iterative optimized of these parameters, dynamic weight assignment to each order of the Taylor expansion is achieved. A parameter-identified nonlinear function model is finally obtained, which can more accurately describe the dynamic behaviour and characteristics of the system. Finally, an arithmetic simulation is carried out through an example to verify the effectiveness of the proposed method.

Adaptive Dynamic Model-Based Path Following Controller Design for an Unmanned Surface Vessel

Abstract The effective design of a path following controller for Unmanned Surface Vessels (USVs) under uncertain influences induced by various factors such as environmental disturbances is a challenging task. In this study, we propose to ful?lling this task through taking benefits from an online parameter identi?cation technique, the discrete-time sliding mode control (DSMC) method, and the improved line of sight (LOS) algorithm. The Particle Swarm Optimization algorithm (PSO) was adopted to provide initial settings for the straightforward online identification method, i.e., the Forgetting Factor Recursive Least Square method (FFRLS). In order to handle the time-varying sideslip angle of a ship that exists in reality due to environmental disturbances, a multi-model course control scheme is proposed to improve the control performance. For this control scheme, a flexible selection mechanism in-between a heading angle or a course angle tracking controller based on the DSMC method is designed. A solution to ?xing the tracking deviation problem of the LOS guidance law is investigated for which the gradient descent method is introduced. A series of experiments are carried out at sea with a USV called Orca to verify and validate the proposed hybrid path following approach. The results showed that tracking errors mainly induced by environmental disturbances existed but the maximum magnitude among them was small enough and remaining within the acceptable range especially from the marine engineering point of view. These results, to a high degree, validated the robustness and precision of the proposed controller.

Online battery model parameters identification approach based on bias-compensated forgetting factor recursive least squares

Accuracy of a lithium-ion battery model is pivotal in faithfully representing actual state of battery, thereby influencing safety of entire electric vehicles. Precise estimation of battery model parameters using key measured signals is essential. However, measured signals inevitably carry random noise due to complex real-world operating environments and sensor errors, potentially diminishing model estimation accuracy. Addressing the challenge of accuracy reduction caused by noise, this paper introduces a Bias-Compensated Forgetting Factor Recursive Least Squares (BCFFRLS) method. Initially, a variational error model is crafted to estimate the average weighted variance of random noise. Subsequently, an augmentation matrix is devised to calculate the bias term using augmented and extended parameter vectors, compensating for bias in the parameter estimates. To assess the proposed method's effectiveness in improving parameter identification accuracy, lithium-ion battery experiments were conducted in three test conditions—Urban Dynamometer Driving Schedule (UDDS), Dynamic Stress Test (DST), and Hybrid Pulse Power Characterization (HPPC). The proposed method, alongside two contrasting methods—the offline identification method and Forgetting Factor Recursive Least Squares (FFRLS)—was employed for battery model parameter identification. Comparative analysis reveals substantial improvements, with the mean absolute error reduced by 25%, 28%, and 15%, and the root mean square error reduced by 25.1%, 42.7%, and 15.9% in UDDS, HPPC, and DST operating conditions, respectively, when compared to the FFRLS method.

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.

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.

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 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.

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.

State of health estimation of the LiFePO4 power battery based on the forgetting factor recursive Total Least Squares and the temperature correction

The decline of the lithium-ion power battery's State of Health (SOH) with usage significantly impacts other state estimation results, such as State of Charge (SOC). Hence, accurate estimation of the lithium-ion power battery's SOH holds vital importance in the battery management system. This paper proposes a SOH estimation method for the lithium-ion power battery, utilizing the Forgetting Factor Recursive Total Least Squares (FFRTLS) and incorporating the temperature correction. The FFRTLS effectively addresses the SOC estimation errors and the terminal current measurement noise simultaneously. The temperature correction method, based on the Arrhenius equation, corrects the influence of the ambient temperature during the SOH estimation process, ensuring that the ambient temperature does not affect the accuracy of the SOH estimation results. Additionally, the capacity convergence coefficient enhances the reliability of the SOH estimation results by preventing abrupt changes of the maximum available capacity. Experimental results on a LiFePO4 power battery under diverse working conditions and varying ambient temperatures, validate the effectiveness of the proposed method. The evaluation indexes, including Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Maximum Absolute Error (Max-AE), demonstrate the high accuracy of the SOH estimation results, with all indexes below 0.21%, 0.25% and 0.35% respectively.

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.

Improved Backward Smoothing—Square Root Cubature Kalman Filtering and Variable Forgetting Factor—Recursive Least Square Modeling Methods for the High-Precision State of Charge Estimation of Lithium-Ion Batteries

Accurate lithium-ion battery charge state estimation is crucial for battery management systems. Modeling of dual polarization—electrical equivalent circuit based on ternary lithium batteries as a research object, a variable forgetting factor recursive least square method is proposed for parameter identification given the insufficient tracking ability of the traditional recursive least squares method for abrupt and time-varying signals in a non- stationary environment. A backward smoothing square root cubature Kalman filtering algorithm is applied to enhance the accuracy and convergence speed of SOC estimation. The algorithm uses the square root update to ensure the numerical stability of the filtering and uses the idea of backward smoothing-forward filtering to improve the filtering accuracy on the basis of the first forward filtering. Finally, variable forgetting factor recursive least square is combined with backward smoothing square root cubature Kalman filtering to achieve the joint estimation of model parameters and state of charge, and the feasibility of the battery state of charge estimation is verified in different working conditions. The simulation results show that the variable forgetting factor recursive least square-backward smoothing square root cubature Kalman filter algorithm improves the study’s filtering accuracy and convergence speed of lithium-ion batteries.

An Ultrafast Variable Forgetting Factor Recursive Least Square Method for Determining the State-of-Health of Li-Ion Batteries

An Ultrafast Variable Forgetting Factor Recursive Least Square Method for Determining the State-of-Health of Li-Ion Batteries

A Novel Multi-Constraint Peak Power Prediction Method Combined with Online Model Parameter Identification and State-of-Charge Co-Estimation of Lithium-Ion Batteries

The accuracy of the peak power is influenced by the accurate battery model, the results of the parameter identification, and the state of charge (SOC). First, to accurately predict the peak power of lithium-ion batteries, this paper proposes an improved Thevenin model to describe the operating state of lithium-ion batteries by introducing model noise into the Thevenin model. Second, to achieve accurate online parameter identification, a Forgetting Factor Recursive Extended Least Squares (FFRELS) method is proposed to identify the parameters of the improved model. To optimize the effect of noise on SOC estimation, an improved adaptive extended Kalman filtering (AEKF) algorithm is proposed. Finally, to obtain higher accuracy of peak power estimation, a multi-constrained peak power prediction method based on state-recursive estimation is used in this paper. Experimental results show that the maximum error of the FFRELS algorithm under different working conditions is 34.35 mV, and the SOC estimation error of the improved AEKF algorithm is less than 0.53%. The improved multi-constraint peak power estimation algorithm has high estimation accuracy under two complex working conditions, and can accurately predict the power input and output capability of the battery.