Forgetting Factor Research Articles

SoC-Modified Core Temperature Estimation of Lithium-Ion Battery Based on Control-Oriented Electro-Thermal Model

Lithium-ion batteries and their control technologies are the key points to electrification and intelligence of transportation. Dynamic thermal management is one of the key technologies for intelligent battery management systems. Real-time monitoring of information about the temperature characteristics inside the battery is important for effective and safe thermal management. This paper firstly constructs a distributed control-oriented electro-thermal coupling model which contains multidimensional internal information about the cell. Based on the proposed model, improved parameter identification methods are used to construct offline database of model parameters. The electrical and thermal parameters are identified by applying recursive least squares with variable forgetting factor (VFFRLS) and particle swarm optimization (PSO) separately. Finally, a SoC-modified core temperature estimation method is proposed, which adopts discrete-time nonlinear observer (DNLO) to modify SoC and adapative Kalman filter (AKF) to estimate core temperature. The method takes into account the sensitivity of the output results to nonlinear, time-varying battery systems. The results show that the root-mean-square error (RMSE) of SoC estimation is 1.75 % and the mean absolute error (MAE) is 0.65 % for the proposed temperature method under wide temperature points (-5, 25, 45 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{\circ }$</tex-math></inline-formula> C). The proposed core temperature estimation method possesses better robustness and universality, with RMSE of 0.61 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{\circ }$</tex-math></inline-formula> C and MAE of 0.56 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^ {\circ }$</tex-math></inline-formula> C. Compared with the open-loop prediction method, the accuracy is improved about 0.5 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^ {\circ }$</tex-math></inline-formula> C under extreme loadfiles with uncertainty.

Sliding Mode Control of Ball Screw Meta-Action Unit Based on Disturbance Compensation and Inertia Identification

To solve the problems of dynamic model parameter perturbation and external disturbances during the operation of the ball screw meta-action unit, an adaptive sliding mode control method based on disturbance compensation and inertia identification is proposed in this paper. First, a model of the ball screw meta-action unit is established and the dynamic equation is derived. Taking into account the uncertainty of the dynamic parameters, a least squares method with a forgetting factor is introduced to identify the moment of inertia in real time, and the identification results are utilized to adaptively adjust the sliding mode control law. Second, a nonlinear disturbance observer is designed to effectively observe the load disturbance, and the observed value is substituted into the sliding mode control as feedforward compensation to improve the anti-interference ability of the controller. Committed to the chattering of traditional sliding mode control, an improved adaptive exponential sliding mode reaching law is exploited to construct a novel sliding mode controller, thereby suppressing the slid mode chattering more thoroughly. Finally, the superiority of the proposed method is verified by MATLAB/Simulink simulation and compared with the other two control methods; the control method proposed in this paper can effectively improve the tracking performance of the system and has good robustness.

Parameter and order estimation algorithms and convergence analysis for lithium‐ion batteries

AbstractThe fractional‐order equivalent circuit model can reflect the internal reaction mechanism of a lithium‐ion battery well. This article aims to design an effective model and optimization method to describe and analyze the operating characteristics of the lithium‐ion battery based on online measurement data. The fractional‐order controlled autoregressive model is derived by exploiting the memory superiorities of the fractional‐order, which comprises the electrochemical impedance spectroscopy and the ‐RC equivalent circuit model as the special cases. The utilization of polynomial properties reduces the difficulty of identification while preserving the ability of the controlled autoregressive model to fit the characteristics of the battery. To realize simultaneous parameter and the order estimation, a weighted gradient descent algorithm is proposed. The approach designs a new gradient direction and fully utilizes the data from the lithium‐ion battery by adding a suitable weighted factor. In addition, the forgetting factor is introduced to speed up convergence and produce more accurate parameter estimation. Furthermore, in order to analyze the convergence of the proposed algorithms, the convergence properties are proved by using martingale convergence theory and stochastic principle. Finally, the experimental simulation result shows the performance of the proposed algorithms.

Research on SOC estimation method of hybrid electric vehicles battery based on the grey wolf optimized particle filter

In this paper, we propose a method called grey wolf optimized particle filter (GWO-PF) to estimate the state of charge (SOC) of the power battery in hybrid electric vehicles (HEVs). The GWO-PF method combines the particle distribution mechanism with grey wolf optimization to achieve accurate SOC estimation. To begin, we compare four different equivalent circuit models of power batteries and select the second-order RC model (RC2 model) as our research focus. Next, we identify the parameters of the RC2 model online using the recursive least square method with a forgetting factor. Finally, we utilize the identified parameters to implement the GWO-PF method for SOC estimation. We compare the performance of the GWO-PF method with two other commonly used methods: the unscented Kalman filter (UKF) and the particle filter (PF). The results demonstrate that the GWO-PF method achieves high precision in SOC estimation, with a controllable relative error within 3.5%.

Joint estimation for SOC and capacity after current measurement offset redress with two-stage forgetting factor recursive least square method

Joint estimation for SOC and capacity after current measurement offset redress with two-stage forgetting factor recursive least square method

Unconventional Cardiovascular Risk Factors and Systematic Coronary Risk Estimation (SCORE) in the Lebanese Rural Population: The Forgotten Factors.

To evaluate the correlation between unconventional risk factors and the Systematic Coronary Risk Estimation (SCORE), and estimate the prevalence of conventional and unconventional cardiovascular (CV) risk factors in the rural Lebanese population in order to assess their CV risk. This is a retrospective descriptive study conducted between November 2017 and June 2019 among the Lebanese rural population. The risk factors were analyzed from the files of the patients who presented for the CV disease screening days organized by a non governmental organization. The CV risk estimation tool is the SCORE. The classification of socio-economic level ranges from zero (low level) to 3 (high level). A total of 433 patients were included. The prevalence of hypertension, diabetes, dyslipidemia, smoking, and metabolic syndrome was 45.1%, 31.2%, 39.2%, 50% and 42.9% respectively. Only 13.6% of hypertensive patients and 6.7% of diabetics were controlled. A total of 0 or 1 point for the classification of socio-economic status was found in 62.6% of cases. A family history of CV diseases was present in 87.3% of participants. The SCORE was correlated with diabetes and metabolic syndrome (p = 0.000), without being correlated to socio-economic status (HR = -0.104; p = 0.059) or to family history (p = 0.834). The socio-economic status and the family history of CV disease must be evaluated in addition to the classical risk calculation of the SCORE to better pinpoint the actual risk of the targeted population. The risk factors are prevalent but poorly controlled, hence the need for a national effort to ensure better care for the rural Lebanese population.

Deformation critical threshold estimation of Xiaowan ultrahigh arch dam with time-varying grey model

The structural behavior of the Xiaowan ultrahigh arch dam is primarily influenced by external loads and time-varying characteristics of dam concrete and foundation rock mass during long-term operation. According to overload testing with a geological model and the measured time series of installed perpendicular lines, the space and time evolution characteristics of the arch dam structure were analyzed, and its mechanical performance was evaluated. Subsequently, the deformation centroid of the deflective curve was suggested to indicate the magnitude and unique distribution rules for a typical dam section using the measured deformation values at multi-monitoring points. The ellipse equations of the critical ellipsoid for the centroid were derived from the historical measured time series. Hydrostatic and seasonal components were extracted from the measured deformation values with a traditional statistical model, and residuals were adopted as a grey component. A time-varying grey model was developed to accurately predict the evolution of the deformation behavior of the ultrahigh arch dam during future operation. In the developed model, constant coefficients were modified so as to be time-dependent functions, and the prediction accuracy was significantly improved through introduction of a forgetting factor. Finally, the critical threshold was estimated, and predicted ellipsoids were derived for the Xiaowan arch dam. The findings of this study can provide technical support for safety evaluation of the actual operation of ultrahigh arch dams and help to provide early warning of abnormal changes.

Parameter Estimation of Fractional Wiener Systems with the Application of Photovoltaic Cell Models

Fractional differential equations are used to construct mathematical models and can describe the characteristics of real systems. In this paper, the parameter estimation problem of a fractional Wiener system is studied by designing linear filters which can obtain smaller tunable parameters and maintain the stability of the parameters in any case. To improve the identification performance of the stochastic gradient algorithm, this paper derives two modified stochastic gradient algorithms for the fractional nonlinear Wiener systems with colored noise. By introducing the forgetting factor, a forgetting factor stochastic gradient algorithm is deduced to improve the convergence rate. To achieve more efficient and accurate algorithms, we propose a multi-innovation forgetting factor stochastic gradient algorithm by means of the multi-innovation theory, which expands the scalar innovation into the innovation vector. To test the developed algorithms, a fractional-order dynamic photovoltaic model is employed in the simulation, and the dynamic elements of this photovoltaic model are estimated using the modified algorithms. Concurrently, a numerical example is given, and the simulation results verify the feasibility and effectiveness of the proposed procedures.

Recursive identification of the time-varying frequency parameters of a space solar power satellite using a robust subspace tracking method based on the variable forgetting factor

Considering changes in the structural configuration caused by the rotation of solar panel arrays in space solar power satellites, this study proposes an improved robust recursive subspace tracking algorithm to identify the time-varying modal frequency parameters of the system. In this algorithm, variable forgetting factor and robust weight coefficient are involved to improve the tracking adaptability of time-varying system and decrease the influence of impulsive disturbance. Then, the time-varying pseudo modal frequency parameters are identified using the recursive projection subspace tracking. In the numerical simulations, the influence of the different rotation speeds of the solar panel arrays on the frequency identification results is studied. The computational results for the different rotation speeds reveal that the tracking performance of the proposed algorithm is better than that of the original method for time-varying system. Under the influence of impulsive disturbances, the relative values of the average relative error under the proposed algorithm are approximately 65.9–75.2% less than those under the original algorithm. Additionally, the results reveal that when the rotation speed of the solar panel arrays is time-varying, the proposed algorithm achieves a better tracking performance than the conventional recursive methods by the adjustment of the variable forgetting factor. When the signal-to-noise ratio is 15 dB, the absolute and relative values of the average relative error under the proposed algorithm are less by approximately 6.4% and 64.8%, respectively, under the two reference methods with a fixed forgetting factor.

Study on Multi-Mode Switching Control of Intelligent Suspension under Full Road Section

The safety, comfort, and energy feedback of active suspension in a single control mode is mutually restricted. To meet the needs of drivers and passengers for vehicle driving performance under different road conditions, this paper proposes a multi-mode switching control strategy of an intelligent suspension system, aiming at improving the stability and comfort of vehicles under different road conditions. In this paper, the adaptive Kalman filter algorithm with a forgetting factor is used to estimate the road input. The accuracy of the algorithm in estimating the road input is verified by simulation and experiment. The single-double threshold logic judgment method is used to formulate the switching rules between each working mode. In the controller, the PID control of the BP neural network and the LQR control optimized by GA are used to optimize and adjust the vehicle driving performance indexes in different modes, which effectively solves the problem of limited adaptability of suspension control optimization objectives under different road driving conditions. Based on the data from the vehicle acceleration sensor and road condition sensor, the modeling and simulation of the switching control system are carried out. The simulation results show that the designed control system can effectively improve the comprehensive performance of the vehicle under different road driving conditions. Compared with the traditional active suspension, the body acceleration is increased by 26% on the B-grade road surface, which effectively improves the user’s ride comfort. Compared with the traditional active suspension, the tire dynamic displacement is increased by 24% on the D-grade road, which can significantly improve the overall performance of the vehicle and meet the design requirements of the system.

A Hierarchical Identification Method for Lithium-Ion Battery SOC Based on the Hammerstein Model

Two-input one-output Hammerstein model consists of two parallel nonlinear static blocks followed by a linear dynamic part. By using Hammerstein structure to map relation between a battery State of Charge (SOC) and its terminal voltage/current, a hierarchical stochastic gradient algorithm is studied to estimate parameters of Hammerstein SOC model, so as to predict battery SOC. Firstly, the Hammerstein model is transformed into a bilinear parameter system with the least number of required parameters. Then, a hierarchical stochastic gradient algorithm with a forgetting factor is used to update the two sets of model parameters of the bilinear parameter system, so as to realize SOC estimation. Furthermore, the experiment platform of lithium-ion battery was built and the data of the urban dynamometer driving schedule (UDDS) profile and the Los Angeles 92 (LA92) profile were collected. Finally, the MATLAB simulation results show that the proposed parameter optimized method based Hammerstein model has the advantages of fast convergence speed and high SOC estimation accuracy.

High-precision State of Charge Estimation of Lithium-ion Batteries Based on Joint Compression Factor Particle Swarm Optimization-Forgetting Factor Recursive Least Square-Adaptive Extended Kalman Filtering

Accurate state of charge (SOC) estimation is an important basis for battery energy management and the applications of lithium-ion batteries. In this paper, an improved compression factor particle swarm optimization-forgetting factor recursive least square (CFPSO -FFRLS) algorithm is proposed, in which the forgetting factor is optimized to identify more accurate parameters for high-precision SOC estimation of lithium-ion battery. In order to improve the SOC estimation accuracy, a dual noise update link is introduced to the traditional extended Kalman filter (EKF), which enhances the algorithm’s ability to adapt to noise by updating the process and measurement noises in real time. The experimental results of parameter identification and SOC estimation show that the CFPSO-FFRLS algorithm proposed significantly improves the accuracy of parameter identification, and the joint CFPSO-FFRLS-AEKF algorithm can accurately estimate the SOC of lithium-ium battery under different working conditions. Under HPPC, BBDST and DST working conditions, the mean absolute errors of SOC estimation are 1.14%, 0.78% and 1.1%, which are improved by 42.71%, 65.79% and 39.56% compared with FFRLS-EKF algorithm, and the root mean square errors are 1.18%, 0.99% and 1.11%, improved by 44.86%, 65.98% and 51.74%, respectively.

Vehicle state estimation using a maximum likelihood based robust adaptive extended kalman filter considering unknown white Gaussian process and measurement noise signal

The stochastic nature of noise signals affects the vehicle’s internal states and the outputs, resulting in the difficulty in estimation. The unknown or time-varying nature of noise signals if not taken into account for estimation, the results will diverge and be highly deteriorated. In this paper, a maximum likelihood principle (MLP) based adaptive robust extended kalman filter for estimating the states of the adopted non-linear vehicle model is proposed. An observability test is done for the purpose of estimation. A covariance matching (CM) based robust adaptive high forgetting factor based fault tolerant technique is also employed on the robust adaptive extended and unscented kalman filters for comparison purpose. The Robustness of the filter is analyzed by varying the parameter of the vehicle through a local sensitivity analysis. The results show that the MLP based approach to the extended kalman filter performs well in three simulations for sinusoidal steering, Double Lance Change, J-Turn, Fishhook, Slalom maneuver in comparison to robust adaptive unscented kalman filter. Friction coefficient of 0.8 (dry road) and 0.4 (wet road) is chosen for the simulation. The sideslip angle RMSE value for MLP based estimation is obtained as 2.62e-05, 4.545e-06 for Sine and DLC maneuver.

Parameter identification of fractional‐order Wiener system based on FF‐ESG and GI algorithms

AbstractFractional‐order calculus has broad application scenarios in engineering and physics. Unlike integer‐order calculus, fractional‐order calculus has the ability to analyze nonclassical phenomena in science and engineering. For industrial processes with strong nonlinear characteristics, nonlinear models such as the Wiener model have become research hotspots. This paper studies the parameter identification of the fractional‐order Wiener system. In this paper, the forgetting factor extended stochastic gradient (FF‐ESG) algorithm and the gradient iterative (GI) algorithm are proposed to identify the parameters of the fractional‐order Wiener system. Then, the convergence of the FF‐ESG algorithm for the fractional‐order Wiener system is analyzed. Both proposed algorithms can obtain exact parameter estimates, which are verified by a numerical example and a case study of a fluid control valve.

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.

A novel combined online method for SOC estimation of a Li-Ion battery with practical and industrial considerations

Estimation of the state of charge (SOC) in the battery management systems (BMS) is very crucial. However, the BMS consistently suffers from inaccuracy of SOC estimation and high computational burden in industrial applications. Herein, we propose a novel combined SOC estimation approach with high accuracy, simplicity in implementation and, robustness that can be implemented on the low-cost microcontrollers. The basis of the method is to online identification the open circuit voltage (OCV) value of the battery simultaneously with other unknown parameters of the battery equivalent circuit model (ECM). Using this identified OCV, SOC is extracted from the OCV-SOC curve, directly. This direct method is an open-loop estimation method and tends to get lower SOC accuracy compared with known methods. To overcome this disadvantage, a combined method is proposed. Hence, to estimate SOC in this method, in the middle part of the OCV-SOC curve (linear part) and after identifying OCV from recursive least square algorithm (RLS) method with a forgetting factor, SOC is estimated directly via OCV-SOC curve. Furthermore, in the other parts of the curve especially non-linear parts, SOC is estimated with the EKF algorithm. In summary, not only estimation accuracy will increase, but also the computational burden of the EKF will decrease. In this paper, voltage and current samples of the battery at each sample time are the inputs of the algorithms and gained from the known “LA-92 dynamic driving cycle” test. To validate the efficiency of the presented method, results are compared with the EKF algorithm and direct method. The experimental results show that the proposed method reduces the EKF calculations by almost 15 % and guarantee high accuracy SOC estimation. The maximum error of the proposed method is <2.5 %.

Insulation fault monitoring of lithium-ion battery pack: Recursive least square with adaptive forgetting factor

The large-scale and high voltage of lithium-ion battery packs have brought severe challenges to the insulation performance of the system. An effective insulation fault diagnosis scheme is of great significance in ensuring the operation of the battery pack. In this work, a battery insulation detection scheme based on an adaptive filtering algorithm is proposed. Firstly, an insulation resistance detection scheme based on signal injection is designed. Then, an insulation resistance estimation algorithm based on the adaptive forgetting factor recursive least square (AFFRLS) algorithm is proposed, which uses fuzzy logic to adaptively correct the forgetting factor. Finally, the proposed insulation detection scheme is verified by four groups of experiments under different dynamic and static conditions. The experimental results show that the AFFRLS algorithm has a significant filtering effect and can suppress the influence of system noise and battery voltage fluctuation on the estimation results. The adaptive forgetting factor ensures the dynamic performance of the algorithm.

Improved lumped electrical characteristic modeling and adaptive forgetting factor recursive least squares-linearized particle swarm optimization full-parameter identification strategy for lithium-ion batteries considering the hysteresis component effect

Electric vehicles, as a new green mode of transportation, have put forward higher demand indicators for accurate modeling and efficient parameter identification strategies for lithium-ion batteries. In this paper, a lumped electrical characteristic model is constructed for lithium-ion batteries considering the hysteresis component effect based on a proposed adaptive forgetting factor recursive least squares-linearized particle swarm optimization (AFFRLS-LPSO) algorithm with strong working condition characterization capability for full parameter identification. First, to characterize the relationship accurately and intuitively between the external characteristics and the internal state quantities of the battery, the charging and discharging measurement information is captured, and the difference in the open circuit voltage (OCV) caused by the hysteresis phenomenon is resolved. Then, the complex working condition experiments is conducted, and through online inspection of experimental data, the fusion strategy concept is introduced to prevent the phenomenon of “filter saturation” and improve the ability of the algorithm to track the variable characteristic parameters of the battery. The full parameter identification results and terminal voltage tracking effects under different identification strategies are compared. Also, the consistency verification results of the adaptive parameter identification strategy under different working conditions are further analyzed. The experimental results show that the voltage tracking error of the model with an added hysteresis component is significantly smaller than the error without hysteresis. Furthermore, at an ambient temperature of 15 °C, the root mean squared error and mean absolute percentage error of the AFFRLS-LPSO algorithm are reduced by 0.0037 V and 0.300 %, respectively, under the dynamic stress test and Beijing bus dynamic stress test working conditions, and the consistency accuracy of the unconstrained parameter estimation is improved by 9.9 %. The fusion strategy provides a theoretical basis for real-time parameter identification models for lithium-ion batteries with high precision and adaptability for electric vehicles.

Parameter estimation of fractional‐order Hammerstein state space system based on the extended Kalman filter

SummaryThis paper addresses the combined estimation issues of the parameters and states for fractional‐order Hammerstein state space systems with colored noises. An extended state estimator is derived by using the parameter estimates to replace the unknown system parameters in Kalman filter. The hierarchical identification principle is introduced to solve the unknown parameters of measurement noises. By introducing the forgetting factor, an extended Kalman filtering‐based hierarchical forgetting factor stochastic gradient algorithm is presented to estimate the unknown states, parameters and fractional‐order. A numerical example is respectively presented to demonstrate the feasibility of the proposed identification algorithm. It can be seen that the estimation errors are relatively small, which reflects the proposed algorithms have good identification effect.