On-line Estimation Research Articles

Data-driven battery capacity estimation based on partial discharging capacity curve for lithium-ion batteries

An accurate maximum capacity estimation is critical to ensure the safety and reliability of lithium-ion batteries (LIBs). In this paper, we first investigate the relationship between discharging capacity corresponding to non-lower cutoff voltage and the maximum capacity based on which, a novel health indicator (HI) derived from the partial constant current discharging capacity curves is proposed. Unlike the previous work on incremental capacity (IC) curves, the capacity at equispaced voltage is extracted as the HI without the subjective differentiating or filtering process. It can be demonstrated that not only the HI and the area enclosed under the IC curve are homologous but also the HI is highly correlated with the maximum capacity by the Pearson correlation coefficient method. The Gaussian process regression (GPR) is employed to capture the mapping relationship between the HI and the maximum capacity. The proposed method is verified on a dataset generated from aging tests of eight 105 Ah batteries, performed under three different aging conditions. The results show that the maximum remaining capacity can be accurately estimated no matter the extrapolation estimation or the online estimation. Further, the influence of the training sample size and the voltage window length on the capacity estimation is also analyzed to evaluate the effectiveness and flexibility of the method. The maximum root mean square percentage error (RMSPE) is below 3.5 % in online capacity estimation only using the data within 10 mV. This method has been demonstrated well adapted to different voltage ranges, charging/discharging rates, and temperatures.

Impedance-Based Online Estimation of Nodal Inertia and Primary Frequency Regulation Capability

Accurate estimation of inertia and primary frequency regulation (PFR) capability is important to ensure frequency stability in low-inertia power systems. This paper investigates how the inertia and PFR capability of a power source node can be evaluated using a non-invasive online estimation method from the impedance perspective. Based on small perturbation injection, a novel approximate relationship between the impedance and corresponding frequency response transfer function (FR(s)) is deduced. The features of the FR(s)&#x2019;s magnitude response curve, i.e., resonance frequency and DC gain, are then used to develop an overall implementation framework for nodal inertia and PFR capability estimation in real time. This method provides new insights with respect to obtain the synchronous and non-synchronous converter interfaced generator&#x0027;s inertia constant and PFR capability for grid operators via impedance calculation and measurements. Case studies on a modified 9-bus system and NETS-NYPS 68-bus system demonstrate the effectiveness of the proposed impedance-based estimation approach.<fn id="fn4" fn-type="other"> This work was supported in part by the National Natural Science Foundation of China (52077066), in part by the Hunan Provincial Natural Science Foundation for Excellent Young Scholars (2020JJ3011), and in part by the Huxiang Young Talents Science and Technology Innovation Program (2020RC3015). (<i>Corresponding author: Yunfeng Wen</i>) W. Zhang and Y. Wen are with the College of Electrical and Information Engineering, Hunan University, Changsha 410082, China (e-mail: ; ). C. Y. Chung is with the Department of Electrical Engineering, The Hong Kong Polytechnic University, Hong Kong 999077, China (e-mail: C.Y.). </fn>

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.

Transport map Bayesian parameter estimation for dynamical systems

AbstractAccurate online state and parameter estimation of uncertain non‐linear dynamical systems is a demanding task that has been traditionally handled by adopting non‐linear Kalman Filters or particle filters. However, in case of Kalman filters the system needs to be linearised and for particle filters the computational demand can be high. Recent advances in optimal transport theory and the application to Bayesian model updating pave the way for other approaches to system and parameter identification. They also provide a way of formulating the problem in such a way that efficient online estimation for complex systems is possible. In this work, we investigate the properties of the transport map approach when compared to standard Markov Chain Monte Carlo in an off‐line setting as a first step towards on‐line parameter estimation. We apply both approaches to an analytical exponential model and a dynamical system with seven unknown parameters subjected to ground displacement. Details on the theory of transport maps and on the used MCMC algorithm are also given.

Human Compatible Stiffness Modulation of a Novel VSA for Physical Human-Robot Interaction

Due to intensive human-robot interaction in exoskeletons, it is desirable to design and control the exoskeletons with behavior compatible to human limbs to achieve natural and energy-efficient motion assistance. This requires both novel variable stiffness actuators and also technologies able to detect human muscle stiffness, upon which exoskeleton joint stiffness can be tuned. In this paper, a novel stiffness modulation method is proposed to achieve variable stiffness with respect to human status. The method is developed upon a novel actuator of nonlinear variable stiffness. Moreover, human joint stiffness is estimated innovatively from Force Myography (FMG) signals. The correlation between the recorded FMG and human joint stiffness is established with Machine Learning methods, which is further used for online estimation. An elbow joint exoskeleton is finally developed and tested. The results validate experimentally the methods for bionic compatible stiffness modulation.

Adaptive Intention-Driven Variable Impedance Control for Wearable Robots With Compliant Actuators

Understanding human motion intention is fundamental to wearable robots, which are designed to provide assistance by assessing the intention of wearers. Although modeling human motion intention during physical interaction reveals the fundamental properties of wearable robots, uncertainty and random noise are commonly neglected in existing works. This article presents an adaptive intention-driven variable impedance controller, where the online estimation of human motion intention is realized subject to physical interaction, stochastic distribution, and random disturbance. Specifically, human motion intention is estimated under a dual-channel structure and is represented as both the immediate desired position of the human limb and its predicted future position. A new variable impedance model is formulated from the estimated intention to regulate the dynamic interaction between the human and the robot. Such an impedance model is defined as the control objective achieved using the adaptive controller for wearable compliantly driven robots. The proposed formulation will be able to improve the estimation accuracy of human motion intention and will allow the robot to match the human’s action in a safe and efficient manner. The stability of the closed-loop system is rigorously proven from the stochastic perspective, and the experimental results on the compliantly driven exoskeleton robot are presented to validate the performance of the proposed controller.

Grey-box modeling for hot-spot temperature prediction of oil-immersed transformers in power distribution networks

Power transformers are one of the most costly assets in power grids. Due to increasing electricity demand and levels of distributed generation, they are more and more often loaded above their rated limits. Transformer ratings are traditionally set as static limits, set in a controlled environment with conservative margins. Through dynamic transformer rating, the rating is instead adapted to the actual working conditions of the transformers. This can help distribution system operators (DSOs) to unlock unused capacity and postpone costly grid investments. To this end, real-time information of the transformer operating conditions, and in particular of its hot-spot and oil temperature, is required. This work proposes a grey-box model that can be used for online estimation and forecasting of the transformer temperature. It relies on a limited set of non-intrusive measurements and was developed using experimental data from a DSO in Jutland, Denmark. The thermal model has proven to be able to predict the temperature of the transformers with a high accuracy and low computational time, which is particularly relevant for online applications. With a six-hour prediction horizon the mean average error was 0.4–0.6 °C. By choosing a stochastic data-driven modeling approach we can also provide prediction intervals and account for the uncertainty.

Adaptive Multi-Parameter Estimation of Inertial Stabilization Platform with Unknown Load

In order to improve the state monitoring and adaptive control capability of inertial stabilization platforms (ISPs) with unknown loads, it is necessary to estimate the dynamic parameters comprehensively online. However, most current online estimation methods regard the system as a linear dual-inertia model which neglects the backlash and nonlinear friction torque. It reduces the accuracy of the model and leads to incomplete and low accuracy of the estimated parameters. The purpose of this research is to achieve a comprehensive and accurate online estimation of multiple parameters of ISPs and lay a foundation for state monitoring and adaptive control of ISPs. First, a dual-inertia model containing backlash and nonlinear friction torque of the motor and load is established. Then, the auto-regressive moving average (ARMA) model of the motor and load is established by the forward Euler method, which clearly expresses the online identification formula of the parameters. On this basis, the adaptive identification method based on the recursive extended least squares (RELS) algorithm is used to realize the online estimation of multiple parameters. The simulation and experimental results show that the proposed adaptive multi-parameter estimation method can realize the simultaneous online identification of the moment of inertia of the load, the damping coefficient of motor and load, the transmission stiffness, the Coulomb friction torque of motor and load, and the backlash, and the steady-state error is less than 10%. Compared with the traditional linear dual-inertia model, the similarity between the model based on the proposed adaptive parameter estimation algorithm and the actual system is increased by 65.3%.

Inferring electrochemical performance and parameters of Li-ion batteries based on deep operator networks

Li-ion battery is a complex physicochemical system that generally takes observable current and terminal voltage as input and output, while leaving some unobservable quantities, e.g., Li-ion concentration, for serving as internal variables (states) of the system. On-line estimation for the unobservable states plays a key role in battery management system since they reflect battery safety and degradation conditions. Several kinds of models that map from current to voltage have been established for state estimation, such as accurate but inefficient physics-based models, and efficient but sometimes inaccurate equivalent circuit and black-box models. To realize accuracy and efficiency simultaneously in battery modeling, we propose to build a data-driven surrogate for a battery system while incorporating the underlying physics as constraints. In this work, we innovatively treat the functional mapping from current curve to terminal voltage as a composite of operators, which is approximated by the powerful deep operator network (DeepONet). Its learning capability is firstly verified through a predictive test for Li-ion concentration at two electrodes. In this experiment, the physics-informed DeepONet is found to be more robust than the purely data-driven DeepONet, especially in temporal extrapolation scenarios. A composite surrogate is then constructed for mapping current curve and solid diffusivity to terminal voltage with three operator networks, in which two parallel physics-informed DeepONets are firstly used to predict Li-ion concentration at two electrodes, and then based on their surface values, a DeepONet is built to give terminal voltage predictions. Since the surrogate is differentiable anywhere, it is endowed with the ability to learn from data directly, which was validated by using terminal voltage measurements to estimate input parameters. The proposed surrogate built upon operator networks possesses great potential to be applied in on-board scenarios, since it integrates efficiency and accuracy by incorporating underlying physics, and also leaves an interface for model refinement through a totally differentiable model structure.

Composite anti-disturbance control for ship dynamic positioning systems with thruster faults

Anti-disturbance control problem is studied for ship dynamic positioning systems with model uncertainties and ocean disturbances under thruster faults. For the ocean disturbance, a stochastic disturbance observer (SDO) is established to give the online estimation. For thruster faults, an adaptive law is used to evaluate, which is obtain from Lyapunov function. For model uncertainties, a robust control term with adaptive technology is used to attenuate it. Then, a composite anti-disturbance control (CADC) strategy is raised by combining disturbance observer-based control (DOBC), adaptive technology, and robust control term, which makes the position and yaw angle of ship reach the desired values. Finally, the simulation example proves the validity of the controller.

Online estimation approach of the steam specific enthalpy for wet steam turbines in nuclear power plants

Wet steam turbines are widely used in pressurized water reactor nuclear power plants. The specific enthalpy of the wet saturated steam is an indispensable variable for the thermodynamic balance and performance monitoring of the wet steam turbines, but it is rarely online measured in practice. In this study, a model-based online estimation approach of the steam specific enthalpy for the wet steam turbine in nuclear power plants is proposed. The wet steam turbine is divided into several stage groups. In each stage group, the steam expansion process, the moisture separation process, and the steam extraction process are captured in mechanism modeling at first. Then, by solving the model, the specific enthalpy and the dryness fraction of the wet saturated steam are obtained. Using the historical operation data of a 1000 MW pressurized water reactor unit, the model-based pseudo-online simulations and the measured data are compared which suggests a high accuracy of the proposed approach.

Accurate power sharing for islanded DC microgrids considering mismatched feeder resistances

Accurate load power sharing and bus voltage regulation are two critical control objectives for ensuring power quality and reliable operation of DC microgrids. Although regulating the DC Bus voltage can be achieved by adopting an external secondary control loop, inaccurate load power/current sharing among converters is a prominent issue due to feeder resistances mismatch. This can lead to undesired overloading of converters, triggering over-current protection relays, and potentially resulting in cascading failure of the whole system. Existing literature uses virtual resistance techniques to improve the power sharing accuracy; however, so far, no explicit relation between the values of the virtual resistances and the feeder resistances mismatch has been formulated, opening the possibility to enhance power sharing even further. Therefore, this paper proposes an accurate power sharing strategy in which the virtual resistances are chosen to account for the feeder resistances mismatch. The proposed technique relies on the optimal tuning of the virtual resistance assigned to the local controller of each converter. An online estimation algorithm of the physical feeder resistances, required for virtual resistance tuning, is embedded into the control loop of each converter. Thus, prior information about the feeder resistances in the design stage is not required. The proposed approach is validated through simulation and experimental results from a Hardware-in-the-Loop setup of a typical islanded DC microgrid. The results demonstrate the approach merits, achieving accurate power sharing among converters and ensuring robust operation, even in scenarios involving communication failures.

Multi-dimensional features based data-driven state of charge estimation method for LiFePO4 batteries

The flat open-circuit voltage (OCV) curve of LiFePO4 (LFP) batteries poses a significant challenge to state of charge (SOC) estimation. To solve this problem, this paper proposes a data-driven SOC estimation method based on multi-dimensional features, especially incorporating force signals. The significant force variation at the middle SOC region section compensates for the flat OCV problem. A long short-term memory (LSTM) neural network model is established to estimate SOC. Battery voltage, current, temperature, and force data sampled only in 5 s are taken as input. The proposed method is validated under different dynamic testing profiles and different temperatures. Experimental results indicate that this method can highly improve SOC estimation accuracy in the middle SOC region, with less than 0.5% root mean square errors and less than 2.5% maximum errors. The validation results at different temperatures also maintain high accuracy with the same model, showing strong robustness and excellent generalization performance. Additionally, the model training process of this method only takes 1.5 h, and the online estimation time is less than 1 s, considerably reducing time cost.

Robust Adaptive Control of Hypersonic Flight Vehicle With Aero-Servo-Elastic Effect

This paper investigates the notch filter based robust adaptive control for the longitudinal dynamics of flexible hyper- sonic flight vehicle using finite-time design and online estimation. Considering the aero-servo-elastic effect caused by the elastic vibration at sensor position, the recursive least-square algorithm is employed to track the natural frequencies of the flexible modes, which then be used as the center frequencies for the cascade-type notch filter. Based on the filtered signal, the robust adaptive control is studied where the neural network is used to handle aerodynamics uncertainty and the disturbance observer is employed to compensate flexible coupling. The prediction error is constructed for the update laws while the nonlinear function is further developed to achieve the finite-time tracking. The uniformly ultimately bounded stability is guaranteed under the proposed approach. The effectiveness of the design is illustrated through the simulation study.

Quantification of Physical and Numerical Mixing in a Coastal Ocean Model Using Salinity Variance Budgets

AbstractNumerical mixing, the spurious mixing primarily generated by the discretization of advection, is often significant in estuarine and coastal models due to sharp, energetic fronts. We compare on‐ and offline estimates of numerical mixing in a submesoscale‐resolving realistic simulation of the ocean state over the Texas‐Louisiana continental shelf. While offline estimates of numerical mixing differ from online estimates, offline methods may be the only analysis available. We use two methods to estimate numerical mixing offline based on the residuals of the salinity squared s2 and volume‐mean salinity variance budgets. The budget overestimates the time‐averaged online numerical mixing by 60% at hourly output. The s2 budget compares poorly due to large truncation errors associated with the tendency and advection terms. The residual of the s2 budget starts to converge to the budget as output frequency increases to 10 min—an unrealistic frequency for long‐term coastal ocean simulations—but neither method unconditionally converges to the online method and therefore cannot be recommended for generic analysis of numerical mixing. We also investigate the effects of horizontal resolution on numerical mixing using a two‐way nested grid with the online method. The volume‐integrated numerical mixing constitutes 57% of the bulk physical mixing—the mixing prescribed by the turbulence closure scheme—in the coarse model and may exceed the physical mixing by half an order of magnitude. We find numerical mixing is reduced by 35% on average in the nested model, likely due to new dynamical processes that emerge in the nested simulation.

Simultaneous Online Registration-Independent Stiffness Identification and Tip Localization of Surgical Instruments in Robot-assisted Eye Surgery.

Notable challenges during retinal surgery lend themselves to robotic assistance which has proven beneficial in providing a safe steady-hand manipulation. Efficient assistance from the robots heavily relies on accurate sensing of surgery states (e.g. instrument tip localization and tool-to-tissue interaction forces). Many of the existing tool tip localization methods require preoperative frame registrations or instrument calibrations. In this study using an iterative approach and by combining vision and force-based methods, we develop calibration- and registration-independent (RI) algorithms to provide online estimates of instrument stiffness (least squares and adaptive). The estimations are then combined with a state-space model based on the forward kinematics (FWK) of the Steady-Hand Eye Robot (SHER) and Fiber Brag Grating (FBG) sensor measurements. This is accomplished using a Kalman Filtering (KF) approach to improve the deflected instrument tip position estimations during robot-assisted eye surgery. The conducted experiments demonstrate that when the online RI stiffness estimations are used, the instrument tip localization results surpass those obtained from pre-operative offline calibrations for stiffness.

IGBT Junction Temperature Estimation Using a Dynamic TSEP Independent of Wire Bonding Faults

Despite that many temperature-sensitive electrical parameters (TSEPs) have been discovered for the online estimation of the junction temperature of IGBT devices, their wide adoption in the field is yet to come. This is because they are most susceptible to both the aging status and operating points of IGBTs, which can result in inaccurate results if not attended. In this study, a novel dynamic TSEP, the gate voltage undershoot <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">GE(np)</sub> of the complementary IGBT switch, is proposed. It is based on the crosstalk effect and measured during the turn- <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">off</small> switching transition of the controlled IGBT switch for its temperature estimation. Its monotonic temperature dependence has been identified with implications for the changing load current and bus voltage, which are experimentally verified using a 1200 V/450 A IGBT module. The theoretical analysis and experimental results also show that <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">GE(np)</sub> is independent of bond wire failures while providing comparatively high relative sensitivity. The MMC power equivalent experimental results are given to verify the feasibility of the proposed method in commercial engineering applications. Finally, the multivariate linear regression method is used to improve the ability to estimate the IGBT's temperature by accounting for the operating point.

A Dual Observer for Parameter-Free Encoderless Control of Doubly-Fed Reluctance Generators

A novel, cascaded model reference adaptive system (MRAS) observer design for speed and reactive power ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf{Q}$</tex-math></inline-formula> ) control of the emerging brushless doubly-fed reluctance generator (BDFRG) without a shaft position sensor, and no machine parameter knowledge, is proposed. The main advantages of the underlying estimation technique over the existing ones reported in the open literature are the intrinsic versatility, robustness, and accuracy, offering entirely decoupled torque (power) and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf{Q}$</tex-math></inline-formula> responses. The reference model of the rotor angular velocity and position MRAS observer is purely based on the current measurements of the converter-fed (secondary) winding, and its adaptive counterpart on the measured grid voltages and currents at line frequency. The latter requires the inductance ratio for calculations, the online estimates of which being generated by the supplementary MRAS observer working in parallel. Doing so, a complete machine parameter independence and stability of the scheme have been achieved, and its viability fully experimentally validated under variable loading conditions of the small-scale BDFRG wind turbine emulated in a laboratory environment.

Online frequency estimation of periodic disturbance based on FFT algorithm with application in repetitive control

In this paper, a new adaptive method is proposed for online frequency estimation of a periodic disturbance by the output measurement based on the fast Fourier transform algorithm. The performance of the proposed algorithm is evaluated in the face of time varying frequency, time varying amplitude, non-sinusoidal periodic disturbance, and different plants. Also, the convergence rate of the method is compared by other estimation methods. Then, the online estimation is used in the repetitive controller structure for eliminating periodic disturbances with unknown frequencies. A new analysis is performed on RC and the stability conditions are determined in a theorem. These are illustrated in simulation results. The effectiveness of this method is shown on the application of ϕ-shaped PZT active suspension and it is compared by existing results.

Multi-State Online Estimation of Lithium-Ion Batteries Based on Multi-Task Learning

Deep learning-based state estimation of lithium batteries is widely used in battery management system (BMS) design. However, due to the limitation of on-board computing resources, multiple single-state estimation models are more difficult to deploy in practice. Therefore, this paper proposes a multi-task learning network (MTL) combining a multi-layer feature extraction structure with separated expert layers for the joint estimation of the state of charge (SOC) and state of energy (SOE) of Li-ion batteries. MTL uses a multi-layer network to extract features, separating task sharing from task-specific parameters. The underlying LSTM initially extracts time-series features. The separated expert layer, consisting of task-specific and shared experts, extracts features specific to different tasks and shared features for multiple tasks. The information extracted by different experts is fused through a gate structure. Tasks are processed based on specific and shared information. Multiple tasks are trained simultaneously to improve performance by sharing the learned knowledge with each other. SOC and SOE are estimated on the Panasonic dataset, and the model is tested for generalization performance on the LG dataset. The Mean Absolute Error (MAE) values for the two tasks are 1.01% and 0.59%, and the Root Mean Square Error (RMSE) values are 1.29% and 0.77%, respectively. For SOE estimation tasks, the MAE and RMSE values are reduced by 0.096% and 0.087%, respectively, when compared with single-task learning models. The MTL model also achieves reductions of up to 0.818% and 0.938% in MAE and RMSE values, respectively, compared to other multi-task learning models. For SOC estimation tasks, the MAE and RMSE values are reduced by 0.051% and 0.078%, respectively, compared to single-task learning models. The MTL model also outperforms other multi-task learning models, achieving reductions of up to 0.398% and 0.578% in MAE and RMSE values, respectively. In the process of simulating online prediction, the MTL model consumes 4.93 ms, which is less than the combined time of multiple single-task learning models and almost the same as that of other multi-task learning models. The results show the effectiveness and superiority of this method.