Combining Non-Parametric and Parametric Models for Stable and Computationally Efficient Battery Health Estimation

2020 ◽  
Author(s):  
Antti Aitio ◽  
David Howey
Keyword(s):  
Latent Variables ◽  
Linear Time ◽  
Full Range ◽  
Real Life ◽  
Internal Resistance ◽  
State Of Charge ◽  
Parametric Models ◽  
Model Parameters ◽  
Battery Management ◽  
Resistance Change

Abstract Equivalent circuit models for batteries are commonly used in electric vehicle battery management systems to estimate state of charge and other important latent variables. They are computationally inexpensive, but suffer from a loss of accuracy over the full range of conditions that may be experienced in real-life. One reason for this is that the model parameters, such as internal resistance, change over the lifetime of the battery due to degradation. However, estimating long term changes is challenging, because parameters also change with state of charge and other variables. To address this, we modelled the internal resistance parameter as a function of state of charge and degradation using a Gaussian process (GP). This was performed computationally efficiently using an algorithm [1] that interprets a GP to be the solution of a linear time-invariant stochastic differential equation. As a result, inference of the posterior distribution of the GP scales as 𝒪(n) and can be implemented recursively using a Kalman filter.

scholarly journals Lithium-Ion Battery Parameters and State of Charge Joint Estimation Using Bias Compensation Least Squares and the Alternate Algorithm

2020 ◽  
Vol 2020 ◽  
pp. 1-16 ◽  
Author(s):  
Wei Xiong ◽  
Yimin Mo ◽  
Cong Yan
Keyword(s):  
Least Squares ◽  
Computational Efficiency ◽  
High Accuracy ◽  
State Of Charge ◽  
Joint Estimation ◽  
Model Parameters ◽  
Battery Management System ◽  
Battery Management ◽  
Soc Estimation ◽  
Bias Compensation

For safe and efficient operation of electric vehicles (EVs), battery management system is essential. Nevertheless, a challenge lying in battery management systems is how to obtain an algorithm for state of charge (SOC) estimation that has both high accuracy and low computational cost. For this purpose, the battery parameters and SOC joint estimation algorithm based on bias compensation least squares and alternate (BCLS-ALT) algorithm are proposed in this paper. The battery model parameters are identified online using the bias compensation least squares (BCLS), while the SOC is estimated applying the alternate (ALT) algorithm, which can switch the computational logic between H-infinity filter (HIF) and ampere-hour integral (AHI) to improve the computational efficiency and accuracy. The experimental results show that the accuracy of the SOC estimated by the BCLS-ALT algorithm is the highest, and the computational efficiency is also high, with the switching threshold SOCALT being set to 25%. Despite the 20% initial error and the 10% current drift, the proposed BCLS-ALT algorithm can obtain high accuracy and robustness of SOC estimation under different ambient temperatures and dynamic load profiles.

scholarly journals A New Extended Model with Bathtub-Shaped Failure Rate: Properties, Inference, Simulation and Applications

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2024
Author(s):  
Alya Al Al Mutairi ◽  
Muhammad Z. Iqbal ◽  
Muhammad Z. Arshad ◽  
Badr Alnssyan ◽  
Hazem Al-Mofleh ◽  
...  
Keyword(s):  
Applied Sciences ◽  
Real Life ◽  
Parametric Models ◽  
Model Parameters ◽  
Extended Model ◽  
Censored Samples ◽  
Real Life Data ◽  
Rate Functions ◽  
Competing Models ◽  
Likelihood Approach

Theoretical and applied researchers have been frequently interested in proposing alternative skewed and symmetric lifetime parametric models that provide greater flexibility in modeling real-life data in several applied sciences. To fill this gap, we introduce a three-parameter bounded lifetime model called the exponentiated new power function (E-NPF) distribution. Some of its mathematical and reliability features are discussed. Furthermore, many possible shapes over certain choices of the model parameters are presented to understand the behavior of the density and hazard rate functions. For the estimation of the model parameters, we utilize eight classical approaches of estimation and provide a simulation study to assess and explore the asymptotic behaviors of these estimators. The maximum likelihood approach is used to estimate the E-NPF parameters under the type II censored samples. The efficiency of the E-NPF distribution is evaluated by modeling three lifetime datasets, showing that the E-NPF distribution gives a better fit over its competing models such as the Kumaraswamy-PF, Weibull-PF, generalized-PF, Kumaraswamy, and beta distributions.

Comprehensive Battery Equivalent Circuit Based Model for Battery Management Application

2013 ◽  
Author(s):  
Shijie Tong ◽  
Matthew P. Klein ◽  
Jae Wan Park
Keyword(s):  
Equivalent Circuit ◽  
Life Time ◽  
State Of Charge ◽  
Model Parameters ◽  
Battery Management System ◽  
Battery Management ◽  
Computationally Efficient ◽  
Battery Model ◽  
Battery State Of Charge ◽  
Dependent Model

This paper presents a comprehensive control oriented battery model. Described first is an equivalent circuit based battery model which captures particular battery characteristics of control interest. Then, the model categorizes the battery dynamics based on their different time constants (transient, long-term, life-time). This model uses a 2-D map representing the temperature and state-of-charge dependent model parameters. Also, the model uses new battery state-of-charge and state-of-health definitions that are more practical for a real battery management system. Battery testing and simulation on various types of batteries and use scenarios was completed to validate that the model is easy to parameterize, computationally efficient and of adequate accuracy.

scholarly journals A Novel Adaptive Function—Dual Kalman Filtering Strategy for Online Battery Model Parameters and State of Charge Co-Estimation

Energies ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 2268
Author(s):  
Yongcun Fan ◽  
Haotian Shi ◽  
Shunli Wang ◽  
Carlos Fernandez ◽  
Wen Cao ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Unscented Kalman Filter ◽  
Initial Period ◽  
Lithium Ion ◽  
Estimation Algorithm ◽  
Maximum Error ◽  
Internal Resistance ◽  
State Of Charge ◽  
Model Parameters ◽  
The Difference

This paper aims to improve the stability and robustness of the state-of-charge estimation algorithm for lithium-ion batteries. A new internal resistance-polarization circuit model is constructed on the basis of the Thevenin equivalent circuit to characterize the difference in internal resistance between charge and discharge. The extended Kalman filter is improved through adding an adaptive noise tracking algorithm and the Kalman gain in the unscented Kalman filter algorithm is improved by introducing a dynamic equation. In addition, for benignization of outliers of the two above-mentioned algorithms, a new dual Kalman algorithm is proposed in this paper by adding a transfer function and through weighted mutation. The model and algorithm accuracy is verified through working condition experiments. The result shows that: the errors of the three algorithms are all maintained within 0.8% during the initial period and middle stages of the discharge; the maximum error of the improved extension of Kalman algorithm is over 1.5%, that of improved unscented Kalman increases to 5%, and the error of the new dual Kalman algorithm is still within 0.4% during the latter period of the discharge. This indicates that the accuracy and robustness of the new dual Kalman algorithm is better than those of traditional algorithm.

scholarly journals Parameter Identification and State-of-Charge Estimation for Lithium-Ion Batteries Using Separated Time Scales and Extended Kalman Filter

Energies ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 1054
Author(s):  
Kuo Yang ◽  
Yugui Tang ◽  
Zhen Zhang
Keyword(s):  
Kalman Filter ◽  
Parameter Identification ◽  
Open Circuit Voltage ◽  
Lithium Ion ◽  
Open Circuit ◽  
State Of Charge ◽  
Recursive Least Squares ◽  
Model Parameters ◽  
Soc Estimation ◽  
Battery Model

With the development of new energy vehicle technology, battery management systems used to monitor the state of the battery have been widely researched. The accuracy of the battery status assessment to a great extent depends on the accuracy of the battery model parameters. This paper proposes an improved method for parameter identification and state-of-charge (SOC) estimation for lithium-ion batteries. Using a two-order equivalent circuit model, the battery model is divided into two parts based on fast dynamics and slow dynamics. The recursive least squares method is used to identify parameters of the battery, and then the SOC and the open-circuit voltage of the model is estimated with the extended Kalman filter. The two-module voltages are calculated using estimated open circuit voltage and initial parameters, and model parameters are constantly updated during iteration. The proposed method can be used to estimate the parameters and the SOC in real time, which does not need to know the state of SOC and the value of open circuit voltage in advance. The method is tested using data from dynamic stress tests, the root means squared error of the accuracy of the prediction model is about 0.01 V, and the average SOC estimation error is 0.0139. Results indicate that the method has higher accuracy in offline parameter identification and online state estimation than traditional recursive least squares methods.

scholarly journals Robustness and Sensitivity Tuning of the Kalman Filter for Speech Enhancement

Signals ◽  
2021 ◽  
Vol 2 (3) ◽  
pp. 434-455
Author(s):  
Sujan Kumar Roy ◽  
Kuldip K. Paliwal
Keyword(s):  
Kalman Filter ◽  
Speech Enhancement ◽  
Linear Prediction ◽  
Real Life ◽  
Model Parameters ◽  
Noise Variance ◽  
Noisy Speech ◽  
Kalman Gain ◽  
Whitening Filter ◽  
Prediction Coefficient

Inaccurate estimates of the linear prediction coefficient (LPC) and noise variance introduce bias in Kalman filter (KF) gain and degrade speech enhancement performance. The existing methods propose a tuning of the biased Kalman gain, particularly in stationary noise conditions. This paper introduces a tuning of the KF gain for speech enhancement in real-life noise conditions. First, we estimate noise from each noisy speech frame using a speech presence probability (SPP) method to compute the noise variance. Then, we construct a whitening filter (with its coefficients computed from the estimated noise) to pre-whiten each noisy speech frame prior to computing the speech LPC parameters. We then construct the KF with the estimated parameters, where the robustness metric offsets the bias in KF gain during speech absence of noisy speech to that of the sensitivity metric during speech presence to achieve better noise reduction. The noise variance and the speech model parameters are adopted as a speech activity detector. The reduced-biased Kalman gain enables the KF to minimize the noise effect significantly, yielding the enhanced speech. Objective and subjective scores on the NOIZEUS corpus demonstrate that the enhanced speech produced by the proposed method exhibits higher quality and intelligibility than some benchmark methods.

scholarly journals Adaptive State-of-Charge Estimation for Lithium-Ion Batteries by Considering Capacity Degradation

Electronics ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 122
Author(s):  
Peipei Xu ◽  
Junqiu Li ◽  
Chao Sun ◽  
Guodong Yang ◽  
Fengchun Sun
Keyword(s):  
Equivalent Circuit Model ◽  
Lithium Ion ◽  
Maximum Error ◽  
State Of Charge ◽  
Recursive Least Squares ◽  
Accurate Estimation ◽  
Model Parameters ◽  
Soc Estimation ◽  
Capacity Degradation ◽  
Battery Capacity

The accurate estimation of a lithium-ion battery’s state of charge (SOC) plays an important role in the operational safety and driving mileage improvement of electrical vehicles (EVs). The Adaptive Extended Kalman filter (AEKF) estimator is commonly used to estimate SOC; however, this method relies on the precise estimation of the battery’s model parameters and capacity. Furthermore, the actual capacity and battery parameters change in real time with the aging of the batteries. Therefore, to eliminate the influence of above-mentioned factors on SOC estimation, the main contributions of this paper are as follows: (1) the equivalent circuit model (ECM) is presented, and the parameter identification of ECM is performed by using the forgetting-factor recursive-least-squares (FFRLS) method; (2) the sensitivity of battery SOC estimation to capacity degradation is analyzed to prove the importance of considering capacity degradation in SOC estimation; and (3) the capacity degradation model is proposed to perform the battery capacity prediction online. Furthermore, an online adaptive SOC estimator based on capacity degradation is proposed to improve the robustness of the AEKF algorithm. Experimental results show that the maximum error of SOC estimation is less than 1.3%.

A GAMMA MOVING AVERAGE PROCESS FOR MODELLING DEPENDENCE ACROSS DEVELOPMENT YEARS IN RUN-OFF TRIANGLES

2020 ◽  
pp. 1-22
Author(s):  
Luis E. Nieto-Barajas ◽  
Rodrigo S. Targino
Keyword(s):  
Latent Variables ◽  
Moving Average ◽  
Real Data ◽  
Model Parameters ◽  
Average Process ◽  
Moving Average Process ◽  
Data Set ◽  
Run Off ◽  
Average Form ◽  
Reserve Estimates

ABSTRACT We propose a stochastic model for claims reserving that captures dependence along development years within a single triangle. This dependence is based on a gamma process with a moving average form of order $p \ge 0$ which is achieved through the use of poisson latent variables. We carry out Bayesian inference on model parameters and borrow strength across several triangles, coming from different lines of businesses or companies, through the use of hierarchical priors. We carry out a simulation study as well as a real data analysis. Results show that reserve estimates, for the real data set studied, are more accurate with our gamma dependence model as compared to the benchmark over-dispersed poisson that assumes independence.

scholarly journals Modeling Northern Hemisphere Summer Heat Extreme Changes and Their Uncertainties Using a Physics Ensemble of Climate Sensitivity Experiments

2006 ◽  
Vol 19 (17) ◽  
pp. 4418-4435 ◽  
Author(s):  
Robin T. Clark ◽  
Simon J. Brown ◽  
James M. Murphy
Keyword(s):  
Structural Changes ◽  
Heat Waves ◽  
Full Range ◽  
Daily Maximum ◽  
Model Parameters ◽  
Mean Values ◽  
Summer Heat ◽  
Modeling Uncertainties ◽  
Physics Ensemble ◽  
Projected Changes

Abstract Changes in extreme daily temperature events are examined using a perturbed physics ensemble of global model simulations under present-day and doubled CO2 climates where ensemble members differ in their representation of various physical processes. Modeling uncertainties are quantified by varying poorly constrained model parameters that control atmospheric processes and feedbacks and analyzing the ensemble spread of simulated changes. In general, uncertainty is up to 50% of projected changes in extreme heat events of the type that occur only once per year. Large changes are seen in distributions of daily maximum temperatures for June, July, and August with significant shifts to warmer conditions. Changes in extremely hot days are shown to be significantly larger than changes in mean values in some regions. The intensity, duration, and frequency of summer heat waves are expected to be substantially greater over all continents. The largest changes are found over Europe, North and South America, and East Asia. Reductions in soil moisture, number of wet days, and nocturnal cooling are identified as significant factors responsible for the changes. Although uncertainty associated with the magnitude of expected changes is large in places, it does not bring into question the sign or nature of the projected changes. Even with the most conservative simulations, hot extreme events are still expected to substantially increase in intensity, duration, and frequency. This ensemble, however, does not represent the full range of uncertainty associated with future projections; for example, the effects of multiple parameter perturbations are neglected, as are the effects of structural changes to the basic nature of the parameterization schemes in the model.

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