Online model

Abstract: The Bayesian framework provides a principled way of model selection. This framework estimates a probability distribution over an ensemble of models, and the prediction is done by averaging over the ensemble of models. Accordingly, the uncertainty of the models is taken into account, and complex models with more degrees of freedom are penalized. However, integration over model parameters is often intractable, and some approximation scheme is needed. Recently, a powerful approximation scheme, called the variational bayes (VB) method, has been proposed. This approach defines the free energy for a trial probability distribution, which approximates a joint posterior probability distribution over model parameters and hidden variables. The exact maximization of the free energy gives the true posterior distribution. The VB method uses factorized trial distributions. The integration over model parameters can be done analytically, and an iterative expectation-maximization-like algorithm, whose convergence is guaranteed, is derived. In this article, we derive an online version of the VB algorithm and prove its convergence by showing that it is a stochastic approximation for finding the maximum of the free energy. By combining sequential model selection procedures, the online VB method provides a fully online learning method with a model selection mechanism. In preliminary experiments using synthetic data, the online VB method was able to adapt the model structure to dynamic environments.

Abstract: An accurate State-of-Charge (SoC) estimation plays a significant role in battery systems used in electric vehicles due to the arduous operation environments and the requirement of ensuring safe and reliable operations of batteries. Among the conventional methods to estimate SoC, the Coulomb counting method is widely used, but its accuracy is limited due to the accumulated error. Another commonly used method is model-based online iterative estimation with the Kalman filters, which improves the estimation accuracy in some extent. To improve the performance of Kalman filters in SoC estimation, the adaptive extended Kalman filter (AEKF), which employs the covariance matching approach, is applied in this paper. First, we built an implementation flowchart of the AEKF for a general system. Second, we built an online open-circuit voltage (OCV) estimation approach with the AEKF algorithm so that we can then get the SoC estimate by looking up the OCV-SoC table. Third, we proposed a robust online model-based SoC estimation approach with the AEKF algorithm. Finally, an evaluation on the SoC estimation approaches is performed by the experiment approach from the aspects of SoC estimation accuracy and robustness. The results indicate that the proposed online SoC estimation with the AEKF algorithm performs optimally, and for different error initial values, the maximum SoC estimation error is less than 2% with close-loop state estimation characteristics.

Abstract: The state-of-charge (SOC) observer with online model adaption generally has high accuracy and robustness. However, the unexpected sensing of noises is shown to cause the biased identification of model parameters. To address this problem, a novel technique which integrates a recursive total least squares (RTLS) with an SOC observer is proposed to enhance the online model identification and SOC estimate. An efficient method is exploited to solve the Rayleigh quotient minimization which lays the basis of the RTLS. The number of multiplies, divides, and square roots is elaborated to show the low computational complexity of the developed RTLS. Simulation and experimental results show that the proposed RTLS-based observer attenuates the model identification bias caused by noise corruption effectively, and, thereby, provides a more reliable estimation of SOC. The proposed method is further compared with several available methods to highlight its superiority in terms of accuracy and the robustness to noise corruption.

Abstract: Learning in real-time applications, e.g., online approximation of the inverse dynamics model for model-based robot control, requires fast online regression techniques. Inspired by local learning, we propose a method to speed up standard Gaussian Process regression (GPR) with local GP models (LGP). The training data is partitioned in local regions, for each an individual GP model is trained. The prediction for a query point is performed by weighted estimation using nearby local models. Unlike other GP approximations, such as mixtures of experts, we use a distance based measure for partitioning of the data and weighted prediction. The proposed method achieves online learning and prediction in real-time. Comparisons with other nonparametric regression methods show that LGP has higher accuracy than LWPR and close to the performance of standard GPR and nu-SVR.