An Iterative Method Based on the Marginalized Particle Filter for Nonlinear B-Spline Data Approximation and Trajectory Optimization

The B-spline function representation is commonly used for data approximation and trajectory definition, but filter-based methods for nonlinear weighted least squares (NWLS) approximation are restricted to a bounded definition range. We present an algorithm termed nonlinear recursive B-spline approximation (NRBA) for an iterative NWLS approximation of an unbounded set of data points by a B-spline function. NRBA is based on a marginalized particle filter (MPF), in which a Kalman filter (KF) solves the linear subproblem optimally while a particle filter (PF) deals with nonlinear approximation goals. NRBA can adjust the bounded definition range of the approximating B-spline function during run-time such that, regardless of the initially chosen definition range, all data points can be processed. In numerical experiments, NRBA achieves approximation results close to those of the Levenberg–Marquardt algorithm. An NWLS approximation problem is a nonlinear optimization problem. The direct trajectory optimization approach also leads to a nonlinear problem. The computational effort of most solution methods grows exponentially with the trajectory length. We demonstrate how NRBA can be applied for a multiobjective trajectory optimization for a battery electric vehicle in order to determine an energy-efficient velocity trajectory. With NRBA, the effort increases only linearly with the processed data points and the trajectory length

Battery State of Health Monitoring via Estimation of Health-Relevant Electrochemical Variables

This dissertation explores and compares the effectiveness of estimating two health-relevant electrochemical variables, the side reaction current density and the number of cyclable Li-ions, as indicators of battery state of health (SOH) in battery management systems of electric vehicles (EV) and hybrid electric vehicles (HEV). The choice of these two electrochemical variables is based on the assumption that battery degradation is mainly caused by consumption of cyclable Li-ions. This assumption is valid for the two widely-used types of EV/HEV batteries considered herein, namely LiFePO4 and LMO-based mixture batteries. This dissertation provides formulations to estimate these two electrochemical variables from measurements of battery terminal voltage and current. Estimation is necessary here because the electrochemical variables cannot be measured on-board. Estimation of the side reaction current density is formulated as a subsystem identification problem and is solved using retrospective-cost subsystem identification. A new subsystem identification algorithm, the two-step filter, is also developed to improve the estimation accuracy of the side reaction current density under the presence of state of charge (SOC) estimation errors. On the contrary, the number of cyclable Li-ions is estimated as an unknown battery parameter using the extended Kalman filter. This dissertation also analyzes the robustness of estimation of the two electrochemical variables by providing a framework to obtain the lower bound of relative estimation errors of each of the two variables under non-ideal conditions for algorithms that estimate the variable by minimizing the error between measured voltage and estimated voltage. This framework determines that the lower bound of the relative estimation error of a variable is proportional to the error in either measurement or estimate of battery terminal voltage caused by non-ideal conditions, and inversely proportional to the sensitivity of the voltage to the variable and the magnitude of the variable itself. This framework also yields the same lower bound for the covariance of unbiased estimates as given by the Fisher information. The effectiveness of estimating the side reaction current density and the number of cyclable Li-ions as SOH indicators is also discussed through comparison. Compared to the number of cyclable Li-ions or other SOH indicators such as capacity and internal resistance, the side reaction current density is a more ideal SOH indicator when it can be estimated accurately, because it can instantaneously indicate battery degradation rate. However, estimation of the side reaction current density under practical non-ideal conditions is fundamentally difficult due to the fact that the sensitivity of the voltage to the side reaction current density and the magnitude of the side reaction current density are both low. On the other hand, the number of cyclable Li-ions is a promising SOH indicator for battery management systems in practice because it provides an indication of the remaining capacity from the first principles, can be estimated using a standard algorithm and simple models, and demonstrates high robustness to non-ideal conditions. Future extensions of this work include i) studying the impact of temperature on estimation of health-relevant electrochemical variables by including thermal dynamics in the model, ii) validating experimentally estimation of the number of cyclable Li-ions, and iii) extending estimation of the side reaction current density to other side-reaction-based battery degradation and safety problems such as Lithium plating and dendrite formation.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/137087/1/zhouxin_1.pd

A recursive algorithm for nonlinear least-squares problems

The solution of nonlinear least-squares problems is investigated. The asymptotic behavior is studied and conditions for convergence are derived. To deal with such problems in a recursive and efficient way, it is proposed an algorithm that is based on a modified extended Kalman filter (MEKF). The error of the MEKF algorithm is proved to be exponentially bounded. Batch and iterated versions of the algorithm are given, too. As an application, the algorithm is used to optimize the parameters in certain nonlinear input\u2013output mappings. Simulation results on interpolation of real data and prediction of chaotic time series are shown