Improving the Convergence of Vector Fitting for Equivalent Circuit Extraction From Noisy Frequency Responses

The vector fitting (VF) algorithm has become a common tool in electromagnetic compatibility and signal integrity studies. This algorithm allows the derivation of a rational approximation to the transfer matrix of a given linear structure starting from measured or simulated frequency responses. This paper addresses the convergence properties of a VF when the frequency samples are affected by noise.We show that small amounts of noise can seriously impair or destroy convergence. This is due to the presence of spurious poles that appear during the iterations. To overcome this problem we suggest a simple modification of the basic VF algorithm, based on the identification and removal of the spurious poles. Also, an incremental pole addition and relocation process is proposed in order to provide automatic order estimation even in the presence of significant noise.We denote the resulting algorithm as vector fitting with adding and skimming (VF-AS). A thorough validation of the VF-AS algorithm is presented using a Monte Carlo analysis on synthetic noisy frequency responses. The results show excellent convergence and significant improvements with respect to the basic VF iteration scheme. Finally, we apply the new VF-AS algorithm to measured scattering responses of interconnect structures and networks typical of high-speed digital systems

Model migration neural network for predicting battery aging trajectories

Accurate prediction of batteries’ future degradation is a key solution to relief users’ anxiety on battery lifespan and electric vehicle’s driving range. Technical challenges arise from the highly nonlinear dynamics of battery aging. In this paper, a feed-forward migration neural network is proposed to predict the batteries’ aging trajectories. Specifically, a base model that describes the capacity decay over time is first established from the existed battery aging dataset. This base model is then transformed by an input-output slope-and-bias-correction (SBC) method structure to capture the degradation of target cell. To enhance the model’s nonlinear transfer capability, the SBC-model is further integrated into a four-layer neural network, and easily trained via the gradient correlation algorithm. The proposed migration neural network is experimentally verified with four different commercial batteries. The predicted RMSEs are all lower than 2.5% when using only the first 30% of aging trajectories for neural network training. In addition, illustrative results demonstrate that a small size feed-forward neural network (down to 1-5-5-1) is sufficient for battery aging trajectory prediction

Kernel Based Model Parametrization and Adaptation with Applications to Battery Management Systems.

With the wide spread use of energy storage systems, battery state of health (SOH) monitoring has become one of the most crucial challenges in power and energy research, as SOH significantly affects the performance and life cycle of batteries as well as the systems they are interacting with. Identifying the SOH and adapting of the battery energy/power management system accordingly are thus two important challenges for applications such as electric vehicles, smart buildings and hybrid power systems. This dissertation focuses on the identification of lithium ion battery capacity fading, and proposes an on-board implementable model parametrization and adaptation framework for SOH monitoring. Both parametric and non-parametric approaches that are based on kernel functions are explored for the modeling of battery charging data and aging signature extraction. A unified parametric open circuit voltage model is first developed to improve the accuracy of battery state estimation. Several analytical and numerical methods are then investigated for the non-parametric modeling of battery data, among which the support vector regression (SVR) algorithm is shown to be the most robust and consistent approach with respect to data sizes and ranges. For data collected on LiFePO4 cells, it is shown that the model developed with the SVR approach is able to predict the battery capacity fading with less than 2% error. Moreover, motivated by the initial success of applying kernel based modeling methods for battery SOH monitoring, this dissertation further exploits the parametric SVR representation for real-time battery characterization supported by test data. Through the study of the invariant properties of the support vectors, a kernel based model parametrization and adaptation framework is developed. The high dimensional optimization problem in the learning algorithm could be reformulated as a parameter estimation problem, that can be solved by standard estimation algorithms such as the least-squares method, using a SVR special parametrization. The resulting framework uses the advantages of both parametric and non-parametric methods to model nonlinear dynamics, and greatly reduces the required effort in model development and on-board computation. The robustness and effectiveness of the developed methods are validated using both single cell and multi-cell module data.PhDNaval Architecture and Marine EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/116688/1/chsweng_1.pd

Development of a Tunable Electromechanical Acoustic Liner for Engine Nacelles

This report describes the development of a tunable electromechanical Helmholtz resonator (EMHR) for engine nacelles using smart materials technology. This effort addresses both near-term and long-term goals for tunable electromechanical acoustic liner technology for the Quiet Aircraft Technology (QAT) Program. Analytical models, i.e. lumped element model (LEM) and transfer matrix (TM) representation of the EMHR, have been developed to predict the acoustic behavior of the EMHR. The models have been implemented in a MATLAB program and used to compare with measurement results. Moreover, the prediction performance of models is further improved with the aid of parameter extraction of the piezoelectric backplate. The EMHR has been experimentally investigated using standard two-microphone method (TMM). The measurement results validated both the LEM and TM models of the EMHR. Good agreement between predicted and measured impedance is obtained. Short- and open circuit loads define the limits of the tuning range using resistive and capacitive loads. There is approximately a 9% tuning limit under these conditions for the non-optimized resonator configuration studied. Inductive shunt loads result in a 3 degree-of-freedom DOF) system and an enhanced tuning range of over 20% that is not restricted by the short- and open-circuit limits. Damping coefficient ' measurements for piezoelectric backplates in a vacuum chamber are also performed and indicate that the damping is dominated by the structural damping losses, such as compliant boundaries, and other intrinsic loss mechanisms. Based on models of the EMHR, a Pareto optimization design of the EMHR has been performed for the EMHR with non-inductive loads. The EMHR with non-inductive loads is a 2DOF system with two resonant fiequencies. The tuning ranges of the two resonant frequencies of the EMHR with non-inductive loads cannot be optimized simultaneously; a trade-off (i.e., a Pareto solution) must be reached. The Pareto solution provides the information for a designer that shows how design trade-offs can be used to satisfy specific design requirements. The optimization design of the EMHR with inductive loads aims at optimal tuning of these three resonant fiequencies. The results indicate that it is possible to keep the acoustic reactance of the resonator close to a constant over a given frequency range. An effort to mimic the second layer of the NASA 2DOF liner using a piezoelectric composite diaphragm has been made. The optimal acoustic reactance of the second layer of the NASA 2DOF liner is achieved using a thin PVDF composite diaphragm, but matching the acoustic resistance requires further investigation. Acoustic energy harvesting is achieved by connecting the EMHR to an energy reclamation circuit that converts the ac voltage signal across the piezoceramic to a conditioned dc signal. Energy harvesting experiment yields 16 m W continuous power for an incident SPL of 153 dB. Such a level is sufficient to power a variety of low power electronic devices. Finally, technology transfer has been achieved by converting the original NASA ZKTL FORTRAN code to a MATLAB code while incorporating the models of the EMHR. Initial studies indicate that the EMHR is a promising technology that may enable lowpower, light weight, tunable engine nacelle liners. This technology, however, is very immature, and additional developments are required. Recommendations for future work include testing of sample EMHR liner designs in NASA Langley s normal incidence dual-waveguide and the grazing-incidence flow facility to evaluating both the impedance characteristics as well as the energy reclamation abilities. Additional design work is required for more complex tuning circuits with greater performance. Poor electromechanical coupling limited the electromechanical tuning capabilities of the proof of concept EMHR. Different materials than those studies and perhaps novel composite material systems may dramatically improvehe electromechanical coupling. Such improvements are essential to improved mimicking of existing double layer liners

LITHIUM-ION BATTERY DEGRADATION EVALUATION THROUGH BAYESIAN NETWORK METHOD FOR RESIDENTIAL ENERGY STORAGE SYSTEMS

Batteries continue to infiltrate in innovative applications with the technological advancements led by Li-ion chemistry in the past decade. Residential energy storage is one such example, made possible by increasing efficiency and decreasing the cost of solar PV. Residential energy storage, charged by rooftop solar PV is tied to the grid, provides household loads. This multi-operation role has a significant effect on battery degradation. These contributing factors especially solar irradiation and weather conditions are highly variable and can only be explained with probabilistic analysis. However, the effect of such external factors on battery degradation is approached in recent literature with mostly deterministic and some limited stochastic processes. Thus, a probabilistic degradation analysis of Li-ion batteries in residential energy storage is required to evaluate aging and relate to the external causal factors. The literature review revealed modified Arrhenius degradation model for Li-ion battery cells. Though originating from an empirical deterministic method, the modified Arrhenius equation relates battery degradation with all the major properties, i.e. state of charge, C-rate, temperature, and total amp-hour throughput. These battery properties are correlated with external factors while evaluation of capacity fade of residential Li-ion battery using a proposed detailed hierarchical Bayesian Network (BN), a hierarchical probabilistic framework suitable to analyze battery degradation stochastically. The BN is developed considering all the uncertainties of the process including, solar irradiance, grid services, weather conditions, and EV schedule. It also includes hidden intermediate variables such as battery power and power generated by solar PV. Markov Chain Monte-Carlo analysis with Metropolis-Hastings algorithm is used to estimate capacity fade along with several other interesting posterior probability distributions from the BN. Various informative and promising results were obtained from multiple case scenarios that were developed to explore the effect of the aforementioned external factors on the battery. Furthermore, the methodologies involved to perform several characterizations and aging test that is essential to evaluate the estimation proposed by the hierarchical BN is explored. These experiments were conducted with conventional and low-cost hardware-in-the-loop systems that were developed and utilized to quantify the quality of estimation of degradation

Interpretable Battery Lifetime Prediction Using Early Degradation Data

Battery lifetime prediction using early degradation data is crucial for optimizing the lifecycle management of batteries from cradle to grave, one example is the management of an increasing number of batteries at the end of their first lives at lower economic and technical risk.In this thesis, we first introduce quantile regression forests (QRF) model to provide both cycle life point prediction and range prediction with uncertainty quantified as the width of the prediction interval. Then two model-agnostic methods are employed to interpret the learned QRF model. Additionally, a machine learning pipeline is proposed to produce the best model among commonly-used machine learning models reported in the battery literature for battery cycle life early prediction. The experimental results illustrate that the QRF model provides the best range prediction performance using a relatively small lab dataset, thanks to its advantage of not assuming any specific distribution of cycle life. Moreover, the two most important input features are identified and their quantitative effect on predicted cycle life is investigated. Furthermore, a generalized capacity knee identification algorithm is developed to identify capacity knee and capacity knee-onset on the capacity fade curve. The proposed knee identification algorithm successfully identifies both the knee and knee-onset on synthetic degradation data as well as experimental degradation data of two chemistry types.In summary, the learned QRF model can facilitate decision-making under uncertainty by providing more information about cycle life prediction than single point prediction alone, for example, selecting a high-cycle-life fast-charging protocol. The two model-agnostic interpretation methods can be easily applied to other data-driven methods with the aim of identifying important features and revealing the battery degradation process. Lastly, the proposed capacity knee identification algorithm can contribute to a successful second-life battery market from multiple aspects