Angel Urbina

Accelerated calendar and pulse life analysis of lithium-ion cells

Abstract Sandia National Laboratories has been studying calendar and pulse discharge life of prototype high-power lithium-ion cells as part of the Advanced Technology Development (ATD) Program. One of the goals of ATD is to establish validated accelerated life test protocols for lithium-ion cells in the hybrid electric vehicle application. In order to accomplish this, aging experiments have been conducted on 18650-size cells containing a chemistry representative of these high-power designs. Loss of power and capacity are accompanied by increasing interfacial impedance at the cathode. These relationships are consistent within a given state-of-charge (SOC) over the range of storage temperatures and times. Inductive models have been used to construct detailed descriptions of the relationships between power fade and aging time and to relate power fade, capacity loss and impedance rise. These models can interpolate among the different experimental conditions and can also describe the error surface when fitting life prediction models to the data.

Quantification of margins and uncertainties of complex systems in the presence of aleatoric and epistemic uncertainty

Abstract Performance assessment of complex systems is ideally done through full system-level testing which is seldom available for high consequence systems. Further, a reality of engineering practice is that some features of system behavior are not known from experimental data, but from expert assessment, only. On the other hand, individual component data, which are part of the full system are more readily available. The lack of system level data and the complexity of the system lead to a need to build computational models of a system in a hierarchical or building block approach (from simple components to the full system). The models are then used for performance prediction in lieu of experiments, to estimate the confidence in the performance of these systems. Central to this are the need to quantify the uncertainties present in the system and to compare the system response to an expected performance measure. This is the basic idea behind Quantification of Margins and Uncertainties (QMU). QMU is applied in decision making—there are many uncertainties caused by inherent variability (aleatoric) in materials, configurations, environments, etc., and lack of information (epistemic) in models for deterministic and random variables that influence system behavior and performance. This paper proposes a methodology to quantify margins and uncertainty in the presence of both aleatoric and epistemic uncertainty. It presents a framework based on Bayes networks to use available data at multiple levels of complexity (i.e. components, subsystem, etc.) and demonstrates a method to incorporate epistemic uncertainty given in terms of intervals on a model parameter.

Inductive modeling of lithium-ion cells

Abstract Sandia National Laboratories has conducted a sequence of studies on the performance of lithium ion and other types of electrochemical cells using inductive models. The objectives of some of these investigations are: (1) to develop procedures to rapidly determine performance degradation rates while these cells undergo life tests; (2) to model cell voltage and capacity in order to simulate cell output under variable load and temperature conditions; (3) to model rechargeable battery degradation under conditions of cyclic charge/discharge, and many others. Among the uses for the models are: (1) to enable efficient predictions of battery life; (2) to characterize system behavior. Inductive models seek to characterize system behavior using experimentally or analytically obtained data in an efficient and robust framework that does not require phenomenological development. There are certain advantages to this. Among these advantages is the ability to avoid making measurements of hard to determine physical parameters or having to understand cell processes sufficiently to write mathematical functions describing their behavior. We have used artificial neural networks (ANNs) for inductive modeling, along with ancillary mathematical tools to improve their accuracy. This paper summarizes efforts to use inductive tools for cell and battery modeling. Examples of numerical results are presented.

Probabilistic Integration of Validation and Calibration Results for Prediction Level Uncertainty Quantification: Application to Structural Dynamics

In many application domains, it is impossible or impractical to perform full-scale experiments on a system in the regime of interest. Instead, data may be collected via experiments at lower levels of the system on individual materials, components, or subsystems. As a result, physics-based models are the only available tool at the full system level and must be used to make predictions in the regime of interest. This scenario poses difficulty when attempting to characterize the uncertainty in the model prediction since no further data is available. This problem has commonly been addressed by characterizing aleatory uncertainty in input variables with probability distributions and then performing calibration to characterize epistemic uncertainty stemming from parameter uncertainty. Calibrated models are then validated by any of a number of available metrics by utilizing a new set of independent data, typically at a higher level of the system hierarchy. Once the models are validated at the subsystem level, the input variability and parameter uncertainty can be propagated through a system-level model to make a prediction in the regime of interest. Standard propagation techniques will yield a probability distribution for a quantity of interest which can then be used to perform reliability analysis and make system assessments. However, common implementations of this approach largely ignore model uncertainty, which may be a leading source of uncertainty in the prediction. The approach presented in this study accounts for the fact that models never perform perfectly in the validation activities. Model validation is typically posed as a single pass/fail decision, but it can instead be viewed probabilistically. The model reliability metric is utilized in this study because it readily allows this probabilistic treatment by computing the probability of model errors exceeding a specified tolerance. We assert that parameters which are calibrated from models which are later partially invalidated should not be fully carried forward to the prediction. Calibration can be performed jointly with all available subsystem models or by using only a subset of them. Thus, from a Bayesian calibration approach we can obtain several posterior distributions of the parameters in addition to the prior distribution. These parameter distributions can then be weighted by the corresponding model probabilities computed in the

Status and Integrated Road-Map for Joints Modeling Research

The constitutive behavior of mechanical joints is largely responsible for the energy dissipation and vibration damping in weapons systems. For reasons arising from the dramatically different length scales associated with those dissipative mechanisms and the length scales characteristic of the overall structure, this physics cannot be captured adequately through direct simulation of the contact mechanics within a structural dynamics analysis. The only practical method for accommodating the nonlinear nature of joint mechanisms within structural dynamic analysis is through constitutive models employing degrees of freedom natural to the scale of structural dynamics. This document discusses a road-map for developing such constitutive models.

Stochastic modeling of rechargeable battery life in a photovoltaic power system

The authors have developed a stochastic model for the power generated by a photovoltaic (PV) power supply system that includes a rechargeable energy storage device. The ultimate objective of this work is to integrate this photovoltaic generator along with other generation sources to perform power flow calculations to estimate the reliability of different electricity grid configurations. For this reason, the photovoltaic power supply model must provide robust, efficient realizations of the photovoltaic electricity output under a variety of conditions and at different geographical locations. This has been achieved by use of a Karhunen-Loeve framework to model the solar insolation data. The capacity of the energy storage device, in this case a lead-acid battery, is represented by a deterministic model that uses an artificial neural network to estimate the reduction in capacity that occurs over time. When combined with an appropriate stochastic load model, all three elements yield a stochastic model for the photovoltaic power system. This model has been operated on the Monte Carlo principle in stand-alone mode to infer the probabilistic behavior of the system. In particular, numerical examples are shown to illustrate the use of the model to estimate battery life. By the end of one year of operation, there is a 50% probability for the test case shown that the battery will be at or below 95% of initial capacity.

Reliability of rechargeable batteries in a photovoltaic power supply system

We investigated the reliability of a rechargeable battery acting as the energy storage component in a photovoltaic power supply system. A model system was constructed for this that includes the solar resource, the photovoltaic power supply system, the rechargeable battery and a load. The solar resource and the system load are modelled as stochastic processes. The photovoltaic system and the rechargeable battery are modelled deterministically, and an artificial neural network is incorporated into the model of the rechargeable battery to simulate damage that occurs during deep discharge cycles. The equations governing system behaviour are solved simultaneously in the Monte Carlo framework, and a first passage problem is solved to assess system reliability.

A Comparison of Methods for Representing and Aggregating Uncertainties Involving Sparsely Sampled Random Variables - More Results

This paper discusses the treatment of uncertainties corresponding to relatively few samples of random-variable quantities. The importance of this topic extends beyond experimental data uncertainty to situations involving uncertainty in model calibration, validation, and prediction. With very sparse samples it is not practical to have a goal of accurately estimating the underlying variability distribution (probability density function, PDF). Rather, a pragmatic goal is that the uncertainty representation should be conservative so as to bound a desired percentage of the actual PDF, say 95% included probability, with reasonable reliability. A second, opposing objective is that the representation not be overly conservative; that it minimally over-estimate the random-variable range corresponding to the desired percentage of the actual PDF. The presence of the two opposing objectives makes the sparse-data uncertainty representation problem an interesting and difficult one. In this paper the performance of five uncertainty representation techniques is characterized on twenty-one test problems (over thousands of trials for each problem) according to these two opposing objectives and other performance measures. Two of the methods exhibit significantly better overall performance than the others according to the objectives and performance measures emphasized.

An Initial Comparison of Methods for Representing and Aggregating Experimental Uncertainties involving Sparse Data.

This paper discusses the handling and treatment of uncertainties corresponding to relatively few data samples in experimental characterization of random quantities. The importance of this topic extends beyond experimental uncertainty to situations where the derived experimental information is used for model validation or calibration. With very sparse data it is not practical to have a goal of accurately estimating the underlying variability distribution (probability density function, PDF). Rather, a pragmatic goal is that the uncertainty representation should be conservative so as to bound a desired percentage of the actual PDF, say 95% included probability, with reasonable reliability. A second, opposing objective is that the representation not be overly conservative; that it minimally over-estimate the random-variable range corresponding to the desired percentage of the actual PDF. The performance of a variety of uncertainty representation techniques is tested and characterized in this paper according to these two opposing objectives. An initial set of test problems and results is presented here from a larger study currently underway.

Optimal Selection of Calibration and Validation Test Samples under Uncertainty.

Frequently, important system properties that parameterize system models must be inferred from experimental data in a calibration problem. The quality of the resulting parameter description is directly linked to the quality and quantity of data. Because economic considerations and experimental limitations often lead to data that is sparse and/or imprecise (sources of epistemic uncertainty), this research will characterize parameter uncertainty within a probabilistic framework. A hierarchical system structure will be considered where data may be collected at different levels of varying complexity and cost (e.g. material, component, subsystem, etc.), leading to a tradeoff decision of cost vs. importance of data. In addition to calibration, data is also needed within the proposed framework to perform probabilistic model validation to characterize model uncertainty. This uncertainty will be carried through the system parameters, thereby increasing the conservatism in the prediction because of the presence of imperfect models. This research proposes a constrained discrete optimization formulation for selecting among the candidate data types (calibration or validation and at what level) to determine the respective quantities of observations to collect in order to best quantify parameter uncertainty and model uncertainty (which propagate to prediction uncertainty).