No abstract

No abstract

The expansion of battery material during lithium intercalation is a concern for the cycle life and performance of lithium ion batteries. In this paper, electrode expansion is quantified from in situ neutron images taken during cycling of pouch cells with lithium iron phosphate positive and graphite negative electrodes. Apart from confirming the overall expansion as a function of state of charge and the correlation with graphite transitions that have been observed in previous dilatometer experiments we show the spatial distribution of the expansion along the individual electrodes of the pouch cell. The experiments were performed on two cells with different electrode areas during low and high c-rate operation. The measurements show how charging straightened the cell layers that were slightly curved by handling of the pouch cell during setup of the experiment. Subsequent high charging rate, that exceeded the suggested operating voltage limits, was shown to have a strong influence on the observed expansion. Specifically, during high-rate cycling, the battery showed a much larger and irreversible expansion of around 1.5% which was correlated with a 4% loss in capacity over 21 cycles.Expansion and contraction of battery material during charging and discharging can lead to fracture of the electrode and eventually capacity loss as particles are no longer electrically connected to the current collector, each other, or the carbon matrix in which they are suspended. The carbon anode material is known to expand upon intercalation of lithium into the host structure that occurs during charging of the battery. Expansion of the graphite can cause deformations as large as 10% of the anode volume 1,2 depending upon the type of carbon. The stress that develops inside the battery is also related to the rate of charging. 3 Lee et al. 4 measured the dimensional changes in lithium cobalt oxide pouch cells during cycling using a specialized dilatometer setup. They found that the expansion of the battery consists of two components: an irreversible thickness increase, corresponding to initial formation of the solid electrolyte interface (SEI), and one which is reversible and follows the battery state of charge, expanding upon charging. 4 They attributed the volume change during cycling, approximately 2% of the total battery initial thickness, to the anode active material since the cobalt oxide does not show significant volume change upon lithium intercalation.In this paper we document the expansion of Lithium Iron Phosphate (LiFePO 4 or LFP) pouch cells upon charging. The measurements are taken using Neutron Imaging (NI), an in situ technique similar to X-ray imaging that is sensitive to lighter elements such as hydrogen and lithium. We also provide a method for quantifying the expansion from the NI data. We observed a 0.5% total cell expansion (after SEI formation), which corresponds to a 1.7% expansion of the graphite material if attributed entirely to the negative electrode active material and ignoring the potential contraction of the ...

No abstract

No abstract

No abstract

SUMMARYIn gradient-based design optimization, the sensitivities of the constraint with respect to the design variables are required. In reliability-based design optimization (RBDO), the probabilistic constraint is evaluated at the most probable point (MPP), and thus the sensitivities of the probabilistic constraints at MPP are required. This paper presents the rigorous analytic derivation of the sensitivities of the probabilistic constraint at MPP for both first-order reliability method (FORM)-based performance measure approach (PMA) and dimension reduction method (DRM)-based PMA. Numerical examples are used to demonstrate that the analytic sensitivities agree very well with the sensitivities obtained from the finite difference method (FDM). However, as the sensitivity calculation at the true DRM-based MPP requires the second-order derivatives and additional MPP search, the sensitivity derivation at the approximated DRM-based MPP, which does not require the second-order derivatives and additional MPP search to find the DRM-based MPP, is proposed in this paper. A convergence study illustrates that the sensitivity at the approximated DRM-based MPP converges to the sensitivity at the true DRM-based MPP as the design approaches the optimum design. Hence, the sensitivity at the approximated DRM-based MPP is proposed to be used for the DRM-based RBDO to enhance the efficiency of the optimization.

In physics-based engineering modeling, the two primary sources of model uncertainty, which account for the differences between computer models and physical experiments, are parameter uncertainty and model discrepancy. Distinguishing the effects of the two sources of uncertainty can be challenging. For situations in which identifiability cannot be achieved using only a single response, we propose to improve identifiability by using multiple responses that share a mutual dependence on a common set of calibration parameters. To that end, we extend the single response modular Bayesian approach for calculating posterior distributions of the calibration parameters and the discrepancy function to multiple responses. Using an engineering example, we demonstrate that including multiple responses can improve identifiability (as measured by posterior standard deviations) by an amount that ranges from minimal to substantial, depending on the characteristics of the specific responses that are combined.