Literature reports show both benefits and negligible impact when including graded electrodes in battery design, depending upon the exact model and conditions used. In this paper, we use two different optimization approaches for a secondary current distribution porous electrode model with nonlinear kinetics to confirm that computed solutions are correct. We use these confirmed optimal solutions to probe several ways that graded porosity can improve electrode performance. Single objective optimization such as reducing the overall electrode resistance using a graded electrode design provides a modest 4-6% reduction in resistance for typical lithium-ion battery parameters. Multiple objective optimization-for example, simultaneously considering electrode resistance and the overpotential variance and eventually the overpotential average as well-shows that multilayer designs open up a much richer feasible design space for achieving multiple goals. The ultimate answer to the value of graded electrodes will be the techno-economic analysis that links the benefits of an expanded optimal design space to the detrimental costs associated with manufacturing multilayer electrodes. An open-access executable code that can give optimal porosity distribution of any specified chemistry and detailed explanation of the two approaches can be found on the Subramanian group's website. Modeling and mathematical optimization can significantly improve the efficiency of battery design, helping to meet the growing demands for various applications. The idea of using modeling for battery design was first introduced by Tiedemann and Newman in 1975. 1 They used an ohmically limited porous electrode model to maximize the cell's effective capacity by changing the electrode thickness and porosity. Newman later applied the reaction-zone model to maximize the specific energy of the system, taking mass into consideration as well.2 For these two models, the objective function can be directly related to the design variables, thus the optimum can be obtained by simply observing the plot or from the analytical solution. They further optimized the thickness and porosity of a lithium iron phosphate 3 electrode, where they maximized the specific energy using the Ragone plots. Ramadesigan et al.4 went one step further by including the linear electrode kinetics to minimize the internal resistance of the electrode. They used control vector parameterization (CVP) to minimize the ohmic resistance in the positive electrode by varying porosity.With the development of battery modeling, more physical processes have been included, and one of the most popular physics based models is the pseudo-2-Dimensional (P2D) model developed by the Newman group. 5 The P2D model involves a set of nonlinear partial differential equations (PDEs) that can only be solved numerically. Therefore, a numerical optimization approach is required to perform optimization on the system. Du et al. proposed a surrogate-modelbased approach, 6 and later developed a sophisticated framework based on th...
A hybrid analytical-collocation approach for fast simulation of the impedance response for a Li-ion battery using the pseudo-two dimensional model is presented. The impedance response of the spherical diffusion equations is solved analytically and collocation is performed on the resulting boundary value problem across the electrode and separator thickness using an orthogonal collocation scheme based on Gauss-Legendre points. The profiles for a frequency range from 0.5 mHz to 10 kHz are compared with the numerical solution obtained by solving the original model in COMSOL Multiphysics. The internal variable profiles across a wide range of frequencies are compared between the two methods and the accuracy, robustness, and computational superiority of the proposed hybrid analytical-collocation approach is presented. The limitations of the proposed approach are also discussed. A freeware for academic use that reads the various battery parameters and frequencies of interest as input, and predicts the battery impedance for a half cell and full cell, is also developed and a means to access it is reported in this paper.
Background The development of the minimum clinical important difference (MCID) can make it easier for researchers or doctors to judge the significance of research results and the effect of intervention measures, and improve the evaluation system of efficacy. This paper is aimed to calculate the MCID based on anchor and to develop MCID for esophageal cancer scale (QLICP-ES). Methods The item Q29 (How do you evaluate your overall health in the past week with 7 grades answers from 1 very poor to 7 excellent)of EORTC QLQ-C30 was used as the subjective anchor to calculate the score difference between each domain at discharge and admission. MCID was established according to two standards, "one grade difference"(A) and "at least one grade difference"(B), and developed by three methods: anchor-based method, ROC curve method and multiple linear regression models. In terms of anchor-based method, the mean of the absolute value of the difference before and after treatments is MCID. The point with the best sensitivity and specificity-Yorden index at the ROC curve is MCID for ROC curve method. In contrast, the predicted mean value based on a multiple linear regression model and the parameters of each factor is MCID. Results Most of the correlation coefficients of Q29 and various domains of the QLICP-ES were higher than 0.30. The rank of MCID values determined by different methods and standards were as follows: standard B > standard A, anchor-based method > ROC curve method > multiple linear regression models. The recommended MCID values of physical domain, psychological domain, social domain, common symptom and side-effects domain, the specific domain and the overall of the QLICP-ES were 7.8, 9.7, 4.7, 3.6, 4.3, 2.3 and 2.9, respectively. Conclusion Different methods have their own advantages and disadvantages, and also different definitions and standards can be adopted according to research purposes and methods. A lot of different MCID values were presented in this paper so that it can be easy and convenient to select by users.
Electrochemical models for the lithium-ion battery are useful in predicting and controlling its performance. The values of the parameters in these models are vital to their accuracy. However, not all parameters can be measured precisely, especially when destructive methods are prohibited. In this paper, we proposed a parameter estimation approach to estimate the open circuit potential of the positive electrode (Up) using piecewise linear approximation together with all the other parameters of a single particle model. Using the genetic algorithm (GA), Up and 10 more parameters were estimated from a single discharge curve without knowledge of the electrode chemistry. Different case studies were presented for estimating Up with different types of parameters of the battery model. The estimated parameters were then validated by comparing simulations at different C rates with experimental data.
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