Abstract
Full battery models are highly complex, which limits their application to tasks such as optimization and uncertainty quantification. To lower the computational burden, sensitivity analysis (SA) can be used as a precursor to identify the most important parameters in the model, but SA itself relies on a high number of full model evaluations, which has motivated the use of emulators. For high-dimensional output problems, emulators are challenging to construct. In this paper we develop a probabilistic framework for SA of high-dimensional output models using a Gaussian process emulator based on dimensionality reduction. This allows us to perform SA under uncertainty for multi-ouput problems, providing error bounds for the emulator predictions of sensitivity measures. We show how this can be achieved using Monte Carlo sampling or possibly by using semi-analytical expressions with highly efficient sampling. Moreover, we can perform SA for multivariate outputs by ranking the sensitivity measures related to (uncorrelated) coefficients in a basis for the output space.
Highlights
The large number of parameters appearing in mathematical models and numerical codes for batteries complicates modelling efforts
We derive an approximate basis for Y using principal component analysis (PCA) [8], i.e., we find a linear transformation w(ξ) = VT y, in which V ∈ Rd×d has orthogonal columns vi and the uncorrelated components wi(ξ) of w(ξ) have decreasing variance with i
A total of 500 simulations were performed by varying the initial state of charge SOCin, the particle diameter in the positive electrode Rp and the positive electrode porosity p
Summary
The large number of parameters appearing in mathematical models and numerical codes for batteries complicates modelling efforts. If the quantity of interest (QoI), which is derived from the output, is a scalar, an alternative is to use an emulator directly between the inputs and QoI It may be the case, that there are multiple QoIs, in which case it would be ideal to emulate the output, especially when other tasks (e.g. UQ) involving different quantities, including perhaps the original output, are to be performed subsequently. To address these issues, we develop an approach for SA of a nonlinear Li-ion battery model by employing a Gaussian process emulator based on dimensionality reduction to approximate entire charge-discharge curves. Using the emulation method we are able to perform a SA of multiple outputs (including in high dimensional spaces) by ranking coefficients in a low-dimensional subspace approximation of the output space
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