Meaning
Mathematical operator used to reconstruct localized internal states from spatially averaged external sensor readings in battery packs. The inverse smearing matrix reverses the blending effect of thermal diffusion to estimate individual cell temperatures. This allows the battery management system to detect localized overheating using fewer sensors.
Spatial Reconstruction
Temperature measurements from the pack casing are typically smoothed out by the thermal mass of the structure. When applying the inverse smearing matrix, the algorithm restores the original peak values of the individual cells. This step is necessary to identify which cell has started to degrade.
Signal Restoration
Linear algebraic solvers resolve the true temperature profile by deconvolving the sensor readings. This use of the inverse smearing matrix is sensitive to the accuracy of the thermal modeling of the pack. If the thermal model is inaccurate, the reconstructed profile will show high levels of error.
Mathematical Limit
Deconvolution is an inherently ill-posed problem that amplifies measurement noise. Adding regularization parameters helps stabilize the calculation and prevents the inverse smearing matrix from generating unphysical values. This step makes the calculation viable for real-time applications.
If the regularization is too strong, it will damp out the localized temperature peaks, defeating the purpose of the spatial reconstruction. Thus, the tuning parameters must be selected based on experimental thermal data from actual cell failure tests.
