A computer maps 3,245 charge–discharge curves from four batteries by their shape alone. Reveal each cycle’s age to see whether the map sorted them by ageing.
Each time a battery is charged and discharged, its voltage traces a curve, and that curve slowly changes as the battery ages. Given only the shapes of these curves, with no cycle numbers, can a computer tell earlier cycles from later ones?
In a map built only from curve shape, earlier and later cycles tend to sit in different regions, with some overlap. Reveal the cycle colours to see the pattern.
One PCA map, fitted on all four batteries.
One charge–discharge curve, with its age hidden.
The charge half and the discharge half are each stretched to 64 points; the voltages are then shifted and scaled so every curve has the same average and spread. The computer never sees the cycle number or the capacity.
Each dot is one cycle, placed by its curve shape alone; nearby dots have similar shapes. Coloured dots belong to the highlighted battery, grey dots to the other three. Click a coloured dot to see its curve.
Reveal cycle colours; point positions stay fixed.
The computer maps differences in curve shape. Reveal cycle colours to see how those differences relate to ageing.
PCA (principal component analysis) finds the directions along which the curve shapes differ most; the map’s axes, PC1 and PC2, are the two strongest. It was fitted once on all 3,245 cycles of the four batteries, without cycle numbers or capacity. Playing steps through 40 of the highlighted battery’s cycles in order; the slider selects any of its cycles.
The map shows the first two principal components of one PCA fitted on all 3,245 cycles: PC1 across, PC2 up. Choosing a battery highlights its points in this same map. Cycle numbers set only the colours; neither axis is a cycle number.
Each cycle enters PCA as 128 standardised voltages: 64 from the charge and 64 from the discharge. Cycle number, capacity and battery identity were not inputs. The first two components carry 89.78% of the shape variation.