Measured world · energy
When does a lithium-ion cell stop being able to deliver what it was built for?
Goal Keep delivering at least 80% of its first capacity
Oxford Battery Degradation Dataset 1: eight 740 mAh lithium-ion pouch cells aged in a 40 C chamber on an Artemis urban drive cycle, characterised every 100 drive cycles.
Attainability
100 means the goal is reachable without extra effort. Below 100 the cell needs effort to hold the goal.
Shift
How far an actor has moved from the cell's own first test (0 = unchanged, 100 = moved by its own starting value or more).
Measured and projected
Measured values are drawn from the data. A projection is a separate, labelled extension past the last reading and carries its own backtested error.
Cell 1: attainability stayed below full from cycle 3000, when the cell still delivered 87.2% of its first capacity. The measured 80% line came at cycle 5800, 2800 cycles later. A plain 'capacity below 90%' rule fired at cycle 2200, before the engine.
measured · measured after the projection was made · projected Drag the chart, or use the arrow keys, to read any cycle.
What the projection said
Made at cycle 2,200, using only the tests up to that point. It put the 80% line at about cycle 5,508 (range 4,624 to 5,725). The cell actually crossed it at cycle 5,800, 292 cycles before the projection.
Range: central minus the largest and smallest errors this method made on the other cells at the same cut. Method: power p=0.75, anchored at the last measurement. The timing comes from a power law on capacity loss; the engine reads the attainability along that projected path.
| Method (all 8 cells, same cut) | Mean error | Tends to |
|---|---|---|
| power law on capacity loss, anchored at the last reading | 467 cycles | predict 294 cycles late |
| straight line through the last five capacity readings | 763 cycles | predict 763 cycles early |
| the three actor tracks combined to predict capacity loss | 631 cycles | predict 419 cycles late |
Key cycles, Cell 1
| Capacity first below 90% | 2,200 |
| Capacity first below 85% | 3,800 |
| Attainability stays below full | 3,000 |
| Effort allowance runs short | 2,900 |
| Measured 80% line | 5,800 |
| impedance leaves its start | 1,000 |
| peak leaves its start | 700 |
| thermal leaves its start | 1,600 |
Leaving its start means the actor has moved 15% from its own first reading.
What moved with the shortfall
These actors move with the failure. They are not shown to be its mechanical cause: lithium inventory and active material are not measured in this dataset.
How much the effort setting matters
Set at 4 times the mean starting intensity (declared default). The sensitivity block per cell shows the same readings at 2 and 8 times.
| Cell 1 | Attainability stays below full | Effort allowance runs short |
|---|---|---|
| Setting x2 | 2,100 | 2,000 |
| Setting x4 (default) | 3,000 | 2,900 |
| Setting x8 | 4,400 | 4,300 |
A dash means it never happened within the measured life. The order of the cells did not change across settings; the timings did.
Across all eight cells
- Attainability stayed below full for three consecutive tests before the cell's capacity reached the 80% line in 7 of 8 cells (Cell 1, Cell 2, Cell 3, Cell 4, Cell 5, Cell 7, Cell 8); lead over the line, in cycles: Cell 1 2800, Cell 2 2600, Cell 3 3100, Cell 4 700, Cell 5 3400, Cell 7 1900, Cell 8 900.
- Against a plain capacity rule the engine is not always earlier: attainability dropped below full before capacity fell below 90% in 1 of 8 cells (Cell 5), and before capacity fell below 85% in 4 of 8 (Cell 1, Cell 2, Cell 3, Cell 5).
- Impedance and Peak shift together in these cells. When the engine assigns the shortfall it points to them, but they are markers that move with the failure, not proven mechanical causes: lithium inventory and active material are not measured in this dataset, and a team that measures them can add them as actors.
- Resistance on its own would have to grow roughly twenty-fold to take a cell to the 80% line by the voltage limit (estimated for cells 1, 4, 6 and 7); the cells showed 1.6 to 2 times. Most of the capacity loss therefore comes from somewhere the three measured actors only mark.
Limits
- One chemistry, eight cells, one test lab.
- The effort allowance is a single declared setting, not measured per cell; timings move with it, the order of the cells did not.
- Cells 4 and 6 reach the 80% line first while the engine reads them as healthy; the three measured actors do not explain their loss.
- The projection's timing comes from a power law on capacity; the actor-track version did not beat it.
What each actor is
- Capacity
- Charge delivered on a 1C discharge, as a share of the cell's first test. Falls with lithium loss, loss of active material and, more weakly, with resistance.
- Impedance
- Resistance proxy: extra voltage drop at 1C compared with the slow 40 mA discharge, divided by current, over 10-60% of the first capacity. Mixes ohmic, charge-transfer and diffusion losses; rises as the surface film grows.
- Peak
- Height of the largest dQ/dV (incremental capacity) peak on the slow discharge. It shrinks with loss of active material and lithium.
- Thermal
- Temperature rise during the 1C discharge in a 40 C chamber. Mostly resistive heating, so it tracks impedance.
Descriptions are general battery literature. A team that measures more (lithium inventory, active material) can add it as another actor, and the engine ranks it with the rest.
Source
Oxford Battery Degradation Dataset 1: eight 740 mAh lithium-ion pouch cells aged in a 40 C chamber on an Artemis urban drive cycle, characterised every 100 drive cycles.
Licence: Open Database License (ODbL 1.0). C. R. Birkl, Oxford Battery Degradation Dataset 1, University of Oxford (see the dataset Readme for the DOI); C. R. Birkl, "Diagnosis and Prognosis of Degradation in Lithium-Ion Batteries", PhD thesis, University of Oxford, 2017.