cs.LGOct 30, 2026

From fleet trajectories to single-cell promises: hierarchically weighted conformal prediction for battery SOH monitoring

Authors: Xiangyu Liu

Organizations: Independent Researcher, Beijing, China

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Abstract

Interval predictions from conformal prediction are usually read as "90% coverage", but on nested battery data that number promises the fleet average, not the individual cell. We measure the gap on 124 public LFP cells under a preregistered three-tier reporting protocol (fleet, batch, cell): pooled coverage looks healthy (0.875-0.906 across splits) while the worst cell is covered 0.1-2% of the time, with exact binomial tests against the nominal level. We then repair part of the gap with a hierarchically weighted conformal engine whose weights consume only side information frozen at prediction time - signature features, batch labels, cycle indices - and never touch residuals. The preregistered repair criterion passes: 10th-percentile cell coverage moves 0.750 to 0.830 (53% of the gap), the worst cell 0.642 to 0.694, with zero deferrals and a flat sensitivity spectrum. What the engine does not repair is localized rather than left open: under protocol drift the frozen weights harm monotonically on the SOH scale (the absolute scale is reported in full), a structural dead end we report instead of tuning away; and repair capacity is bounded by calibration-pool battery diversity, measured on both datasets. On a cross-chemistry external set the calibrated intervals collapse (0.286), while the within-domain skeleton replicates (pooled 0.933, worst cell 0.686). The deliverable is a reporting protocol - three tiers of promise anchored to measured regimes, worst-cell statistics, deferral share - that makes per-cell interval claims auditable before deployment.

Figures & tables

Figure 1: The object of the guarantee and the three-tier reading (concept figure; numbers from panel A, SOH scale, Table 1). (a) Calibration cycles nest inside cells; cells nest inside protocol batches. The conformal guarantee attaches to a draw from the pooled cycle set; maintenance decisions attach to one cell. (b) The same experiment read at three tiers: fleet pooled coverage 0.906, minimum batch coverage 0.787, worst single cell 0.642, against nominal 0.90; 28% of cells fall below 0.85. The headline tier passes while the decision-relevant tier fails.
scalepanelpooledmin batchworst cellpbonfp_{\mathrm{bonf}}frac <0.85<0.85perm. pp
SOHA (random, 5-seed median)0.9060.7870.6424.2e-5528%—
SOHC (official split)0.8750.7900.014 (b2c1)<10−300<10^{-300}35%—
SOHB (2017 →\rightarrow 2018 drift)0.799—0.001 (b3c29)——<0.001
absA0.8970.790—6.1e-5828%—
absC0.8880.7780.020 (b2c1)<10−300<10^{-300}27%—
absB0.810—0.001 (b3c29)——<0.001
Table 1: Baseline split conformal, six gate cells (E1). Cell identifiers read batch, then cell within batch.
Figure 2: Per-cell coverage under baseline split conformal (SOH scale, nominal 90%). (a) Random split (panel A): five splits (thin) and their pointwise median (bold); the fleet-level number (0.906) sits on nominal while 28% of cells fall below 0.85 and the median worst cell is 0.642. (b) Official split (panel C): 83 test cells ranked by coverage; the worst cell (b2c1) is covered 1.4% of the time. A healthy bulk with a disastrous tail is the object the reporting protocol of §7 is built to expose.
armpooledq10min batchworstfrac <0.85<0.85deferral
baseline0.9060.7500.7870.64228%0%
engine0.9090.8300.8840.69416%0%
Table 2: Baseline vs. engine, panel A (SOH). Registered line: q10 ≥\geq 0.825.
Figure 3: Engine sensitivity and the drift dead end (SOH scale). (a, b) q10 and worst-cell coverage vs. the battery-level ESS target (log axis); gray lines mark the unweighted baseline. Panel A is flat (q10 0.804–0.830) with no knife-edge at the registered head value ESS_batt = 5; panel C peaks at ESS_batt = 1 with worst-cell repair 0.014 →\rightarrow 0.311. (c) Under protocol drift (panel B) the engine degrades monotonically toward the baseline from below — the harm is the mechanism, not the setting. Target 20 saturates at achieved ESS ≈\approx 18 (cap flag, §8.3).
armpooledq10min batchworstwidth q^\hat{q}fallback
baseline0.9060.7500.7870.6420.0019—
engine (ours)0.9090.8300.8840.6940.00210%
Mondrian (within-batch)0.8990.8250.8690.6310.00220% (A)
GP posterior0.9650.9130.9320.7860.0011none possible
BHM-lite0.9530.8630.9100.8310.0039 (2 ×\times )0% (A)
Table 3: Five arms, panel A (SOH), five-seed medians.
Figure 4: Feature families divide the labor across two axes (baseline arm, SOH; interval half-width on log scale). (a) Panel A: removing the trajectory family leaves q10 apparently better (0.870) at 29 ×\times width — coverage surviving as an artifact of width. (b) Panel C: removing the environment/position family collapses q10 (0.726 →\rightarrow 0.543) at unchanged width — the cycle index carries batch signature, echoing §8.1. The electrochemical family is mild on both axes: its point sits essentially on the full-feature anchor.
armpooledworstreading
cross-domain plain (Severson pool →\rightarrow Oxford)0.2860.137 (oxc2)pbonfp_{\mathrm{bonf}} 4.5e-36; 100% of cells below 0.85
cross-domain engine0.3760.216+0.09; not saved
within-domain plain (LOO ×\times 8)0.9330.686 (oxc2)oxc2 binomial pp 2.3e-05; Bonferroni 1.9e-04
within-domain engine0.9330.686identical to plain; ESS_batt ceiling 3.73 (cap flag)
Table 4: Oxford, four arms (SOH, IR-free feature subset, n = 8 cells; full distributions, no percentiles).
#prediction (summary)outcome
P1Mondrian: batch tier repaired, cell tier untouched✓\checkmark , sharpened: q10 repaired cosmetically while worst unmoved
P2GP: overconfident, worst-cell disaster×\times reshaped: conservative via non-converged hyperparameters; conclusion (no trustworthy σ\sigma ) holds with rewritten mechanism
P3BHM between base and Mondrianhalf ✓\checkmark : conservative coverage at 2 ×\times width; drift “win” is a 100% fallback artifact
P4sim-only reverses the median×\times reversed: no reversal under battery-level pools; cause relocated to pool narrowness
P5bal-only ≈\approx base, tail kept✓\checkmark ; plus unexpected +0.037 pooled on the drift panel
P6trajectory family hurts coverage mostreshaped to the width axis: 29 ×\times width, worst-cell collapse, q10 improves
Table 5: P1–P10, written before execution, reconciled after.
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