A Controlled Benchmark Ablation of Fréchet-Window Battery Early Warning and Global Routing

Abstract

Researchers often propose candidate algorithms for embedded monitoring and routing with added machinery, such as windowed curve-similarity measures or iterative rerouting, before testing their value; hardware testing or labelled field data collection is slow and, for battery faults, hazardous. This article presents a synthetic-benchmark screening of two such designs, with explicit hypotheses and outcomes. Study A examines early warning of a simulated battery thermal-runaway precursor. Eight detectors, including an instantaneous voltage-temperature distance, a persistence rule, Fréchet windows, and an open-end Fréchet variant, were compared in five healthy-data scenarios, calibrated to about 2% false alarms, with 200 fault trials per setting. A robustness study added step and intermittent faults, heavy-tailed noise, and a local-outlier-factor baseline. The study proves that, for first-crossing alarms, a standard Fréchet window is exactly equivalent to the instantaneous distance; thresholds, false alarm counts, and median latencies were identical in all scenarios. The open-end variant was up to 1.1 s slower, and the local-outlier-factor baseline was slower than all simpler detectors. Persistence was decisive under heavy-tailed noise, detecting 199 of 200 one-degree steps against 42 for the instantaneous distance and Fréchet windows. Study B examines global routing on 20 × 20 and 32 × 32 grids. Rip-up and reroute removed all overflow in 15 of 15 netlists at 55% utilization and halved overflow at 85% relative to a congestion-aware single pass (paired Wilcoxon p < 0.001); a negotiated-congestion variant performed similarly. All data are synthetic. The results show where added complexity does not pay and provide a reusable benchmark and protocol for real-data testing.