Identity Collapse: A Measurable Degradation Regime in Bearing and Battery Systems

We study adaptive threshold detection in two physical degradation settings: rolling element bearings monitored by vibration RMS and lithium-ion batteries monitored by discharge capacity. Applying a scalar identity metric derived from the ratio between baseline and current signal state, we find that the two domains occupy structurally different degradation regimes. Batteries degrade while preserving high identity (I approximately 0. 58 to 0. 72 in our sample). Bearings undergo identity collapse, losing most of their baseline signal character before failure (I as low as 0. 04 in our sample). More importantly, a system can be deep in identity collapse while its temporal coherence remains high, as shown by Bearing1₁ (I = 0. 108, rho = 0. 978). These are not the same quantity, and the adaptive threshold formula treats them as separate terms. This distinction has a direct consequence for threshold correction. Linear identity modulation collapses the correction multiplier too far toward zero in the extreme-collapse regime, making it ineffective. In the documented Bearing2₄ development path, linear modulation yielded F1 = 0. 455; square-root identity dampening preserved a stronger correction and yielded F1 = 0. 957 on the same bearing. Across the tested XJTU-SY bearing set, all 10 validated passing bearings fall below an empirical rescue boundary near I approximately 0. 25, while the reported failing cases lie outside the effective rescue regime or lack a usable degradation signal. All three NASA batteries pass with strong F1 scores (0. 949 to 0. 975) using a domain-specific coupling constant alpha = 0. 034, compared to alpha = 0. 1 for bearings. We document a failure case in which an incorrect alpha setting caused F1 drops of 37 to 43 percentage points before correction. All experiments use real published datasets with no synthetic data. We report explicit negative results, including five bearings for which the correction did not succeed and one domain in which an incorrect alpha setting caused large performance drops before correction. The methods described in this paper are the subject of U. S. Provisional Patent Application No. 63/921, 348 (filed November 20, 2025). No license to implement or commercialize the described methods is granted by this publication. All rights reserved.