Baseline-Referenced S-Parameter Fault Diagnosis Under Environmental Drift: Profile Likelihood, Identifiability Limits, and Hierarchical Localization

Fault identification from measured scattering parameters is complicated by manufacturing offsets, environmental drift, frequency-correlated measurement noise, and structural indistinguishability. This paper studies a baseline-referenced pipeline for detecting changes in complex two-port scattering responses and classifying resonator detuning, coupling reduction, and excess internal loss. A whitened local model separates environmental nuisance directions from candidate fault signatures. We derive the exact relationship between nuisance projection and a profile generalized likelihood-ratio test (GLRT) in the linear Gaussian regime, demonstrate the condition under which a fault is locally unidentifiable, and report indistinguishable nodes as symmetry-aware diagnostic regions. Reproducible synthetic experiments on branched and inline five-resonator models compare uncorrected change energy, projected residual energy, and a one-sided matched GLRT. Under moderate simulated drift, the GLRT achieves 51.9% and 60.1% detection on deliberately weak faults, compared with 10.8% and 11.9% for uncorrected energy, while false-alarm rates are 5.3% and 4.3%, respectively. Strong out-of-calibration drift increases false alarms to 12.5% and 17.0%, showing that nuisance projection is not a universal remedy. These findings support an explicit three-way reporting policy: identified region, ambiguous/weak evidence, or suspected model mismatch. No physical electromagnetic simulation or vector-network-analyzer data are claimed.