Identifiability Limits of Discrete Axial Screw-Wear Diagnosis from Thermal and Electrical Process Signals During Soybean Extrusion

This retrospective study audits whether a two-campaign soybean-extrusion archive supports section-specific inference in a linear geometry-associated signal model. The archive contains 3966 records (2091 worn and 1875 new) with four temperature and three phase-current channels. Descriptive statistics and complete recorded trajectories characterize the signal differences without treating time samples as independent experimental replicates. Eight section-associated predictor columns are assigned once per campaign from the available geometry documentation. With unrestricted campaign effects, these columns lie exactly in the campaign-indicator space: their added rank is zero and their coefficient nullity is eight per channel. Intercept-only adjustment retains at most one between-campaign contrast, whose physical cause cannot be isolated. An explicit reparameterization example illustrates identical fitted responses from different regression coefficients. The geometry audit reproduces source-cell formulas and establishes the discrete order 1–5–2–6–3–7–4–8, while identifying reversed endpoint labels, different percentage conventions, and absent measurement pairing and uncertainty documentation. These findings delimit inference for the specified archive and model; they do not establish a universal impossibility of thermal or electrical wear diagnosis. A reproducible audit sequence and maintenance decision criteria connect the results to mechanical engineering practice.