Compressor fouling reduces air mass flow and compressor efficiency together. The characteristic pattern is falling corrected mass flow with a falling pressure ratio, output down, heat rate up, and compressor discharge temperature rising relative to what the pressure ratio would imply.
Hot section deterioration and increased clearances show differently. Where turbine efficiency has fallen, exhaust temperature rises for a given firing condition, and the relationship between fuel flow, output and exhaust temperature moves in a way that fouling does not reproduce.
Neither is diagnosable from a single parameter. Output alone is ambiguous, heat rate alone is ambiguous, and it is the combination across mass flow, pressure ratio, discharge temperature and exhaust temperature that carries the answer. This is precisely the case where a physical model earns its place, because the constraint that ties those quantities together is what makes an inconsistent set of readings visible.
Filtration condition belongs in the same analysis. A differential pressure rising across the inlet filters produces a loss that looks like fouling in the output data and is fixed by a different action entirely.