Module multivariate_observer 

Multivariate observer — ingests PCA/FDC residual streams and provides structural interpretation via the StructuralPCA module.

Design: Monitoring the Monitor

Existing FDC systems reduce the multivariate residual space to two scalar statistics:

• Hotelling’s T² — squared Mahalanobis distance in the principal component subspace; detects changes in the modelled variation.
• Q-Statistic (SPE) — sum of squared residuals in the complement subspace; detects changes in the unmodelled variation.

Neither statistic explains which process variables are responsible for the excursion, nor how the residual vector is oriented in physical space.

The StructuralPCA module provides the “why” to the PCA “what”: it decomposes the PCA residual vector into its principal loading directions, identifies the dominant physical dimensions, and maps the result to a DSFB grammar state and semiotic label.

Observer-Only Pattern

No upstream controller state is modified. The multivariate observer is a read-only side-channel that consumes statistics already produced by the FDC system. If a measurement is unavailable the observer degrades gracefully by returning StructuralVerdict::Unavailable.

Structs

MultivariateObserver

High-level observer that ingests PCA/FDC statistics from an upstream monitoring system and produces DSFB structural interpretations.

PcaObservation

A single multivariate process observation expressed in terms of the PCA residual statistics already computed by the upstream FDC system.

StructuralInterpretation

The full structural interpretation record emitted by StructuralPCA::interpret.

StructuralPCA

Structural PCA module — provides the “why” to the PCA “what”.

Enums

StructuralVerdict

The structural interpretation the DSFB engine infers from the PCA/FDC statistics.