Δ.72 on SKAB Benchmark

Key Results

Across 34 SKAB industrial experiments, the Δ coherence metric achieved 97% detection rate with a mean F1 of 0.429. Variance-based detection scored F1 of 0.517. While variance achieves near-perfect recall (0.999), it does so at the cost of precision (0.350). Δ wins on F1 in 6 of 34 experiments, showing stronger precision where it matters.

Method Comparison

Category Breakdown

Three fault categories: valve1 (16 experiments), valve2 (4 experiments), and other (14 experiments). Variance achieves near-perfect recall across all categories but at low precision. Δ trades recall for meaningfully higher precision, reducing false positives.

Experiment Plots

Plot 01

Example Experiment — Sensor Traces & Coherence

Top: 8 sensor traces (normalized) showing industrial valve behavior before and after fault onset. Middle: system-level Δ coherence with alert threshold. Bottom: per-sensor Δ decomposition.

Sensor readings shift subtly at fault onset. Δ coherence captures the cross-sensor structural departure from baseline, providing an interpretable anomaly signal. Interpretable

Plot 02

F1 Score Comparison

Per-experiment F1 scores for Δ coherence vs variance across all 34 experiments.

Δ wins on F1 in 6 of 34 experiments. Where Δ wins, the margin is often substantial — driven by higher precision on the anomalous segments. Mixed

Plot 03

Detection Timeline

When does each method first detect the anomaly relative to the labeled onset? Comparison of lead times across all experiments.

Both methods detect faults before the labeled onset in most cases. Variance tends to alert earlier on average (531 vs 415 samples), but this comes at the cost of more false positives. Early Detection

Plot 04

Sensor Heatmap

Per-sensor Δ coherence values across experiments. Which sensors contribute most to fault detection?

The heatmap reveals which sensor channels carry the strongest fault signatures. Accelerometer and pressure sensors tend to show the earliest coherence departure, consistent with mechanical valve fault physics. Physics-Aligned

Plot 05

Summary Overview

Combined summary: detection rates, F1 distributions, precision-recall tradeoff, and per-category performance.

The summary confirms that Δ coherence provides a viable alternative to variance-based detection on industrial data, with a fundamentally different precision-recall tradeoff. Confirmed

All Experiments

Dataset & Configuration

SKAB (Skoltech Anomaly Benchmark) — Industrial testbed with water circulation system, valves, and 8 sensor channels. 34 experiments across 3 fault categories (valve1, valve2, other). Each experiment contains labeled anomaly onset points. Source: Skoltech / GitHub.

Configuration — Window: 60 samples, step 10. Δ threshold: 0.3. Memory threshold: 0.4. Recovery threshold: 0.4. Variance z-score: 2.5.

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