Δ.72 on UCI Power

Key Results

Across 34,190 hours of household power data (1,418 rolling windows), the Δ coherence metric triggered 432 alerts while variance-based detection found only 1. Of the Δ alerts, 431 were coherence-only detections — structural regime shifts invisible to variance. The mean Δ value of 0.425 indicates sustained departure from baseline coherence across the dataset.

Method Comparison

Experiment Plots

Plot 01

Coherence Overview

Full timeline of Δ coherence across 34,190 hours. Top: raw power signals. Middle: system-level Δ with alert threshold. Bottom: per-feature Δ decomposition.

Clear seasonal structure in coherence: winter months show higher Δ (more departure from baseline), while summer months are more stable. The framework captures both gradual seasonal drift and abrupt consumption regime changes. Seasonal Signal

Plot 02

Monthly Coherence Heatmap

Month-by-month coherence levels across all 4 years. Color intensity maps to mean Δ value.

The heatmap reveals a repeating annual pattern: coherence peaks in winter (Dec–Feb) and troughs in summer (Jul–Aug). 7 months exceed the high-coherence threshold while 19 remain in the low range. Repeatable

Plot 03

Daily Consumption Profile

Average hourly power consumption profile showing intra-day patterns and their relationship to coherence dynamics.

Daily profiles show distinct morning and evening peaks typical of residential consumption. Δ is sensitive to changes in these temporal patterns — a shift in peak timing registers as a coherence change even if total consumption remains constant. Temporal Sensitivity

Plot 04

Alert Distribution

Distribution of Δ alerts across the timeline. Where and when does the coherence framework detect structural shifts?

Alerts cluster around seasonal transitions and holiday periods, consistent with genuine changes in household energy behavior. The 431 coherence-only alerts represent events completely invisible to variance-based monitoring. Behavioral Shifts

Plot 05

Multi-Feature Coherence

Per-feature Δ decomposition across all 7 electrical measurements. Which features drive the coherence signal?

Sub-metering channels show the most variable coherence profiles, reflecting appliance-level usage pattern changes. Global active power and intensity track closely, while voltage maintains lower Δ values throughout — consistent with grid stability. Feature Decomposition

Monthly Coherence

48 months analyzed. Coherence levels: High ≥ 0.6   Moderate 0.35–0.6   Low < 0.35

Dataset

UCI Household Electric Power Consumption — Measurements from a single household in Sceaux, France. 4 years of data (Dec 2006 – Nov 2010) at 1-minute resolution, resampled to hourly (34,190 readings). 7 electrical features covering global power, voltage, intensity, and 3 sub-metering circuits. Source: UCI Machine Learning Repository.

Configuration — Baseline: first 8 weeks. Window: 168 hours (1 week), step 24 hours. Δ threshold: 0.3. Resample: 1h. Variance z-score: 2.5.

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