Vibration Depth Index (VDI): A Cross-Domain Structural Signal Instrument — Validation Across EEG, Mechanical Fault Detection, and Network Intrusion Detection

Standard signal analysis methods characterise signals primarily through amplitude, frequency content, and statistical distribution. These representations are not designed to capture whether a signal reflects a structurally coherent underlying process. This paper presents the Vibration Depth Index (VDI), a domain-agnostic measurement instrument designed to quantify a structural property of signals distinct from amplitude and frequency. VDI is defined explicitly as an instrument rather than a predictive model or analytical framework. Three independent empirical validations are reported: (1) pre-ictal state detection in scalp EEG recordings using the CHB-MIT dataset; (2) early mechanical bearing fault detection using the CWRU Bearing Data Center dataset; (3) structural anomaly detection in network traffic using the UNSW-NB15 dataset, achieving 99.8% alert reduction at zero false positives and zero false negatives. Core computational mechanisms are proprietary and are not disclosed in this paper.