Condition Monitoring & Machine Health

Condition Monitoring & Machine Health

Sofia Engine transforms raw time-series telemetry into actionable mechanical condition assessments using statistical anomaly detectors, deterministic diagnostic rule matrices, and uncertainty-bounded health scores.

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1. Vibration Severity Framework (ISO 10816 / ISO 20816)

Industrial condition monitoring classifies vibration severity based on machine size, mounting stiffness, and power rating:

Zone	Severity Status	Operational Guidance
Zone A	Newly Commissioned	Normal, vibration of newly commissioned machines.
Zone B	Unrestricted Operation	Acceptable for long-term continuous operation without restriction.
Zone C	Restricted Operation	Unsatisfactory for long-term continuous operation; plan remedial action.
Zone D	Damage Probable	Vibration severity is sufficient to cause damage to the machine. Trip/Shutdown required.

Sofia evaluates RMS velocity ($\text{mm/s}$) and RMS acceleration ($g$) against configurable boundary thresholds derived from these standards.

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2. Statistical Anomaly Detectors

Sofia Engine provides a collection of pluggable statistical detectors in sofia_ai.inference.detectors:

1. Robust Median Absolute Deviation (MAD)

Unlike standard deviation, which is easily distorted by fault transients, MAD provides a 50% breakdown point:

$$\text{MAD} = \text{median}\left(\left|x_i - \text{median}(\mathbf{x})\right|\right)$$

The normalized robust $z$-score is:

$$M_i = \frac{0.6745 \cdot (x_i - \text{median}(\mathbf{x}))}{\text{MAD}}$$

An anomaly is flagged when $|M_i| > \theta$ (typically $\theta = 3.0$ or $3.5$).

2. Exponentially Weighted Moving Average (EWMA)

For detecting subtle, progressive drifts in bearing temperature or baseline vibration:

$$Z_t = \lambda x_t + (1 - \lambda) Z_{t-1}, \quad \lambda \in (0, 1]$$

The control limits at time $t$ are:

$$\text{UCL/LCL} = \mu_0 \pm L \sigma \sqrt{\frac{\lambda}{2 - \lambda}\left[1 - (1 - \lambda)^{2t}\right]}$$

3. Cumulative Sum Control Chart (CUSUM)

Detects small persistent shifts in mean level:

$$S_t^+ = \max(0, S_{t-1}^+ + x_t - \mu_0 - K)$$ $$S_t^- = \max(0, S_{t-1}^- - x_t + \mu_0 - K)$$

Where $K$ is the reference value (allowable slack) and an alarm triggers if $S_t^+ > H$ or $S_t^- > H$.

4. Rolling Z-Score & Interquartile Range (IQR)

• Z-Score: $$z = \frac{x_t - \mu_w}{\sigma_w}$$
• IQR: $$\text{IQR} = Q_3 - Q_1, \quad \text{Bounds} = [Q_1 - 1.5 \cdot \text{IQR}, Q_3 + 1.5 \cdot \text{IQR}]$$

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3. Data Quality & Confidence Degradation

Sofia's diagnostic pipeline scales its confidence based on the integrity of the underlying data:

flowchart TD
    S["Raw Sensor Input"] --> V{"Validation Filter"}
    V -->|Non-finite NaN / Inf| INV["Quality: INVALID\n(Discard / Count)"]
    V -->|Out of Physical Range| OOR["Quality: OUT_OF_RANGE\n(Confidence Scaled: 0.2)"]
    V -->|Duplicate Timestamp| DUP["Quality: DUPLICATE\n(Confidence Scaled: 0.3)"]
    V -->|Age > max_age_s| STL["Quality: STALE\n(Confidence Scaled: 0.5)"]
    V -->|Normal| GD["Quality: GOOD\n(Confidence Scaled: 1.0)"]
    
    INV & OOR & DUP & STL & GD --> DIAG["Diagnostic Engine"]

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The Confidence Rule

Sofia Engine enforces SOFIA-DQ-003: $$\text{Confidence}{final} = \text{Confidence}{model} \cdot Q_{factor}$$

Where:

• $Q(\text{GOOD}) = 1.0$
• $Q(\text{STALE}) = 0.5$
• $Q(\text{DUPLICATE}) = 0.3$
• $Q(\text{OUT_OF_RANGE}) = 0.2$
• $Q(\text{MISSING}) = 0.0$

A degraded data stream never produces a falsely confident critical diagnosis.

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4. Holistic Machine Health Scoring

The compute_health_score() function maps all active HealthEvents into a single 0–100 index:

$$H = 100 - \min\left(100, \sum_{i=1}^{K} w_i \cdot \mathcal{S}_i \cdot Q_i\right)$$

• $w_i$: Diagnostic rule weight $\in [0, 1]$
• $\mathcal{S}_i$: Event severity penalty:
  • NORMAL: $0$
  • LOW: $15$
  • MEDIUM: $35$
  • HIGH: $65$
  • CRITICAL: $100$
• $Q_i$: Quality factor of the source telemetry

Dynamic Uncertainty Bounds

The uncertainty interval $[H_{lower}, H_{upper}]$ is dynamically computed:

$$H_{lower} = \max(0, H - \delta), \quad H_{upper} = \min(100, H + \delta)$$

Where $\delta = \sum_{i=1}^K u_i \cdot \mathcal{S}_i$ aggregates individual event uncertainties $u_i$. If telemetry quality drops or sensor drift is observed, the uncertainty band widens, alerting engineers that diagnostic certainty has diminished.