-
Notifications
You must be signed in to change notification settings - Fork 0
Multi Domain Signal Processing
Sofia Engine extends far beyond mechanical vibration, providing comprehensive digital signal processing for electrical power grids, acoustic emissions, process telemetry, and multi-axis inertial dynamics.
These algorithms are derived and ported from Rootcastle REI SignalLab.
Electrical telemetry from voltage ($v(t)$) and current ($i(t)$) probes is analyzed for power efficiency and power quality disturbances:
-
Active Power (
$P$ ):$$P = \frac{1}{N} \sum_{n=0}^{N-1} v_n \cdot i_n$$ -
Apparent Power (
$S$ ):$$S = V_{rms} \cdot I_{rms}$$ -
Reactive Power (
$Q$ ):$$Q = \sqrt{S^2 - P^2}$$ -
Power Factor (
$PF$ ):$$PF = \frac{P}{S}, \quad PF \in [-1.0, 1.0]$$
Evaluated up to the 50th harmonic order:
Where individual harmonic magnitudes are verified against IEEE 519 limits (
For 3-phase unbalanced AC power systems, Sofia decomposes line voltages into symmetrical components: $$\begin{bmatrix} V_0 \ V_1 \ V_2 \end{bmatrix} = \frac{1}{3} \begin{bmatrix} 1 & 1 & 1 \ 1 & a & a^2 \ 1 & a^2 & a \end{bmatrix} \begin{bmatrix} V_a \ V_b \ V_c \end{bmatrix}, \quad a = e^{j 120^\circ}$$
-
Voltage Unbalance Factor (
$\text{VUF}$ ):$$\text{VUF} = \frac{|V_2|}{|V_1|} \times 100%$$ A$\text{VUF} > 2.0%$ triggers warnings for three-phase motor de-rating.
-
Voltage Sag:
$V_{rms} \in [10%, 90%]$ of nominal. -
Voltage Swell:
$V_{rms} > 110%$ of nominal. -
Interruption:
$V_{rms} < 10%$ of nominal. -
Inrush Current: Instantaneous peak-to-RMS ratio
$> 3.0$ .
High-frequency acoustic emission (AE) and ultrasound telemetry detect stress wave bursts from micro-cracking, partial electrical discharge, and fluid cavitation:
-
AE Energy:
$$E_{AE} = \sum_{n=0}^{N-1} v_n^2 \Delta t$$ -
Counts: Number of rising threshold crossings (
$> 3\sigma$ ). - Rise Time: Elapsed time from first threshold crossing to peak amplitude.
- Duration: Total time the burst envelope remains above threshold.
-
Cavitation Index (
$C_p$ ):$$C_p = \frac{\sum_{k: 5\text{kHz} \le f_k \le 20\text{kHz}} |X_k|^2}{\sum_k |X_k|^2}$$ Detects pump and valve cavitation before mechanical pitting occurs.
-
Temperature Rate of Change:
$\frac{dT}{dt}$ (in$^\circ\text{C/s}$ or$^\circ\text{C/min}$ ) identifies sudden thermal runaways or heat-sink failures. - Thermal Inertia & Delta: Dynamic difference between peak and ambient process temperature.
- Hydraulic Pressure Pulsation: Peak-to-peak pressure swings and pressure crest factor for detecting water hammer and valve chatter.
-
Acceleration Vector Magnitude:
$$|\mathbf{a}| = \sqrt{a_x^2 + a_y^2 + a_z^2}$$ -
Dynamic Tilt (Pitch & Roll):
$$\text{Pitch} = \text{atan2}(-a_x, \sqrt{a_y^2 + a_z^2}), \quad \text{Roll} = \text{atan2}(a_y, a_z)$$ -
Dynamic Jerk:
$$\mathbf{j} = \frac{d\mathbf{a}}{dt}$$ Monitors mechanical shock and high-stress robot arm reversals.