Lighting Control System

Mathematical Representation of Metrics

Let \(P_i\) be the PPFD at the \(i\)-th point; \(n\) is the number of points.

1. Average PPFD \((\text{PPFD}_{\text{avg}})\):
   \[ \text{PPFD}_{\text{avg}}=\frac{1}{n}\sum_{i=1}^{n} P_i \]
2. Root Mean Squared Error (RMSE):
   \[ \text{RMSE}=\sqrt{\frac{1}{n}\sum_{i=1}^{n}\bigl(P_i-\text{PPFD}_{\text{avg}}\bigr)^2} \]
3. Degree of Uniformity (DOU):
   \[ \text{DOU}=100\times\Bigl(1-\frac{\text{RMSE}}{\text{PPFD}_{\text{avg}}}\Bigr) \]
4. Mean Absolute Deviation (MAD):
   \[ \text{MAD}=\frac{1}{n}\sum_{i=1}^{n}\lvert P_i-\text{PPFD}_{\text{avg}}\rvert \]
5. Coefficient of Variation (CV):
   \[ \sigma=\sqrt{\frac{1}{n}\sum_{i=1}^{n}\bigl(P_i-\text{PPFD}_{\text{avg}}\bigr)^2},\quad \text{CV}=100\times\frac{\sigma}{\text{PPFD}_{\text{avg}}} \]