Alright, let’s pull back the curtain on that last step so the score numbers in ITACA REXELweb make total sense.
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## ⚖️ How the Normalization Works
In ITACA REXELweb, the raw RMSE in spectral units (like cm/s²) is **scaled** by the average size of the target values in the matching period range. This removes the unit dependency and gives a dimensionless “score” you can compare across different spectra.
The formula looks like:
\[
\text{Score} = \frac{\sqrt{\frac{\sum_{i=1}^{N} \left( S_\text{record}(T_i) - S_\text{target}(T_i) \right)^2}{N}}}
{\frac{\sum_{i=1}^{N} S_\text{target}(T_i)}{N}}
\]
Where the denominator is just the **mean target ordinate** over those N periods.
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## 🔢 Continuing Our Example
From the fake numbers before:
- RMSE = 12.65 cm/s²
- Mean target value = \( (200 + 320 + 270 + 250 + 190) / 5 = 246 \) cm/s²
So:
\[
\text{Score} = \frac{12.65}{246} \approx 0.0514
\]
Voilà — your “0.05” score.
This now represents a **5.1 % average RMS deviation** from the target spectrum in the match window, independent of the actual amplitude scale.
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## 🗝️ Why This Matters
- **Dimensionless** → lets you compare different projects or design levels directly.
- **More intuitive** → you can think of it as a “percent fit error.”
- **Consistent** → whether your target peak is 100 or 1,000 cm/s², the interpretation is the same.
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If you’d like, I can also give you a **visual mini‑plot** showing how the record and target spectra differ in that example, so you can see exactly where the deviations creep in — would you like me to?
