Table 1 Nomenclature.

From: A multi dataset validation model for hybrid feature selection in wind energy maximum power point tracking systems

Symbol

Description

Problem formulation

\({\varvec{X}}=\{{{\varvec{x}}}_{1},...,{{\varvec{x}}}_{{\varvec{d}}}\}\)

Complete feature set from SCADA sensors

\({\varvec{S}}\subseteq {\varvec{X}}\)

Selected feature subset after optimization

\({\varvec{z}}\in \{0,1{\}}^{{\varvec{d}}}\)

Binary selection vector (\({z}_{i}=1\) if feature included)

\({\varvec{Y}}\)

Target variable (active power or rotor speed)

\({{\varvec{n}}}_{{\varvec{m}}{\varvec{i}}{\varvec{n}}},{{\varvec{n}}}_{{\varvec{m}}{\varvec{a}}{\varvec{x}}}\)

Feature count constraints (minimum for stability, maximum for computational feasibility)

Objective functions

\({{\varvec{f}}}_{1}({\varvec{S}})\)

Validation loss (prediction accuracy)

\({{\varvec{f}}}_{2}({\varvec{S}})\)

Normalized subset size $(

\({\varvec{L}}({\varvec{M}},{\varvec{S}})\)

Cross-validation MSE of model trained on subset \(S\)

Mutual information

\({\varvec{M}}{\varvec{I}}({{\varvec{X}}}_{{\varvec{i}}},{\varvec{Y}})\)

Mutual information between feature \({X}_{i}\) and target

\({\varvec{H}}(\cdot )\)

Shannon entropy

\({\varvec{\beta}}\)

Retention ratio (proportion of top-ranked features retained)

\({\varvec{\theta}}\)

MI filtering threshold

\({\varvec{h}}\)

Silverman’s bandwidth parameter

AMO-BHS parameters

HMCR \(\left({\varvec{t}}\right)\)

Harmony memory considering rate (exploration–exploitation balance)

PAR \(\left({\varvec{t}}\right)\)

Pitch adjustment rate (local search intensity)

\({\boldsymbol{\alpha }}_{{\varvec{H}}{\varvec{M}}{\varvec{C}}{\varvec{R}}}\)

Power-law exponent for HMCR adaptation (Eq. 23)

\({\boldsymbol{\alpha }}_{{\varvec{P}}{\varvec{A}}{\varvec{R}}}\)

Exponential decay coefficient for PAR adaptation (Eq. 24)

\({\varvec{H}}{\varvec{M}}\)

Harmony memory (current solution population)

\({\varvec{E}}\)

Elite archive (non-dominated solutions)

\({\mathcal{P}}^{\boldsymbol{*}}\)

Final Pareto front