Optimization and early warning strategy for wind turbine blade acoustic signature monitoring array based on wind farm simulation | International Journal for Simulation and Multidisciplinary Design Optimization (IJSMDO)

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Table 2

Description of key symbols.

Symbol	Meaning/Description
$x_{s} = (x_{s}, y_{s}, z_{s})$	Spatial coordinates of the sound source point
$x_{m}^{(k)} = (x_{m}^{(k)}, y_{m}^{(k)}, z_{m}^{(k)})$	Spatial coordinates of the k-th microphone sensor
N_m	Total number of sensors in the microphone array
p(x,t)	Time-domain sound pressure signal at spatial point x
$P (x, ω)$	Complex amplitude of sound pressure in frequency domain at angular frequency ω
f_c	Center frequency for voiceprint feature analysis
u	Mean incoming wind velocity vector
θ_y	Yaw angle of the wind turbine rotor
c₀	Ambient sound speed
$k = ω / c_{0}$	Wave number
$H (x_{m}, x_{s}, ω)$	Frequency-domain transfer function from sound source to sensor
$\hat{H} (x_{m}, x_{s}, ω)$	Transfer function corrected for shear layer refraction
SNR(A)	Average SNR over the monitoring region for array configuration A
$A = x m^{(k)} k = 1^{N_{m}}$	Spatial configuration of the microphone array
d_min	Minimum spacing constraint between adjacent sensors
${\hat{f}}_{Krig} (A)$	Predicted objective function value from the Kriging surrogate model
$σ_{Krig}^{2} (A)$	Prediction variance of the Kriging surrogate model
$F \in ℝ^{T \times F}$	Time-frequency feature map output from beamforming
$W_{Q}, W_{K}, W_{V}$	Query, key, and value projection matrices in attention mechanism
$α_{i j}$	Attention weight between the i-th and j-th feature positions
$L_{BCE}$	Binary cross-entropy loss function
$L_{CL}$	Contrastive learning loss function
$L_{total}$	Total loss function for joint training
λ₁,λ₂	Weighting coefficients for loss terms
τ	Warning decision threshold
B	Budget parameter for surrogate model updating

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