338 lines
11 KiB
TeX
338 lines
11 KiB
TeX
% --- Glossary Definitions ---
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% Note: Descriptions are based on the provided Indonesian text but translated to English
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% for typical glossary conventions. You can adjust the language as needed.
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\newglossaryentry{not:signal}{
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name={\ensuremath{S}},
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description={vektor sinyal akselerometer berdimensi 1$\times$262144},
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sort={s},
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type=notation,
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}
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\newglossaryentry{not:sampling_freq}{
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name={\ensuremath{f_s}},
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description={frekuensi dengan nilai \textit{sampling} ($s$) di mana sinyal kontinu didigitalkan},
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sort={fs},
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type=notation,
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}
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\newglossaryentry{not:time_length}{
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name={\ensuremath{t}},
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description={panjang waktu data dalam detik},
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sort={t},
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type=notation,
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}
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\newglossaryentry{not:dataset_A}{
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name={\ensuremath{\mathcal{A}}},
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description={matriks dataset A},
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sort={adataset},
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type=notation,
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}
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\newglossaryentry{not:dataset_B}{
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name={\ensuremath{\mathcal{B}}},
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description={matriks dataset B},
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sort={bdataset},
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type=notation,
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}
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\newglossaryentry{not:damage_file}{
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name={\ensuremath{\mathbf{D}}},
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description={matriks akselerometer untuk setiap berkas dengan bentuk $262144\times30$},
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sort={filedamage},
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type=notation,
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}
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\newglossaryentry{not:joint_index}{
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name={\ensuremath{n}},
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description={indeks atau nomor kerusakan \textit{joint}},
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sort={indexjoint},
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type=notation,
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}
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\newglossaryentry{not:damage_file_set_case}{
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name={\ensuremath{\mathbf{d}}},
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description={set matriks kerusakan},
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sort={damagefilesetcase},
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type=notation,
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}
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\newglossaryentry{not:k}{
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name={$k$},
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description={Index for measurement nodes, an integer ranging from 0 to 29.},
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sort={k},
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type=notation,
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}
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\newglossaryentry{not:Fk}{
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name={$F_{k}$},
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description={Filename string for the raw time-domain signal from node $k$. The specific format mentioned is \texttt{zzzAD}$k$\texttt{.TXT}.},
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sort={Fk},
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type=notation,
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}
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\newglossaryentry{not:nkFk}{
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name={$n_{k}^{F_{k}}$},
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description={Represents the measurement \textit{node} with index $k$. The raw time-domain signal data from this node, $x_k$, has a length of $L=262144$ samples.},
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sort={nkFk},
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type=notation,
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}
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\newglossaryentry{not:i}{
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name={$i$},
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description={Index for ``damage-case'' folders, an integer ranging from 0 to 5.},
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sort={i},
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type=notation,
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}
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\newglossaryentry{not:di}{
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name={\ensuremath{d_{i}}},
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description={Set representing the $i$-th damage scenario, containing data from five consecutive nodes: $\bigl\{\,n_{5i}^{F_{5i}},\;n_{5i+1}^{F_{5i+1}},\;\dots,\;n_{5i+4}^{F_{5i+4}}\bigr\}$. Cardinality: $|d_i|=5$ nodes.},
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sort={di},
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type=notation,
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}
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\newglossaryentry{not:diTD}{
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name={$d_{i}^{\mathrm{TD}}$},
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description={Time-domain subset of nodes from damage case $d_i$, containing only the first and last nodes: $\bigl\{\,n_{5i}^{F_{5i}},\;n_{5i+4}^{F_{5i+4}}\bigr\}$. Cardinality: $|d_{i}^{\mathrm{TD}}| = 2$ nodes.},
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sort={diTD},
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type=notation,
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}
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\newglossaryentry{not:calT}{
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name={$\mathcal{T}$},
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description={Short-Time Fourier Transform (STFT) operator. It maps a raw time-domain signal $n_k^{F_k}$ (or $x_k$) from $\mathbb{R}^{L}$ (with $L=262144$) to a magnitude spectrogram matrix $\widetilde{n}_k^{F_k}$ in $\mathbb{R}^{513 \times 513}$.},
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sort={Tcal},
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type=notation,
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}
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\newglossaryentry{not:L}{
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name={$L$},
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description={Length of the raw time-domain signal, $L=262144$ samples.},
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sort={L},
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type=notation,
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}
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\newglossaryentry{not:Nw}{
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name={$N_{w}$},
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description={Length of the Hanning window used in the STFT, $N_{w}=1024$ samples.},
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sort={Nw},
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type=notation,
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}
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\newglossaryentry{not:Nh}{
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name={$N_{h}$},
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description={Hop size (or step size) used in the STFT, $N_{h}=512$ samples.},
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sort={Nh},
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type=notation,
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}
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\newglossaryentry{not:wn}{
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name={$w[n]$},
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description={Value of the Hanning window function at sample index $n$. The window spans $N_w$ samples.},
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sort={wn},
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type=notation,
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}
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\newglossaryentry{not:n_summation}{
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name={$n$},
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description={Sample index within the Hanning window and for the STFT summation, an integer ranging from $0$ to $N_w-1$.},
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sort={n_summation},
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type=notation,
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}
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\newglossaryentry{not:xkm}{
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name={$x_k[m]$}, % Or x_k if it's treated as the whole signal vector
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description={Represents the raw time-domain signal for node $k$. As a discrete signal, it consists of $L=262144$ samples. $x_k[m]$ would be the $m$-th sample.},
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sort={xkm},
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type=notation,
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}
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\newglossaryentry{not:Skpt}{
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name={$S_k(p,t)$},
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description={Complex-valued result of the STFT for node $k$ at frequency bin $p$ and time frame $t$. This is a scalar value for each $(p,t)$ pair.},
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sort={Skpt},
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type=notation,
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}
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\newglossaryentry{not:p}{
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name={$p$},
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description={Frequency bin index in the STFT or spectrogram, an integer ranging from $0$ to $512$.},
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sort={p},
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type=notation,
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}
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\newglossaryentry{not:t_stft}{ % Differentiating t for STFT time frame and t for feature vector time slice if necessary
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name={$t$},
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description={Time frame index in the STFT or spectrogram, an integer ranging from $0$ to $512$. Also used as the time slice index for extracting feature vectors $\mathbf{x}_{i,s,r,t}$ from spectrograms.},
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sort={t},
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type=notation,
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}
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\newglossaryentry{not:ntildekFk}{ % New entry for the matrix
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name={$\widetilde{n}_k^{F_k}$},
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description={The magnitude spectrogram matrix for node $k$, obtained by applying the STFT operator $\mathcal{T}$ to the time-domain signal $n_k^{F_k}$. This matrix is an element of $\mathbb{R}^{513 \times 513}$.},
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sort={ntildekFk},
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type=notation,
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}
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\newglossaryentry{not:ntildekFkpt}{ % Modified entry for the element
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name={$\widetilde{n}_k^{F_k}(p,t)$},
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description={Scalar value representing the magnitude of the STFT for node $k$ at frequency bin $p$ and time frame $t$; specifically, $\widetilde{n}_k^{F_k}(p,t) = |S_k(p,t)|$. This is an element of the spectrogram matrix $\widetilde{n}_k^{F_k}$.},
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sort={ntildekFkpt},
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type=notation,
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}
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\newglossaryentry{not:R}{
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name={\ensuremath{\mathbb{R}}},
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description={The set of real numbers. Used to denote vector spaces like $\mathbb{R}^{N}$ (N-dimensional real vectors) or $\mathbb{R}^{M \times N}$ (M-by-N real matrices).},
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sort={Rbb},
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type=notation,
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}
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\newglossaryentry{not:diFD}{
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name={$d_{i}^{\mathrm{FD}}$},
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description={Frequency-domain subset for damage case $i$. It contains two spectrogram matrices: $\bigl\{\,\widetilde{n}_{5i}^{F_{5i}},\; \widetilde{n}_{5i+4}^{F_{5i+4}}\,\bigr\}$, where each spectrogram $\widetilde{n}$ is in $\mathbb{R}^{513 \times 513}$. Cardinality: $|d_{i}^{\mathrm{FD}}| = 2$ spectrograms.},
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sort={diFD},
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type=notation,
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}
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\newglossaryentry{not:r_repetition}{
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name={$r$},
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description={Repetition index within a single damage case, an integer ranging from $0$ to $4$.},
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sort={r_repetition},
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type=notation,
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}
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\newglossaryentry{not:xboldisr}{
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name={$\mathbf{x}_{i,s,r,t}$},
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description={Feature vector (a row or column, often referred to as a time slice) taken from the $r$-th spectrogram repetition, for damage case $i$ and sensor side $s$, at time slice $t$. This vector is an element of $\mathbb{R}^{513}$.},
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sort={xisrt_bold},
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type=notation,
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}
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% Efficiency metrics
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\newglossaryentry{not:S_i}{
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name={\ensuremath{S_i}},
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description={Rata-rata skor akurasi hasil \textit{fold cross-validation} pada \textit{grid-search} (0–1)},
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sort={S_i},
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type=notation,
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}
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\newglossaryentry{not:T_i}{
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name={\ensuremath{T_i}},
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description={Rata-rata waktu latih hasil \textit{fold cross-validation} pada \textit{grid-search} (dalam detik)},
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sort={T_i},
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type=notation,
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}
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\newglossaryentry{not:E_i}{
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name={\ensuremath{E_i}},
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description={Metrik efisiensi untuk rasio antara akurasi dan waktu latih \textit{fold} pada \textit{grid-search}},
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sort={E_i},
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type=notation,
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}
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% SVM Hyperparameters
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\newglossaryentry{not:C}{
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name={\ensuremath{C}},
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description={Parameter regulasi pada SVM yang mengontrol \textit{trade-off} antara memaksimalkan margin dan meminimalkan kesalahan klasifikasi pada data pelatihan. Nilai yang lebih besar memberikan penalti lebih tinggi untuk kesalahan klasifikasi, sehingga menghasilkan margin yang lebih sempit.},
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sort={C},
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type=notation,
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}
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\newglossaryentry{not:gamma}{
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name={\ensuremath{\gamma}},
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description={Parameter kernel pada SVM dengan kernel RBF yang menentukan jangkauan pengaruh dari satu sampel pelatihan. Nilai kecil berarti jangkauan pengaruh yang luas, sedangkan nilai besar berarti jangkauan yang sempit.},
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sort={gamma},
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type=notation,
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}
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\newglossaryentry{not:s_sensor}{
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name={$s$},
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description={Index representing the sensor side (e.g., identifying Sensor A or Sensor B).},
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sort={s_sensor},
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type=notation,
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}
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\newglossaryentry{not:yi}{
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name={$y_{i}$},
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description={Scalar label for the damage case $i$, defined as $y_i = i$. This is an integer value from 0 to 5.},
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sort={yi},
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type=notation,
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}
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\newglossaryentry{not:Lambda}{
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name={$\Lambda(i,s,r,t)$},
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description={Slicing function that concatenates a feature vector $\mathbf{x}_{i,s,r,t} \in \mathbb{R}^{513}$ with its corresponding damage case label $y_i \in \mathbb{R}$, resulting in a combined vector $\bigl[\,\mathbf{x}_{i,s,r,t}, \;y_{i}\bigr] \in \mathbb{R}^{514}$.},
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sort={Lambda},
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type=notation,
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}
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\newglossaryentry{not:calDs}{
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name={$\mathcal{D}^{(s)}$},
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description={The complete dataset for sensor side $s$. It is a collection of $15390$ data points, where each point is a vector in $\mathbb{R}^{514}$ (513 features + 1 label). Thus, the dataset can be viewed as a matrix of size $15390 \times 514$.},
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sort={Dcal_s},
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type=notation,
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}
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% --- End Glossary Definitions ---
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% --- Added Missing Notations ---
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\newglossaryentry{not:U}{
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name={\ensuremath{\mathbf{U}}},
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description={Matrix representing undamaged data, $\mathbf{U} \in \mathbb{R}^{262144 \times 30}$},
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sort={U},
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type=notation,
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}
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\newglossaryentry{not:Dn}{
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name={\ensuremath{\mathbf{D}^{(n)}}},
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description={Matrix representing damaged data for joint $n$, $\mathbf{D}^{(n)} \in \mathbb{R}^{262144 \times 30}$},
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sort={Dn},
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type=notation,
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}
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\newglossaryentry{not:aj}{
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name={\ensuremath{\mathbf{a}_{j}^{(n)}}},
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description={Acceleration vector for joint $j$ in case $n$, $\mathbf{a}_{j}^{(n)} \in \mathbb{R}^{262144}$},
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sort={aj},
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type=notation,
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}
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\newglossaryentry{not:Cn}{
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name={\ensuremath{\mathcal{C}(n)}},
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description={Set of healthy complementary pairs for file $n$},
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sort={Cn},
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type=notation,
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}
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\newglossaryentry{not:CU}{
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name={\ensuremath{\mathcal{C}_{\mathbf{U}}}},
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description={Set of pairs from undamaged data $\mathbf{U}$},
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sort={CU},
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type=notation,
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}
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\newglossaryentry{not:DA}{
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name={\ensuremath{\mathcal{D}_A}},
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description={Dataset for the upper sensor channel},
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sort={DA},
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type=notation,
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}
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\newglossaryentry{not:DB}{
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name={\ensuremath{\mathcal{D}_B}},
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description={Dataset for the lower sensor channel},
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sort={DB},
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type=notation,
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}
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\newglossaryentry{not:D}{
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name={\ensuremath{\mathcal{D}}},
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description={Labeled dataset containing features and labels},
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sort={D},
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type=notation,
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}
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\newglossaryentry{not:concat_time}{
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name={\ensuremath{\operatorname{concat}_{\text{time}}}},
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description={Concatenation operator over time},
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sort={concat_time},
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type=notation,
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}
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% --- End Added Missing Notations --- |