diff --git a/latex/chapters/id/04_results.tex b/latex/chapters/id/04_results.tex index 567f9f6..4f2e6fa 100644 --- a/latex/chapters/id/04_results.tex +++ b/latex/chapters/id/04_results.tex @@ -1,149 +1,666 @@ \chapter{Hasil Penelitian dan Pembahasan} +Bab ini menyajikan hasil dari proses ekstraksi fitur, analisis eksplorasi data, +pengembangan model klasifikasi, serta evaluasi kinerja model. +Hasil yang diperoleh selanjutnya dianalisis untuk menilai kemampuan model dengan fitur yang telah diekstraksi +dalam mendeteksi dan mengklasifikasikan lokasi kerusakan struktur \textit{grid}. +% \section{Pendahuluan Singkat} +% Bab ini menyajikan hasil evaluasi model untuk prediksi lokasi kerusakan berbasis fitur domain waktu dan frekuensi yang diekstrak dari STFT. Tujuan utama evaluasi adalah menguji apakah kombinasi fitur waktu--frekuensi dapat meningkatkan kinerja klasifikasi dibandingkan masing-masing domain secara terpisah, serta menilai kelayakan pendekatan sensor terbatas untuk penerapan di lapangan. -\section{Pendahuluan Singkat} -Bab ini menyajikan hasil evaluasi model untuk prediksi lokasi kerusakan berbasis fitur domain waktu dan frekuensi yang diekstrak dari STFT. Tujuan utama evaluasi adalah menguji apakah kombinasi fitur waktu--frekuensi dapat meningkatkan kinerja klasifikasi dibandingkan masing-masing domain secara terpisah, serta menilai kelayakan pendekatan sensor terbatas untuk penerapan di lapangan. +% Secara ringkas, kami menampilkan: (i) performa utama pada data uji, (ii) analisis per-kelas dan pola kesalahan, (iii) studi ablation dan sensitivitas mencakup fitur, parameter STFT, serta jumlah/posisi sensor, dan (iv) uji robustness serta implikasi implementasi. Detail metodologi eksperimen telah diuraikan pada Bab Metodologi; bagian ini berfokus pada temuan empiris dan interpretasinya. -Secara ringkas, kami menampilkan: (i) performa utama pada data uji, (ii) analisis per-kelas dan pola kesalahan, (iii) studi ablation dan sensitivitas mencakup fitur, parameter STFT, serta jumlah/posisi sensor, dan (iv) uji robustness serta implikasi implementasi. Detail metodologi eksperimen telah diuraikan pada Bab Metodologi; bagian ini berfokus pada temuan empiris dan interpretasinya. +\section{Hasil Ekstraksi Fitur STFT} +Bagian ini menyajikan contoh hasil transformasi STFT yang diterapkan +pada sinyal percepatan dari sensor atas dan bawah. +Analisis dilakukan untuk memastikan konsistensi pola spektral +dan kesetaraan ukuran data antar kelas sebelum proses pelatihan model. -\section{Rancangan Evaluasi} -\subsection{Dataset dan Pembagian Data} -Evaluasi dilakukan pada himpunan data berlabel yang terdiri dari \textit{[N\_total]} sampel dengan \textit{[K]} kelas lokasi kerusakan. Data dibagi menjadi \textit{[N\_train]} sampel pelatihan, \textit{[N\_val]} validasi, dan \textit{[N\_test]} pengujian, atau menggunakan skema \textit{k}-fold dengan \textit{[k]} lipatan (rincian skema dipertahankan konsisten dengan Bab Metodologi). Potensi ketidakseimbangan kelas dicatat dengan rasio maksimum/minimum sekitar \textit{[imbalance\_ratio:1]}. - -\subsection{Pra-pemrosesan dan Ekstraksi Fitur} -Sinyal diproses dengan normalisasi \textit{[jenis normalisasi/standarisasi]}, dan augmentasi \textit{[jenis augmentasi, jika ada]}. Fitur domain waktu dan frekuensi diekstraksi; komponen frekuensi diperoleh dari STFT dengan window Hann, ukuran jendela \textit{[win\_size]} sampel, overlap - -\subsection{Model dan Metrik Evaluasi} -Model utama adalah SVM dengan kernel \textit{[RBF/Linear]} dan pemilihan hyperparameter (\textit{C}, \textit{gamma}) melalui \textit{[grid/random/bayes] search} pada data validasi. Metrik evaluasi meliputi Akurasi, Macro-F1, Macro-Precision, Macro-Recall, Balanced Accuracy, serta Cohen's Kappa. Untuk analisis multi-kelas yang lebih tajam, kami juga melaporkan metrik per-kelas dan Confusion Matrix. - -\section{Hasil Utama} -\begin{table}[htbp] - \centering - \caption{Hasil utama pada data uji untuk beberapa konfigurasi fitur dan model. Nilai diisi dari eksperimen akhir.} - \label{tab:main-results} - \begin{tabular}{lccc} - \hline - Konfigurasi & Akurasi & Macro-F1 & Kappa \\ - \hline - Time-domain + SVM-RBF & -- & -- & -- \\ - Freq-domain + SVM-RBF & -- & -- & -- \\ - Kombinasi (Time+Freq) + SVM-RBF & \textbf{--} & \textbf{--} & \textbf{--} \\ - \hline - \end{tabular} -\end{table} - -Konfigurasi terbaik diperoleh pada kombinasi fitur waktu--frekuensi dengan SVM-\textit{[kernel]}, menghasilkan Akurasi sebesar \textit{[acc\_best]}\%, Macro-F1 sebesar \textit{[f1\_best]}\%, dan Kappa sebesar \textit{[kappa\_best]} pada data uji (Tabel~\ref{tab:main-results}). Dibandingkan baseline domain waktu saja, Macro-F1 meningkat sekitar \textit{[delta\_f1\_time]} poin persentase; dibandingkan domain frekuensi saja, peningkatan mencapai \textit{[delta\_f1\_freq]} poin persentase. Hasil ini mengindikasikan bahwa informasi pelengkap antara dinamika temporal dan spektral berkontribusi nyata terhadap separabilitas kelas. - -Performa pada metrik Balanced Accuracy dan Macro-Recall juga konsisten, menandakan model tidak terlalu bias pada kelas mayoritas. Nilai Kappa \textit{[kappa\_best]} mengindikasikan tingkat kesepakatan yang \textit{[moderat/tinggi]} melampaui kebetulan. - -\section{Analisis Per-Kelas dan Kesalahan} +Gambar~\ref{fig:stft-undamaged} memperlihatkan hasil STFT gabungan (\textit{aggregated}) untuk seluruh titik join tanpa kerusakan (kelas 0). \begin{figure}[htbp] \centering - % \includegraphics[width=0.8\textwidth]{img/confusion_matrix.pdf} - \fbox{\begin{minipage}[c][0.30\textheight][c]{0.80\textwidth}\centering - Placeholder Confusion Matrix - \end{minipage}} - \caption{Confusion matrix pada data uji. Isikan gambar aktual dari pipeline evaluasi.} - \label{fig:cm} + \begin{minipage}{0.48\textwidth} + \centering + \includesvg[width=\textwidth, pretex=\tiny]{chapters/img/sensor1/stft-undamaged-1} + % \caption{Caption for the first image.} + % \label{fig:image1} + \end{minipage}\hfill + \begin{minipage}{0.48\textwidth} + \centering + \includesvg[width=\textwidth, pretex=\tiny]{chapters/img/sensor2/stft-undamaged-2} + % \caption{Caption for the second image.} + % \label{fig:image2} + \end{minipage} + \caption{STFT tanpa kerusakan (undamaged). Sensor A (kiri) dan Sensor B (kanan)} + \label{fig:stft-undamaged} \end{figure} -\begin{table}[htbp] - \centering - \caption{Metrik per-kelas pada data uji. Gunakan bila diperlukan untuk melengkapi Confusion Matrix.} - \label{tab:per-class} - \begin{tabular}{lccc} - \hline - Kelas & Precision & Recall & F1 \\ - \hline - A & -- & -- & -- \\ - B & -- & -- & -- \\ - C & -- & -- & -- \\ - % ... tambah baris sesuai jumlah kelas - \hline - \end{tabular} -\end{table} - -Confusion Matrix pada Gambar~\ref{fig:cm} menunjukkan pola salah klasifikasi yang dominan antara kelas \textit{[kelas\_A]} dan \textit{[kelas\_B]}. Dua kelas ini memiliki respons spektral yang mirip pada rentang \textit{[f\_low--f\_high]} Hz, sehingga kesalahan terutama terjadi ketika amplitudo sinyal rendah atau \textit{signal-to-noise ratio} menurun. Sebaliknya, kelas \textit{[kelas\_C]} memperlihatkan separasi yang baik dengan Recall \textit{[recall\_C]}\% dan F1 \textit{[f1\_C]}\% (Tabel~\ref{tab:per-class}). - -Analisis kesalahan kasus-per-kasus menunjukkan bahwa \textit{[proporsi\_\%]}\% prediksi keliru terjadi pada sampel dengan \textit{[ciri sinyal/condisi uji]} dan \textit{[konfigurasi sensor]}. Hal ini menyarankan perlunya \textit{[strategi perbaikan, mis. penambahan fitur bandpass tertentu atau penyeimbangan kelas]}. - -\section{Ablasi dan Sensitivitas} -\subsection{Ablasi Fitur} +Gambar~\ref{fig:stft-damaged-multiple-a} dan Gambar~\ref{fig:stft-damaged-multiple-b} memperlihatkan hasil STFT gabungan (\textit{aggregated}) untuk seluruh titik join dengan kerusakan (kelas 1--6). Setiap 513 segmen waktu merepresentasikan kolom sensor yang ditinjau. \begin{figure}[htbp] \centering - \includegraphics[width=0.75\textwidth]{example-image-a} - \fbox{\begin{minipage}[c][0.22\textheight][c]{0.70\textwidth}\centering - Placeholder Bar Chart: Time vs Freq vs Kombinasi - \end{minipage}} - \caption{Perbandingan performa berdasarkan jenis fitur.} - \label{fig:ablation-features} + \includesvg[width=\textwidth, pretex=\tiny, inkscapelatex=true]{chapters/img/sensor1/stft-damaged-multiple-1.svg} + \caption{STFT sensor A dengan kerusakan (damaged $d_1$\textemdash $d_6$).} + \label{fig:stft-damaged-multiple-a} \end{figure} - -Studi ablation pada Gambar~\ref{fig:ablation-features} menegaskan bahwa kombinasi fitur memberikan peningkatan \textit{[delta\_ablation]} poin persentase pada Macro-F1 dibandingkan fitur domain waktu saja. Hal ini mengindikasikan bahwa karakteristik harmonik dan komponen frekuensi transien yang ditangkap STFT berkontribusi pada pemisahan kelas yang lebih baik. - -\subsection{Parameter STFT dan Windowing} -\begin{table}[htbp] - \centering - \caption{Sensitivitas terhadap parameter STFT pada data validasi.} - \label{tab:stft-sensitivity} - \begin{tabular}{lcccc} - \hline - Window & n\_fft & Overlap & Akurasi & Macro-F1 \\ - \hline - Hann & -- & -- & -- & -- \\ - Hann & -- & -- & -- & -- \\ - (Tanpa window) & -- & -- & -- & -- \\ - \hline - \end{tabular} -\end{table} - -Eksperimen sensitivitas pada Tabel~\ref{tab:stft-sensitivity} memperlihatkan adanya \textit{trade-off} antara resolusi waktu dan frekuensi. Peningkatan \textit{n\_fft} cenderung memperhalus resolusi frekuensi namun mengurangi ketelitian temporal, sedangkan overlap yang lebih besar \textit{[overlap\_\% range]}\% membantu stabilitas estimasi fitur pada sinyal bising. Penggunaan window Hann memberikan kenaikan Macro-F1 sekitar \textit{[delta\_hann]} poin dibanding tanpa window, menegaskan peran pengurangan \textit{spectral leakage}. - -\subsection{Pendekatan Sensor Terbatas} \begin{figure}[htbp] \centering - % placeholder - \includegraphics[width=0.75\textwidth]{example-image-a} - \fbox{\begin{minipage}[c][0.22\textheight][c]{0.70\textwidth}\centering - Placeholder: Performa vs Jumlah/Posisi Sensor - \end{minipage}} - \caption{Dampak jumlah/konfigurasi sensor terhadap performa.} - \label{fig:sensor-limited} + \includesvg[width=1\textwidth, pretex=\tiny, inkscapelatex=true]{chapters/img/sensor2/stft-damaged-multiple-2.svg} + \caption{STFT sensor B dengan kerusakan (damaged $d_1$\textemdash $d_6$).} + \label{fig:stft-damaged-multiple-b} \end{figure} -Hasil pada Gambar~\ref{fig:sensor-limited} menunjukkan bahwa pengurangan dari \textit{[n\_sensors\_full]} menjadi \textit{[n\_sensors\_min]} sensor hanya menurunkan Macro-F1 sekitar \textit{[delta\_perf\_sensors]} poin, khususnya ketika sensor ditempatkan pada \textit{[posisi sensor terbaik]}. Ini mengindikasikan bahwa pendekatan sensor terbatas tetap layak untuk implementasi dengan biaya perangkat keras yang lebih rendah, selama pemilihan posisi sensor dioptimalkan. -\section{Robustness dan Generalisasi} -\begin{table}[htbp] +\section{Analisis Eksplorasi Data} +\label{sec:eda} + +Sebelum tahap pelatihan model dilakukan, diperlukan analisis eksplorasi +untuk memahami distribusi dan karakteristik data fitur hasil ekstraksi +STFT pada himpunan $\mathcal{D}_A$ dan $\mathcal{D}_B$. +Analisis ini bertujuan untuk menilai sejauh mana fitur yang diperoleh +mampu merepresentasikan perbedaan kondisi struktur +serta menentukan parameter reduksi dimensi yang sesuai +pada tahap pemodelan berikutnya. + +\subsection{Analisis Komponen Utama (PCA)} +Transformasi \gls{pca} diterapkan terhadap data fitur berdimensi +$513$ untuk mengevaluasi proporsi variansi yang dapat dijelaskan +oleh setiap komponen utama. +Dengan menghitung \textit{explained variance ratio}, diperoleh +diagram \textit{scree} seperti pada Gambar~\ref{fig:scree_plot}, +yang menunjukkan kontribusi masing-masing komponen terhadap +total variansi data. + +\begin{figure}[H] \centering - \caption{Ringkasan kinerja antar-fold (jika menggunakan k-fold).} - \label{tab:kfold} - \begin{tabular}{lcc} - \hline - Metrik & Rata-rata & Deviasi Standar \\ - \hline - Macro-F1 & -- & -- \\ - Akurasi & -- & -- \\ - \hline - \end{tabular} -\end{table} + \includegraphics[width=.75\textwidth]{chapters/img/sensor1/scree_plot.png} + \caption{Diagram \textit{scree} hasil analisis PCA pada dataset $\mathcal{D}_A$ dan $\mathcal{D}_B$.} + \label{fig:scree_plot} +\end{figure} -Pada skema validasi silang \textit{k}-fold, variasi performa relatif rendah dengan simpangan baku Macro-F1 sebesar \textit{[std\_f1]} (Tabel~\ref{tab:kfold}), menandakan stabilitas model terhadap variasi subset data. Penambahan noise sintetis pada tingkat SNR \textit{[snr levels]} menunjukkan penurunan performa yang \textit{[ringan/sedang/bermakna]} sekitar \textit{[delta\_snr]} poin; augmentasi \textit{[jenis augmentasi]} membantu mengkompensasi sebagian penurunan tersebut. +Dari Gambar~\ref{fig:scree_plot} terlihat bahwa \textit{explained ratio cumulative} 0.95 dicapai pada sekitar 300 komponen utama, +% Sebagai contoh, sepuluh komponen pertama menjelaskan sekitar +% $\alpha\%$ variansi kumulatif pada kanal sensor~A +% dan $\beta\%$ pada kanal sensor~B. +% Hasil ini menunjukkan bahwa terdapat redundansi di antara fitur-fitur +% frekuensi yang diekstraksi, sehingga reduksi dimensi +% dapat dilakukan tanpa kehilangan informasi signifikan. -Pada skenario \textit{domain shift} \textit{[nama skenario]}, model mempertahankan Macro-F1 sebesar \textit{[f1\_shift]}\%, yang menunjukkan \textit{[derajat generalisasi]} terhadap kondisi yang berbeda dari data pelatihan. +\subsection{Reduksi Dimensi Sebelum Visualisasi} +Sebelum diterapkan metode reduksi dimensi non-linear seperti \gls{tsne} +dan \gls{pacmap}, terlebih dahulu dilakukan reduksi dimensi linear +menggunakan \gls{pca} untuk menghilangkan derau dan mengurangi kompleksitas +fitur STFT yang berukuran tinggi ($513$ dimensi). +Langkah ini umum digunakan untuk meningkatkan stabilitas dan efisiensi +proses embedding \parencite{JMLR:v9:vandermaaten08a}. -\section{Perbandingan dengan Pustaka/Baseline} -Temuan kami selaras dengan tren yang dilaporkan oleh \textcite{abdeljaber2017}, khususnya mengenai pentingnya informasi frekuensi untuk mendeteksi lokasi kerusakan. Meskipun demikian, perbedaan \textit{setup} eksperimen (\textit{[jenis struktur/skenario uji]}, konfigurasi sensor, dan definisi kelas) membuat angka metrik tidak dapat dibandingkan secara langsung. Oleh karena itu, perbandingan difokuskan pada pola dan arah peningkatan, bukan nilai absolut. +Pada penelitian ini, beberapa nilai komponen PCA digunakan \\ +($n_\text{components}\in\{512,128,32,8\}$) +untuk menilai pengaruh tingkat reduksi terhadap hasil proyeksi t-SNE +dan PaCMAP. +Gambar~\ref{fig:pca_tsne_pacmap} memperlihatkan contoh visualisasi +dua dimensi hasil reduksi berurutan PCA $\rightarrow$ t-SNE dan +PCA $\rightarrow$ PaCMAP pada dataset $\mathcal{D}_A$. -\section{Kompleksitas dan Implementasi} -Model SVM dengan fitur \textit{[jenis fitur terbaik]} menawarkan waktu inferensi sekitar \textit{[t\_infer\_ms]} ms per sampel pada \textit{[perangkat/CPU/GPU]}. Tahap ekstraksi STFT memerlukan \textit{[t\_stft\_ms]} ms per segmen dengan parameter \textit{[n\_fft]}, overlap \textit{[overlap\_\%]}\%, dan window Hann. Secara keseluruhan, latensi ujung-ke-ujung diperkirakan \textit{[t\_end2end\_ms]} ms, yang \textit{[memadai/belum memadai]} untuk aplikasi \textit{[real-time/near real-time]}. +\begin{figure}[H] + \centering + \subfloat[PCA=512]{\includegraphics[width=.24\textwidth]{chapters/img/sensor1/tsne_original.png}} + \subfloat[PCA=16]{\includegraphics[width=.24\textwidth]{chapters/img/sensor1/tsne_pca16.png}} + \subfloat[PCA=8]{\includegraphics[width=.24\textwidth]{chapters/img/sensor1/tsne_pca8.png}} + \subfloat[PCA=4]{\includegraphics[width=.24\textwidth]{chapters/img/sensor1/tsne_pca4.png}} \\[1ex] + \subfloat[PCA=512]{\includegraphics[width=.24\textwidth]{chapters/img/sensor1/pacmap_original.png}} + \subfloat[PCA=16]{\includegraphics[width=.24\textwidth]{chapters/img/sensor1/pacmap_pca16.png}} + \subfloat[PCA=8]{\includegraphics[width=.24\textwidth]{chapters/img/sensor1/pacmap_pca8.png}} + \subfloat[PCA=4]{\includegraphics[width=.24\textwidth]{chapters/img/sensor1/pacmap_pca4.png}} + \caption{Visualisasi hasil reduksi bertahap pada $\mathcal{D}_A$ dengan PCA $\rightarrow$ t-SNE (baris atas) + dan PCA $\rightarrow$ PaCMAP (baris bawah).} + \label{fig:pca_tsne_pacmap_A} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[PCA=512]{\includegraphics[width=.24\textwidth]{chapters/img/sensor2/tsne_original.png}} + \subfloat[PCA=16]{\includegraphics[width=.24\textwidth]{chapters/img/sensor2/tsne_pca16.png}} + \subfloat[PCA=8]{\includegraphics[width=.24\textwidth]{chapters/img/sensor2/tsne_pca8.png}} + \subfloat[PCA=4]{\includegraphics[width=.24\textwidth]{chapters/img/sensor2/tsne_pca4.png}} \\[1ex] + \subfloat[PCA=512]{\includegraphics[width=.24\textwidth]{chapters/img/sensor2/pacmap_original.png}} + \subfloat[PCA=16]{\includegraphics[width=.24\textwidth]{chapters/img/sensor2/pacmap_pca16.png}} + \subfloat[PCA=8]{\includegraphics[width=.24\textwidth]{chapters/img/sensor2/pacmap_pca8.png}} + \subfloat[PCA=4]{\includegraphics[width=.24\textwidth]{chapters/img/sensor2/pacmap_pca4.png}} + \caption{Visualisasi hasil reduksi bertahap pada $\mathcal{D}_B$ dengan PCA $\rightarrow$ t-SNE (baris atas) + dan PCA $\rightarrow$ PaCMAP (baris bawah).} + \label{fig:pca_tsne_pacmap_B} +\end{figure} -Dengan \textit{[n\_sensors\_min]} sensor, kebutuhan komputasi dan bandwidth data berkurang \textit{[proporsi pengurangan]} dibanding konfigurasi penuh, yang memperbaiki kelayakan implementasi lapangan tanpa mengorbankan akurasi secara signifikan. +Hasil pada Gambar~\ref{fig:pca_tsne_pacmap} menunjukkan bahwa +pengurangan jumlah komponen PCA hingga 8 dimensi +masih mempertahankan pemisahan antar kelas secara visual, +sedangkan reduksi lebih jauh (misalnya $n_\text{components}=4$) +menyebabkan beberapa klaster saling tumpang tindih (\textit{overlap}). +Temuan ini mendukung pemilihan nilai $n_\text{components}$ +sebagai salah satu parameter penting yang diuji dalam +pencarian \textit{grid} pada tahap optimasi model untuk mengurangi kompleksitas model dan efisiensi komputasi. -\section{Ringkasan Bab} +% \subsection{Visualisasi Ruang Fitur Non-Linear} +% Selain PCA, digunakan dua metode reduksi dimensi non-linear, +% yaitu \gls{tsne} dan \gls{pacmap}, +% untuk memvisualisasikan struktur data dalam ruang dua dimensi. +% Kedua metode ini memproyeksikan vektor fitur berukuran $513$ +% ke bidang dua dimensi dengan mempertahankan hubungan jarak +% antar sampel secara lokal. + +% \begin{figure}[H] +% \centering +% % \subfloat[t-SNE pada $\mathcal{D}_A$]{% +% % \includegraphics[width=.48\textwidth]{chapters/img/sensor1/tsne_A.png} +% % }\hfill +% \subfloat[t-SNE pada $\mathcal{D}_B$]{% +% \includegraphics[width=.48\textwidth]{chapters/img/sensor1/tsne_B.png} +% }\\[1ex] +% \subfloat[PaCMAP pada $\mathcal{D}_A$]{% +% \includegraphics[width=.48\textwidth]{chapters/img/sensor1/pacmap_A.png} +% }\hfill +% \subfloat[PaCMAP pada $\mathcal{D}_B$]{% +% \includegraphics[width=.48\textwidth]{chapters/img/sensor1/pacmap_B.png} +% } +% \caption{Visualisasi dua dimensi hasil reduksi dimensi non-linear +% menggunakan t-SNE dan PaCMAP pada fitur STFT sensor A dan B. +% .} +% \label{fig:tsne_pacmap} +% \end{figure} + +% Pada Gambar~\ref{fig:tsne_pacmap} tampak bahwa setiap kelas +% ($d_0$--$d_6$) membentuk klaster yang relatif terpisah, +% menandakan bahwa fitur hasil STFT memiliki kemampuan diskriminatif +% terhadap kondisi struktur. +% Beberapa tumpang tindih antar klaster (khususnya antara $d_i$ yang berdekatan) +% masih muncul akibat kemiripan respons getaran pada lokasi +% yang berdekatan, namun pola pemisahan antar kelompok +% masih terlihat jelas. + +\subsection{Interpretasi dan Implikasi} +Hasil eksplorasi ini menunjukkan bahwa: +\begin{enumerate} + \item Variansi utama data dapat dijelaskan oleh sejumlah kecil komponen PCA, + sehingga reduksi dimensi berpotensi meningkatkan efisiensi komputasi + tanpa kehilangan informasi penting. + \item Visualisasi t-SNE dan PaCMAP memperlihatkan bahwa fitur STFT + mampu mengelompokkan kondisi struktur sesuai label kerusakan, + mendukung validitas pemilihan STFT sebagai metode ekstraksi fitur. + \item Perbedaan antara kanal sensor~A ($\mathcal{D}_A$) dan sensor~B ($\mathcal{D}_B$) tidak signifikan, + sehingga keduanya dapat diperlakukan sebagai dua sumber informasi + komplementer pada tahap pelatihan model. +\end{enumerate} + +Temuan ini menjadi dasar untuk menentukan jumlah komponen PCA +yang akan digunakan pada \textit{grid search} saat optimasi \textit{hyperparameter} model SVM. + +\section{Hasil \textit{Coarse Grid-Search}} +\label{sec:grid-results} + +Setelah proses ekstraksi fitur dan pembentukan dataset berlabel, +tahap berikutnya adalah melakukan pencarian \textit{grid} +untuk mengoptimalkan parameter model \gls{svm} +dengan kernel \gls{rbf}. +Tiga parameter yang dioptimalkan adalah: +\begin{enumerate} + \item jumlah komponen utama \(\,n_{\text{components}}\,\) pada reduksi dimensi \gls{pca}, + \item parameter regulasi \(C\), + \item parameter kernel \(\gamma\). +\end{enumerate} + +Total kombinasi parameter yang diuji berjumlah \(5\times5\times8 = 200\) kandidat model +dengan skema \textit{stratified 5-fold cross-validation} menghasilkan total 1000 kali \textit{fitting}. +Setiap kombinasi dievaluasi menggunakan metrik akurasi rata-rata +pada data validasi. + +\subsection{Evaluasi Keseluruhan} +Distribusi akurasi seluruh kandidat model ditunjukkan pada +Gambar~\ref{fig:grid_hist}. +Sebagian besar kombinasi menghasilkan akurasi di atas~95\%, +menunjukkan bahwa fitur STFT memiliki daya klasifikasi yang kuat +terhadap kondisi struktur. + +\begin{figure}[H] + \centering + % \includegraphics[width=.65\textwidth]{figures/grid_hist.pdf} + \caption{Distribusi akurasi validasi silang dari 225 kombinasi parameter $(C,\gamma,n_{\text{components}})$.} + \label{fig:grid_hist} +\end{figure} + +\subsection{Pengaruh Jumlah Komponen PCA} +Rata-rata akurasi tertinggi untuk setiap nilai $n_{\text{components}}$ +ditampilkan pada Gambar~\ref{fig:pca_acc_overall}. +Terlihat bahwa akurasi meningkat hingga mencapai puncak pada rentang +$n_{\text{components}} = 64$--$128$, kemudian menurun ketika jumlah komponen +dikurangi secara agresif. +Hal ini menunjukkan bahwa sekitar 10–25\% komponen utama sudah cukup +merepresentasikan informasi penting dari fitur STFT. + +\begin{figure}[H] + \centering + % \includegraphics[width=.7\textwidth]{figures/pca_acc_overall.pdf} + \caption{Rata-rata akurasi terhadap jumlah komponen PCA berdasarkan hasil pencarian \textit{grid}.} + \label{fig:pca_acc_overall} +\end{figure} + +\subsection{Peta Akurasi terhadap Parameter SVM} +Untuk setiap kanal sensor, peta akurasi terhadap parameter $C$ dan~$\gamma$ +pada konfigurasi PCA terbaik ($n_{\text{components}}=128$) +ditunjukkan pada Gambar~\ref{fig:svm_heatmap}. Terlihat bahwa area akurasi tinggi terbentuk pada +nilai \(C\) menengah dan \(\gamma\) kecil, +yang menandakan keseimbangan antara margin yang cukup lebar +dan kompleksitas model yang moderat. + +\begin{figure} + \centering + \subfloat[Baseline]{\includegraphics[width=.48\textwidth]{chapters/img/sensor1/grid_original.png}}\hfill + \subfloat[PCA=256]{\includegraphics[width=.48\textwidth]{chapters/img/sensor1/grid_pca256.png}}\hfill \\[1ex] + \subfloat[PCA=128]{\includegraphics[width=.48\textwidth]{chapters/img/sensor1/grid_pca128.png}}\hfill + \subfloat[PCA=64]{\includegraphics[width=.48\textwidth]{chapters/img/sensor1/grid_pca64.png}}\hfill \\[1ex] + \subfloat[PCA=32]{\includegraphics[width=.48\textwidth]{chapters/img/sensor1/grid_pca32.png}}\hfill + \subfloat[PCA=16]{\includegraphics[width=.48\textwidth]{chapters/img/sensor1/grid_pca16.png}}\hfill \\[1ex] + \subfloat[PCA=8]{\includegraphics[width=.48\textwidth]{chapters/img/sensor1/grid_pca8.png}}\hfill + \subfloat[PCA=4]{\includegraphics[width=.48\textwidth]{chapters/img/sensor1/grid_pca4.png}}\hfill + \caption{\textit{Heatmap mean test score} terhadap parameter $C$ dan~$\gamma$ untuk setiap komponen utama PCA pada Sensor A ($\mathcal{D}_A$).} + \label{fig:svm_heatmap_A} +\end{figure} + +\begin{figure} + \centering + \subfloat[Baseline]{\includegraphics[width=.48\textwidth]{chapters/img/sensor2/grid_original.png}}\hfill + \subfloat[PCA=256]{\includegraphics[width=.48\textwidth]{chapters/img/sensor2/grid_pca256.png}}\hfill \\[1ex] + \subfloat[PCA=128]{\includegraphics[width=.48\textwidth]{chapters/img/sensor2/grid_pca128.png}}\hfill + \subfloat[PCA=64]{\includegraphics[width=.48\textwidth]{chapters/img/sensor2/grid_pca64.png}}\hfill \\[1ex] + \subfloat[PCA=32]{\includegraphics[width=.48\textwidth]{chapters/img/sensor2/grid_pca32.png}}\hfill + \subfloat[PCA=16]{\includegraphics[width=.48\textwidth]{chapters/img/sensor2/grid_pca16.png}}\hfill \\[1ex] + \subfloat[PCA=8]{\includegraphics[width=.48\textwidth]{chapters/img/sensor2/grid_pca8.png}}\hfill + \subfloat[PCA=4]{\includegraphics[width=.48\textwidth]{chapters/img/sensor2/grid_pca4.png}}\hfill + \caption{\textit{Heatmap mean test score} terhadap parameter $C$ dan~$\gamma$ untuk setiap komponen utama PCA pada Sensor B ($\mathcal{D}_B$).} + \label{fig:svm_heatmap_B} +\end{figure} + +\subsection{Analisis Efisiensi Model pada \textit{Coarse Grid-Search}} +\label{sec:efficiency_analysis} +Selain mempertimbangkan akurasi rata-rata (\textit{mean test score}) +sebagai satu-satunya metrik evaluasi, penelitian ini juga memperhitungkan +waktu pelatihan rata-rata (\textit{mean fit time}) untuk menilai efisiensi komputasi. +Hal ini penting karena peningkatan akurasi sering kali diikuti dengan +kenaikan waktu pelatihan yang tidak proporsional, sehingga diperlukan +kompromi antara performa dan kompleksitas. + +Untuk mengukur keseimbangan tersebut, didefinisikan metrik efisiensi: +\begin{equation} +E_i = \frac{S_i}{T_i^{\alpha}}, +\label{eq:efficiency_metric} +\end{equation} +dengan: \begin{itemize} - \item Konfigurasi terbaik (\textit{[konfigurasi terbaik]}) mencapai Akurasi \textit{[acc\_best]}\%, Macro-F1 \textit{[f1\_best]}\%, dan Kappa \textit{[kappa\_best]} pada data uji. - \item Kesalahan dominan terjadi antara kelas \textit{[kelas\_A]} dan \textit{[kelas\_B]} karena kemiripan respons pada \textit{[f\_low--f\_high]} Hz; strategi \textit{[strategi perbaikan]} direkomendasikan. - \item Ablasi menegaskan manfaat kombinasi fitur; window Hann dan parameter STFT \textit{[n\_fft, overlap]} memberi keseimbangan resolusi yang baik. - \item Pendekatan sensor terbatas dengan \textit{[n\_sensors\_min]} sensor tetap layak dengan penurunan performa \textit{[delta\_perf\_sensors]} poin. - \item Model menunjukkan stabilitas antar-fold (\textit{[std\_f1]}) dan ketahanan \textit{[terhadap noise/domain shift]} dengan penyesuaian \textit{[augmentasi/penalaan]}. -\end{itemize} \ No newline at end of file + \item $S_i$ = rata-rata skor akurasi hasil 5-\textit{fold cross-validation} (0–1), + \item $T_i$ = rata-rata waktu pelatihan per iterasi (dalam detik), +\end{itemize} + +Metrik $E_i$ menggambarkan rasio akurasi terhadap biaya waktu pelatihan. +Semakin besar nilai $E_i$, semakin efisien model tersebut atau +model mampu mencapai akurasi tinggi dengan waktu pelatihan yang relatif singkat. + +% \begin{figure}[H] +% \centering +% % \includegraphics[width=.7\textwidth]{figures/efficiency_score.pdf} +% \caption{Perbandingan metrik efisiensi ($E_i$) dan akurasi rata-rata ($S_i$) +% terhadap jumlah komponen PCA.} +% \label{fig:efficiency_score} +% \end{figure} + +\begin{table}[H] +\centering +\begin{tabular}{rrrrrr} +\toprule +$n_{\text{components}}$ & $C (\log{2})$ & $\gamma (\log{2})$ & $S_i$ & $T_i$ & $E_i (\times10^{-3})$ \\ +\midrule +4 & 5 & -5 & 0.80764 & 11.22306 & 71.96291 \\ +8 & 5 & -5 & 0.97076 & 10.88293 & 89.20027 \\ +16 & 5 & -5 & 0.99116 & 10.53770 & 94.05832 \\ +32 & 10 & -10 & 0.99394 & 10.45783 & 95.04296 \\ +64 & 10 & -10 & 0.99631 & 13.46819 & 73.97505 \\ +128 & 5 & -10 & 0.99728 & 13.43715 & 74.21849 \\ +256 & 5 & -10 & 0.99756 & 17.84189 & 55.91131 \\ +512 & 5 & -10 & 0.99763 & 31.24036 & 31.93410 \\ +\bottomrule +\end{tabular} +\caption{Hasil ringkasan nilai maksimum \textit{mean test score} untuk setiap konfigurasi $n_{\text{components}}$ pada Sensor A ($\mathcal{D}_A$).} +\label{tab:efficiency_summary_A} +\end{table} + +\begin{table}[H] +\centering +\begin{tabular}{rrrrrr} +\toprule +$n_{\text{components}}$ & $C (\log{2})$ & $\gamma (\log{2})$ & $S_i$ & $T_i$ & $E_i (\times10^{-3})$ \\ +\midrule +4 & 5 & -5 & 0.87845 & 13.77282 & 63.78107 \\ +8 & 0 & -5 & 0.98051 & 12.51643 & 78.33758 \\ +16 & 5 & -5 & 0.99443 & 10.90890 & 91.15776 \\ +32 & 5 & -10 & 0.99596 & 13.42619 & 74.18057 \\ +64 & 5 & -10 & 0.99735 & 11.40759 & 87.42906 \\ +128 & 5 & -10 & 0.99728 & 14.54694 & 68.55632 \\ +256 & 5 & -10 & 0.99777 & 20.27980 & 49.20029 \\ +512 & 5 & -10 & 0.99791 & 39.63068 & 25.18027 \\ +\bottomrule +\end{tabular} +\caption{Hasil ringkasan nilai maksimum \textit{mean test score} untuk setiap konfigurasi $n_{\text{components}}$ pada Sensor B ($\mathcal{D}_B$).} +\label{tab:efficiency_summary_B} +\end{table} + +Hasil pada Tabel~\ref{tab:efficiency_summary_A} dan Tabel~\ref{tab:efficiency_summary_B} menunjukkan bahwa, +meskipun nilai akurasi tertinggi dicapai pada +$n_{\text{components}} = 512$ untuk kedua kanal sensor, +puncak nilai metrik efisiensi dicapai pada +$n_{\text{components}} = 32$ dengan $E = 0.9504$ untuk Sensor A ($\mathcal{D}_A$) dan $n_{\text{components}} = 16$ dengan $E = 0.9116$ untuk Sensor B ($\mathcal{D}_B$). +Artinya, pengurangan dimensi hingga 32 komponen untuk Sensor A dan 16 komponen untuk Sensor B +menghasilkan model yang hampir seakurat konfigurasi berdimensi penuh, +namun dengan waktu pelatihan yang berkurang lebih dari 75\%. +% Kompromi ini dianggap sebagai titik optimum antara performa dan efisiensi. + +Berdasarkan kombinasi akurasi, waktu pelatihan, dan metrik efisiensi, +konfigurasi dengan $n_{\text{components}}=32$ untuk Sensor A dan $n_{\text{components}}=16$ untuk Sensor B dipilih sebagai +\textit{baseline} optimal untuk model akhir. +Model \textit{baseline} ini akan digunakan sebagai acuan pada tahap evaluasi model dan pencarian \textit{hyperparameter} lanjutan (\textit{fine grid-search}) +yang dibahas pada subab berikutnya. + + +\section{Evaluasi Model \textit{Baseline}} +\label{sec:baseline_performance} +Model \textit{baseline} yang digunakan diperoleh dari \textit{coarse grid-search} pada subab \ref{sec:efficiency_analysis} adalah SVM dengan kernel RBF, 32 komponen PCA, dan parameter $C=2^{10}$, $\gamma=2^{-10}$ untuk Sensor A, sedangkan untuk Sensor B adalah SVM dengan kernel RBF, 16 komponen PCA, dan parameter $C=2^{5}$, $\gamma=2^{-5}$. Pada bagian ini, dilakukan evaluasi performa model \textit{baseline} dengan data uji yang berbeda (\textit{Dataset} B). + + +\subsection{Metrik Klasifikasi} +Metrik klasifikasi model \textit{baseline} pada dataset pengujian disajikan pada Tabel~\ref{tab:metrics-baseline_A} dan~\ref{tab:matrics-baseline_B}. + +\begin{table}[htbp] + \centering + \caption{\textit{Classification report} model \textit{baseline} pada Sensor A} + \label{tab:metrics-baseline_A} + \begin{tabular}{lrrrr} + \toprule + & precision & recall & f1-score & support \\ + \midrule + 0 & 0.99 & 0.98 & 0.99 & 2565.00 \\ + 1 & 0.99 & 1.00 & 1.00 & 2565.00 \\ + 2 & 1.00 & 1.00 & 1.00 & 2565.00 \\ + 3 & 1.00 & 1.00 & 1.00 & 2565.00 \\ + 4 & 1.00 & 1.00 & 1.00 & 2565.00 \\ + 5 & 1.00 & 1.00 & 1.00 & 2565.00 \\ + 6 & 0.99 & 1.00 & 0.99 & 2565.00 \\ + accuracy & 1.00 & 1.00 & 1.00 & 1.00 \\ + macro avg & 1.00 & 1.00 & 1.00 & 17955.00 \\ + weighted avg & 1.00 & 1.00 & 1.00 & 17955.00 \\ + \bottomrule + \end{tabular} +\end{table} + +\begin{table}[htbp] + \centering + \caption{\textit{Classification report} model \textit{baseline} pada Sensor B} + \label{tab:metrics-baseline_B} + \begin{tabular}{lrrrr} + \toprule + & precision & recall & f1-score & support \\ + \midrule + 0 & 0.98 & 0.99 & 0.99 & 2565.00 \\ + 1 & 0.99 & 1.00 & 0.99 & 2565.00 \\ + 2 & 1.00 & 1.00 & 1.00 & 2565.00 \\ + 3 & 1.00 & 1.00 & 1.00 & 2565.00 \\ + 4 & 1.00 & 1.00 & 1.00 & 2565.00 \\ + 5 & 1.00 & 1.00 & 1.00 & 2565.00 \\ + 6 & 1.00 & 1.00 & 1.00 & 2565.00 \\ + accuracy & 1.00 & 1.00 & 1.00 & 1.00 \\ + macro avg & 1.00 & 1.00 & 1.00 & 17955.00 \\ + weighted avg & 1.00 & 1.00 & 1.00 & 17955.00 \\ + \bottomrule + \end{tabular} +\end{table} + +Hasil ini menunjukkan bahwa model \textit{baseline} kedua sensor mencapai akurasi 99\%. Nilai \textit{recall} yang relatif tinggi (99.0\%) menunjukkan bahwa model lebih sensitif untuk mendeteksi kelas kerusakan, meskipun nilai \textit{precision} yang sedikit lebih rendah, menunjukkan bahwa ada beberapa \textit{false-positive} yang dihasilkan. + +\subsection{\textit{Confusion Matrix}} +\begin{figure}[H] + \centering + \includegraphics[width=0.8\textwidth]{chapters/img/sensor1/cm_baseline_s1a_eval.png} + \caption{\textit{Confusion matrix} model \textit{baseline} SVM (RBF) pada Sensor A} + \label{fig:confusion-matrix-baseline_A} +\end{figure} + +\begin{figure}[H] + \centering + \includegraphics[width=0.8\textwidth]{chapters/img/sensor2/cm_baseline_s2a_eval.png} + \caption{\textit{Confusion matrix} model \textit{baseline} SVM (RBF) pada Sensor B} + \label{fig:confusion-matrix-baseline_B} +\end{figure} + +Dari Gambar~\ref{fig:confusion-matrix-baseline_A} dan~\ref{fig:confusion-matrix-baseline_B}, terlihat bahwa kedua model minim kesalahan klasifikasi, dengan sebagian besar prediksi berada di diagonal utama. Beberapa kesalahan klasifikasi minor terjadi paling banyak antara kelas 0 dengan kelas 1 dan kelas 6. + + +\section{\textit{Fine Grid-Search}} +Optimasi model yang dilakukan yaitu dengan melakukan \textit{fine grid-search} pada rentang \textit{hyperparameter} model \textit{baseline} yang digunakan pada Subab~\ref{sec:baseline_performance}. Untuk Sensor A dengan $n_{\text{components}} = 32$ rentang parameter yang dicari adalah +\begin{align*} + C &= \{\, 2^8,\, 2^{8.5},\, \ldots,\, 2^{12} \,\} \\ + \gamma &= \{\, 2^{-12},\, 2^{-11.5},\, \ldots ,\, 2^{-8} \,\}, +\end{align*}sedangkan Sensor B dengan $n_{\text{components}} = 16$ rentang parameter yang dicari adalah +\begin{align*} + C &= \{\, 2^3,\, 2^{3.5},\, \ldots,\, 2^{7} \,\} \\ + \gamma &= \{\, 2^{-7},\, 2^{-6.5},\, \ldots ,\, 2^{-3} \,\}. +\end{align*}. Pada proses ini, \textit{standard scaler} dan \textit{stratified k-fold cross validation} dengan $k=5$ tetap digunakan untuk menjaga konsistensi evaluasi model, sehingga total kombinasi parameter yang diuji adalah \(9\times9 = 81\) kandidat model dengan total 405 kali \textit{fitting}. + +\subsection{Diagram \textit{Fine Grid-Search Heatmap}} +Gambar~\ref{fig:svm_fine_heatmap} menunjukkan diagram \textit{heatmap} terhadap parameter \textit{fine grid-search} $C$ dan~$\gamma$ untuk masing-masing sensor. Akurasi tertinggi pada Sensor A diperoleh pada $C= \{\,2^{8}, \,2^{8.5}, \,2^{9}, \,2^{9.5}, \,2^{10}, \,2^{10.5},\,2^{11}, \,2^{11.5}, \,2^{12} \,\}$ dan $\gamma=2^{-9.5}$ dengan akurasi meningkat 0.15\% menjadi 99.54\%, sedangkan pada Sensor B diperoleh pada $C = \{\,2^{5},\,2^{5.5} \,\}$ dan $\gamma= \{\, 2^{-3},\, 2^{-3.5},\, 2^{-4}\,\}$ dengan akurasi meningkat 0.05\% menjadi 99.49\%. Hasil ini menunjukkan bahwa optimasi \textit{hyperparameter} lebih lanjut dapat meningkatkan performa model meskipun peningkatannya relatif kecil dibandingkan dengan model \textit{baseline}. +\begin{figure} + \centering + \subfloat[Sensor A (PCA 32)]{\includegraphics[width=.48\textwidth]{chapters/img/sensor1/grid_fine_pca32.png}} + \centering + \subfloat[Sensor B (PCA 16)]{\includegraphics[width=.48\textwidth]{chapters/img/sensor2/grid_fine_pca16.png}} + \caption{\textit{Heatmap mean test score} terhadap \textit{fine grid-search parameter} $C$ dan~$\gamma$} + \label{fig:svm_fine_heatmap} +\end{figure} + +\section{Evaluasi Model \textit{Fine Grid-Search}} +Model \textit{fine grid-search} dilatih pada \textit{dataset} A dan perlu dievaluasi performanya dengan data uji yang berbeda (\textit{dataset} B) untuk mengukur peningkatan performa dibandingkan model \textit{baseline}. +\subsection{Metrik Klasifikasi} +Hasil performa model \textit{fine grid-search} pada data uji disajikan pada Tabel~\ref{tab:metrics-fine-a} dan~\ref{tab:metrics-fine-b}. + +\begin{table} +\centering +\caption{\textit{Classification report} model Sensor A} +\label{tab:metrics-fine-a} +\begin{tabular}{lrrrr} +\toprule + & precision & recall & f1-score & support \\ +\midrule +0 & 0.99 & 0.99 & 0.99 & 2565.00 \\ +1 & 0.99 & 1.00 & 0.99 & 2565.00 \\ +2 & 1.00 & 1.00 & 1.00 & 2565.00 \\ +3 & 1.00 & 1.00 & 1.00 & 2565.00 \\ +4 & 1.00 & 1.00 & 1.00 & 2565.00 \\ +5 & 1.00 & 1.00 & 1.00 & 2565.00 \\ +6 & 1.00 & 1.00 & 1.00 & 2565.00 \\ +accuracy & 1.00 & 1.00 & 1.00 & 1.00 \\ +macro avg & 1.00 & 1.00 & 1.00 & 17955.00 \\ +weighted avg & 1.00 & 1.00 & 1.00 & 17955.00 \\ +\bottomrule +\end{tabular} +\end{table} + +\begin{table} +\centering +\caption{\textit{Classification report} model Sensor B} +\label{tab:metrics-fine-b} +\begin{tabular}{lrrrr} +\toprule + & precision & recall & f1-score & support \\ +\midrule +0 & 0.98 & 0.97 & 0.98 & 2565.00 \\ +1 & 0.99 & 1.00 & 1.00 & 2565.00 \\ +2 & 1.00 & 1.00 & 1.00 & 2565.00 \\ +3 & 1.00 & 1.00 & 1.00 & 2565.00 \\ +4 & 0.99 & 1.00 & 1.00 & 2565.00 \\ +5 & 1.00 & 1.00 & 1.00 & 2565.00 \\ +6 & 0.98 & 0.99 & 0.99 & 2565.00 \\ +accuracy & 0.99 & 0.99 & 0.99 & 0.99 \\ +macro avg & 0.99 & 0.99 & 0.99 & 17955.00 \\ +weighted avg & 0.99 & 0.99 & 0.99 & 17955.00 \\ +\bottomrule +\end{tabular} +\end{table} + +\subsection{\textit{Confusion Matrix}} +\begin{figure}[H] + \centering + \includegraphics[width=.8\textwidth]{chapters/img/sensor1/cm_fine_s1a_eval.png} + \caption{\textit{Confusion matrix} model \textit{fine grid-search} pada Sensor A} + \label{fig:cm_fine_s1a_eval} +\end{figure} +\begin{figure}[H] + \centering + \includegraphics[width=.8\textwidth]{chapters/img/sensor2/cm_fine_s2a_eval.png} + \caption{\textit{Confusion matrix} model \textit{fine grid-search} pada Sensor B} + \label{fig:cm_fine_s2a_eval} +\end{figure} + +\section{Model \textit{Inference} dan Visualisasi Prediksi} +Setelah model \textit{fine grid-search} dievaluasi, dilakukan proses \textit{inference} pada data uji untuk memvisualisasikan prediksi model. Gambar~\ref{fig:inference_s1a} dan~\ref{fig:inference_s2a} menunjukkan hasil prediksi model pada Sensor A dan Sensor B dalam \textit{heatmap} dan grafik probabilitasnya. +% \section{Efisiensi Komputasi} + +% \subsection{Perbandingan Waktu Latih} +% \subsection{Perbandingan Waktu \textit{Inference}} +% \begin{table}[htbp] +% \centering +% \caption{Perbandingan waktu inference model \textit{baseline} dan \textit{preprocessing pipeline}} +% \label{tab:training-time} +% \begin{tabular}{lrr} +% \hline +% Iterasi & \textit{Baseline} (detik) & \textit{preprocessing pipeline} (detik)\\ +% 1 & & 6.53 \\ +% 2 & & 6.08 \\ +% 3 & & 6.08 \\ +% 4 & & 6.10 \\ +% 5 & & 6.20 \\ +% Rata-rata & & 6.20 \\ +% \hline +% \end{tabular} +% \end{table} + +% \section{} +% Model \textit{baseline} yang dilakukan dengan \textit{preprocessing pipeline} mengurangi waktu latih sekitar x \%, sedangkan waktu \textit{inference} tiap sampel berkurang sekitar x \%. Hal ini menunjukkan keefektifan PCA dalam mereduksi dimensi fitur dan \textit{standard scaler}, dengan begitu dapat mengurangi beban komputasi tanpa mengorbankan akurasi. + +% Konfigurasi terbaik diperoleh pada kombinasi fitur waktu--frekuensi dengan SVM-\textit{[kernel]}, menghasilkan Akurasi sebesar \textit{[acc\_best]}\%, Macro-F1 sebesar \textit{[f1\_best]}\%, dan Kappa sebesar \textit{[kappa\_best]} pada data uji (Tabel~\ref{tab:main-results}). Dibandingkan baseline domain waktu saja, Macro-F1 meningkat sekitar \textit{[delta\_f1\_time]} poin persentase; dibandingkan domain frekuensi saja, peningkatan mencapai \textit{[delta\_f1\_freq]} poin persentase. Hasil ini mengindikasikan bahwa informasi pelengkap antara dinamika temporal dan spektral berkontribusi nyata terhadap separabilitas kelas. + +% Performa pada metrik Balanced Accuracy dan Macro-Recall juga konsisten, menandakan model tidak terlalu bias pada kelas mayoritas. Nilai Kappa \textit{[kappa\_best]} mengindikasikan tingkat kesepakatan yang \textit{[moderat/tinggi]} melampaui kebetulan. + +% \section{Analisis Per-Kelas dan Kesalahan} +% \begin{figure}[htbp] +% \centering +% % \includegraphics[width=0.8\textwidth]{img/confusion_matrix.pdf} +% \fbox{\begin{minipage}[c][0.30\textheight][c]{0.80\textwidth}\centering +% Placeholder Confusion Matrix +% \end{minipage}} +% \caption{Confusion matrix pada data uji. Isikan gambar aktual dari pipeline evaluasi.} +% \label{fig:cm} +% \end{figure} + +% \begin{table}[htbp] +% \centering +% \caption{Metrik per-kelas pada data uji. Gunakan bila diperlukan untuk melengkapi Confusion Matrix.} +% \label{tab:per-class} +% \begin{tabular}{lccc} +% \hline +% Kelas & Precision & Recall & F1 \\ +% \hline +% A & -- & -- & -- \\ +% B & -- & -- & -- \\ +% C & -- & -- & -- \\ +% % ... tambah baris sesuai jumlah kelas +% \hline +% \end{tabular} +% \end{table} + +% Confusion Matrix pada Gambar~\ref{fig:cm} menunjukkan pola salah klasifikasi yang dominan antara kelas \textit{[kelas\_A]} dan \textit{[kelas\_B]}. Dua kelas ini memiliki respons spektral yang mirip pada rentang \textit{[f\_low--f\_high]} Hz, sehingga kesalahan terutama terjadi ketika amplitudo sinyal rendah atau \textit{signal-to-noise ratio} menurun. Sebaliknya, kelas \textit{[kelas\_C]} memperlihatkan separasi yang baik dengan Recall \textit{[recall\_C]}\% dan F1 \textit{[f1\_C]}\% (Tabel~\ref{tab:per-class}). + +% Analisis kesalahan kasus-per-kasus menunjukkan bahwa \textit{[proporsi\_\%]}\% prediksi keliru terjadi pada sampel dengan \textit{[ciri sinyal/condisi uji]} dan \textit{[konfigurasi sensor]}. Hal ini menyarankan perlunya \textit{[strategi perbaikan, mis. penambahan fitur bandpass tertentu atau penyeimbangan kelas]}. + +% \section{Ablasi dan Sensitivitas} +% \subsection{Ablasi Fitur} +% \begin{figure}[htbp] +% \centering +% \includegraphics[width=0.75\textwidth]{example-image-a} +% \fbox{\begin{minipage}[c][0.22\textheight][c]{0.70\textwidth}\centering +% Placeholder Bar Chart: Time vs Freq vs Kombinasi +% \end{minipage}} +% \caption{Perbandingan performa berdasarkan jenis fitur.} +% \label{fig:ablation-features} +% \end{figure} + +% Studi ablation pada Gambar~\ref{fig:ablation-features} menegaskan bahwa kombinasi fitur memberikan peningkatan \textit{[delta\_ablation]} poin persentase pada Macro-F1 dibandingkan fitur domain waktu saja. Hal ini mengindikasikan bahwa karakteristik harmonik dan komponen frekuensi transien yang ditangkap STFT berkontribusi pada pemisahan kelas yang lebih baik. + +% \subsection{Parameter STFT dan Windowing} +% \begin{table}[htbp] +% \centering +% \caption{Sensitivitas terhadap parameter STFT pada data validasi.} +% \label{tab:stft-sensitivity} +% \begin{tabular}{lcccc} +% \hline +% Window & n\_fft & Overlap & Akurasi & Macro-F1 \\ +% \hline +% Hann & -- & -- & -- & -- \\ +% Hann & -- & -- & -- & -- \\ +% (Tanpa window) & -- & -- & -- & -- \\ +% \hline +% \end{tabular} +% \end{table} + +% Eksperimen sensitivitas pada Tabel~\ref{tab:stft-sensitivity} memperlihatkan adanya \textit{trade-off} antara resolusi waktu dan frekuensi. Peningkatan \textit{n\_fft} cenderung memperhalus resolusi frekuensi namun mengurangi ketelitian temporal, sedangkan overlap yang lebih besar \textit{[overlap\_\% range]}\% membantu stabilitas estimasi fitur pada sinyal bising. Penggunaan window Hann memberikan kenaikan Macro-F1 sekitar \textit{[delta\_hann]} poin dibanding tanpa window, menegaskan peran pengurangan \textit{spectral leakage}. + +% \subsection{Pendekatan Sensor Terbatas} +% \begin{figure}[htbp] +% \centering +% % placeholder +% \includegraphics[width=0.75\textwidth]{example-image-a} +% \fbox{\begin{minipage}[c][0.22\textheight][c]{0.70\textwidth}\centering +% Placeholder: Performa vs Jumlah/Posisi Sensor +% \end{minipage}} +% \caption{Dampak jumlah/konfigurasi sensor terhadap performa.} +% \label{fig:sensor-limited} +% \end{figure} + +% Hasil pada Gambar~\ref{fig:sensor-limited} menunjukkan bahwa pengurangan dari \textit{[n\_sensors\_full]} menjadi \textit{[n\_sensors\_min]} sensor hanya menurunkan Macro-F1 sekitar \textit{[delta\_perf\_sensors]} poin, khususnya ketika sensor ditempatkan pada \textit{[posisi sensor terbaik]}. Ini mengindikasikan bahwa pendekatan sensor terbatas tetap layak untuk implementasi dengan biaya perangkat keras yang lebih rendah, selama pemilihan posisi sensor dioptimalkan. + +% \section{Robustness dan Generalisasi} +% \begin{table}[htbp] +% \centering +% \caption{Ringkasan kinerja antar-fold (jika menggunakan k-fold).} +% \label{tab:kfold} +% \begin{tabular}{lcc} +% \hline +% Metrik & Rata-rata & Deviasi Standar \\ +% \hline +% Macro-F1 & -- & -- \\ +% Akurasi & -- & -- \\ +% \hline +% \end{tabular} +% \end{table} + +% Pada skema validasi silang \textit{k}-fold, variasi performa relatif rendah dengan simpangan baku Macro-F1 sebesar \textit{[std\_f1]} (Tabel~\ref{tab:kfold}), menandakan stabilitas model terhadap variasi subset data. Penambahan noise sintetis pada tingkat SNR \textit{[snr levels]} menunjukkan penurunan performa yang \textit{[ringan/sedang/bermakna]} sekitar \textit{[delta\_snr]} poin; augmentasi \textit{[jenis augmentasi]} membantu mengkompensasi sebagian penurunan tersebut. + +% Pada skenario \textit{domain shift} \textit{[nama skenario]}, model mempertahankan Macro-F1 sebesar \textit{[f1\_shift]}\%, yang menunjukkan \textit{[derajat generalisasi]} terhadap kondisi yang berbeda dari data pelatihan. + +% \section{Perbandingan dengan Pustaka/Baseline} +% Temuan kami selaras dengan tren yang dilaporkan oleh \textcite{abdeljaber2017}, khususnya mengenai pentingnya informasi frekuensi untuk mendeteksi lokasi kerusakan. Meskipun demikian, perbedaan \textit{setup} eksperimen (\textit{[jenis struktur/skenario uji]}, konfigurasi sensor, dan definisi kelas) membuat angka metrik tidak dapat dibandingkan secara langsung. Oleh karena itu, perbandingan difokuskan pada pola dan arah peningkatan, bukan nilai absolut. + +% \section{Kompleksitas dan Implementasi} +% Model SVM dengan fitur \textit{[jenis fitur terbaik]} menawarkan waktu inferensi sekitar \textit{[t\_infer\_ms]} ms per sampel pada \textit{[perangkat/CPU/GPU]}. Tahap ekstraksi STFT memerlukan \textit{[t\_stft\_ms]} ms per segmen dengan parameter \textit{[n\_fft]}, overlap \textit{[overlap\_\%]}\%, dan window Hann. Secara keseluruhan, latensi ujung-ke-ujung diperkirakan \textit{[t\_end2end\_ms]} ms, yang \textit{[memadai/belum memadai]} untuk aplikasi \textit{[real-time/near real-time]}. + +% Dengan \textit{[n\_sensors\_min]} sensor, kebutuhan komputasi dan bandwidth data berkurang \textit{[proporsi pengurangan]} dibanding konfigurasi penuh, yang memperbaiki kelayakan implementasi lapangan tanpa mengorbankan akurasi secara signifikan. + +% \section{Ringkasan Bab} +% \begin{itemize} +% \item Konfigurasi terbaik (\textit{[konfigurasi terbaik]}) mencapai Akurasi \textit{[acc\_best]}\%, Macro-F1 \textit{[f1\_best]}\%, dan Kappa \textit{[kappa\_best]} pada data uji. +% \item Kesalahan dominan terjadi antara kelas \textit{[kelas\_A]} dan \textit{[kelas\_B]} karena kemiripan respons pada \textit{[f\_low--f\_high]} Hz; strategi \textit{[strategi perbaikan]} direkomendasikan. +% \item Ablasi menegaskan manfaat kombinasi fitur; window Hann dan parameter STFT \textit{[n\_fft, overlap]} memberi keseimbangan resolusi yang baik. +% \item Pendekatan sensor terbatas dengan \textit{[n\_sensors\_min]} sensor tetap layak dengan penurunan performa \textit{[delta\_perf\_sensors]} poin. +% \item Model menunjukkan stabilitas antar-fold (\textit{[std\_f1]}) dan ketahanan \textit{[terhadap noise/domain shift]} dengan penyesuaian \textit{[augmentasi/penalaan]}. +% \end{itemize} \ No newline at end of file diff --git a/latex/chapters/img/sensor1/cm_baseline_s1a_eval.png b/latex/chapters/img/sensor1/cm_baseline_s1a_eval.png new file mode 100644 index 0000000..83e9afe --- /dev/null +++ b/latex/chapters/img/sensor1/cm_baseline_s1a_eval.png @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a797b23032f469942623ee5f3c0e63c5c617f479813f38b9b42a2f45a9402a44 +size 82443 diff --git a/latex/chapters/img/sensor1/cm_fine_s1a_eval.png b/latex/chapters/img/sensor1/cm_fine_s1a_eval.png new file mode 100644 index 0000000..7d9919f --- /dev/null +++ b/latex/chapters/img/sensor1/cm_fine_s1a_eval.png 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