Unsupervised Novelty Detection Methods Benchmarking with Wavelet Decomposition

TL;DR

This work addresses unsupervised novelty detection in vibration signals by proposing a framework that delivers a continuous novelty metric $NM$ and validating it with a shaker-based dataset. It combines wavelet-based feature extraction with statistical features, and compares six UML models across three feature-transformations (undercomplete AE, overcomplete AE, and PCA). The study demonstrates that certain models (K-Means, DBSCAN, GMM, LOF) yield meaningful degradation metrics under suitable preprocessing, while others (nuSVM, Isolation Forest) can behave more like binary indicators. The findings emphasize the pivotal role of feature extraction and transformation in enabling robust, real-time novelty assessment with potential for edge deployment and broader industrial validation.

Abstract

Novelty detection is a critical task in various engineering fields. Numerous approaches to novelty detection rely on supervised or semi-supervised learning, which requires labelled datasets for training. However, acquiring labelled data, when feasible, can be expensive and time-consuming. For these reasons, unsupervised learning is a powerful alternative that allows performing novelty detection without needing labelled samples. In this study, numerous unsupervised machine learning algorithms for novelty detection are compared, highlighting their strengths and weaknesses in the context of vibration sensing. The proposed framework uses a continuous metric, unlike most traditional methods that merely flag anomalous samples without quantifying the degree of anomaly. Moreover, a new dataset is gathered from an actuator vibrating at specific frequencies to benchmark the algorithms and evaluate the framework. Novel conditions are introduced by altering the input wave signal. Our findings offer valuable insights into the adaptability and robustness of unsupervised learning techniques for real-world novelty detection applications.

Figures (7)

• Figure 1: The proposed framework architecture consists of three main blocks. The feature extraction block uses WPD to extract wavelet coefficients. These coefficients, along with statistical measures, form the output of this block. The feature transformation block employs either Autoencoder or PCA to transform the extracted features, enabling the detection of different behaviours in the novelty metric computation. Finally, the feature evaluation block uses six unsupervised machine learning models to compute the novelty metric of the transformed features.
• Figure 2: Wavelet Packet Decomposition features extraction architecture. At each level of decomposition, the input signal is split into two sub-band signals, each with a dimension of $N/2$. This process is repeated through $L$ levels, resulting in $2^L$ sub-band signals. For each sub-band signal, the $l_2$ norm is computed, condensing each array into a single value. These values are then aggregated into a final array of dimension $2^L$, forming the complete WPD feature array that encapsulates the characteristics of the original time series data.
• Figure 3: Architecture of the proposed undercomplete autoencoder feature transformation algorithm. The NN model is composed of fully connected layers with the following shape: $N_{E2} < N_{E1}< N_{feat}$ and $N_{E2} < N_{D1} < N_{feat}$. The input is the preprocessed data obtained after the statistical and wavelet transformation.
• Figure 4: Architecture of the proposed overcomplete autoencoder feature transformation algorithm. The NN model is composed of fully connected layers with the following shape: $N_{feat} < N_{E1} < N_{E2}$ and $N_{feat} < N_{D1} < N_{E2}$.
• Figure 5: Graphical representation of performance metrics reported on Table \ref{['tab:shak_results']}. All the $y$ axes are displayed in a logarithmic scale. AEA is the overcomplete autoencoder, AER is the undercomplete autoencoder and OF is the original features.