arXiv subjects

Rafal Zdunek

Publications and source records attributed to Rafal Zdunek.

6 recordsLinked to original sources

arXiv2026

Non-negative tensor factorization-based dependence map analysis for local damage detection in presence of non-Gaussian noise

The time-frequency map (TFM) is frequently used in condition monitoring, necessitating further processing to select an informative frequency band (IFB) or directly detect damage. However, selecting an IFB is challenging due to the complexity of spectral structures, non-Gaussian disturbances, and overlapping fault signatures in vibration signals. Additionally, dynamic operating conditions and low signal-to-noise ratio further complicate the identification of relevant features that indicate damage. To solve this problem, the present work proposes a novel method for informative band selection and local damage detection in rolling element bearings, utilizing non-negative tensor factorization (NTF)-based dependence map analysis. The recently introduced concept of the dependence map is leveraged, with a set of these maps being factorized to separate informative components from non-informative ones. Dependence maps provide valuable information on the auto-similarity of spectral content, while NTF, a powerful tool commonly used in image processing for feature extraction, enhances this process. The combination of these methods allows for the extraction of IFBs, forming the basis for local damage detection. The effectiveness of the proposed method has been validated using both synthetic and real vibration signals corrupted with non-Gaussian disturbances.

eess.SP↗

arXiv2025

Sparse Hyperparametric Itakura-Saito Nonnegative Matrix Factorization via Bi-Level Optimization

The selection of penalty hyperparameters is a critical aspect in Nonnegative Matrix Factorization (NMF), since these values control the trade-off between reconstruction accuracy and adherence to desired constraints. In this work, we focus on an NMF problem involving the Itakura-Saito (IS) divergence, which is particularly effective for extracting low spectral density components from spectrograms of mixed signals, and benefits from the introduction of sparsity constraints. We propose a new algorithm called SHINBO, which introduces a bi-level optimization framework to automatically and adaptively tune the row-dependent penalty hyperparameters, enhancing the ability of IS-NMF to isolate sparse, periodic signals in noisy environments. Experimental results demonstrate that SHINBO achieves accurate spectral decompositions and demonstrates superior performance in both synthetic and real-world applications. In the latter case, SHINBO is particularly useful for noninvasive vibration-based fault detection in rolling bearings, where the desired signal components often reside in high-frequency subbands but are obscured by stronger, spectrally broader noise. By addressing the critical issue of hyperparameter selection, SHINBO improves the state-of-the-art in signal recovery for complex, noise-dominated environments.

cs.LG↗

arXiv2024

Non-negative tensor factorization for vibration-based local damage detection

In this study, a novel non-negative tensor factorization (NTF)-based method for vibration-based local damage detection in rolling element bearings is proposed. As the diagnostic signal registered from a faulty machine is non-stationary, the time-frequency method is frequently used as a primary decomposition technique. It is proposed here to extract multi-linear NTF-based components from a 3D array of time-frequency representations of an observed signal partitioned into blocks. As a result, frequency and temporal informative components can be efficiently separated from non-informative ones. The experiments performed on synthetic and real signals demonstrate the high efficiency of the proposed method with respect to the already known non-negative matrix factorization approach.

eess.SP↗

arXiv2024

Non-negative matrix underapproximation as optimal frequency band selector

Time-frequency representation (TFR) is often used for non-stationary signal analysis. The most intuitive and interpretable TFR is the spectrogram. Recently, a concept of non-negative matrix factorization (NMF) has been successfully applied to local damage detection in rolling elements of bearings via spectrogram factorization. NMF applied to the spectrogram allows one to find an informative frequency band, which could be further used as a filter characteristic. However, the obtained filter characteristics mostly detect the informative frequency band, which also encompasses a lot of noise. In the case where noise is more problematic, as is the case for acoustic signals from industrial machines, the NMF hardly detects the damage. To solve this problem and obtain more selective filters, which are more robust to noise, we propose the non-negative matrix under-approximation (NMU) as an informative frequency band selector. Due to the more sparse parts-based representation of the NMU compared to NMF, NMU provides more selective filter characteristics, which neglect the non-informative frequency bands related to the noise. In practice, it means that NMU gives a better signal-to-noise ratio for the filtered signal. The efficiency of the proposed approach has been validated on the vibration signal from the test rig and the acoustic signal from an idler.

eess.SP↗

arXiv2024

Bearing damage detection with orthogonal and non-negative low-rank feature extraction

Local damage of bearings can be detected as a weak cyclic and impulsive component in a highly noisy measured signal. A key problem is how to extract the signal of interest (SOI) from the raw signal, i.e., how to identify and design an optimal filter. To tackle this problem, we propose to use stochastic sampled orthogonal non-negative matrix factorization for extracting frequency-based features from a spectrogram of the measured signal. The proposed algorithm finds a selective filter that is tailored to the frequency band of the SOI. We show that our approach outperforms the other state-of-the-art selectors that were previously used in condition monitoring. The efficiency of the proposed method is illustrated using both a simulation study and the following real signals: (a) vibration signal from a test rig in the laboratory and (b) acoustic signal from a belt conveyor.

eess.SP↗

arXiv2023

Bi-level algorithm for optimizing hyperparameters in penalized nonnegative matrix factorization

Learning approaches rely on hyperparameters that impact the algorithm's performance and affect the knowledge extraction process from data. Recently, Nonnegative Matrix Factorization (NMF) has attracted a growing interest as a learning algorithm. This technique captures the latent information embedded in large datasets while preserving feature properties. NMF can be formalized as a penalized optimization task in which tuning the penalty hyperparameters is an open issue. The current literature does not provide any general framework addressing this task. This study proposes to express the penalty hyperparameters problem in NMF in terms of a bi-level optimization. We design a novel algorithm, named Alternating Bi-level (AltBi), which incorporates the hyperparameters tuning procedure into the updates of NMF factors. Results of the existence and convergence of numerical solutions, under appropriate assumptions, are studied, and numerical experiments are provided.

math.NA↗