Failure Mode Classification for Rolling Element Bearings Using Time-Domain Transformer-Based Encoder.

In this paper, we propose a Transformer-based encoder architecture integrated with an unsupervised denoising method to learn meaningful and sparse representations of vibration signals without the need for data transformation or pre-trained data. Existing Transformer models often require transformed data or extensive computational resources, limiting their practical adoption. We propose a simple yet competitive modification of the Transformer model, integrating a trainable noise reduction method specifically tailored for failure mode classification using vibration data directly in the time domain without converting them into other domains or images. Furthermore, we present the key architectural components and algorithms underlying our model, emphasizing interpretability and trustworthiness. Our model is trained and validated using two benchmark datasets: the IMS dataset (four failure modes) and the CWRU dataset (four and ten failure modes). Notably, our model performs competitively, especially when using an unbalanced test set and a lightweight architecture.

Dual Residual Denoising Autoencoder with Channel Attention Mechanism for Modulation of Signals.

Aiming to address the problems of the high bit error rate (BER) of demodulation or low classification accuracy of modulation signals with a low signal-to-noise ratio (SNR), we propose a double-residual denoising autoencoder method with a channel attention mechanism, referred to as DRdA-CA, to improve the SNR of modulation signals. The proposed DRdA-CA consists of an encoding module and a decoding module. A squeeze-and-excitation (SE) ResNet module containing one residual connection is modified and then introduced into the autoencoder as the channel attention mechanism, to better extract the characteristics of the modulation signals and reduce the computational complexity of the model. Moreover, the other residual connection is further added inside the encoding and decoding modules to optimize the network degradation problem, which is beneficial for fully exploiting the multi-level features of modulation signals and improving the reconstruction quality of the signal. The ablation experiments prove that both the improved SE module and dual residual connections in the proposed method play an important role in improving the denoising performance. The subsequent experimental results show that the proposed DRdA-CA significantly improves the SNR values of eight modulation types in the range of -12 dB to 8 dB. Especially for 16QAM and 64QAM, the SNR is improved by 8.38 dB and 8.27 dB on average, respectively. Compared to the DnCNN denoising method, the proposed DRdA-CA makes the average classification accuracy increase by 67.59∼74.94% over the entire SNR range. When it comes to the demodulation, compared with the RLS and the DnCNN denoising algorithms, the proposed denoising method reduces the BER of 16QAM by an average of 63.5% and 40.5%, and reduces the BER of 64QAM by an average of 46.7% and 18.6%. The above results show that the proposed DRdA-CA achieves the optimal noise reduction effect.

An Internal Defect Detection Algorithm for Concrete Blocks Based on Local Mean Decomposition-Singular Value Decomposition and Weighted Spatial-Spectral Entropy.

Within the scope of concrete internal defect detection via laser Doppler vibrometry (LDV), the acquired signals frequently suffer from low signal-to-noise ratios (SNR) due to the heterogeneity of the concrete's material properties and its rough surface structure. Consequently, these factors make the defect signal characteristics challenging to discern precisely. In response to this challenge, we propose an internal defect detection algorithm that incorporates local mean decomposition-singular value decomposition (LMD-SVD) and weighted spatial-spectral entropy (WSSE). Initially, the LDV vibration signal undergoes denoising via LMD and the SVD algorithms to reduce noise interference. Subsequently, the distribution of each frequency in the scan plane is analyzed utilizing the WSSE algorithm. Since the vibrational energy of the frequencies caused by the defect resonance is concentrated in the defect region, its energy distribution in the scan plane is non-uniform, resulting in a significant difference between the defect resonance frequencies' SSE values and the other frequencies' SSE values. This feature is used to estimate the resonant frequencies of internal defects. Ultimately, the defects are characterized based on the modal vibration patterns of the defect resonant frequencies. Tests were performed on two concrete blocks with simulated cavity defects, using an ultrasonic transducer as the excitation device to generate ultrasonic vibrations directly from the back of the blocks and applying an LDV as the acquisition device to collect vibration signals from their front sides. The results demonstrate the algorithm's capacity to effectively pinpoint the information on the location and shape of shallow defects within the concrete, underscoring its practical significance for concrete internal defect detection in practical engineering scenarios.

Application of Variational Mode Decomposition and Whale Optimization Algorithm to Laser Ultrasonic Signal Denoising.

Laser ultrasound signal echoes are easily drowned out by the surrounding environmental noise in industrial field applications, and it is worthwhile to study methods of retaining the weak ultrasound signal during signal processing. To address this problem, this paper proposes to adopt the parameters optimized by the whale optimization algorithm to the variational mode decomposition (VMD) of laser ultrasound signals. The optimized parameters can avoid the frequency mixing and incomplete noise separation caused by the choice of artificial VMD parameters. The Hausdorff distance is applied in the process of reconstructing the signal to help accurately select the relevant modes and improve the signal-to-noise ratio. Simulation and experimental results show that the proposed method is feasible and effective compared with the other three available denoising methods.

A New De-Noising Method Based on Enhanced Time-Frequency Manifold and Kurtosis-Wavelet Dictionary for Rolling Bearing Fault Vibration Signal.

The transient pulses caused by local faults of rolling bearings are an important measurement information for fault diagnosis. However, extracting transient pulses from complex nonstationary vibration signals with a large amount of background noise is challenging, especially in the early stage. To improve the anti-noise ability and detect incipient faults, a novel signal de-noising method based on enhanced time-frequency manifold (ETFM) and kurtosis-wavelet dictionary is proposed. First, to mine the high-dimensional features, the C-C method and Cao's method are combined to determine the embedding dimension and delay time of phase space reconstruction. Second, the input parameters of the liner local tangent space arrangement (LLTSA) algorithm are determined by the grid search method based on Renyi entropy, and the dimension is reduced by manifold learning to obtain the ETFM with the highest time-frequency aggregation. Finally, a kurtosis-wavelet dictionary is constructed for selecting the best atom and eliminating the noise and reconstruct the defective signal. Actual simulations showed that the proposed method is more effective in noise suppression than traditional algorithms and that it can accurately reproduce the amplitude and phase information of the raw signal.

EEMD and Multiscale PCA-Based Signal Denoising Method and Its Application to Seismic P-Phase Arrival Picking.

Signal denoising is one of the most important issues in signal processing, and various techniques have been proposed to address this issue. A combined method involving wavelet decomposition and multiscale principal component analysis (MSPCA) has been proposed and exhibits a strong signal denoising performance. This technique takes advantage of several signals that have similar noises to conduct denoising; however, noises are usually quite different between signals, and wavelet decomposition has limited adaptive decomposition abilities for complex signals. To address this issue, we propose a signal denoising method based on ensemble empirical mode decomposition (EEMD) and MSPCA. The proposed method can conduct MSPCA-based denoising for a single signal compared with the former MSPCA-based denoising methods. The main steps of the proposed denoising method are as follows: First, EEMD is used for adaptive decomposition of a signal, and the variance contribution rate is selected to remove components with high-frequency noises. Subsequently, the Hankel matrix is constructed on each component to obtain a higher order matrix, and the main score and load vectors of the PCA are adopted to denoise the Hankel matrix. Next, the PCA-denoised component is denoised using soft thresholding. Finally, the stacking of PCA- and soft thresholding-denoised components is treated as the final denoised signal. Synthetic tests demonstrate that the EEMD-MSPCA-based method can provide good signal denoising results and is superior to the low-pass filter, wavelet reconstruction, EEMD reconstruction, Hankel-SVD, EEMD-Hankel-SVD, and wavelet-MSPCA-based denoising methods. Moreover, the proposed method in combination with the AIC picking method shows good prospects for processing microseismic waves.

X-ray Pulsar Signal Denoising Based on Variational Mode Decomposition.

Pulsars, especially X-ray pulsars detectable for small-size detectors, are highly accurate natural clocks suggesting potential applications such as interplanetary navigation control. Due to various complex cosmic background noise, the original pulsar signals, namely photon sequences, observed by detectors have low signal-to-noise ratios (SNRs) that obstruct the practical uses. This paper presents the pulsar denoising strategy developed based on the variational mode decomposition (VMD) approach. It is actually the initial work of our interplanetary navigation control research. The original pulsar signals are decomposed into intrinsic mode functions (IMFs) via VMD, by which the Gaussian noise contaminating the pulsar signals can be attenuated because of the filtering effect during signal decomposition and reconstruction. Comparison experiments based on both simulation and HEASARC-archived X-ray pulsar signals are carried out to validate the effectiveness of the proposed pulsar denoising strategy.

A New Method Based on Time-Varying Filtering Intrinsic Time-Scale Decomposition and General Refined Composite Multiscale Sample Entropy for Rolling-Bearing Feature Extraction.

The early fault diagnosis of rolling bearings has always been a difficult problem due to the interference of strong noise. This paper proposes a new method of early fault diagnosis for rolling bearings with entropy participation. First, a new signal decomposition method is proposed in this paper: intrinsic time-scale decomposition based on time-varying filtering. It is introduced into the framework of complete ensemble intrinsic time-scale decomposition with adaptive noise (CEITDAN). Compared with traditional intrinsic time-scale decomposition, intrinsic time-scale decomposition based on time-varying filtering can improve frequency-separation performance. It has strong robustness in the presence of noise interference. However, decomposition parameters (the bandwidth threshold and B-spline order) have significant impacts on the decomposition results of this method, and they need to be artificially set. Aiming to address this problem, this paper proposes rolling-bearing fault diagnosis optimization based on an improved coyote optimization algorithm (COA). First, the minimal generalized refined composite multiscale sample entropy parameter was used as the objective function. Through the improved COA algorithm, optimal intrinsic time-scale decomposition parameters based on time-varying filtering that match the input signal are obtained. By analyzing generalized refined composite multiscale sample entropy (GRCMSE), whether the mode component is dominated by the fault signal is determined. The signal is reconstructed and decomposed again. Finally, the mode component with the highest energy in the central frequency band is selected for envelope spectrum variation for fault diagnosis. Lastly, simulated and experimental signals were used to verify the effectiveness of the proposed method.

Spectral State Compression of Markov Processes.

Model reduction of Markov processes is a basic problem in modeling state-transition systems. Motivated by the state aggregation approach rooted in control theory, we study the statistical state compression of a discrete-state Markov chain from empirical trajectories. Through the lens of spectral decomposition, we study the rank and features of Markov processes, as well as properties like representability, aggregability, and lumpability. We develop spectral methods for estimating the transition matrix of a low-rank Markov model, estimating the leading subspace spanned by Markov features, and recovering latent structures like state aggregation and lumpable partition of the state space. We prove statistical upper bounds for the estimation errors and nearly matching minimax lower bounds. Numerical studies are performed on synthetic data and a dataset of New York City taxi trips.

An Ultra-Short Baseline Underwater Positioning System with Kalman Filtering.

The ultra-short baseline underwater positioning is one of the most widely applied methods in underwater positioning and navigation due to its simplicity, efficiency, low cost, and accuracy. However, there exists environmental noise, which has negative impacts on the positioning accuracy during the ultra-short baseline (USBL) positioning process, which results in a large positioning error. The positioning result may lead to wrong decision-making in the latter processing. So, it is necessary to consider the error sources, and take effective measurements to minimize the negative impact of the noise. In our work, we propose a USBL positioning system with Kalman filtering to improve the positioning accuracy. In this system, we first explore a new kind of element array to accurately capture the acoustic signals from the object. We then organically combine the Kalman filters with the array elements to filter the acoustic signals, using the minimum mean-square error rule to obtain accurate acoustic signals. We got the high-precision phase difference information based on the non-equidistant quaternary original array and the phase difference acquisition mechanism. Finally, on account of the obtained accurate phase difference information and position calculation, we determined the coordinates of the underwater target. Comprehensive evaluation results demonstrate that our proposed USBL positioning method based on the Kalman filter algorithm can effectively enhance the positioning accuracy.

Gravitational-Wave Burst Signals Denoising Based on the Adaptive Modification of the Intersection of Confidence Intervals Rule.

Gravitational-wave data (discovered first in 2015 by the Advanced LIGO interferometers and awarded by the Nobel Prize in 2017) are characterized by non-Gaussian and non-stationary noise. The ever-increasing amount of acquired data requires the development of efficient denoising algorithms that will enable the detection of gravitational-wave events embedded in low signal-to-noise-ratio (SNR) environments. In this paper, an algorithm based on the local polynomial approximation (LPA) combined with the relative intersection of confidence intervals (RICI) rule for the filter support selection is proposed to denoise the gravitational-wave burst signals from core collapse supernovae. The LPA-RICI denoising method's performance is tested on three different burst signals, numerically generated and injected into the real-life noise data collected by the Advanced LIGO detector. The analysis of the experimental results obtained by several case studies (conducted at different signal source distances corresponding to the different SNR values) indicates that the LPA-RICI method efficiently removes the noise and simultaneously preserves the morphology of the gravitational-wave burst signals. The technique offers reliable denoising performance even at the very low SNR values. Moreover, the analysis shows that the LPA-RICI method outperforms the approach combining LPA and the original intersection of confidence intervals (ICI) rule, total-variation (TV) based method, the method based on the neighboring thresholding in the short-time Fourier transform (STFT) domain, and three wavelet-based denoising techniques by increasing the improvement in the SNR by up to 118.94% and the peak SNR by up to 138.52%, as well as by reducing the root mean squared error by up to 64.59%, the mean absolute error by up to 55.60%, and the maximum absolute error by up to 84.79%.

A Denoising Method for Fiber Optic Gyroscope Based on Variational Mode Decomposition and Beetle Swarm Antenna Search Algorithm.

Fiber optic gyroscope (FOG) is one of the important components of Inertial Navigation Systems (INS). In order to improve the accuracy of the INS, it is necessary to suppress the random error of the FOG signal. In this paper, a variational mode decomposition (VMD) denoising method based on beetle swarm antenna search (BSAS) algorithm is proposed to reduce the noise in FOG signal. Firstly, the BSAS algorithm is introduced in detail. Then, the permutation entropy of the band-limited intrinsic mode functions (BLIMFs) is taken as the optimization index, and two key parameters of VMD algorithm, including decomposition mode number K and quadratic penalty factor α , are optimized by using the BSAS algorithm. Next, a new method based on Hausdorff distance (HD) between the probability density function (PDF) of all BLIMFs and that of the original signal is proposed in this paper to determine the relevant modes. Finally, the selected BLIMF components are reconstructed to get the denoised signal. In addition, the simulation results show that the proposed scheme is better than the existing schemes in terms of noise reduction performance. Two experiments further demonstrate the priority of the proposed scheme in the FOG noise reduction compared with other schemes.

Signal Denoising Method Using AIC-SVD and Its Application to Micro-Vibration in Reaction Wheels.

To suppress noise in signals, a denoising method called AIC-SVD is proposed on the basis of the singular value decomposition (SVD) and the Akaike information criterion (AIC). First, the Hankel matrix is chosen as the trajectory matrix of the signals, and its optimal number of rows and columns is selected according to the maximum energy of the singular values. On the basis of the improved AIC, the valid order of the optimal matrix is determined for the vibration signals mixed with Gaussian white noise and colored noise. Subsequently, the denoised signals are reconstructed by inverse operation of SVD and the averaging method. To verify the effectiveness of AIC-SVD, it is compared with wavelet threshold denoising (WTD) and empirical mode decomposition with Savitzky-Golay filter (EMD-SG). Furthermore, a comprehensive indicator of denoising (CID) is introduced to describe the denoising performance. The results show that the denoising effect of AIC-SVD is significantly better than those of WTD and EMD-SG. On applying AIC-SVD to the micro-vibration signals of reaction wheels, the weak harmonic parameters can be successfully extracted during pre-processing. The proposed method is self-adaptable and robust while avoiding the occurrence of over-denoising.

Noise Reduction for MEMS Gyroscope Signal: A Novel Method Combining ACMP with Adaptive Multiscale SG Filter Based on AMA.

In this paper, a novel hybrid method combining adaptive chirp mode pursuit (ACMP) with an adaptive multiscale Savitzky-Golay filter (AMSGF) based on adaptive moving average (AMA) is proposed for offline denoising micro-electromechanical system (MEMS) gyroscope signal. The denoising scheme includes preliminary denoising and further denoising. At the preliminary denoising stage, the original gyroscope signal is decomposed into signal modes one by one using ACMP with modified stopping criterion based on mutual information. Useful information is extracted while most noise is discarded in the residue at this stage. Then, AMSGF is proposed to further denoise the signal modes. Sample variance based on AMA is used to adjust the window size of AMSGF adaptively. Practical MEMS gyroscope signal denoising results under different motion conditions show the superior performance of the proposed method over empirical mode decomposition (EMD)-based denoising, discrete wavelet threshold denoising, and variational mode decomposition (VMD)-based denoising. Moreover, AMSGF is proven to gain a better denoising effect than some other common smoothing methods.

A Gyroscope Signal Denoising Method Based on Empirical Mode Decomposition and Signal Reconstruction.

To suppress the random drift error of a gyroscope signal, this paper proposes a novel denoising method, which is based on processing the intrinsic mode functions (IMFs) obtained by empirical mode decomposition (EMD). Considering that a gyroscope signal contains colored noise in addition to Gaussian white noise, fractal Gaussian noise (FGN) was introduced to quantify the noise in the gyroscope data. The proposed denoising method combines the FGN energy model and the modified method of Hausdorff distance (HD) to adaptively divide the IMFs into three categories (pure noise, pure information, and mixed components of noise and information). Then, the information IMFs and the mixed components after thresholding were selected to give the optimal signal reconstruction. Static and dynamic signal tests of the fiber optic gyroscope (FOG) were carried out to illustrate the performance of the proposed method, and compared with other traditional EMD denoising methods, such as the Euclidean norm measure method (EMD-l2-norm) and the sliding average filtering method (EMD-SA). The results of the analysis of both the static and dynamic signal tests indicate the effectiveness of the proposed method.

A Wavelet Transform-Based Neural Network Denoising Algorithm for Mobile Phonocardiography.

Cardiovascular pathologies cause 23.5% of human deaths, worldwide. An auto-diagnostic system monitoring heart activity, which can identify the early symptoms of cardiac illnesses, might reduce the death rate caused by these problems. Phonocardiography (PCG) is one of the possible techniques able to detect heart problems. Nevertheless, acoustic signal enhancement is required since it is exposed to various disturbances coming from different sources. The most common denoising enhancement is based on the Wavelet Transform (WT). However, the WT is highly susceptible to variations in the noise frequency distribution. This paper proposes a new adaptive denoising algorithm, which combines WT and Time Delay Neural Networks (TDNN). The acquired signal is decomposed by means of the WT using the coif five-wavelet basis at the tenth decomposition level and then provided as input to the TDNN. Besides the advantage of adaptive thresholding, the reason for using TDNNs is their capacity of estimating the Inverse Wavelet Transform (IWT). The best parameters of the TDNN were found for a NN consisting of 25 neurons in the first and 15 in the second layer and the delay block of 12 samples. The method was evaluated on several pathological heart sounds and on signals recorded in a noisy environment. The performance of the developed system with respect to other wavelet-based denoising approaches was validated by the online questionnaire.

K - Shrinkage Function for ECG Signal Denoising.

ECG signals is a graphical way of recording the electrical actions of the heart for the various diagnostic purposes. ECG signals are affected by various noises such as Electrode Contact, Baseline Wandering, Motion artifact, Power-line interference, Muscle Contractions, and Electrosurgical noise during data acquisition. Denoising is a technique which is used for removing the noise in ECG signals which keeps the useful information. In this paper, a new category of Wavelet shrinkage methods is proposed. The white Gaussian noise is mixed with the ECGs for simulation and tested with the new class of shrinkage function and is compared with the other wavelet shrinkage functions such as hard and soft shrinkage. The performance measures such as Signal to Noise Ratio (SNR) and Percent Root mean - square Difference (PRD) etc. are used to examine the performance of various shrinkage functions. The experimental result shows that it gives better MSE over conventional shrinkage functions.

Towards a Continuous Biometric System Based on ECG Signals Acquired on the Steering Wheel.

Electrocardiogram signals acquired through a steering wheel could be the key to seamless, highly comfortable, and continuous human recognition in driving settings. This paper focuses on the enhancement of the unprecedented lesser quality of such signals, through the combination of Savitzky-Golay and moving average filters, followed by outlier detection and removal based on normalised cross-correlation and clustering, which was able to render ensemble heartbeats of significantly higher quality. Discrete Cosine Transform (DCT) and Haar transform features were extracted and fed to decision methods based on Support Vector Machines (SVM), k-Nearest Neighbours (kNN), Multilayer Perceptrons (MLP), and Gaussian Mixture Models - Universal Background Models (GMM-UBM) classifiers, for both identification and authentication tasks. Additional techniques of user-tuned authentication and past score weighting were also studied. The method's performance was comparable to some of the best recent state-of-the-art methods (94.9% identification rate (IDR) and 2.66% authentication equal error rate (EER)), despite lesser results with scarce train data (70.9% IDR and 11.8% EER). It was concluded that the method was suitable for biometric recognition with driving electrocardiogram signals, and could, with future developments, be used on a continuous system in seamless and highly noisy settings.

Electrocardiogram Signal Denoising Using Extreme-Point Symmetric Mode Decomposition and Nonlocal Means.

Electrocardiogram (ECG) signals contain a great deal of essential information which can be utilized by physicians for the diagnosis of heart diseases. Unfortunately, ECG signals are inevitably corrupted by noise which will severely affect the accuracy of cardiovascular disease diagnosis. Existing ECG signal denoising methods based on wavelet shrinkage, empirical mode decomposition and nonlocal means (NLM) cannot provide sufficient noise reduction or well-detailed preservation, especially with high noise corruption. To address this problem, we have proposed a hybrid ECG signal denoising scheme by combining extreme-point symmetric mode decomposition (ESMD) with NLM. In the proposed method, the noisy ECG signals will first be decomposed into several intrinsic mode functions (IMFs) and adaptive global mean using ESMD. Then, the first several IMFs will be filtered by the NLM method according to the frequency of IMFs while the QRS complex detected from these IMFs as the dominant feature of the ECG signal and the remaining IMFs will be left unprocessed. The denoised IMFs and unprocessed IMFs are combined to produce the final denoised ECG signals. Experiments on both simulated ECG signals and real ECG signals from the MIT-BIH database demonstrate that the proposed method can suppress noise in ECG signals effectively while preserving the details very well, and it outperforms several state-of-the-art ECG signal denoising methods in terms of signal-to-noise ratio (SNR), root mean squared error (RMSE), percent root mean square difference (PRD) and mean opinion score (MOS) error index.

An Ultrahigh Frequency Partial Discharge Signal De-Noising Method Based on a Generalized S-Transform and Module Time-Frequency Matrix.

Due to electromagnetic interference in power substations, the partial discharge (PD) signals detected by ultrahigh frequency (UHF) antenna sensors often contain various background noises, which may hamper high voltage apparatus fault diagnosis and localization. This paper proposes a novel de-noising method based on the generalized S-transform and module time-frequency matrix to suppress noise in UHF PD signals. The sub-matrix maximum module value method is employed to calculate the frequencies and amplitudes of periodic narrowband noise, and suppress noise through the reverse phase cancellation technique. In addition, a singular value decomposition de-noising method is employed to suppress Gaussian white noise in UHF PD signals. Effective singular values are selected by employing the fuzzy c-means clustering method to recover the PD signals. De-noising results of simulated and field detected UHF PD signals prove the feasibility of the proposed method. Compared with four conventional de-noising methods, the results show that the proposed method can suppress background noise in the UHF PD signal effectively, with higher signal-to-noise ratio and less waveform distortion.