Noise Robustness Research Articles

A robust intelligent fault diagnosis method for rotating machinery under noisy labels

Despite achieving considerable success, the fault diagnosis methods will still be disturbed by noisy labels, this causes the model’s degradation and reduced diagnostic precision. Focused on solving the above issues, a robust intelligent fault diagnosis approach for rotating machinery under noisy labels is proposed. Firstly, we maintain two deep neural networks (DNNs) and alternatively execute parameters updating and models optimization by referring to the Co-teaching strategy, which can maximize filtering different error types and implement pre-training of DNNs. Secondly, adopting a two-component Gaussian mixture model (GMM) to fit training dataset’s cross-entropy (CE) loss and realize the clean and noisy labels division according to the threshold. Then, a data augmentation method called Mixup operation is employed in semi-supervised learning (SSL) to increase noise robustness and avoid error accumulation, subsequently, performing fine-tuning and correction for clean and noisy samples. Challenging experiments on a transmission gearbox dataset under different noisy labels levels show that the proposed method has robustness to noise and significantly surpasses other approaches, which provides an important reference value for accurate fault diagnosis for rotating equipment parts with noisy labels.

State-space modeling approach for fringe pattern demodulation.

A spatial carrier fringe demodulation technique is proposed based on a state-space modeling approach for phase estimation. The fringe background intensity, carrier frequency, and phase quadrature components are considered to be the elements of the state vector, which are estimated simultaneously. The state estimation is performed using the extended Kalman filter. The simulation and experimental results are provided to demonstrate the performance comparison of the proposed method with popular and state-of-the-art methods in terms of noise robustness and phase estimation accuracy.

Distributed sub-Nyquist sampling and parameters measurement of common frequency support MEDS signals

Parameters measurement of multiple exponentially damped sinusoids (MEDS) signals is of great significance in many areas. However, recent technologies are most based on Nyquist sampling theory and thus require very high sampling rate for wide band signals. In this paper, a distributed sub-Nyquist sampling and parameters measurement method is proposed for common frequency support MEDS signals. The proposed method can measure the parameters of P common frequency support MEDS signals by P+1 distributed sub-Nyquist sampling channels. A subspace based parameters estimation algorithm is proposed to estimate the unknown amplitudes, frequencies and damping factors of the measured MEDS signals. It can be determined that K(P+1)+P⌈K/P⌉ samples are sufficient for parameters measuring of P MEDS signals with K common frequency components, which is much smaller than previous works. Finally, we design a hardware prototype to verify the effectiveness of the proposed method. Simulation and hardware experiments have demonstrated the effectiveness and noise robustness of the proposed method.

On the Uncertainty Analysis of the Data-Enabled Physics-Informed Neural Network for Solving Neutron Diffusion Eigenvalue Problem

We performed uncertainty analysis and further numerical studies on the data-enabled physics-informed neural network (DEPINN). The purpose of DEPINN is to accurately and efficiently use a small amount of prior data to solve the neutron diffusion eigenvalue equations based on the physics-informed neural network. However, in practical engineering experiments, these prior data are acquired through different kinds of sensors, which are inevitably polluted by noise. Numerical results of three typical benchmark problems show that the classical DEPINN is not so robust with respect to noise. To improve the noise robustness, we propose an interval loss function to deal with the noisy prior data term; the weight of the noisy prior data term is also set to be noise dependent. Numerical results show that the proposed framework effectively enhances the robustness of DEPINN and improves the efficiency of utilizing the noisy prior data and thus promotes the engineering application of DEPINN.

Optimization-inspired Cumulative Transmission Network for image compressive sensing

Compressive Sensing (CS) techniques enable accurate signal reconstruction with few measurements. Deep Unfolding Networks (DUNs) have recently been shown to increase the efficiency of CS by emulating iterative CS optimization procedures by neural networks. However, most of these DUNs suffer from redundant update procedures or complex matrix operations, which can impair their reconstruction performances. Here we propose the optimization-inspired Cumulative Transmission Network (CT-Net), a DUN approach for natural image CS. We formulate an optimization procedure introducing an auxiliary variable similar to Half Quadratic Splitting (HQS). Unfolding this procedure defines the basic structure of our neural architecture, which is then further refined. A CT-Net is composed of Reconstruction Fidelity Modules (RFMs) for minimizing the reconstruction error and Constraint Gradient Approximation (CGA) modules for approximating (the gradient of) sparsity constraints instead of relying on an analytic solutions such as soft-thresholding. Furthermore, a lightweight Cumulative Transmission (CT) between CGAs in each reconstruction stage is proposed to facilitate a better feature representation. Experiments on several widely used natural image benchmarks illustrate the effectiveness of CT-Net with significant performance improvements and fewer network parameters compared to existing state-of-the-art methods. The experiments also demonstrate the scene and noise robustness of the proposed method.

A vibration-based 1DCNN-BiLSTM model for structural state recognition of RC beams

The vibration signal analysis-based structural health monitoring (SHM) system has been widely used for bridge condition identification. With the development of artificial intelligence (AI), machine learning (ML) has made numerous breakthroughs in the detection of civil engineering structures. However, conventional data-driven ML methods heavily rely on prior knowledge for their performance. This paper proposes a deep learning (DL) model 1DCNN-BiLSTM for detecting small local structural changes of reinforced concrete (RC) beams, which applies the structure of the Inception module in GoogLeNet to one-dimensional convolution neural networks (1DCNNs) for feature extraction at different scales, and combines the advantages of bidirectional long short-term memory (BiLSTM) modules for processing long time-series data. Firstly, a three-dimensional numerical model of the RC beam was established using finite element software, and the accuracy of the numerical model was verified by comparing it with the test results. Based on the numerical model, tests on RC beams impacted by falling hammers were carried out, and the acceleration signals of the beam in different states were collected as a dataset. The proposed DL model can automatically extract the spatial and temporal domain features in the signals, accurately identify the location of small bridge local variations, the accuracy in the test set is 98.8% compared to 92.6% for a traditional ML model, and has better noise immunity performance and robustness to the missing data than the traditional ML model. Finally, the internal inference process of the model was explored and visualized, illustrating that the model has adaptive learning capabilities.

Improving the stability of phase retrieval algorithm in speckle autocorrelation imaging by Huber penalty sparsity constraint

One of the most widely used methods for reconstructing images through a scattering medium is the Hybrid Input Output (HIO) phase retrieval algorithm. However, the stability and noise robustness of the HIO method are poor, as they are affected by initial values and noise during the imaging process. This paper presents an optimized HIO phase retrieval algorithm that utilizes the Huber penalty as a sparsity constraint to effectively enhance the quality and stability of the reconstruction algorithm. The introduced constraint is designed to guide the iteration process away from local optimal solutions, ensuring superior recovery images even with random initial values. Additionally, an adaptive step size parameter is incorporated to control the iterations and convergence steps, resulting in stronger robustness against noise effects. Moreover, the error criterion for image restoration is defined as the sum of the Fourier transform amplitude of the gradient. Experimental results demonstrate that the proposed phase retrieval algorithm achieves superior quality in the recovered images, while significantly improving noise immunity and stability for randomly selected initial values.

Local time-reassigned synchrosqueezing transform and its application in bearing fault characteristic extraction

Rolling bearing fault signals and other types of impulse signals present transient broadband and fast time-varying characteristics in the time–frequency plane, which makes accurately locating the time–frequency trajectory of the signal a challenging task. In this paper, a new time–frequency analysis method is proposed to achieve a high energy-concentrated time–frequency representation for impulsive-like signals. At first, the points on the time–frequency ridges are detected to construct a fixed point set as the reassignment target of the fuzzy energy. Then the local blurred energy is directly assigned to the nearest ridge according to the reassignment direction of time–frequency points. The proposed method ensures a high concentration of energy and supports perfect signal reconstruction. The results of numerical validation prove that the new time–frequency analysis method has excellent noise robustness and energy concentration capability. Finally, the application of bearing fault diagnosis under multiple operating conditions confirms the excellence in the fault diagnosis field.

A weighted local‐spherical grid based lightweight descriptor for 3D point cloud registration

AbstractEstablishing effective feature descriptors is a crucial step in 3D point cloud registration task. Existing manual‐based methods are noise‐susceptible and time‐consuming when running on low‐cost edge computing devices. To this end, the authors proposed a Local Reference Frame (LRF) based approach that can quickly and robustly register point clouds by using a novel lightweight local‐spherical grid weighted descriptor (LSGWD). Firstly, the LRF of the proposed algorithm is established by the covariance matrix eigenvector of KeyPoint's spherical support set and the centroid vector's projection on its orthogonal plane. Then the spherical support is grided to 32 bins, and the 4D geometric features of each subset are constructed by the centroid moment and the cosine value of the angles between the centroid vector and axes of LRF. Secondly, to restrain the insufficient discriminative information presented in the purely geometric features, the Gaussian projection and gradient mapping are proposed to calculate the smooth density and the correlation of structural characteristics, which are obtained as the distribution information of each bin to weigh the feature representation. Finally, the 32 × 4‐dimensional KeyPoint descriptor is obtained and used in the 3D point cloud registration framework. Experiments are carried out on three test datasets and real scene data. Compared to previous baselines, our descriptor achieves the state‐of‐the‐art performance in terms of efficiency and accuracy owing to its compact structure and noise robustness. The proposed method enhances the recognition and registration performance of 3D point cloud matching in low‐cost edge computing applications.

2D-supervised fast neural fluid reconstruction technique for time-resolved volumetric flame reconstruction

The volumetric tomography reconstruction technique (VTRT) can calculate and restore the three-dimensional physical field based on the multi-view projection information of the flame and similar flow fields, which plays an important role in the research of volumetric targets. However, the reconstruction of three-dimensional scalar/vector fields representing the physical information of the flow field (temperature, density, chemical composition, etc.) requires a significant amount of computational resources and time, especially in the turbulent flame flow field, which requires high spatial and temporal resolutions. Based on the said background, in this work, we proposed a Fast Neural Fluid Reconstruction Technique (Fast-NFRT) based on deep learning. In this investigation, we first test the reconstruction accuracy, speed, and noise robustness of Fast-NFRT using numerically simulated flames. Then Fast-NFRT is used to reconstruct the experimental turbulent jet flame under two different conditions. Finally, with the camera settings preserved, the Fast-NFRT model was tested for transfer learning between the numerical simulation flame and the two experimental jet flames to examine the generalization performance of the reconstruction. It is found that the proposed Fast-NFRT model can achieve a temporal resolution of 50-500 fps with a similar reconstruction fidelity to traditional algebraic reconstruction methods, which demonstrates the capacity of the Fast-NFRT model and its potential in real-time reconstruction applications and dynamic analysis for complex flow dynamics.

Noise robustness of an operational modal-based structural damage-detection scheme using impact-synchronous modal analysis

Noise robustness of an operational modal-based structural damage-detection scheme using impact-synchronous modal analysis

Rolling bearing fault diagnosis under time-varying speeds based on time-characteristic order spectrum and multi-scale domain adaptation network

In practical industrial applications, rolling bearing generally operates under variable conditions and its vibration signal significantly fluctuates in amplitude and frequency. This increases the feature distribution differences of the bearing fault samples and makes the health status identification of the bearing more difficult. To this end, a new intelligent fault diagnosis method for bearing under time-varying speed conditions is proposed based on time-characteristic order (TCO) spectrum and multi-scale domain adaptation network (MSDAN). Firstly, by using the good noise robustness and high time–frequency aggregation properties of the synchrosqueezed wave packet transform (SSWPT), the TCO spectrum method based on SSWPT is proposed to eliminate the impact of speed fluctuation, reducing the distribution shift of bearing data under time-varying speeds. Secondly, an MSDAN model based on global-local feature fusion is established to extract the domain-invariant features closely related to the bearing fault state from the TCO spectrum. Finally, the local maximum distribution discrepancy is introduced to capture the discriminative fine-grained features. The feasibility of the proposed method is verified in various transfer tasks on two different bearing datasets with time-varying speeds. Compared with some state-of-art methods, the proposed method can eliminate the sample distribution differences under time-varying speeds, significantly improving its accuracy and generalization performance in cross-domain fault diagnosis of rolling bearing.

The Power-Normalized Cepstral Coefficient (PNCC) for convolutional neural networks-based robust speech command recognition

While implementations of speech recognition grow rapidly in recent years and are slowly being integrated into our daily devices, the problem of noise robustness is still a challenging task, even with the recent advancement of deep learning technologies for speech recognition. The presence of noise may cause a mismatch between training, which is performed in clean conditions, and noisy testing conditions. This paper proposes a method to extract features for speech recognition by employing features derived under the power law scale, i.e., the Power-Normalized Cepstral Coefficient (PNCC). The power-law can provide better compression in low-energy regions so that it is not sensitive when the speech signal is distorted by noise. The features are implemented on speech recognition based on Convolutional Neural Networks (CNNs). The experiments were carried out by TensorFlow’s Speech Command Dataset mixed with various signal-to-noise ratio to evaluate the method. The experimental findings indicate that the accuracy ranges from 81% to 86%.

Noise robust Zernike phase retrieval via learning based algorithm only with 2-step phase shift measurements.

We present a noise robust deep learning based aberration analysis method using 2-step phase shift measurement data. We first propose a realistic aberration pattern generation method to synthesize a sufficient amount of real-world-like aberration patterns for training a deep neural network by exploiting the asymptotic statistical distribution parameters of the real-world Zernike coefficients extracted from a finite number of experimentally measured real-world aberration patterns. As a result, we generate a real-world-like synthetic dataset of 200,000 different aberrations from 15 sets of real-world aberration patterns obtained by a Michelson interferometer under a variety of measurement conditions using the 4-step derivative fitting method together with the exploitation of the Gaussian density estimation. We then train the deep neural network with the real-world-like synthetic dataset, using two types of network architectures, GoogLeNet and ResNet101. By applying the proposed learning based 2-step aberration analysis method to the analysis of numerically generated aberrations formed under 100 different conditions, we verify that the proposed 2-step method can clearly outperform the existing 4-step iterative methods based on 4-step measurements, including the derivative fitting, transport of intensity equation (TIE), and robust TIE methods, in terms of noise robustness, root mean square error (RMSE), and inference time. By applying the proposed 2-step method to the analysis of the real-world aberrations experimentally obtained under a variety of measurement conditions, we also verify that the proposed 2-step method achieves compatible performance in terms of the RMSE between the reconstructed and measured aberration patterns, and also exhibits qualitative superiority in terms of reconstructing more realistic fringe patterns and phase distributions compared to the existing 4-step iterative methods. Since the proposed 2-step method can be extended to an even more general analysis of aberrations of any higher order, we expect that it will be able to provide a practical way for comprehensive aberration analysis and that further studies will extend its usefulness and improve its operational performance in terms of algorithm compactness, noise robustness, and computational speed.

Spectral–Spatial Features Exploitation Using Lightweight HResNeXt Model for Hyperspectral Image Classification

Hyperspectral image classification is vital for various remote sensing applications; however, it remains challenging due to the complex and high-dimensional nature of hyperspectral data. This paper introduces a novel approach to address this challenge by leveraging spectral and spatial features through a lightweight HResNeXt model. The proposed model is designed to overcome the limitations of traditional methods by combining residual connections and cardinality to enable efficient and effective feature extraction from hyperspectral images, capturing both spectral and spatial information simultaneously. Furthermore, the paper includes an in-depth analysis of the learned spectral–spatial features, providing valuable insights into the discriminative power of the proposed approach. The extracted features exhibit strong discriminative capabilities, enabling accurate classification even in challenging scenarios with limited training samples and complex spectral variations. Extensive experimental evaluations are conducted on four benchmark hyperspectral data sets, the Pavia university (PU), Kennedy Space Center (KSC), Salinas scene (SA), and Indian Pines (IP). The performance of the proposed method is compared with the state-of-the-art methods. The quantitative and visual results demonstrate the proposed approach’s high classification accuracy, noise robustness, and computational efficiency superiority. The HResNeXt obtained an overall accuracy on PU, KSC, SA, and IP, 99.46%, 81.46%, 99.75%, and 98.64%, respectively. Notably, the lightweight HResNeXt model achieves competitive results while requiring fewer computational resources, making it well-suited for real-time applications.

M2GF: Multi-Scale and Multi-Directional Gabor Filters for Image Edge Detection

An image edge detection algorithm using multi-directional and multi-scale Gabor filters is proposed in this paper. The main merit of this method is that high edge detection accuracy can be obtained while maintaining noise robustness. The approach proposed in this paper consists of three procedures: firstly, the transformation to the CIE L*a*b* color space, which has a wide shading area and uniform distribution; secondly, under different scales, the edge feature information of the image is extracted from several different directions by Gabor filters, and a new edge strength map is obtained by feature fusion; thirdly, the new fused edge strength map is enhanced with local features, and a noise-resistant image edge detector is obtained under a novel hysteresis threshold calculation. The experiments illustrate that, compared to the methods involved, the designed edge detector outperforms by about 2% to 4%, and also shows competitive performance regarding the ability to handle noise.

Study on a hybrid algorithm for accurate ripple detection in DC microgrids

AbstractWith the advantages of the low cost of transmission lines and high efficiency, the DC microgrid has become a rising star in the low‐voltage network. However, multi‐source and multi‐transformation characteristics in DC microgrids will lead to the existence of various forms of ripple generation sources in the system. The existence of a large amount of ripple not only directly cause the reduction of power quality of DC microgrids, but also decreases the accuracy of electricity billing. It is vital to achieving accurate ripple detection for the reliable power supply of the DC microgrid. A DC‐side ripple detection method, which combines the Whale Optimization Algorithm (WOA), Variational Modal Decomposition (VMD), and Hilbert Transform (HT), is therefore investigated and proposed here. Firstly, the sample entropy (SampEn) is used as the fitness function, applied the whale optimization algorithm, is to determine the optimal decomposition scale and penalty factor, of the variational modal decomposition; then, the ripple‐containing DC signal is decomposed into a series of eigenmodal components (imf) by the optimized variational modal decomposition algorithm. Finally, the Hilbert Transform is performed to obtain the amplitude and frequency of the ripple components. To prove the effectiveness, the proposed method is compared with the conventional Empirical Mode Decomposition (EMD) and the VMD algorithm, by testing simulated DC signals without and with noise. Results show that the proposed method has higher accuracy and noise robustness than the EMD and VMD algorithms.

Detecting Bell Correlations in Multipartite Non-Gaussian Spin States.

We expand the toolbox for studying Bell correlations in multipartite systems by introducing permutationally invariant Bell inequalities (PIBIs) involving few-body correlators. First, we present around twenty families of PIBIs with up to three- or four-body correlators, that are valid for an arbitrary number of particles. Compared to known inequalities, these show higher noise robustness, or the capability to detect Bell correlations in highly non-Gaussian spin states. We then focus on finding PIBIs that are of practical experimental implementation, in the sense that the associated operators require collective spin measurements along only a few directions. To this end, we formulate this search problem as a semidefinite program that embeds the constraints required to look for PIBIs of the desired form.

Reliable modal estimation of high-rise structures via synergistic usage of multiple stabilization diagram-based operational modal analysis techniques

In operational modal analysis, typically only structural responses are available. Errors and uncertainties may exist in modal estimates, thereby leading to discrepancies in the results by different modal identification approaches even analyzing the same data set. To this end, a synergistic usage of multiple stabilization diagram-based modal identification techniques is presented in this paper to reduce the errors and uncertainties in modal estimates associated with modal identification techniques or modeling ideas. The effectiveness and noise robustness of the synergistic strategy are validated via numerical simulation study of a frame structure. Additionally, the synergistic strategy is further utilized to evaluate the dynamic characteristics of a supertall building with 600 m height during a typhoon event. The application of the synergistic strategy to field measurements reveal that the building natural frequencies varied during the typhoon and exhibited significant amplitude-dependent features. Meanwhile, the damping ratios of the skyscraper for all concerned modes remained roughly stable within a range of [0.16%, 0.94%]. This paper aims to provide a practical way or effective tool to enhance the accuracy and confidence in modal estimation of high-rise buildings, thus further revealing the dynamic characteristics of large-scale structures under severe wind excitations.

Improved On-Orbit MTF Measurement Method Based on Point Source Arrays

The modulation transfer function (MTF) is a key characteristic used to assess the performance of optical remote sensing satellite sensors. MTF detection can directly measure a sensor’s two-dimensional (2D) point spread function (PSF); therefore, it has been applied to various high-resolution remote sensing satellites (e.g., Pleiades) using point sources. However, current point source methods mainly use 2D Gaussian functions to fit the discrete digital number (DN) of the point source on the image to extract the center of the point source and fit the PSF after encrypting multiple point sources; thus, noise robustness is poor and measurement accuracy varies widely. In this study, we developed a noise-resistant on-orbit MTF detection method based on the object space constraint among point source arrays. Utilizing object space constraint relationships among points in a point source array, a homography transformation model was established, enabling accurate extraction of sub-pixel coordinates for each point source response. Subsequently, aligning the luminosity distribution of all point sources concerning a reference point source, the encrypted PSF was obtained and then fitted to obtain the MTF. To validate the method, Gaofen-2 (GF-2) satellite images were used to conduct an in-orbit imaging experiment on the point source array of the Chinese Zhongwei remote sensing satellite calibration site. Compared with the Gaussian model methods, the proposed method yielded more accurate peak positions for each point source. Standard deviations of peak position constant ratios in along- and cross-track directions improved by 2.8 and 4.8 times, respectively. The root-mean-square error (RMSE) of the collinearity test results increased by 92%, and the noise resistance of the MTF curve improved by two times. Dynamic MTF values at the Nyquist frequency for the GF-2 panchromatic band in along- and cross-track directions were 0.0476 and 0.0705, respectively, and MTF values in different directions were well distinguished.