Bispectrum Analysis Research Articles

Bispectrum Analysis of Thermal Images for the Classification of Retinal Vascular Diseases

In the field of medicine, thermal imaging provides a non-invasive means to diagnose diseases by displaying temperature variations. Specifically, thermal images of the ocular region are proving effective in diagnosing retinal diseases like diabetic retinopathy (DR), diabetic macular edema (DME), age-related macular degeneration (AMD), and wet AMD. This study explores the use of bispectrum analysis on ocular thermal images. The bispectrum, derived from third-order statistics (cumulants), is estimated using parametric (ARMA) and non-parametric methods (direct and indirect). Various entropy measures are extracted as features from these bispectrum images. The effectiveness of these features is evaluated through experiments employing different machine learning algorithms: discriminant analysis (DA), K-nearest neighbour (KNN), decision tree (DT), and Naïve Bayes Classifier (NBC). The results indicate that the KNN classifier achieves the highest accuracy when using features extracted via the indirect method of bispectrum estimation. Meanwhile, the DT classifier performs exceptionally well with bispectrum features extracted through the direct method, outperforming other feature extraction approaches.

Catalog-level blinding on the bispectrum for DESI-like galaxy surveys

We evaluate the performance of the catalog-level blind analysis technique (blinding) presented in Brieden et al. (2020) in the context of a fixed template power spectrum and bispectrum analysis. This blinding scheme, which is tailored for galaxy redshift surveys similar to the Dark Energy Spectroscopic Instrument (DESI), has two components: the so-called “AP blinding” (concerning the dilation parameters α ∥, α ⊥) and “RSD blinding” (redshift space distortions, affecting the growth rate parameter f). Through extensive testing, including checks for the RSD part in cubic boxes, the impact of AP blinding on mocks with realistic survey sky coverage, and the implementation of a full AP+RSD blinding pipeline, our analysis demonstrates the effectiveness of the technique in preserving the integrity of cosmological parameter estimation when the analysis includes the bispectrum statistic. We emphasize the critical role of sophisticated — and difficult to accidentally unblind — blinding methods in precision cosmology.

Impact of the Epoch of Reionization sources on the 21-cm bispectrum

The morphology of the 21-cm signal emitted by the neutral hydrogen present in the intergalactic medium (IGM) during the Epoch of Reionization (EoR) depends both on the properties of the sources of ionizing radiation and on the underlying physical processes within the IGM. Variation in the morphology of the IGM 21-cm signal due to the different sources of the EoR is expected to have a significant impact on the 21-cm bispectrum, which is one of the crucial observable statistics that can evaluate the non-Gaussianity present in the signal and which can be estimated from radio interferometric observations of the EoR. Here we present the 21-cm bispectrum for different reionization scenarios assuming different simulated models for the sources of reionization. We also demonstrate how well the 21-cm bispectrum can distinguish between different IGM 21-cm signal morphologies, arising due to the differences in the reionization scenarios, which will help us shed light on the nature of the sources of ionizing photons. Our estimated large-scale bispectrum for all unique k-triangle shapes shows a significant difference in the magnitude and sign across different reionization scenarios. Additionally, our focused analysis of bispectrum for a few specific k-triangle shapes (e.g. squeezed-limit, linear, and shapes in the vicinity of the squeezed-limit) shows that the large scale 21-cm bispectrum can distinguish between reionization scenarios that show inside-out, outside-in and a combination of inside-out and outside-in morphologies. These results highlight the potential of using the 21-cm bispectrum for constraining different reionization scenarios.

Numerical investigation of triadic interactions during wave propagation over a submerged bar using a fully nonlinear numerical wave tank

This study models wave propagation over a submerged trapezoidal bar problem with a Higher Order Boundary Element Method (HOBEM) based on a two-dimensional fully nonlinear numerical wave tank (NWT). A Mixed Eulerian-Lagrangian technique is implemented, and the NWT is validated using the experimental results available from the existing literature. A numerical investigation is conducted on the individual wave harmonics as it propagates across the numerical wave tank over the submerged bar. The amplitude spectrum is obtained from the time histories of wave elevation across the tank at various locations over the trapezoidal bar and compared with the experimental results. The redistribution of the energy spectrum across the domain is recorded as the regular long wave propagates and undergoes deformations because of shoaling followed by de-shoaling. This phenomenon is investigated using a higher-order statistical analysis method viz. Bispectrum. The mechanics of the redistribution of energy among the harmonics is quantified through bispectrum analysis. Further, regular and irregular wave propagation over the submerged bar in the presence of the following and opposing currents is simulated. The effect of current is studied using the amplitude spectrum and the harmonic interaction for each case is compared using bispectrum analysis.

Acoustic emission monitoring for damage diagnosis in composite laminates based on deep learning with attention mechanism

During service, advanced composite materials are susceptible to various forms of damage. Developing an efficient real-time Structural Health Monitoring (SHM) method is of profound significance to ensure the normal operational integrity of the advanced composite structures. This study introduces a novel end-to-end SHM approach employing acoustic emission (AE) techniques and a deep learning model with attention mechanisms (AM) to automate the damage diagnosis process and improve prediction accuracy. Low-velocity impact (LVI) experiments were carried out, recording AE signals for subsequent bi-spectrum analysis. Three dedicated AM-based Convolutional Neural Network (CNN) architectures were designed for damage diagnosis, utilizing 2D bi-spectrum contour images as input data. A comparison was made between the proposed CNN model, deep learning and traditional machine learning models in the context of damage diagnostics, revealing that CNN models combined AM exhibit significantly higher accuracy in pattern recognition tasks. The accuracies of the baseline CNN, self-attention-CNN, multi-head attention-CNN and convolutional block attention module-CNN are 98.22%, 98.50%, 98.85%, and 98.87%, respectively. The CNN embedded with AM demonstrated superior predictive performance and fewer instances of misclassification. Considering the specific demands of damage diagnostics in composite materials, the CBAM-CNN is better suited for composite material health monitoring tasks.

Tool condition monitoring for cavity milling based on bispectrum analysis and Bayesian optimized SVM

Tool condition monitoring for cavity milling based on bispectrum analysis and Bayesian optimized SVM

Toward accurate extraction of bearing fault modulation characteristics with novel time–frequency modulation bispectrum and modulation Gini index analysis

Rolling bearings are extremely critical rotating mechanical components, and when they fail, they can damage the equipment, causing safety threats or economic losses. Collecting and analyzing vibration signals of faulty bearings is a common fault diagnosis method. Modulation signal bispectrum (MSB) can utilize the inherent modulation characteristics of the signal to achieve fault feature recognition, but it is easily affected by strong background noise and other modulation signals, making it difficult to detect the fault feature frequency in the end. Based on this, a time–frequency modulation bispectrum (TFMB) method is proposed in this paper. The signal is first transformed into the time–frequency domain through short-time Fourier transform, retaining both time and frequency information. It reduces the amplitude of bispectral noise, highlights spectral lines related to fault information, and displays modulation information more clearly, making the demodulation results more accurate. Based on the characteristics of bispectrum, a two-dimensional singular value decomposition (2D SVD) strategy is designed to reduce the amplitude of the noise components in the bispectrum, and the relative change rate is proposed to automatically determine the number of effective singular values. At the same time, considering that the Gini index has good sparse property, the modulation Gini index (MGI) is proposed based on the Gini index, which can identify the repetitive pulses in the signal, suppress the random pulses and noise interference, and extract the modulation component. MGI can be used to evaluate the proportion of fault information contained in TFMB slices and select the optimal frequency slice. The simulation signal verifies the effectiveness of the method in fault diagnosis of rolling bearing, and the proposed method is applied to the diagnosis of rolling bearing outer ring fault, inner ring fault, and compound fault respectively. The experimental results show that the method can effectively reduce noise amplitude, enhance fault information in the bispectrum, and extract the optimal frequency slice to accurately detect bearing fault characteristic frequencies. The proposed method is compared with MSB detector, Fast Kurtogram and Autogram, which proves the superiority of TFMB method in extraction of rolling bearing fault characteristics.

Parameterisation and evolution of non-breaking wave nonlinearity over flexible vegetation

Wave nonlinearity significantly influences wave attenuation and can cause sediment transport imbalances in vegetated zones, impacting shoreline stability and ecosystem-based coastal defences. Despite its importance, the parameterisation and mechanisms of wave nonlinearity evolution over flexible vegetation remain unclear. This study examines the mechanisms behind non-breaking wave nonlinearity evolution over flexible vegetation and provides parameterisation of wave nonlinearity, based on experimental data collected by Anderson and Smith (2014). The study derives a new set of empirical formulae for predicting wave nonlinearity in Spartina alterniflora, which considers Ursell number, relative vegetation width, vegetation submergence, and vegetation density. The predictions made using these formulae are in good agreement with the measurements. The results indicate a decrease in wave skewness across the span of vegetation, whereas wave asymmetry increases until it reaches a maximum before decreasing. The findings suggest a preferential dissipation of high harmonics compared to low harmonics in the vegetation zone. Additionally, bispectrum analysis reveals that vegetation enhances the difference interaction while suppressing the sum interaction between wave components. The findings enable improvements in our understanding of wave nonlinearity in vegetation, providing better predictive capabilities for wave attenuation and sediment transport, which are crucial for the design and optimization of coastal defence systems.

Cosmological constraints from the redshift-space galaxy skew spectra

Extracting the non-Gaussian information of the cosmic large-scale structure (LSS) is vital in unlocking the full potential of the rich datasets from the upcoming stage-IV galaxy surveys. Galaxy skew spectra serve as efficient beyond-two-point statistics, encapsulating essential bispectrum information with computational efficiency akin to power spectrum analysis. This paper presents the first cosmological constraints from analyzing the full set of redshift-space galaxy skew spectra of the data from the SDSS-III BOSS, accessing cosmological information down to nonlinear scales. Employing the forward modeling framework and simulation-based inference via normalizing flows, we analyze the CMASS-SGC subsample, which constitute approximately 10% of the full BOSS data. Analyzing the scales up to kmax=0.5 h−1 Mpc, we find that the skew spectra improve the constraints on Ωm,Ωb,h, and ns by 34%, 35%, 18%, 10%, respectively, compared to constraints from previous power spectrum multipoles analysis, yielding Ωm=0.288−0.034+0.024, Ωb=0.043−0.007+0.005, h=0.759−0.050+0.104, ns=0.918−0.090+0.041 (at 68% confidence limit). On the other hand, the constraints on σ8 are weaker than from the power spectrum. Including the big bang nucleosynthesis (BBN) prior on baryon density reduces the uncertainty on the Hubble parameter further, achieving h=0.750−0.032+0.034, which is a 38% improvement over the constraint from the power spectrum with the same prior. Compared to the bispectrum (monopole) analysis, skew spectra offer comparable constraints on larger scales (kmax<0.3 h−1 Mpc) for most parameters except for σ8. Published by the American Physical Society 2024

Angular bispectrum and trispectrum of scalar-induced gravitational waves: all contributions from primordial non-Gaussianity f NL and g NL

Studying the primordial non-Gaussianity of inflationary perturbations is crucial for testing the inflation paradigm of the early universe. In this work, we conduct a comprehensive analysis of the angular bispectrum and trispectrum of scalar-induced gravitational waves (SIGWs) in the presence of local-type primordial non-Gaussianity parameterized by f NL and g NL, deriving their semi-analytical formulae for the first time. Our findings indicate that it is the presence of primordial non-Gaussianity that leads to a non-Gaussian SIGW background, suggesting that the angular bispectrum and trispectrum of SIGWs could serve as probes of the primordial non-Gaussianity. Our numerical results further illustrate that f NL and g NL exert significant impacts on the spectral amplitudes, potentially reaching up to 10-5 for the former and 10-8 for the latter. In particular, we demonstrate that the angular bispectrum and trispectrum exhibit characteristic dependence on the angular multipoles and frequency bands. They hold potentials to be measured by gravitational-wave detectors that may advance our understanding of the origin of the universe.

The BOSS bispectrum analysis at one loop from the Effective Field Theory of Large-Scale Structure

We analyze the BOSS power spectrum monopole and quadrupole, and the bispectrum monopole and quadrupole data, using the predictions from the Effective Field Theory of Large-Scale Structure (EFTofLSS). Specifically, we use the one loop prediction for the power spectrum and the bispectrum monopole, and the tree level for the bispectrum quadrupole. After validating our pipeline against numerical simulations as well as checking for several internal consistencies, we apply it to the observational data. We find that analyzing the bispectrum monopole to higher wavenumbers thanks to the one-loop prediction, as well as the addition of the tree-level quadrupole, significantly reduces the error bars with respect to our original analysis of the power spectrum at one loop and bispectrum monopole at tree level. After fixing the spectral tilt to Planck preferred value and using a Big Bang Nucleosynthesis prior, we measure σ 8 = 0.794 ± 0.037, h = 0.692 ± 0.011, and Ω m = 0.311 ± 0.010 to about 4.7%, 1.6%, and 3.2%, at 68% CL, respectively.This represents an error bar reduction with respect to the power spectrum-only analysis of about 30%, 18%, and 13% respectively. Remarkably, the results are compatible with the ones obtained with a power-spectrum-only analysis, showing the power of the EFTofLSS in simultaneously predicting several observables. We find no tension with Planck.

Micro-crack localization for steel strands using nonlinear vibro-acoustic modulation based on modified signal bispectrum analysis

Under continuous environmental erosion and long-time high tension, fatigue micro-cracks of bridge cables appear frequently to challenge the reliability of cables. The vibro-acoustic modulation analysis is adopted because of its sensitivity to contact-type defects, especially fatigue cracks. In this paper, using multiple sets of low-frequency vibration and high-frequency ultrasonic excitation, the propagation of the ultrasonic wave in the steel strands is studied. Then, the modulated signal bispectrum is proposed to improve the detection reliability of nonlinear modulation components in the nonlinear vibro-acoustic modulation signal of the contact-type defect. The numerical simulations and laboratory tests of straight wire, helical wire, and multi-wire strands are carried out for micro-crack detection to verify the robustness of the proposed method. Compared with the traditional method, the modulated signal bispectrum can still produce clearer peak detection under high noise conditions. The results show that it provides a promising, dynamic and rapid cable defect detection technique.

Diagnosing simultaneous bearing and misalignment faults in an induction motor using sensor fusion

A monitoring system for induction motors (IMs) is essential for most industrial plants. Bearing faults and shaft misalignment are common mechanical defects in induction motors. Since one fault could cause another fault in the system, multiple faults can occur simultaneously and change the vibration (electrical) behaviour of the induction motors from that of a single fault condition. This paper aims to identify two common faults (shaft misalignment and defective bearing) simultaneously in IMs using data fusion of vibration and current measurements. Sensor fusion of accelerometer and Hall-effect sensor signals is used to combine the vibration and current signals. The proposed method is applied via a laboratory test-rig based on data fusion to detect multiple defects simultaneously in induction motors. Then, by extracting the important features using a principal component analysis (PCA) algorithm, the K-nearest neighbours (KNN) classification algorithm is used to detect defects and make decisions. The results show that the fusion of both current and vibration signal analyses significantly improves the efficiency and reliability of multiple fault detection. Also, bispectrum analysis of the current signal is highly sensitive to misalignment and can be an effective method for detecting such faults.

A Single-Shot Scattering Medium Imaging Method via Bispectrum Truncation.

Imaging using scattering media is a very important yet challenging technology. As one of the most widely used scattering imaging methods, speckle autocorrelation technology has important applications in several fields. However, traditional speckle autocorrelation imaging methods usually use iterative phase recovery algorithms to obtain the Fourier phase of hidden objects, posing issues such as large data calculation volumes and uncertain reconstruction results. Here, we propose a single-shot scattering imaging method based on the bispectrum truncation method. The bispectrum analysis is utilized for hidden object phase recovery, the truncation method is used to avoid the computation of redundant data when calculating the bispectrum data, and the method is experimentally verified. The experimental results show that our method does not require uncertain iterative calculations and can reduce the bispectrum data computation by more than 80% by adjusting the truncation factor without damaging the imaging quality, which greatly improves imaging efficiency. This method paves the way for rapid imaging through scattering media and brings benefits for imaging in dynamic situations.

Characterization of Fatigue Damage in Hadfield Steel Using Acoustic Emission and Machine Learning-Based Methods.

Structural health monitoring (SHM) of fatigue cracks is essential for ensuring the safe operation of engineering equipment. The acoustic emission (AE) technique is one of the SHM techniques that is capable of monitoring fatigue-crack growth (FCG) in real time. In this study, fatigue-damage evolution of Hadfield steel was characterized using acoustic emission (AE) and machine learning-based methods. The AE signals generated from the entire fatigue-load process were acquired and correlated with fatigue-damage evolution. The AE-source mechanisms were discussed based on waveform characteristics and bispectrum analysis. Moreover, multiple machine learning algorithms were used to classify fatigue sub-stages, and the results show the effectiveness of classification of fatigue sub-stages using machine learning algorithms. The novelty of this research lies in the use of machine learning algorithms for the classification of fatigue sub-stages, unlike the existing methodology, which requires prior knowledge of AE-loading history and calculation of ∆K.

Efficiently evaluating loop integrals in the EFTofLSS using QFT integrals with massive propagators

We develop a new way to analytically calculate loop integrals in the Effective Field Theory of Large Scale-Structure. Previous available methods show severe limitations beyond the one-loop power spectrum due to analytical challenges and computational and memory costs. Our new method is based on fitting the linear power spectrum with cosmology-independent functions that resemble integer powers of quantum field theory massive propagators with complex masses. A remarkably small number of them is sufficient to reach enough accuracy. Similarly to former approaches, the cosmology dependence is encoded in the coordinate vector of the expansion of the linear power spectrum in our basis. We first produce cosmology-independent tensors where each entry is the loop integral evaluated on a given combination of basis vectors. For each cosmology, the evaluation of a loop integral amounts to contracting this tensor with the coordinate vector of the linear power spectrum. The 3-dimensional loop integrals for our basis functions can be evaluated using techniques familiar to particle physics, such as recursion relations and Feynman parametrization. We apply our formalism to evaluate the one-loop bispectrum of galaxies in redshift space. The final analytical expressions are quite simple and can be evaluated with little computational and memory cost. We show that the same expressions resolve the integration of all one-loop N-point function in the EFTofLSS. This method, which is originally presented here, has already been applied in the first one-loop bispectrum analysis of the BOSS data to constraint ΛCDM parameters and primordial non-Gaussianities [1, 2].

Abnormal noise identification of engines based on wavelet packet transform and bispectrum analysis

Abnormal noise is the most prominent problem for motorcycles and affects the consumers’ purchasing desire and driving experience and the enterprise’s competitiveness. Usually, the noise from a newly assembled engine is detected by manual auscultation (MA) to determine if the engine is operating normally. However, MA is also affected by subjective and objective factors with severe labor intensity, and its accuracy greatly fluctuates. Importantly, MA cannot be applied in a corporation with mass production and high-quality requirements. To improve the efficiency and accuracy of motorcycle engine quality inspection and achieve intelligent production, an online engine abnormal noise detection method was proposed based on wavelet packet transform (WPT) and bispectrum analysis (BA); this method improved the accuracy and stability of the identification of the abnormal noise engine and reduced the cost of the check. First, the acoustic signal of the engine of the motorcycle was acquired by using a free-field microphone. Second, the background noise of signals was eliminated by using the wavelet correlation coefficient (WCC) theory, and the signal features were extracted by applying WPT and BA. Third, the feature vectors were normalized before being used as support vector machine (SVM) samples. Fourth, an appropriate kernel function and parameters were selected to train the vector machine using the training sets. Finally, the testing sets were used to inspect the accuracy of the vector machines. The result showed that the training accuracy is 95% and the testing accuracy is 97.5 of the samples were suitable by using the method of wavelet packet transform-bispectrum analysis-support vector machines (WPT-BA-SVM). WPT-BA-SVM effectively identified engine fault types and provided the theoretical foundation for the establishment of an engine abnormal noise online detection system.

A comprehensive framework for advanced protein classification and function prediction using synergistic approaches: Integrating bispectral analysis, machine learning, and deep learning

Proteins are fundamental components of diverse cellular systems and play crucial roles in a variety of disease processes. Consequently, it is crucial to comprehend their structure, function, and intricate interconnections. Classifying proteins into families or groups with comparable structural and functional characteristics is a crucial aspect of this comprehension. This classification is crucial for evolutionary research, predicting protein function, and identifying potential therapeutic targets. Sequence alignment and structure-based alignment are frequently ineffective techniques for identifying protein families.This study addresses the need for a more efficient and accurate technique for feature extraction and protein classification. The research proposes a novel method that integrates bispectrum characteristics, deep learning techniques, and machine learning algorithms to overcome the limitations of conventional methods. The proposed method uses numbers to represent protein sequences, utilizes bispectrum analysis, uses different topologies for convolutional neural networks to pull out features, and chooses robust features to classify protein families. The goal is to outperform existing methods for identifying protein families, thereby enhancing classification metrics. The materials consist of numerous protein datasets, whereas the methods incorporate bispectrum characteristics and deep learning strategies. The results of this study demonstrate that the proposed method for identifying protein families is superior to conventional approaches. Significantly enhanced quality metrics demonstrated the efficacy of the combined bispectrum and deep learning approaches. These findings have the potential to advance the field of protein biology and facilitate pharmaceutical innovation. In conclusion, this study presents a novel method that employs bispectrum characteristics and deep learning techniques to improve the precision and efficiency of protein family identification. The demonstrated advancements in classification metrics demonstrate this method’s applicability to numerous scientific disciplines. This furthers our understanding of protein function and its implications for disease and treatment.

Deep learning algorithm using bispectrum analysis energy feature maps based on ultrasound radiofrequency signals to detect breast cancer.

Ultrasonography is an important imaging method for clinical breast cancer screening. As the original echo signals of ultrasonography, ultrasound radiofrequency (RF) signals provide abundant tissue macroscopic and microscopic information and have important development and utilization value in breast cancer detection. In this study, we proposed a deep learning method based on bispectrum analysis feature maps to process RF signals and realize breast cancer detection. The bispectrum analysis energy feature maps with frequency subdivision were first proposed and applied to breast cancer detection in this study. Our deep learning network was based on a weight sharing network framework for the input of multiple feature maps. A feature map attention module was designed for multiple feature maps input of the network to adaptively learn both feature maps and features that were conducive to classification. We also designed a similarity constraint factor, learning the similarity and difference between feature maps by cosine distance. The experiment results showed that the areas under the receiver operating characteristic curves of our proposed method in the validation set and two independent test sets for benign and malignant breast tumor classification were 0.913, 0.900, and 0.885, respectively. The performance of the model combining four ultrasound bispectrum analysis energy feature maps in breast cancer detection was superior to that of the model using an ultrasound grayscale image and the model using a single bispectrum analysis energy feature map in this study. The combination of deep learning technology and our proposed ultrasound bispectrum analysis energy feature maps effectively realized breast cancer detection and was an efficient method of feature extraction and utilization of ultrasound RF signals.

Monitoring of ball bearings via vibration analysis and envelope technique for predictive maintenance purposes

Bearings are one of the primary and most crucial machine components in the industry and transportation systems, since they are critical components in these systems, their failure can lead to various losses and significant damages. Despite the advanced stages of development and manufacturing processes, approximately 90% of unplanned machine shutdowns are attributed to bearing failures. These failures can occur in various ways, making it essential to monitor the bearing's deterioration to replace it before it reaches a critical condition for the industry, machine or vehicle's operation. To monitor ball bearing failures, a range of vibration monitoring techniques are employed, encompassing envelope analysis, kurtosis, bi-spectrum, and wavelet analysis. In this case, frequency graphs based in the signals of the bearings inner race will be generated, through a new signal acquisition system, using of envelope analysis by frequency filters, Hilbert Transform and Fast Fourier Transform (FFT). However, detecting and analyzing these signals can be challenging due to weak signals and noise masking vibration patterns. Although current techniques are effective, they have limitations, such as requiring expert analysis, difficulty in detecting early-stage faults, and inability to differentiate between different fault types. Current techniques, such as envelope and wavelet analysis, are effective but have limitations. New technologies and methods, are being explored to improve fault detection and classification, providing early detection of faults and differentiation between different fault types, ultimately reducing the impact of ball bearing failures on machines and industries. This paper proposed to present a study of the ball bearing failure through vibration analysis from early-stage to advanced-stage of damage for predictive maintenance purposes, applying the envelope and FFT together with programming, to enable the identification of defects in the bearing, especially in the inner race, through a signal acquisition system that can explain the presence of the defect through frequency graphs. Thus, obtaining results that show the presence of defects in three different bearings, with gradual defect magnitudes, differentiating these data from an ideal bearing. The next step we will intend to explore the new technologies like machine learning and artificial intelligence, to also analyze all variants of defects in a bearing.