Window Function Research Articles

Improved SE-ResNet Acoustic–Vibration Fusion for Rolling Bearing Composite Fault Diagnosis

An enhanced fault diagnosis approach for rolling bearings with composite faults using an optimized Squeeze and Excitation ResNet (SE-ResNet) model is proposed. This method integrates grid search (GS), support vector regression (SVR), ensemble empirical mode decomposition (EEMD), and low-rank multimodal fusion (LMF) to effectively handle the signals of acoustic–vibration fusion. By combining these techniques, the aim is to improve the accuracy and reliability of rolling bearing fault diagnosis. Firstly, improved EEMD combined with GS-SVR and a window function is used for rolling bearing vibration signal decomposition. Singular value methods are used to filter and reconstruct the results. Secondly, Markov transition fields (MTFs) are used to encode vibration signals into 2D images. LMF is used for the fusion of vibration and sound signals. An improved Squeeze and Excitation ResNet50 network is proposed for feature identification and classification of rolling bearing composite fault data. Finally, the method undergoes rigorous testing and evaluation using rolling bearing data. The experimental outcomes demonstrate that, in comparison to traditional neural networks, the enhanced SE-ResNet, integrated with GS-SVR-EEMD and LMF, attains superior diagnostic accuracy. Additionally, the proposed approach can be effectively utilized for diagnosing rolling bearing composite faults.

Quantification in high-energy resolution Auger electron spectroscopy; Proposal of a reference target convolution technique for direct spectra

Currently, high-energy resolution Auger electron spectroscopy (AES) is utilized for chemical-state qualitative analysis, such as x-ray photoelectron spectroscopy. It is highly desirable to perform quantitative analysis using the high-energy resolution direct spectra used for qualitative analysis. However, AES analysis parameters, such as relative sensitivity factors (RSFs), derived from conventional-energy resolution differentiated spectra cannot be adopted for high-energy resolution direct spectra. Furthermore, for quantification by high-energy resolution direct spectra, there is no established method for determining peak intensity, and no database of RSFs is available in surface analysis communities. Therefore, we tasked ourselves with investigating the use of the analysis parameters obtained from conventional-energy resolution-differentiated spectra obtained with a cylindrical mirror analyzer (CMA)-type AES instrument for high-energy resolution direct spectra measured with a spherical capacitor analyzer (SCA)-type AES instrument. The convolution technique proposed here is achieved by using a conventional-energy resolution spectral dataset obtained with CMA-AES as a target. By applying the convolution with the window function of the convoluted function of the Gaussian function and rectangular function, high-energy resolution direct spectra containing the inherent nature of fine structures are converted to the similar shapes of conventional-energy resolution direct spectra after the Shirley type background subtraction [Watanabe et al., J. Vac. Sci. Technol. A 41, 043209 (2023)]. Results revealed that for all spectra of conventional-energy resolution spectra taken with CMA-AES, as well as high-energy resolution spectra taken with SCA-AES with various energy resolutions, the ratios of the background-subtracted direct peak areas and the differentiated peak-to-peak intensities were well-aligned along the identical parabolic curve as a function of the kinetic energy (KE). Experimental results also revealed that the generalized conversion function f(KE;ΔE)=IareacmaIareaconv.sca(KE;ΔE), which is the ratio of the conventional-energy resolution spectral area (Iareacma) and the convoluted high-energy resolution spectral area (Iareaconv.sca), which can transform differentiated intensities of convoluted high-energy resolution spectra, such that they are similar to those of conventional-energy resolution spectra obtained using the CMA-AES instrument, being a function of KE and the energy resolution ΔE. By applying the conversion function, the historically accumulated AES analysis parameters for conventional-energy resolution differentiated spectra can be adopted to differentiated high-energy resolution spectra. Finally, the results revealed the sufficiency of the conversion function obtained by the actual measurements of the four reference specimens for the practical quantification of high-energy resolution AES direct spectra.

Influence of Power-Weighted Center of Echo Signal Within Window Function on Local Strain Rate Distribution in Left Ventricular Wall

ObjectiveThe deviation of the power-weighted center of the echo signal from the geometric center within the velocity estimation window for calculating strain rate (SR) causes an estimation error. This study aimed to confirm whether an erroneous multilayer pattern in the SR distribution of the left ventricular wall could be corrected by considering the power-weighted center of the echo signal. MethodsThe SR distributions were measured locally in the transmural direction around the pre-ejection and early diastolic phases in healthy volunteers. The estimation error related to the power-weighted center of the echo signal was corrected using a previously proposed method, and the effectiveness of the correction was confirmed based on the accuracy of the estimated myocardial displacement. ResultsThe SR distribution in early diastole was observed as multilayers of low- and high-amplitude negative SRs. However, this multilayer pattern disappeared after correction. In the pre-ejection phase, multilayers of positive and negative SRs were observed in the SR distributions with and without correction. This correction was sufficiently effective in accurately tracking the local peak of the echo signal. ConclusionThe multilayer pattern of low- and high-amplitude positive or negative SRs is caused by estimation errors related to the power-weighted center of the echo signal. The multilayer pattern of positive and negative SRs might not be caused by these errors and might relate to the actual change in myocardial thickness because the estimation errors do not convert the negative (positive) SR to positive (negative) in a homogeneous negative (positive) SR distribution.

Research laser scanning damage detection method in f-k domain for laminate composite material

The use of composite plate structures has become increasingly prevalent in industries such as civil engineering, aerospace, high-speed rail, automotive, and wind power. However, the propagation of ultrasonic Lamb waves in these structures is subject to multi-modal and frequency dispersion effects, which, coupled with the complicated anisotropic propagation mechanism of composite materials, makes it challenging to extract damage scatter signals without a health signal as a reference. In this study, we apply the frequency-wavenumber ( f- k) domain filter wavefront modal method to carbon fiber reinforced polymer (CFRP) materials and use a three-dimensional (3D) window function to achieve different modalities and their corresponding damage reflection signals in the absence of a reference dispersion curve. Single modal damage imaging is achieved using a common source method (CSM) by laser vibration scanning experiment. To effectively extract single modalities in laminate material damage detection, a 3D filter window function was constructed. Considering the skew angle correction, it can effectively remove the direct wave signal, so as to realize the imaging of the damage.

An uncertainty principle for the windowed Bochner–Fourier transform with the complex-valued window function

Abstract The generalization of Hardy uncertainty principle for the windowed Bochner–Fourier transform on the Heisenberg group is proved. We consider a Bochner measurable function Ψ : G → X {\Psi:G\to X} , where X is a completely separable Hilbert space X and Let G be a completely separable, unimodular, connected nilpotent Lie group. We establish that if ϕ ∈ C C ⁢ ( G ) {\phi\in C_{C}(G)} is a non-trivial window function and Ψ ∈ L 2 ⁢ ( G ) {\Psi\in L^{2}(G)} satisfies ∥ V ϕ ⁢ ( Ψ ) ⁢ ( g , χ ) ∥ HB ≤ c 2 ⁢ ( g ) ⁢ exp ⁡ ( - β ⁢ ∥ χ ∥ 2 ) \|V_{\phi}(\Psi)(g,\chi)\|_{\rm HB}\leq c_{2}(g)\exp(-\beta\|\chi\|^{2}) , β > 0 {\beta>0} , then Ψ = 0 {\Psi=0} almost everywhere.

Instantaneous frequency identification for nonstationary signals of time-varying structures using enhanced synchroextracting wavelet transform and dynamic optimization

Civil engineering structures under ambient excitations are essentially time-varying and nonlinear structural systems and the resultant response signals exhibit non-stationarity. To reveal the time-varying characteristics of non-stationary signals, time frequency analysis methods with high resolutions are required. Although synchroextracting short time Fourier transform (SESTFT) is able to generate more energy concentrated time frequency representations and allow signal reconstruction, its major disadvantage is the window function is fixed. To address this issue, an enhanced synchroextracting wavelet transform (ESEWT) method is proposed to refine frequency bands by combing synchroextracting and continuous wavelet transform. After that, dynamic optimization (DO) is used to extract instantaneous frequency (IF) curves within the refined frequency bands. Two numerical examples and an experimental study case are investigated to illustrate the effectiveness and accuracy of the proposed method. The results demonstrate that the proposed ESEWT is capable of extracting frequency bands more accurately and its combination with DO identifies IFs of non-stationary signals better than current time frequency analysis methods such as SESTFT.

A defect location method for power cable based on Burg power spectral

AbstractThe frequency‐domain reflection (FDR) has been demonstrated to be a trustworthy technique in solving the defect location of power cable by field experiments. However, the location spectrum of the FDR requires manual window smoothing and can be disturbed by spurious peaks. Aiming at these shortcomings of FDR, a new method of cable defect location based on Burg power spectral (BPS) is introduced in this paper. The idea of this method is to use linear difference variance to fit the distribution of reflection coefficient spectrum and build an auto‐regressive (AR) model. The Burg algorithm is employed to estimate the coefficients model and calculate the power distribution of the AR model. Then, the cable defects will be located by BPS with high precision and resolution. In this method, the fast Fourier transform (FFT) with windowed function is replaced by an AR model without windowed function. This suppressed the impact of spurious peaks or spectrum leakage in FFT on the localization defects, and the localization resolution is higher. Finally, we validate the feasibility and effectiveness of BPS through experiments conducted on a 500 m laboratory cable and a 9.6 km submarine cable.

Phaseless Sampling on Square-Root Lattices

AbstractDue to its appearance in a remarkably wide field of applications, such as audio processing and coherent diffraction imaging, the short-time Fourier transform (STFT) phase retrieval problem has seen a great deal of attention in recent years. A central problem in STFT phase retrieval concerns the question for which window functions $$g \in {L^2({\mathbb R}^d)}$$ g ∈ L 2 ( R d ) and which sampling sets $$\Lambda \subseteq {\mathbb R}^{2d}$$ Λ ⊆ R 2 d is every $$f \in {L^2({\mathbb R}^d)}$$ f ∈ L 2 ( R d ) uniquely determined (up to a global phase factor) by phaseless samples of the form $$\begin{aligned} |V_gf(\Lambda )| = \left\{ |V_gf(\lambda )|: \lambda \in \Lambda \right\} , \end{aligned}$$ | V g f ( Λ ) | = | V g f ( λ ) | : λ ∈ Λ , where $$V_gf$$ V g f denotes the STFT of f with respect to g. The investigation of this question constitutes a key step towards making the problem computationally tractable. However, it deviates from ordinary sampling tasks in a fundamental and subtle manner: recent results demonstrate that uniqueness is unachievable if $$\Lambda $$ Λ is a lattice, i.e $$\Lambda = A{\mathbb Z}^{2d}, A \in \textrm{GL}(2d,{\mathbb R})$$ Λ = A Z 2 d , A ∈ GL ( 2 d , R ) . Driven by this discretization barrier, the present article centers around the initiation of a novel sampling scheme which allows for unique recovery of any square-integrable function via phaseless STFT-sampling. Specifically, we show that square-root lattices, i.e., sets of the form $$\begin{aligned} \Lambda = A \left( \sqrt{{\mathbb Z}} \right) ^{2d}, \ \sqrt{{\mathbb Z}} = \{ \pm \sqrt{n}: n \in {\mathbb N}_0 \}, \end{aligned}$$ Λ = A Z 2 d , Z = { ± n : n ∈ N 0 } , guarantee uniqueness of the STFT phase retrieval problem. The result holds for a large class of window functions, including Gaussians

Flat-sky angular power spectra revisited

We revisit the flat-sky approximation for evaluating the angular power spectra of projected random fields by retaining information about the correlations along the line of sight. For the case of projections with broad, overlapping radial window functions, these line-of-sight correlations are suppressed and are ignored in the commonly adopted Limber approximation. However, retaining the correlations is important for narrow window functions or unequal-time spectra but introduces significant computational difficulties due to the highly oscillatory nature of the integrands involved. We deal with the integral over line-of-sight wave-modes in the flat-sky approximation analytically, using the FFTlog expansion of the 3D power spectrum. This results in an efficient computational method, which is a substantial improvement compared to any full-sky approaches. We apply our results to galaxy clustering (with and without redshift-space distortions), CMB lensing and galaxy lensing observables in a flat ΛCDM universe. In the case of galaxy clustering, we find excellent agreement with the full-sky results on large (percent-level agreement) and intermediate or small (subpercent agreement) scales, dramatically out-performing the Limber approximation for both wide and narrow window functions, and in equal- and unequal-time cases. In the cases of lensing, we show on the full-sky that the angular power spectrum of the lensing convergence can be very well approximated by projecting the 3D Laplacian (rather than the correct angular Laplacian) of the gravitational potential, even on large scales. Combining this approximation with our flat-sky techniques provides an efficient and accurate evaluation of the CMB lensing angular power spectrum on all scales. We further analyse the clustering and lensing angular power spectra by isolating the projection effects due to the observable- and survey-specific window functions, separating them from the effects due to integration along the line of sight and unequal-time mixing in the 3D power spectrum. All of the angular power spectrum results presented in this paper are obtained using a Python code implementation, which we make publicly available.

Pre-processing data and window function testing on wave spectrum analysis

Pre-processing data in oceanographic data research is an important step in processing data into the required information. This phase often takes longer and more rigorous time to present the correct data. Data pre-processing involves the selection of data, and the modification of data so that it can be readable in a computational algorithm. The data selection process includes selection of sample numbers, correction and filling of data gaps.The data used in spectrum analysis is the recording of the water surface profile of the wave in the data resolution of 1 second. The data needs to be corrected by the process of detrending against the tidal height which become the still water level. The spectral analysis is processed using the pwelch function on MATLAB. The frequency spectrum curve of the measurement is obtained from the calculation of the power spectral density value. In order to obtain a stable power spectral density curve, the Hann window function is used with the number of window elements, nfft/16.

Helmholtz decomposition based windowed Green function methods for elastic scattering problems on a half-space

This paper proposes a new Helmholtz decomposition based windowed Green function (HD-WGF) method for solving the time-harmonic elastic scattering problems on a half-space with Dirichlet boundary conditions in both 2D and 3D. The Helmholtz decomposition is applied to separate the pressure and shear waves, which satisfy the Helmholtz and Helmholtz/Maxwell equations, respectively, and the corresponding boundary integral equations of type (I+T)ϕ=f, that couple these two waves on the unbounded surface, are derived based on the free-space fundamental solution of Helmholtz equation. This approach avoids the treatment of the complex elastic displacement tensor and traction operator that involved in the classical integral equation method for elastic problems. Then a smooth “slow-rise” windowing function is introduced to truncate the boundary integral equations and a “correction” strategy is proposed to ensure the uniformly fast convergence for all incident angles of plane incidence. Numerical experiments for both two and three dimensional problems are presented to demonstrate the accuracy and efficiency of the proposed method.

A Rapid Single-view Radar Imaging Method with Window Functions

Monostatic rapid single-view radar imaging technology is a technique that employs single incidence angle and single frequency point information to implement rapid monostatic radar imaging within a small angular field. Owing to its analytical expression, this technique can substitute the traditional frequency-angle-scanning imaging in a small angular range, facilitating the rapid generation of highly realistic radar imaging data slices for complex targets and environments. This technology has been significantly applied in scatter hotspot diagnostics and target recognition. In order to achieve the windowing effect equivalent to that of frequency-angle-scanning imaging, and to enhance the scattering feature of monostatic imaging while controlling sidelobes, this paper derives analytic windowed imaging formulas for monostatic radar. It then obtains analytical expressions for various typical monostatic windowing rapid radar imaging scenarios. This enables the monostatic rapid imaging technology to maintain high efficiency in its analytical expressions while achieving the windowing effect equivalent to traditional imaging. The validity and correctness of the analytical formula and software implementation have been confirmed through 1D, 2D, and 3D imaging verifications. This technology can provide a vast amount of training data for modern radars.

The short-time Wigner–Ville distribution

The Wigner–Ville distribution (WD) and ambiguity function (AF) are serviceable tools for the global analysis of non-stationary signals. However, when dealing with time-varying signals that exhibit changing characteristics and require real-time signal processing, they have high limitations due to the existence of cross-items. In this paper, we propose the short-time Wigner–Ville distribution (STWD) as a novel approach that effectively analyzes time-varying signals with changing characteristics. First, the definition of STWD and short-time ambiguity function (STAF) and their properties are advanced. Next, three uncertainty principles that define the lower bound for the product of signal spread and its bandwidth are derived. Then, the discrete STWD (DSTWD) and the process of computerization are also proposed which can be used more widely in practice. Finally, the optimization of window functions based on Rényi entropy is discussed. Simulation experiments show that the STWD can be effectively applied for the analysis of local change characteristics and real-time processing of signals with valid and accurate results.

Accurate halo mass functions from the simplest excursion set theory

ABSTRACT Excursion set theory is a powerful and widely used tool for describing the distribution of dark matter haloes, but it is normally applied with simplifying approximations. We use numerical sampling methods to study the mass functions predicted by the theory without approximations. With a spherical top-hat window and a constant δ = 1.5 threshold, the theory accurately predicts mass functions with the M200 mass definition, both unconditional and conditional, in simulations of a range of matter-dominated cosmologies. For Λ cold dark matter at the present epoch, predictions lie between the M200m and M200c mass functions. In contrast, with the same window function, a non-constant threshold based on ellipsoidal collapse predicts uniformly too few haloes. This work indicates a new way to simply and accurately evaluate halo mass functions, clustering bias, and assembly histories for a range of cosmologies. We provide a fitting function that accurately represents the predictions of the theory for a wide range of parameters.

In-situ material damping measurements using the crosshole seismic method

Crosshole seismic testing is commonly used to determine detailed and reliable wave velocity profiles. Material damping measurements can also be performed in crosshole seismic testing, but these measurements require a window function to maintain similar amplitude shapes over the frequency range of interest for the calculation. In-situ seismic testing, including downhole and seismic cone penetration testing (SCPT), also requires a window function for the material damping calculations. However, the length of the window function has the largest influence on the material damping calculation. Therefore, the half-power bandwidth method is introduced to determine the material damping ratio without the window function in crosshole testing by replicating the unconfined, free-free, resonant column (Fr-Fr) test. To demonstrate the influence in the length of the window function, the first cycle of the signal is used in the material damping calculation. The half- power bandwidth method is verified using synthetic signals and field data. Two sets of crosshole and downhole tests were performed, one at a backfill test pad and the second at a Hornsby Bend research site operated by the University of Texas at Austin. The in-situ material damping ratio calculated from these two sets of crosshole tests using the half-power bandwidth method are compare with the Spectral Ratio Slope (SRS) method applied to the downhole testing at these sites. The material damping calculated from the half-power bandwidth method using the full signal results in a reliable and precise damping value compared to the SRS method applied to the downhole data.

Deep Filtered Back Projection for CT Reconstruction.

Filtered back projection (FBP) is a classic analytical algorithm for computed tomography (CT) reconstruction, with high computational efficiency. However, images reconstructed by FBP often suffer from excessive noise and artifacts. The original FBP algorithm uses a window function to smooth signals and a linear interpolation to estimate projection values at un-sampled locations. In this study, we propose a novel framework named DeepFBP in which an optimized filter and an optimized nonlinear interpolation operator are learned with neural networks. Specifically, the learned filter can be considered as the product of an optimized window function and the ramp filter, and the learned interpolation can be considered as an optimized way to utilize projection information of nearby locations through nonlinear combination. The proposed method remains the high computational efficiency of the original FBP and achieves much better reconstruction quality at different noise levels. It also outperforms the TV-based statistical iterative algorithm, with computational time being reduced in an order of two, and state-of-the-art post-processing deep learning methods that have deeper and more complicated network structures.

Localization of the window functions of dual and tight Gabor frames generated by the Gaussian function

Gabor frames generated by the Gaussian function are considered. The localization of the window functions of dual frames is estimated in terms of the uncertainty constants, it its dependence on the relation between the parameters of the time-frequency window and the degree of overcompleteness. It is shown that localization worsens rapidly with the increasing disproportion in the parameters of the window. On the other hand, the higher the system of functions forming the frame is overdetermined, the better the window function of the dual frame is localized. For a tight frame the localization of the window function with the same set of parameters is much better than that for the dual frame. This problem is closely related to the problem of interpolation by we have uniform shifts of the Gaussian function. Both the nodal interpolation function and the window function of the dual frame are constructed from the same coefficients. These coefficients play an important role also in the derivation of formulae for the uncertainty constants. This is why their properties related to sign alternation and the monotonicity of decrease of the absolute value are considered in the paper. Bibliography: 38 titles.

The Effect of Information Entropy Analysis in Computer-Assisted English Translation on Improving Translation Naturalness

Abstract This paper borrows the concept of entropy and refers the information entropy to the computer-aided English translation to build up the information entropy assessment and evaluation model and the information entropy-based English translation optimization model. The information entropy operation formula is used to calculate the fuzziness between the original text and the target translated text, and at the same time, the segmentation function is utilized to find the approximation value of the information entropy value obtained in a sufficiently fine segmentation of the translated text. Obtain the rectangular window function of semantic Gaussian marginalization, project the information entropy data, add the semantic correlation factors of words, identify the features of semantic information, and realize the optimization of English translation. Simulation experiments are carried out to verify the performance of the model. The information entropy evaluation and analysis model in this paper can achieve convergence after 45 iterations. In contrast, the word error rate and the cut-off error rate of the English translation optimization model are both lower than 10%, and the feature recognition and classification are higher than 80%. The fuzzy statements in Chinese writer Lao She’s work “Teahouse” are selected to explore the naturalness of translation. The information entropy value of the translation optimization model in this paper is closer to the original text, and the English translation’s naturalness is better than that of the GLR model.

Comparison of Typical Window Function Characteristics in Interferometric Imaging Spectroscopy Restoration

Comparison of Typical Window Function Characteristics in Interferometric Imaging Spectroscopy Restoration

Analytical Solutions for Charge and Flux in HP Ideal Generic Memristor Model With Joglekar and Prodromakis Window Functions

Analytical Solutions for Charge and Flux in HP Ideal Generic Memristor Model With Joglekar and Prodromakis Window Functions