FFT-based Method Research Articles

New evaluation method for defects propagation in toroidal roller bearings using dominant frequency of acoustic emission

ABSTRACT The increased use of roller bearings in recent years has made it vital to develop techniques for Condition Monitoring (CM) of these valuable assets. Toroidal Roller Bearings (TRB) are one of the recent inventions that has revolutionised some industries because of its unique design. In this study, newly produced TRBs were tested using Acoustic Emission (AE), vibration and temperature, on a specially designed test rig. The AE signal was recorded, processed, and analysed using FFT-based methods to transform from the time domain to the frequency domain, and to specify the Dominant Frequency (DF) of each hit in the signal. The result of the analysis was a layout on the time domain of the DFs of all AE hits along with RMSAE and other parameters, this layout was called DF map. The test was divided into three phases, and the DF bands were divided horizontally into three band groups. The aim is to establish a correlation between the phases and DF bands. Knowing the type of defects that are typical for each phase in the test provided insights to what are the DFs of that type. Promising results can be achieved using this measuring method on other types of bearings.

Nonstationary random vibration analysis of hysteretic systems with fractional derivatives by FFT-based frequency domain method

Nonstationary random vibration problems of nonlinear fractional systems are challenging and drawing increasing attention. This study presents an efficient numerical method for the random vibration analysis of large-scale nonlinear fractional systems subjected to fully nonstationary excitations. Firstly, the fast Fourier transform (FFT)-based frequency domain method originally proposed for the nonstationary random vibration analysis of linear integer-order systems is extended to linear fractional systems, in which the explicit expression of dynamic responses of fractional systems is derived based on the load superposition principle and Newmark method. Secondly, an equivalent linearization analysis framework is constructed to solve the nonstationary responses of hysteretic systems with fractional derivatives, in which the nonstationary response analyses of equivalent linear systems are accomplished by the FFT-based frequency domain method. The presented method can account for nonstationary excitations with arbitrary forms of evolutionary power spectrum, even of the non-separable one. Two numerical examples are used to confirm its superior performance in terms of accuracy and computational efficiency.

Fast Fourier Transform periodic interpolation method for superposition sums in a periodic unit cell

We propose a Fast Fourier Transform based Periodic Interpolation Method (FFT-PIM), a flexible and computationally efficient approach for computing the scalar potential given by a superposition sum in a unit cell of an infinitely periodic array. Under the same umbrella, FFT-PIM allows computing the potential for 1D, 2D, and 3D periodicities for dynamic problems involving the Helmholtz potential and static problems involving Coulomb potential, including problems with and without a periodic phase shift. The computational complexity of the FFT-PIM is of O(Nlog⁡N) for N spatially coinciding sources and observer points. The FFT-PIM uses rapidly converging series representations of the Green's function serving as a kernel in the superposition sum. Based on these representations, the FFT-PIM splits the potential into its near-zone component, which includes a small number of images surrounding the unit cell of interest, and far-zone component, which includes the rest of an infinite number of images. The far-zone component is evaluated by projecting the non-uniform sources onto a sparse uniform grid, performing superposition sums on this sparse grid, and interpolating the potential from the uniform grid to the non-uniform observation points. The near-zone component is evaluated using an FFT-based method, which is adapted to efficiently handle non-uniform source-observer distributions within the periodic unit cell. The FFT-PIM can be used for a broad range of applications, such as periodic problems involving integral equations for wave propagation in electromagnetics and acoustics, micromagnetic solvers, and density functional theory solvers.

Quasi-random frequency sampling for optical turbulence simulations

Optical turbulence modeling and simulation are crucial for developing astronomical ground-based instruments, laser communication, laser metrology, or any application where light propagates through a turbulent medium. In the context of spectrum-based optical turbulence Monte-Carlo simulations, we present an alternative approach to the methods based on the fast Fourier transform (FFT) using a quasi-random frequency sampling heuristic. This approach provides complete control over the spectral information expressed in the simulated measurable without the drawbacks encountered with FFT-based methods such as high-frequency aliasing, low-frequency under-sampling, and static sampling statistics. The method’s heuristics, implementation, and an application example from the study of differential piston fluctuations are discussed.

An FFT-based adaptive polarization method for infinitely contrasted media with guaranteed convergence

We propose an FFT-based iterative algorithm for solving the Lippmann–Schwinger equation in the context of periodic homogenization of infinitely contrasted linear elastic composites. Our work initially reformulates the Moulinec–Suquet, Eyre–Milton and Monchiet–Bonnet schemes using a residual formulation. Subsequently, we introduce an enhanced scheme, termed Adaptive Eyre–Milton (AEM), as a natural extension of the EM scheme where we optimize a relaxation parameter to minimize the residual. We demonstrate the unconditional linear convergence of the AEM scheme, regardless of initialization and the chosen reference material. The paper further extends the AEM scheme to handle composites with both pores and infinitely rigid inclusions. Practical implementation aspects and illustrative applications in two- and three-dimensional settings are discussed, highlighting the efficiency of the proposed AEM scheme. We particularly emphasize the scheme’s robustness for materials with infinitely large contrasts in elastic properties.

Local Distributed Node for Power Quality Event Detection Based on Multi-Sine Fitting Algorithm.

The new power generation systems, the increasing number of equipment connected to the power grid, and the introduction of technologies such as the smart grid, underline the importance and complexity of the Power Quality (PQ) evaluation. In this scenario, an Automatic PQ Events Classifier (APQEC) that detects, segments, and classifies the anomaly in the power signal is needed for the timely intervention and maintenance of the grid. Due to the extension and complexity of the network, the number of points to be monitored is large, making the cost of the infrastructure unreasonable. To reduce the cost, a new architecture for an APQEC is proposed. This architecture is composed of several Locally Distributed Nodes (LDNs) and a Central Classification Unit (CCU). The LDNs are in charge of the acquisition, the detection of PQ events, and the segmentation of the power signal. Instead, the CCU receives the information from the nodes to classify the PQ events. A low-computational capability characterizes low-cost LDNs. For this reason, a suitable PQ event detection and segmentation method with low resource requirements is proposed. It is based on the use of a sliding observation window that establishes a reasonable time interval, which is also useful for signal classification and the multi-sine fitting algorithm to decompose the input signal in harmonic components. These components can be compared with established threshold values to detect if a PQ event occurs. Only in this case, the signal is sent to the CCU for the classification; otherwise, it is discarded. Numerical tests are performed to set the sliding window size and observe the behavior of the proposed method with the main PQ events presented in the literature, even when the SNR varies. Experimental results confirm the effectiveness of the proposal, highlighting the correspondence with numerical results and the reduced execution time when compared to FFT-based methods.

Stationary Detection for Zero Velocity Update of IMU Based on the Vibrational FFT Feature of Land Vehicle

Stationary Detection for Zero Velocity Update of IMU Based on the Vibrational FFT Feature of Land Vehicle

Homogenizing the viscosity of shear-thinning fiber suspensions with an FFT-based computational method

Homogenizing the viscosity of shear-thinning fiber suspensions with an FFT-based computational method

FFT-Based Numerical Method for Nonlinear Elastic Contact

In theoretical research pertaining to sealing, a contact model must be used to obtain the leakage channel. However, for elastoplastic contact, current numerical methods require a long calculation time. Hyperelastic contact is typically simplified to a linear elastic contact problem, which must be improved in terms of calculation accuracy. Based on the fast Fourier transform, a numerical method suitable for elastoplastic and hyperelastic frictionless contact that can be used for solving two-dimensional and three-dimensional (3D) contact problems is proposed herein. The nonlinear elastic contact problem is converted into a linear elastic contact problem considering residual deformation (or the equivalent residual deformation). Results from numerical simulations for elastic, elastoplastic, and hyperelastic contact between a hemisphere and a rigid plane are compared with those obtained using the finite element method to verify the accuracy of the numerical method. Compared with the existing elastoplastic contact numerical methods, the proposed method achieves a higher calculation efficiency while ensuring a certain calculation accuracy (i.e., the pressure error does not exceed 15%, whereas the calculation time does not exceed 10 min in a 64 × 64 grid). For hyperelastic contact, the proposed method reduces the dependence of the approximation result on the load, as in a linear elastic approximation. Finally, using the sealing application as an example, the contact and leakage rates between complicated 3D rough surfaces are calculated. Despite a certain error, the simplified numerical method yields a better approximation result than the linear elastic contact approximation. Additionally, the result can be used as fast solutions in engineering applications.

Use of 2D FFT and DTW in Protein Sequence Comparison.

Protein sequence comparison remains a challenging work for the researchers owing to the computational complexity due to the presence of 20 amino acids compared with only four nucleotides in Genome sequences. Further, protein sequences of different species are of different lengths; it throws additional changes to the researchers to develop methods, specially alignment-free methods, to compare protein sequences. In this work, an efficient technique to compare protein sequences is developed by a graphical representation. First, the classified grouping of 20 amino acids with a cardinality of 4 based on polar class is considered to narrow down the representational range from 20 to 4. Then a unit vector technique based on a two-quadrant Cartesian system is proposed to provide a new two-dimensional graphical representation of the protein sequence. Now, two approaches are proposed to cope with the varying lengths of protein sequences from various species: one uses Dynamic Time Warping (DTW), while the other one uses a two-dimensional Fast Fourier Transform (2D FFT). Next, the effectiveness of these two techniques is analyzed using two evaluation criteria-quantitative measures based on symmetric distance (SD) and computational speed. An analysis is performed on five data sets of 9 ND4, 9 ND5, 9 ND6, 12 Baculovirus, and 24 TF proteins under the two methods. It is found that the FFT-based method produces the same results as DTW but in less computational time. It is found that the result of the proposed method agrees with the known biological reference. Further, the present method produces better clustering than the existing ones.

FFT-Based Approach for the Mechanical Analysis of Superconducting Rutherford-Type Cables

Low-temperature superconductors are widely used in high field accelerator magnets, mostly within Rutherford type cables. We have proposed the “CoCaSCOPE” approach in order to build a numerical model of impregnated low-temperature Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn superconducting Rutherford-type cables dedicated to mechanical computation. Here the strand structure is described as a bi-metallic material: a copper core, a superconducting bundle region and an outer copper ring. In this paper, we explore the use of the distributed solver AMITEX_FFTP based on Fast Fourier Transform (FFT). The main interest of this method is to reduce the simulation time. This approach is investigated for structures with linear material behavior in this paper. This work compares the results from the FFT approach (using AMITEX) and from the 3D Finite Elements approach (using Cast3M). In this way, we can demonstrate the higher performances of FFT-based solving method compared to the finite elements method for multi-scale structure such as Rutherford-type cables in terms of computation time. With this approach, we can reduce the computation time or, alternatively, increase the size of our models in order to analyze the behavior of a macroscale model under mechanical solicitation.

Numerical estimation of the permeability of granular soils using the DEM and LBM or FFT-based fluid computation method

Numerical estimation of the permeability of granular soils using the DEM and LBM or FFT-based fluid computation method

Experimental Study on Entropy Features in Machining Vibrations of A Thin-walled Tubular Workpiece

In machining processes, chatter vibrations are always regarded as one of the major limitations for production quality and efficiency. Accurate and timely monitoring of chatter is helpful to maintain stable machining operations. At present, most chatter monitoring methods are based on the energy level at specified chatter frequencies or frequency bands. However, the spectral features of chatter could change during machining operations due to complexity and time-varying dynamics of the physical machining process. The purpose of this paper is to investigate the time-varying chatter features in turning of thin-walled tubular workpieces from the perspective of entropy. The airborne acoustics was selected as the source of information for machining condition monitoring. First, corresponding to the distinguishing surface topographies relevant to machining conditions, the features of the sound signal emitted during turning of the thin-walled cylindrical workpieces were extracted using the spectral analysis and wavelet packet transform, respectively. It was shown that the dominant vibration frequency as well as the energy distribution could shift with the transition of the machining status. After that, two relative entropy indicators based on the spectrum and the wavelet packet energy were constructed to identify chattering events in turning of the thin-walled tubes. The experimental results demonstrate that the proposed indicators could accurately reflect the transition of machining conditions with high sensitivity and robustness in comparison with the traditional FFT-based methods. The achievement of this study lays the foundations of the online chatter monitoring and control technique for turning of the thin-walled tubular workpieces.

The GMRT High Resolution Southern Sky Survey for Pulsars and Transients. IV. Discovery of Four New Pulsars with an FFA Search

The fast Fourier transform (FFT) based periodicity search methods provide an efficient way to search for millisecond and binary pulsars but encounter significant sensitivity degradation while searching for long period and short duty cycle pulsars. An alternative to FFT-based search methods called the fast folding algorithm (FFA) search provides superior sensitivity to search for signals with long periods and short duty cycles. In the GMRT High Resolution Southern Sky (GHRSS) survey, we are using an FFA-based pipeline to search for isolated pulsars in a period range of 100 ms to 100 s. We have processed 2800 degree2 of the sky coverage away from the Galactic plane and discovered six new pulsars. Here, we report the discovery of four of these pulsars with the FFA search pipeline. This includes a narrow duty cycle pulsar, J1936−30, which shows nulling behavior with an extreme nulling fraction of ∼90%. Two of the GHRSS discoveries from the FFA search lie in narrow duty cycle ranges beyond the limit of the existing population. The implementation of FFA search in the GHRSS survey and other pulsar surveys is expected to recover the missing population of long period and short duty cycle pulsars.

An FFT-based method for estimating the in-plane elastic properties of honeycomb considering geometric imperfections at large elastic deformation

The geometric imperfections in honeycomb cells inevitably arise during the manufacturing process and can affect the honeycomb’s mechanical performance. Hence, it is critical to identify and quantify the geometric imperfections and characterize the effects of these imperfections on the effective mechanical properties of honeycomb. In this study, the geometric imperfections inside the honeycomb were identified from micro-CT scan data. Using the obtained geometric topology, a Fast Fourier Transform (FFT) based method was employed in combination with the composite pixel method to predict the effective in-plane elastic properties of honeycomb at large elastic deformations. The results of the nonlinear homogenized prediction were compared with the experimental data and the prediction values from analytical models to investigate the effects of geometric imperfections. It was found that the predictions from the FFT-based method agreed well with the experimental results. However, the predictions from the analytical models significantly overestimated or underestimated the elastic properties, indicating that the geometric imperfections inside the honeycomb significantly influence its in-plane elastic properties.

FFT-BASED FILTERING APPROACH TO FUSE PHOTOGRAMMETRY AND PHOTOMETRIC STEREO 3D DATA

Abstract. Image-based 3D reconstruction has been successfully employed for micro-measurements and industrial quality control purposes. However, obtaining a highly-detailed and reliable 3D reconstruction and inspection of non-collaborative surfaces is still an open issue. Photometric stereo (PS) offers the high spatial frequencies of the surface, but the low frequency is erroneous due to the mathematical model's assumptions and simplifications on how light interacts with the object surface. Photogrammetry, on the other hand, gives precise low-frequency information but fails to utilize high frequencies. As a result, in this research, we present a fusion strategy in Fourier domain to replace the low spatial frequencies of PS with the corresponding photogrammetric frequencies in order to have correct low frequencies while maintaining high frequencies from PS. The proposed method was tested on three different objects. Different cloud-to-cloud comparisons were provided between reference data and the 3D points derived from the proposed method to evaluate high and low frequency information. The obtained 3D findings demonstrated how the proposed methodology generates a high-detail 3D reconstruction of the surface topography (below 20 µm) while maintaining low-frequency information (0.09 µm on average for three different testing objects) by fusing photogrammetric and PS depth data with the proposed FFT-based method.

An implicit FFT-based method for wave propagation in elastic heterogeneous media

An FFT-based algorithm is developed to simulate the propagation of elastic waves in heterogeneous d-dimensional rectangular shape domains. The method allows one to prescribe the displacement as a function of time in a subregion of the domain, emulating the application of Dirichlet boundary conditions on an outer face. Time discretization is performed using an unconditionally stable beta-Newmark approach. The implicit problem for obtaining the displacement at each time step is solved by transforming the equilibrium equations into Fourier space and solving the corresponding linear system with a preconditioned Krylov solver. The resulting method is validated against analytical solutions and compared with implicit and explicit finite element simulations and with an explicit FFT approach. The accuracy of the method is similar to or better than that of finite elements, and the numerical performance is clearly superior, allowing the use of much larger models. To illustrate the capabilities of the method, some numerical examples are presented, including the propagation of planar, circular, and spherical waves and the simulation of the propagation of a pulse in a polycrystalline medium.

Hybrid Subcarrier Selection Method for Vital Sign Monitoring With Long-Term and Short-Term Data Considerations

Tracking vital signs during sleeping is important because the breathing and heart rates can be used to detect breathing diseases and heart disorders. However, existing work for breathing and heart rate estimations only considered long-term data, while ignoring the fact that people could turn over frequently in practice, which results in different data lengths of breathing and heart rate signals. In addition, most systems based on channel state information (CSI) only adopted either amplitude or phase information to select subcarrier, which could degrade the performance of breathing and heart rate estimations. In this article, in order to improve the performance, we first propose a new subcarrier selection method by jointly considering the CSI amplitude and phase information. Then, based on the proposed subcarrier selection scheme, a new breathing and heart rate estimations scheme is proposed under the consideration of different data lengths, where the peak detection and the FFT-based methods are, respectively, used for long-term and short-term breathing signals, while the FFT-based method is used to estimate the heart rate for both long-term and short-term signals. Experiment results demonstrate that our work can achieve accuracies of 96.1% and 94.3% for breathing and heart rate estimations.

Exact simulation of normal tempered stable processes of OU type with applications

We study the Ornstein-Uhlenbeck process having a symmetric normal tempered stable stationary law and represent its transition distribution in terms of the sum of independent laws. In addition, we write the background driving Lévy process as the sum of two independent Lévy components. Accordingly, we can design two alternate algorithms for the simulation of the skeleton of the Ornstein-Uhlenbeck process. The solution based on the transition law turns out to be faster since it is based on a lower number of computational steps, as confirmed by extensive numerical experiments. We also calculate the characteristic function of the transition density which is instrumental for the application of the FFT-based method of Carr and Madan (J Comput Finance 2:61–73, 1999) to the pricing of a strip of call options written on markets whose price evolution is modeled by such an Ornstein-Uhlenbeck dynamics. This setting is indeed common for spot prices in the energy field. Finally, we show how to extend the range of applications to future markets.

An FFT-based method for uncertainty quantification of Nomex honeycomb’s in-plane elastic properties

The honeycomb manufacturing process involves complex and inter-related procedures spanning multiple physics domains and scales. The geometry heterogeneity in honeycomb cells inevitably exists and propagates to the uncertainty of the honeycomb’s mechanical performance. Quantitatively characterizing the effect of cell geometry variability on the effective mechanical properties of honeycomb hence becomes critically important. In this study, a Fast Fourier Transform (FFT) based method was developed to predict the effective in-plane elastic properties of irregular hexagonal honeycomb. The honeycomb geometry heterogeneity was identified with a digital image technology by examining a large number of cells. Correlation analysis on the resulting statistical data enables determining the interdependence of cell wall lengths and angles. Using a Representative Unit Cell (RUC) with varying cell wall lengths and angles, an analytical function for the effective in-plane elastic parameters was established by incorporating the dependencies. The statistical quantification of cell geometry and the propagation of RUC’s elastic characteristics were further integrated into the FFT-based multiscale framework for predicting the in-plane elastic moduli of irregular honeycomb. The tensile and shear tests on the irregular honeycombs, together with the corresponding finite element analysis, were used to verify the proposed method. Both experimental and numerical results confirmed that the uncertainty of elastic moduli achieved by the FFT-based method provides a reasonable estimation.