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The massive environmental noise interference and insufficient effective sample degradation data of the intelligent fault diagnosis performance methods pose an extremely concerning issue. Realising the challenge of developing a facile and straightforward model that resolves these problems, this study proposed the One-Dimensional Convolutional Neural Network (1D-CNN) based on frequency-domain signal processing. The Fast Fourier Transform (FFT) analysis is initially utilised to transform the signals from the time domain to the frequency domain; the data was represented using a phasor notation, which separates magnitude and phase and then fed to the 1D-CNN. Subsequently, the model is trained with White Gaussian Noise (WGN) to improve its robustness and resilience to noise. Based on the findings, the proposed model successfully achieved 100% classification accuracy from clean signals and simultaneously achieved considerable robustness to noise and exceptional domain adaptation ability. The diagnosis accuracy retained up to 97.37%, which was higher than the accuracy of the CNN without training under noisy conditions at only 43.75%. Furthermore, the model achieved an accuracy of up to 98.1% under different working conditions, which was superior to other reported models. In addition, the proposed model outperformed the state-of-art methods as the Signal-to-Noise Ratio (SNR) was lowered to -10 dB achieving 97.37% accuracy. In short, the proposed 1D-CNN model is a promising effective rolling bearing fault diagnosis.

Deepfake-generated fake faces, commonly utilized in identity-related activities such as political propaganda, celebrity impersonations, evidence forgery, and familiar fraud, pose new societal threats. Although current deepfake generators strive for high realism in visual effects, they do not replicate biometric signals indicative of cardiac activity. Addressing this gap, many researchers have developed detection methods focusing on biometric characteristics. These methods utilize classification networks to analyze both temporal and spectral domain features of the remote photoplethysmography (rPPG) signal, resulting in high detection accuracy. However, in the spectral analysis, existing approaches often only consider the power spectral density and neglect the amplitude spectrum--both crucial for assessing cardiac activity. We introduce a novel method that extracts rPPG signals from multiple regions of interest through remote photoplethysmography and processes themusing Fast Fourier Transform (FFT). The resultant time-frequency domain signal samples are organized into matrices to create Matrix Visualization Heatmaps (MVHM), which are then utilized to train an image classification network. Additionally, we explored various combinations of time-frequency domain representations of rPPG signals and the impact of attention mechanisms. Our experimental results show that our algorithm achieves a remarkable detection accuracy of 99.22% in identifying fake videos, significantly outperforming main stream algorithms and demonstrating the effectiveness of Fourier Transform and attention mechanisms in detecting fake faces. [ABSTRACT FROM AUTHOR]

In general, when using infrared thermography (IRT) techniques to excite a heat source on the surface of an inspection object, the heat source is focused on the center of the image of the infrared (IR) camera. If the object to be inspected is small, uniform excitation of the heat source is possible, but if the area is large, the heat source is concentrated locally, resulting in uneven heat distribution. Therefore, in this study, heat distribution was analyzed after inducing a non-uniform heat source by exciting the heat source at different locations. Additionally, the fast Fourier transform (FFT) algorithm with Gaussian filtering was applied to resolve the non-uniform distribution of the heat sources. Excellent results were obtained from the amplitude image, and the effectiveness of the FFT algorithm was verified using the Otsu algorithm. Finally, the signal-to-noise ratio (SNR) was calculated, and the detection ability according to each thinning rate was analyzed. [ABSTRACT FROM AUTHOR]

Based on the splitting form of the Green's function, a hybrid fast algorithm is proposed for efficient analysis of multiscale problems. In this algorithm, the Green's function is a priori split into two parts: a spectrally band-limited part and a spatially localized part. Then, the fast Fourier transforms (FFT) utilizing the global Cartesian grid and the matrix compression method aided by an adaptive octree grouping are implemented for these two parts, respectively. Compared with the traditional methods which only employ the FFT for acceleration, the proposed hybrid fast algorithm is capable of maintaining low memory consumption in multiscale problems without compromising time cost. Moreover, the proposed algorithm does not need cumbersome geometric treatment to implement the hybridization, and can be established in a concise and straightforward manner. Several numerical examples discretized with multiscale meshes are provided to demonstrate the computational performance of proposed hybrid fast algorithm. [ABSTRACT FROM AUTHOR]

For front-end wireless applications in small battery-powered devices, discrete Fourier transform (DFT) is a critical processing method for discrete time signals. Advanced radix structures are created to reduce the impact of transistor malfunction. To develop DFT, with radix sizes 4, 8, etc., is a complex and tricky issue for algorithm designers. The main reason for this is that the butterfly algorithm's lower-radix-level equations were manually estimated. This requires the selection of a new design process. As a result of fewer calculations and smaller memory requirements for computationally intensive scientific applications, this research focuses on the radix-4 fast Fourier-transform (FFT) technique. A new 64-point DFT method based on radix-4 FFT and multi-stage strategy to solve DFT-related issues is presented in this paper. Based on the results of simulations with Xilinx ISE, it can be concluded that the algorithm developed is faster than conventional approaches, with an 18.963 ns delay and 12.68 mW of power consumption. It was found that the computed picture compression drop ratios of 0.10, 0.31, 0.61 and 0.83 had a direct relationship to the varied tolerances tested, 0.0007625, 0.003246, 0.013075 and 0.03924. Fast reconstruction techniques, wireless medical devices and other applications benefit from this FFT's low power consumption, small storage requirements, and high processing speed. [ABSTRACT FROM AUTHOR]

This article deals with efficient vectorization of the fast Fourier transform algorithm while focusing on Cooley–Tukey versions with power-of-two radixes. Aside from examples of optimizations for 256 and 512-bit vectors, this work also discusses relations between individual radix-based versions, vectorization and OpenMP threading. Ideas are progressing into a timeless design of the FFT algorithm, which can work with any vector size and radix version through conversion into radix-2 output permutation. Furthermore, the implementation of the Cache Optimized Bit-Reversal algorithm, which doubles the performance of its predecessor, is introduced. [ABSTRACT FROM AUTHOR]

Digital image compression is the technique in digital image processing where special attention is provided in decreasing the number of bits required to represent a digital image. A wide range of techniques have been developed over the years, and novel approaches continue to emerge. This paper proposes a new technique for optimizing image compression using Fast Fourier Transform (FFT) and Intelligent Water Drop (IWD) algorithm. IWD-based FFT Compression is a emerging methodology, and we expect compression findings to be much better than the methods currently being applied in the domain. This work aims to enhance the degree of compression of the image while maintaining the features that contribute most. It optimizes the FFT threshold values using swarm-based optimization technique (IWD) and compares the results in terms of Structural Similarity Index Measure (SSIM). The criterion of structural similarity of image quality is based on the premise that the human visual system is highly adapted to obtain structural information from the scene, so a measure of structural similarity provides a reasonable estimate of the perceived image quality. [ABSTRACT FROM AUTHOR]

Populations are ageing and the healthcare costs are increasing accordingly. Humanoid Robots (HRs) perform basic but crucial health checkups such as the heart rate can efficiently meet the healthcare demands. This paper develops a 9-stage heart rate estimation algorithm and implements it to an HR. The 9-stages cover the recognition of the face with the Viola–Jones algorithm, determination of the facial regions with the geometric-based facial distance measurement technique, extraction of the forehead and cheek regions, tracking of these facial regions with the Hierarchical Multi Resolution algorithm, decomposition of the facial regions in the Red–Green–Blue (RGB) color channels, averaging and normalization of the RGB color data, elimination of the artifacts with the Adaptive Independent Component Analysis (ICA) technique, calculating the power spectrum of the data with the Fast Fourier Transform (FFT) technique, and finally determining the peaks inside the threshold reflecting the human heart rate boundaries. One of the key contributions of this paper is building and incorporating the Hierarchical Multi Resolution technique in the heart rate estimation algorithm to eliminate the deteriorating effects of the human and camera motions. A further contribution of this paper is generating a rule-based approach to discard the effects of the sudden movements. These two contributions have noticeably improved the accuracy of the heart rate estimation algorithm in the dynamic environments. The algorithm has been assessed extensively with 5 different experimental scenarios consisting of 33 conditions. [ABSTRACT FROM AUTHOR]

Purpose: Most commercially available treatment planning systems (TPSs) approximate the continuous delivery of volumetric modulated arc therapy (VMAT) plans with a series of discretized static beams for treatment planning, which can make VMAT dose computation extremely inefficient. In this study, we developed a polar‐coordinate‐based pencil beam (PB) algorithm for efficient VMAT dose computation with high‐resolution gantry angle sampling that can improve the computational efficiency and reduce the dose discrepancy due to the angular under‐sampling effect. Methods and Materials: 6 MV 1×1mm2$1 \times 1{\rm{\;m}}{{\rm{m}}^2}$ pencil beams were simulated on a uniform cylindrical phantom under an EGSnrc Monte Carlo (MC) environment. The MC‐generated PB kernels were collected in the polar coordinate system for each bixel on a 40×40cm2$40 \times 40{\rm{\;c}}{{\rm{m}}^2}$ fluence map and subsequently fitted via a series of Gaussians. The fluence was calculated using a detectors' eye view with off‐axis and MLC transmission factors corrected. Doses of VMAT arc on the phantom were computed by summing the convolution results between the corresponding PB kernels and fluence for each bixel in the polar coordinate system. The convolution was performed using fast Fourier transform to expedite the computing speed. The calculated doses were converted to the Cartesian coordinate system and compared with the reference dose computed by a collapsed cone convolution (CCC) algorithm of the TPS. A heterogeneous phantom was created to study the heterogeneity corrections using the proposed algorithm. Ten VMAT arcs were included to evaluate the algorithm performance. Gamma analysis and computation complexity theory were used to measure the dosimetric accuracy and computational efficiency, respectively. Results: The dosimetric comparisons on the homogeneous phantom between the proposed PB algorithm and the CCC algorithm for 10 VMAT arcs demonstrate that the proposed algorithm can achieve a dosimetric accuracy comparable to that of the CCC algorithm with average gamma passing rates of 96% (2%/2mm) and 98% (3%/3mm). In addition, the proposed algorithm can provide better computational efficiency for VMAT dose computation using a PC equipped with a 4‐core processor, compared to the CCC algorithm utilizing a dual 10‐core server. Moreover, the computation complexity theory reveals that the proposed algorithm has a great advantage with regard to computational efficiency for VMAT dose computation on homogeneous medium, especially when a fine angular sampling rate is applied. This can support a reduction in dose errors from the angular under‐sampling effect by using a finer angular sampling rate, while still preserving a practical computing speed. For dose calculation on the heterogeneous phantom, the proposed algorithm with heterogeneity corrections can still offer a reasonable dosimetric accuracy with comparable computational efficiency to that of the CCC algorithm. Conclusions: We proposed a novel polar‐coordinate‐based pencil beam algorithm for VMAT dose computation that enables a better computational efficiency while maintaining clinically acceptable dosimetric accuracy and reducing dose error caused by the angular under‐sampling effect. It also provides a flexible VMAT dose computation structure that allows adjustable sampling rates and direct dose computation in regions of interest, which makes the algorithm potentially useful for clinical applications such as independent dose verification for VMAT patient‐specific QA. [ABSTRACT FROM AUTHOR]

This paper presents a methodology to study non-twist invariant circles and their bifurcations for area preserving maps, which is supported on the theoretical framework developed in Gonzalez-Enriquez et al. (Mem. Amer. Math. Soc. 227:vi+115, 2014). We recall that non-twist invariant circles are characterized not only by being invariant, but also by having some specified normal behavior. The normal behavior may endow them with extra stability properties (e.g., against external noise), and hence, they appear as design goals in some applications, e.g., in plasma physics, astrodynamics and oceanography. The methodology leads to efficient algorithms to compute and continue, with respect to parameters, non-twist invariant circles. The algorithms are quadratically convergent and, when implemented using FFT, have low storage requirement and low operations count per step. Furthermore, the algorithms are backed up by rigorous a posteriori theorems, proved and discussed in detail in Gonzalez-Enriquez et al. (Mem. Amer. Math. Soc. 227:vi+115, 2014), which give sufficient conditions guaranteeing the existence of a true non-twist invariant circle, provided an approximate invariant circle is known. Hence, one can compute confidently even very close to breakdown. With some extra effort, the calculations could be turned into computer-assisted proofs, see Figueras et al. (Found. Comput. Math. 17:1123–1193, 2017) for examples of the latter. The algorithms are also guaranteed to converge up to the breakdown of the invariant circles, and then, they are suitable to compute regions of parameters where the non-twist invariant circles exist. The calculations involved in the computation of the boundary of these regions are very robust, and they do not require symmetries and can run without continuous manual adjustments, largely improving methods based on the computation of very long period periodic orbits to approximate invariant circles. This paper contains a detailed description of our algorithms, the corresponding implementation and some numerical results, obtained by running the computer programs. In particular, we include calculations for two-dimensional parameter regions where non-twist invariant circles (with a prescribed frequency) exist. Indeed, we present systematic results in systems that do not contain symmetry lines, which seem to be unaccessible for previous methods. These numerical explorations lead to some open questions, also included here. [ABSTRACT FROM AUTHOR]

A new algorithm for stable solution of a three-dimensional scalar inverse problem of acoustic sensing of an inhomogeneous medium in a cylindrical domain is proposed. Data for its solution is the complex amplitude of the wave field measured outside the acoustic inhomogeneities in the cylindrical layer. With the help of the Fourier transform and Fourier series, the inverse problem is reduced to a set of one-dimensional Fredholm integral equations of the first kind. Next, the complex amplitude of the wave field is computed in the inhomogeneity region and the desired sonic velocity field is found in this region. When run on a moderate-performance personal computer, the algorithm takes tens of seconds to solve the inverse problem on rather fine three-dimensional grids. The accuracy of the algorithm is analyzed numerically as applied to test inverse problems at different frequencies, and the stability of the algorithm with respect to data perturbations is investigated. [ABSTRACT FROM AUTHOR]

A novel higher-order probe correction algorithm is introduced for the spherical near field antenna measurements. The measured signal is processed by the fast Fourier transform along ϕ direction and integrated numerically along θ direction, thus converting the transmission formula into a series of small matrix equations. In a virtual example simulated using FEKO, a Yagi antenna is used as a higher-order probe to measure a Taylor array. It is shown that the proposed method is faster, more accurate and more stable than the FFT/matrix inverse method. Furthermore, the number of sampling points of the former is only half of that of the latter. [ABSTRACT FROM AUTHOR]

Optoacoustic signals are typically reconstructed into images using inversion algorithms applied in the time-domain. However, time-domain reconstructions can be computationally intensive and therefore slow when large amounts of raw data are collected from an optoacoustic scan. Here we considered a fast weighted ${\omega }-{k}$ (FWOK) algorithm operating in the frequency domain to accelerate the inversion in raster-scan optoacoustic mesoscopy (RSOM), while seamlessly incorporating impulse response correction with minimum computational burden. We investigated the FWOK performance with RSOM measurements from phantoms and mice in vivo and obtained 360-fold speed improvement over inversions based on the back-projection algorithm in the time-domain. This previously unexplored inversion of in vivo optoacoustic data with impulse response correction in frequency domain reconstructions points to a promising strategy of accelerating optoacoustic imaging computations, toward video-rate tomography. [ABSTRACT FROM AUTHOR]

This paper presents an efficient implementation of the inversion algorithm based on the conjugate-gradient method (CGM) for solving inverse scattering problems. The original CGM provides good image reconstruction and robustness to noise-corrupted data. This method requires the solution of the forward scattering problem and the Fréchet derivative operator of the cost function at each iteration step. However, these procedures can make the computational cost prohibitive, even for moderately sized problems. To avoid the computational burden, a two-step conjugate gradient fast Fourier transform (CG-FFT) procedure is proposed. Such an approach reduces the computational cost and storage requirements of the CGM implementation. The efficient CGM is found to share a computational complexity similar to the distorted-Born iterative method (DBIM). Thus the convergence speed and accuracy of the CGM is compared with the DBIM. Numerical tests using both synthetic and experimental data show effectiveness for solving 2D inverse scattering problems. [ABSTRACT FROM AUTHOR]

Mass of an object is an important characteristic for quality assessment. However, in some cases, it is hard to measure the mass of objects with instruments directly. In this paper, we proposed a novel method based on Fuzzy c-means (FCM) to measure the mass of an object by analyzing the deformation degree in a grid pattern. In the spatial field, thin plate spline (TPS) algorithm was adopted to calculate the minimum deformation bending energy in order to give a quantitative analysis of the weight; In frequency domain, the Fast Fourier Transform (FFT) algorithm was used to calculate the spectrum within a deformation frequency area before and after the change of grids, from which the relationship between weight and spectrum was investigated using FCM algorithm. Two different equations evaluated by the above two methods were proposed in order to calculate the mass of an object. Both of them showed a high level of explanatory power of R2 (R2 = 0.9833 and R2 = 0.9698, respectively). The equations were then used to determine the estimated mass. Estimated and measured values were plotted against each other. A high correlation (R2 = 0.9833 and R2 = 0.9698, respectively) was found between actual and calculated mass. Finally, Bland-Altman plot was introduced to access the agreement of the calculated mass and the actual mass. The average bias was –54.408 g and –0.007 g for spatial domain method and frequency domain method, respectively. Theoretical analysis and experiments were performed to verify the effectiveness of our approaches. [ABSTRACT FROM AUTHOR]

This paper proposes method of series direct current (DC) arc fault protection using low cost microcontroller. Series DC arc fault occurs when gap between conductor or wire flows a current. Series DC arc fault can cause fire hazard if do not detected and protected. However, Series DC arc fault is difficult to detected using conventional protection. To detect series DC arc fault accurately using fast Fourier transform (FFT). FFT is used to transform signal in time domain to frequency domain. Series DC arc fault has different characteristic compared by normal current in frequency domain. Therefore, the proposed algorithm for protection of series DC arc fault based on magnitudes of the current in frequency domain. Hardware system is implemented by 100 V DC power supply and DC arc fault generator. Test result is conducted experimentally under varying of load current such as 2 A, 2.5 A, 3 A, 3.5 A, 4 A and 5 A. Experimental testing results show that Series DC arc fault protection has time for trip of 0.48 s, 0.26 s, 1.04 s, 0.68 s, 0.44 s and 0.48, respectively. The fastest time for trip is 0.26 s with current of 2.5 A. Therefore, the proposed algorithm for series DC arc fault protection can operate to trip accurately and have the good performance. [ABSTRACT FROM AUTHOR]

The proliferation of renewable-based distributed generators poses protection challenges for the overcurrent relays due to the intermittent nature and control schemes. Converters present in the AC side restrict the fault current up to two per unit. Therefore, the overcurrent relay present in the AC microgrid maloperates during the fault. The proposed technique is based on the corresponding sum of the current samples obtained after every half-cycle (Ts/2), computed for each phase, and utilized to derive an index to detect the fault. The index thus derived is robust to noises, load variations, and other transients in the system. However, the technique requires removing transients and other noises before comparing the threshold for fault detection, which is resolved using the fast Fourier transform (FFT). Further, the magnitude of decaying DC (as another index) present in the signal is calculated using the least square technique for detecting the three-phase fault. The proposed algorithm is tested on an IEEE 14-bus system and a Real-Time Digital Simulator microgrid model. The fault detection technique is accurate for different faults under different operating conditions like noise, CT saturation, sudden load change, etc. [ABSTRACT FROM AUTHOR]

The pulse with intra-pulse modulation plays an important role in the design of radar systems. The first class of the signals type is the linear frequency modulation technique. The linear frequency modulation is used to resolve range resolution problems. This paper provides a new algorithm for detecting linear frequency modulation signals at a low signal-to-noise ratio. The core idea of the proposed method is firstly to analyse the linear frequency modulation signals via Fast Fourier Transform; and then to accumulate all energy to achieve signal detection using cross-correlation methods. The proposed algorithm showed better results in comparison with current algorithms, which are used to estimate the parameters of the linear frequency modulation signals at a low signal-to-noise ratio. [ABSTRACT FROM AUTHOR]

In this paper, a simple removable post-processing method was employed to improve the pixel-angle resolutions for different surface plasmon resonance (SPR) biochemical sensors. Compared with conventional centroid algorithm, dip span and height proportion of our enhanced algorithm were optimized simultaneously. To improve sensing stability when resonance angle shifting, the calculation region varies with the resonance angle. Besides, FFT algorithm and adjacent-averaging smoothing algorithm were also introduced into our proposed algorithm. It was found that FFT algorithm could reduce standard deviation of resonance angle for dynamic baseline algorithm. Adjacent-averaging smoothing algorithm with an average number of 10 points could also reduce standard deviation of resonance angle. The refractive index (RI) resolution could reach 1.55 ​× ​10−6 RIU, 5.52 ​× ​10−7 RIU and 8.47 ​× ​10−7 RIU for conventional Au-based SPR sensor, MSF and PAA-based plasmonic waveguide resonance (PWR) sensors, respectively. In biochemical sensing experiments, the limit of detection (LOD) of Zn2+ ion for MSF-based PWR chemical sensor could obtain 14.86 ​nM. The LOD of BSA protein could obtain 5.68 pM for PAA-based PWR biosensor. Further, Ag-based SPR biosensor modified with rabbit IgG was used to detect goat anti-rabbit IgG and a LOD of 9.93 pM was achieved. • A simple removable and enhanced centroid algorithm was proposed to improve resolution of plasmonic sensor. • The refractive index (RI) resolution could reach the level of ​10−7 RIU for plasmonic waveguide sensor, respectively. • A LOD of 9.93 pM for IgG protein was obtained for Ag-based SPR biosensor. [ABSTRACT FROM AUTHOR]

[Display omitted] • Mathematical modelling of misaligned sensors and flexible rotor-AMB system. • Dynamic effects of AMBs and sensors residual misalignments. • Innovative virtual trial misalignment (VTM) approach. • Identification of unbalance, sensors and AMBs residual misalignment. • Estimation of AMBs force-displacement and force-current stiffness parameters. A model-based identification algorithm derived from an innovative virtual trial misalignment (VTM) strategy is developed to identify the rotor unbalance, active magnetic bearings (AMBs) residual misalignment and their displacement and current stiffness parameters. The VTM approach is aligned with the similar concept of trial unbalance utilized in balancing of the rotor. This virtual method for providing the trial misalignment to the rotor is more reliable and effective than the physical trial misalignment, as the method does not need test runs and a precise model of the rotor-sensor-bearing system. The mathematical modelling for the non-contact displacement sensors offset from the rotor center has also been presented and even the offset amounts are identified using this novel approach. To illustrate the proposed methodology, an unbalanced and misaligned flexible rotor system mounted on multiple AMBs has been considered. Non-collinearity between the rotor operating axis and the axis of supported AMBs is the prime cause of misalignment (combination of parallel and angular) fault. A finite element method with a gyroscopic dynamic condensation scheme is employed for acquiring the reduced form of system equations. The numerically generated frequency domain responses are further employed in the identification algorithm for estimating the rotor-AMB system and faults parameters. Besides this, the different levels of the random noise signal as well as rotor modelling errors are added in the developed VTM based methodology to check its efficacy and sensitiveness in a practical rotor model. [ABSTRACT FROM AUTHOR]

A numerical method to compute the Effective Thermal Conductivity (ETC) of granular media surrounded by a stagnant fluid is presented. Based on the geometry and size of grains, a Representative Volume Elements (RVE) of the granular media is created using the Discrete Element Method (DEM) while the ETC of this RVE is estimated with Fast Fourier Transform (FFT) computations. To bridge the gap between the DEM and the FFT, a discretization algorithm (voxelization of convex polyhedra) was developed. Since their physical properties are poorly defined, "fuzzy" voxels associated with solid–gas interfaces or solid–solid contacts, domains inherent in a granular medium, are clearly identified during this step. The assignment of extreme properties to these voxels, assuming negligible radiation, allows to establish lower and upper ETC bounds. This methodology is applied to granular media of Uranium dioxide particles immersed in stagnant Helium; packed beds for which experimental data are available in the literature. First, the effect of RVE and discretization sizes on the simulated ETC are investigated and optimal values of RVE size and discretization ratio are defined. Next, the significant deviation of simulated DEM-FFT ETC bounds, observed at high solid to gas conductivity contrasts, exhibits the key role of interfaces on the computed ETCs. An improved modelling of solid–gas interfaces based on the Knudsen effect and a modelling correction for solid–solid interfaces is therefore proposed. The new modelling is shown to adequately bound and estimate the ETC of considered granular media at high (∼ 100) solid to gas thermal conductivity contrasts. [ABSTRACT FROM AUTHOR]