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In this study, we propose a method for recommending appropriate combinations of stocks based on the waveforms of stock price changes. Many Japanese prefer to maintain stability when managing their assets. Specialized knowledge is required to invest in stocks while reducing risk. Hence, stock recommendation methods with different characteristics are required. Stock price movements can be captured as waveforms. Dynamic time warping (DTW), cross–correlation functions, and fast Fourier transforms (FFTs) are used to compare the features of the waveforms. A combination of stocks with different waveforms avoids the risk of simultaneous crashes. In the current experiment, one–year stock waveforms are used to obtain the recommended stock. The combined stocks selected using the DTW, cross–correlation functions, and FFT are shown to be suitable. [ABSTRACT FROM AUTHOR]

We present a new term-structure model for commodity futures prices based on Trolle and Schwartz (2009), which we extend by incorporating seasonal stochastic volatility represented with two different sinusoidal expressions. We obtain a quasi-analytical representation of the characteristic function of the futures log-prices and closed-form expressions for standard European options' prices using the fast Fourier transform algorithm. We price plain vanilla options on the Henry Hub natural gas futures contracts, using our model and extant models. We obtain higher accuracy levels with our model than with the extant models. [ABSTRACT FROM AUTHOR]

As one of the main components of the Earth orientation parameters, short-term prediction of the geodetic polar motion series is crucial in the field of deep-space exploration, high-precision positioning, and timing services, which require high real-time performance. Additionally, its middle- and long-term prediction is equally important in climate forecasting and geodynamics research. In this study, we propose the combined BiLSTM+ARIMA model, which is based on bidirectional long- and short-term memory (BiLSTM) and autoregression integrated moving average (ARIMA). First, ensemble empirical mode decomposition (EEMD) is performed as a filter to decompose the polar motion time series to obtain low- and high-frequency signals. The EOP14 C04 time series provided by International Earth Rotation and Reference Systems Service and decomposed by EEMD includes low-frequency signals like the long-term trend, decadal oscillation, Chandler wobble, and prograde annual wobble, along with shorter-period high-frequency signals. Second, low- and high-frequency signals are predicted using BiLSTM and ARIMA models, respectively. Finally, the low- and high-frequency signal forecast components are reconstructed to obtain geodetic polar motion predictions. In middle- and long-term polar motion prediction, the results show that the proposed model can improve the prediction accuracy by up to 42% and 17%, respectively. This demonstrated that the BiLSTM+ARIMA model can effectively improve the accuracy of polar motion prediction. [ABSTRACT FROM AUTHOR]

Human activity recognition (HAR) with wearable inertial sensors is a burgeoning field, propelled by advances in sensor technology. Deep learning methods for HAR have notably enhanced recognition accuracy in recent years. Nonetheless, the complexity of previous models often impedes their use in real-life scenarios, particularly in online applications. Addressing this gap, we introduce SenseMLP, a novel approach employing a multi-layer perceptron (MLP) neural network architecture. SenseMLP features three parallel MLP branches that independently process and integrate features across the time, channel, and frequency dimensions. This structure not only simplifies the model but also significantly reduces the number of required parameters compared to previous deep learning HAR frameworks. We conducted comprehensive evaluations of SenseMLP against benchmark HAR datasets, including PAMAP2, OPPORTUNITY, USC-HAD, and SKODA. Our findings demonstrate that SenseMLP not only achieves state-of-the-art performance in terms of accuracy but also boasts fewer parameters and lower floating-point operations per second. For further research and application in the field, the source code of SenseMLP is available at [ABSTRACT FROM AUTHOR]

In IoT applications, prediction models have fundamental challenges such as real-time processing, producing results with considerable/without delay, and taking action against pattern drift. While existing models can excel when data statistics remain relatively stable, real-time systems may encounter difficulties, particularly when confronted with dynamic shifts in data behavior. Analyzing data streams generated by different IoT applications and detecting complex pattern on the fly has become an open area of research. Complex event processing with adaptivity is a must to get desired features in such models. To address this issue, a comprehensive model for prediction has been proposed in this paper. It consists of two phases: (1) the basic model is constructed using historical data, (2) a fast Fourier transform-based adaptive support vector regression (FFT-ASVR) approach is proposed to predict events embedded in IoT data streams. FFT-ASVR predicts abnormal events by experiencing a change in data streams with real-time model updation. The performance of FFT-ASVR with a similar existing method SVM-RBF is presented using real-time traffic data of Madrid city. The proposed approach has significant improvement in terms of mean absolute percentage error (MAPE) for prediction, is adaptive in nature, and is also capable of handling the issue of pattern drift. [ABSTRACT FROM AUTHOR]

In this paper, we consider a general notion of convolution. Let D be a finite domain and let D n be the set of n-length vectors (tuples) of D . Let f : D × D → D be a function and let ⊕ f be a coordinate-wise application of f. The f -Convolution of two functions g , h : D n → { - M , ... , M } is (g ⊛ f h) (v) : = ∑ v g , v h ∈ D n s.t. v = v g ⊕ f v h g (v g) · h (v h) for every v ∈ D n . This problem generalizes many fundamental convolutions such as Subset Convolution, XOR Product, Covering Product or Packing Product, etc. For arbitrary function f and domain D we can compute f -Convolution via brute-force enumeration in O ~ (| D | 2 n · polylog (M)) time. Our main result is an improvement over this naive algorithm. We show that f -Convolution can be computed exactly in O ~ ((c · | D | 2 ) n · polylog (M)) for constant c : = 3 / 4 when D has even cardinality. Our main observation is that a cyclic partition of a function f : D × D → D can be used to speed up the computation of f -Convolution, and we show that an appropriate cyclic partition exists for every f. Furthermore, we demonstrate that a single entry of the f -Convolution can be computed more efficiently. In this variant, we are given two functions g , h : D n → { - M , ... , M } alongside with a vector v ∈ D n and the task of the f -Query problem is to compute integer (g ⊛ f h) (v) . This is a generalization of the well-known Orthogonal Vectors problem. We show that f -Query can be computed in O ~ (| D | ω 2 n · polylog (M)) time, where ω ∈ [ 2 , 2.372) is the exponent of currently fastest matrix multiplication algorithm. [ABSTRACT FROM AUTHOR]

Dataflow architecture is an alternative to traditional von Neumann computing architecture. However, known variants of dataflow architecture have a range of serious problems with no effective solutions up to the present day. This paper represents Hybrid Recurrent Signal Processor's (HRSP) hardware verification results. It describes HRSP's register transfer level model implementing its architectural specification and hardware prototype on the HAN Pilot Platform development board with Intel Arria10 field-programmable gate array. HRSP consists of a von Neumann master processor on a control layer and a recurrent dataflow unit on an operational layer. Dataflow unit includes four computing cores. HRSP's hardware model combines either software or hardware implementation of the control processor and the hardware model of the operational layer. Testing the HRSP's hardware prototype on the development board using an isolated word recognizer (IWR) as a typical data processing application has proven that the hardware model is bit-exact with both HRSP's imitation model and the original IWR C++ model. The HRSP's hardware prototype's achieved performance ensures IWR's operation in real-time mode on the development board. It is slightly better than the performance of the TMSC55x (Texas Instruments) digital signal processor. Verification of the HRSP's hardware implementation on synthetic tests showed that its average performance is 5% higher than the performance of the DSP TMSC55x digital signal processor. The results of the proposed optimization of hardware support for Fast Fourier Transform (FFT) in HRSP prove that such an optimization speeds up the FFT calculation, significantly reduces the capsule size, reduces the required hardware resources and simplifies FFT scaling. [ABSTRACT FROM AUTHOR]

This paper reports on a comparative experimental study of the current waveforms accompanying the propagation of creeping discharges over different liquid/pressboard interfaces under both negative and positive lightning impulse voltages; the investigated insulating liquids are mineral oil (MO), a synthetic ester (SE), a natural ester (NE) and an extra virgin olive oil (OO). Two different arrangements are used; in the first one, the point electrode was positioned in a perpendicular direction to the pressboard, and in the second one, the pressboard was positioned parallel to the axis of the point electrode. Due to the similarity of the recorded creeping discharge current shapes, it is hard to differentiate between the currents measured for each type of interface with time domain approaches. To circumvent this difficulty and identify the specific feature(s) associated to each type of interface, two techniques are used to analyze the signal of the discharge currents, namely discrete wavelet and fast Fourier-transform methods. It is shown that: (1) for the first arrangement, there is a particular spectral signature for each type of liquid/pressboard interface, and (2) for the second arrangement, the obtained results are in accordance to those obtained for the first arrangement only in some cases. [ABSTRACT FROM AUTHOR]

Although deep learning makes great success in increasing the accuracy for long sequence time-series forecasting, its complex neural network structure, which comprises many different types of layers and each layer containing hundreds and thousands of neurons, challenges the computing and memory capability of embedded platforms. This paper proposes a lightweight and efficient neural network called TTFNet, which forecasts long time series using three types of features (i.e., the Trend, Temporal attention, and Frequency attention) extracted from raw time series. In TTFNet, we perform a pooling operation on the historical data in a recent time window to extract a general trend, use a multi-layer perceptron to discover the temporal correlation between data as temporal attention, and apply the fast Fourier transforms on data to obtain frequency information as frequency attention. Each feature is separately extracted from its neural network branch with an output result, and we weight the three results to generate the final prediction while optimal weights are learnt. Also, the three prediction results can run in parallel since they are independent from one another. The experimental results show that the proposed method reduces the memory overhead and runtime by 62% and 81% of the five counterpart methods on average while achieving comparable performance. [ABSTRACT FROM AUTHOR]

This research paper introduces a novel approach using dominant frequency analysis to diagnose inner race faults in rolling ball bearings of three-phase induction motor. The main objective of the proposed scheme is to identify damaged bearings by analyzing their characteristic frequency components within a specific time interval in segmented signal. This work has been carried out on vibration signal data provided by Bearing Center Case Reserve Western University (CWRU), USA. In this study, IR007, IR014 and IR021 bearing defects are analyzed by Frequency Statistical Analysis in MATLAB. Mean and standard deviation of dominant frequencies are computed from the recorded vibration signals after dividing the signal into multiple segments of equal length. It is observed that both frequency mean, and standard deviation have been found to be highly sensitive with variations of motor speed and connected load. Therefore, motor speed is also studied to calculate the statistical parameters. The test results suggest that the proposed scheme provides comprehensive information about fault analysis through vibration data and could potentially aid researchers in fault analysis using the CRWU datasets. Overall, this paper presents a promising approach to diagnose the faults in the inner race of rolling ball bearings using frequency domain analysis and statistical parameters. [ABSTRACT FROM AUTHOR]

In this paper we compare three different orthogonal systems in L 2 (R) which can be used in the construction of a spectral method for solving the semi-classically scaled time dependent Schrödinger equation on the real line, specifically, stretched Fourier functions, Hermite functions and Malmquist–Takenaka functions. All three have banded skew-Hermitian differentiation matrices, which greatly simplifies their implementation in a spectral method, while ensuring that the numerical solution is unitary—this is essential in order to respect the Born interpretation in quantum mechanics and, as a byproduct, ensures numerical stability with respect to the L 2 (R) norm. We derive asymptotic approximations of the coefficients for a wave packet in each of these bases, which are extremely accurate in the high frequency regime. We show that the Malmquist–Takenaka basis is superior, in a practical sense, to the more commonly used Hermite functions and stretched Fourier expansions for approximating wave packets. [ABSTRACT FROM AUTHOR]

Based on a brief review of forward algorithms for the computation of topographic gravitational and magnetic effects, including spatial, spectral and hybrid-domain algorithms working in either Cartesian or spherical coordinate systems, we introduce a new algorithm, namely the CP-FFT algorithm, for fast computation of terrain-induced gravitational and magnetic effects on arbitrary undulating surfaces. The CP-FFT algorithm, working in the hybrid spatial-spectral domain, is based on a combination of CANDECOMP/PARAFAC (CP) tensor decomposition of gravitational integral kernels and 2D Fast Fourier Transform (FFT) evaluation of discrete convolutions. By replacing the binomial expansion in classical FFT-based terrain correction algorithms using CP decomposition, convergence of the outer-zone computation can be achieved with significantly reduced inner-zone radius. Additionally, a Gaussian quadrature mass line model is introduced to accelerate the computation of the inner zone effect. We validate our algorithm by computing the gravitational potential, the gravitational vector, the gravity gradient tensor, and magnetic fields caused by densely-sampled topographic and bathymetric digital elevation models of selected mountainous areas around the globe. Both constant and variable density/magnetization models, with computation surfaces on, above and below the topography are considered. Comparisons between our new method and space-domain rigorous solutions show that with modeling errors well below existing instrumentation error levels, the calculation speed is accelerated thousands of times in all numerical tests. We release a set of open-source code written in MATLAB language to meet the needs of geodesists and geophysicists in related fields to carry out more efficiently topographic modeling in Cartesian coordinates under planar approximation. [ABSTRACT FROM AUTHOR]

We address two computational issues common to open-population N-mixture models, hidden integer-valued autoregressive models, and some hidden Markov models. The first issue is computation time, which can be dramatically improved through the use of a fast Fourier transform. The second issue is tractability of the model likelihood function for large numbers of hidden states, which can be solved by improving numerical stability of calculations. As an illustrative example, we detail the application of these methods to the open-population N-mixture models. We compare computational efficiency and precision between these methods and standard methods employed by state-of-the-art ecological software. We show faster computing times (a ∼ 6 to ∼ 30 times speed improvement for population size upper bounds of 500 and 1000, respectively) over state-of-the-art ecological software for N-mixture models. We also apply our methods to compute the size of a large elk population using an N-mixture model and show that while our methods converge, previous software cannot produce estimates due to numerical issues. These solutions can be applied to many ecological models to improve precision when logs of sums exist in the likelihood function and to improve computational efficiency when convolutions are present in the likelihood function. Supplementary materials accompanying this paper appear online. [ABSTRACT FROM AUTHOR]

The harmonic inversion (HI) problem in nuclear magnetic resonance spectroscopy (NMR) is conventionally considered by means of parameter estimations. It consists of extracting the fundamental pairs of complex frequencies and amplitudes from the encoded time signals. This problem is linear in the amplitudes and nonlinear in the frequencies that are entrenched in the complex damped exponentials (harmonics) within the time signal. Nonlinear problems are usually solved approximately by some suitable linearization procedures. However, with the equidistantly sampled time signals, the HI problem can be linearized exactly. The solution is obtained by relying exclusively upon linear algebra, the workhorse of computer science. The fast Padé transform (FPT) can solve the HI problem. The exact analytical solution is obtained uniquely for time signals with at most four complex harmonics (four metabolites in a sample). Moreover, using only the computer linear algebra, the unique numerical solutions, within machine accuracy (the machine epsilon), is obtained for any level of complexity of the chemical composition in the specimen from which the time signals are encoded. The complex frequencies in the fundamental harmonics are recovered by rooting the secular or characteristic polynomial through the equivalent linear operation, which solves the extremely sparse Hessenberg or companion matrix eigenvalue problem. The complex amplitudes are obtained analytically as a closed formula by employing the Cauchy residue calculus. From the frequencies and amplitudes, the components are built and their sum gives the total shape spectrum or envelope. The component spectra in the magnitude mode are described quantitatively by the found peak positions, widths and heights of all the physical resonances. The key question is whether the same components and their said quantifiers can be reconstructed by shape estimations alone. This is uniquely possible with the derivative fast Padé transform (dFPT) applied as a nonparametric processor (shape estimator) at the onset of the analysis. In the end, this signal analyzer can determine all the true components from the input nonparametric envelope. In other words, it can quantify the input time signal. Its performance is presently illustrated utilizing the time signals encoded at a high-field proton NMR spectrometer. The scanned samples are for ovarian cyst fluid from two patients, one histopathologically diagnosed as having a benign lesion and the other with a malignant lesion. These findings are presently correlated with the NMR reconstruction results from the Padé-based solution of the HI problem. Special attention is paid to the citrate metabolites in the benign and malignant samples. The goal of this focus is to see whether the citrates could also be considered as cancer biomarkers as they are now for prostate (low in cancerous, high in normal or benign tissue). Cancer biomarkers are metabolites whose concentration levels can help discriminate between benign and malignant lesions. [ABSTRACT FROM AUTHOR]

Accurate fault diagnosis and prognosis can significantly reduce maintenance costs, increase the safety and availability of engineering systems that have become increasingly complex. It has been observed that very limited researches have been reported on fault diagnosis where multi-component degradation are presented. This is essentially a challenging Complex Systems problem where features multiple components interacting simultaneously and nonlinearly with each other and its environment on multiple levels. Even the degradation of a single component can lead to a misidentification of the fault severity level. This paper introduces a new test rig to simulate the multi-component degradation of the aircraft fuel system. A machine learning-based data analytical approach based on the classification of clustering features from both time and frequency domains is proposed. The scope of this framework is the identification of the location and severity of not only the system fault but also the multi-component degradation. The results illustrate that (a) the fault can be detected with accuracy > 99%; (b) the severity of fault can be identified with an accuracy of almost 100%; (c) the degradation level can be successfully identified with the R-square value > 0.9. [ABSTRACT FROM AUTHOR]

Computational homogenization is the gold standard for concurrent multi-scale simulations (e.g., FE2) in scale-bridging applications. Often the simulations are based on experimental and synthetic material microstructures represented by high-resolution 3D image data. The computational complexity of simulations operating on such voxel data is distinct. The inability of voxelized 3D geometries to capture smooth material interfaces accurately, along with the necessity for complexity reduction, has motivated a special local coarse-graining technique called composite voxels (Kabel et al. Comput Methods Appl Mech Eng 294: 168–188, 2015). They condense multiple fine-scale voxels into a single voxel, whose constitutive model is derived from the laminate theory. Our contribution generalizes composite voxels towards composite boxels (ComBo) that are non-equiaxed, a feature that can pay off for materials with a preferred direction such as pseudo-uni-directional fiber composites. A novel image-based normal detection algorithm is devised which (i) allows for boxels in the firsts place and (ii) reduces the error in the phase-averaged stresses by around 30% against the orientation cf. Kabel et al. (Comput Methods Appl Mech Eng 294: 168–188, 2015) even for equiaxed voxels. Further, the use of ComBo for finite strain simulations is studied in detail. An efficient and robust implementation is proposed, featuring an essential selective back-projection algorithm preventing physically inadmissible states. Various examples show the efficiency of ComBo against the original proposal by Kabel et al. (Comput Methods Appl Mech Eng 294: 168–188, 2015) and the proposed algorithmic enhancements for nonlinear mechanical problems. The general usability is emphasized by examining various Fast Fourier Transform (FFT) based solvers, including a detailed description of the Doubly-Fine Material Grid (DFMG) for finite strains. All of the studied schemes benefit from the ComBo discretization. [ABSTRACT FROM AUTHOR]

A high-accuracy economical iterative method is proposed for calculating the potential and the strength of the electric field in a three-dimensional inhomogeneous spatially periodic dielectric placed in an initially uniform electric field. The idea underlying the algorithm is that the potential is represented as a sum of a linear function and a spatially periodic correction, which can be expressed as an expansion in eigenfunctions of the Laplace operator that satisfy the appropriate periodicity conditions. The fast Fourier transform is used for an efficient numerical implementation of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Fast and accurate calculation of gravitational effects on a regional or global scale with complex density environment is a critical issue in gravitational forward modelling. Most existing significant developments with tessroid-based modelling are limited to homogeneous density models or polynomial ones of a limited order. Moreover, the total gravitational effects of tesseroids are often calculated by pure summation in these methods, which makes the calculation extremely time-consuming. A new efficient and accurate method based on tesseroids with a polynomial density up to an arbitrary order in depth is developed for 3D large-scale gravitational forward modelling. The method divides the source region into a number of tesseroids, and the density in each tesseroid is assumed to be a polynomial function of arbitrary degree. To guarantee the computational accuracy and efficiency, two key points are involved: (1) the volume Newton’s integral is decomposed into a one-dimensional integral with a polynomial density in the radial direction, for which a simple analytical recursive formula is derived for efficient calculation, and a surface integral over the horizontal directions evaluated by the Gauss–Legendre quadrature (GLQ) combined with a 2D adaptive discretization strategy; (2) a fast and flexible discrete convolution algorithm based on 1D fast Fourier transform (FFT) and a general Toepritz form of weight coefficient matrices is adopted in the longitudinal dimension to speed up the computation of the cumulative contributions from all tesseroids. Numerical examples show that the gravitational fields predicted by the new method have a good agreement with the corresponding analytical solutions for spherical shell models with both polynomial and non-polynomial density variations in depth. Compared with the 3D GLQ methods, the new algorithm is computationally more accurate and efficient. The calculation time is significantly reduced by 3 orders of magnitude as compared with the traditional 3D GLQ methods. Application of the new algorithm in the global crustal CRUST1.0 model further verifies its reliability and practicability in real cases. The proposed method will provide a powerful numerical tool for large-scale gravity modelling and also an efficient forward engine for inversion and continuation problems. [ABSTRACT FROM AUTHOR]

The topic of this study is in vitro proton magnetic resonance spectroscopy (MRS). The theme is on theoretical analysis of time signals encoded at a high magnetic field 14.1T, using a Bruker spectrometer, operating at a Larmor frequency of 600 MHz. The samples, dissolved in a D 2 O buffer, are from histopathologically analyzed ovarian cyst fluid from two patients. The benign and malignant diagnoses were serous cystadenoma and serous cystadenocarcinoma, respectively. It is of vital clinical importance to determine whether certain specific patterns, inferred from the analyzed/interpreted MRS data could be correlated with this and similar histopathologic findings for other patients. Encoded time signals contain the fingerprint of the examined sample, its metabolic content. Therefore, to detect the sought patterns from MRS data, the salient characteristics of a malignant tumor, implied by the diagnostically most relevant metabolites (including recognized cancer biomarkers, e.g. lactic acids, cholines,...), need to be unambiguously identified by their significant departures from the associated control data of benign biomaterial, ovarian cyst fluid (serous cystadenoma) in the diagnostic problem under the present consideration. Such identifications are unfeasible by visualization in the domain of encoding (time domain). A direct inspection of the graphed waveforms of an encoded time signal would give no clue about its structure nor about the sample content. However, merely visualizing the plots of the equivalent, information-preserving spectral lineshape profiles in the frequency domain would make transparent at least some of clinically useful, discernible features of MRS data, a number of resonances assignable to the known and unknown metabolites. For instance, the size of each resonance (peak area) is proportional to the concentration of the given metabolite. This is a key quantitative measure, which could help differentiate a malignant from a benign specimen by reference to the normal standards. A number of metabolites (choline, alanine, lactate, threonine, β -hydroxybuturate, valine, isolecine, leucine,...) have substantially different concentrations in the malignant compared with normal samples. Time signals can be processed by two substantially different categories of mathematical transforms, shape and parameter estimators. The former processors are alternatively called nonparametric estimators. They have been employed for envelopes in our recent study on this problem, which will presently be addressed with the prime focus on reconstructions of the corresponding components. Components and envelopes are partial and total shape spectra, respectively. The sum of all the component lineshapes (one per metabolite) yields the envelope nondegenerate spectrum representation of the entire sample. Presently, a deeper diagnostically valid insight is gained about the metabolic content of the scanned sample through the reported exact component spectra. The employed parameter estimators are the high-resolution, noise-suppressing nonderivative and derivative fast Padé transforms. Detailed are several critical achievements by the parametric Padé processing of direct clinical relevance. Importantly, all the accomplishments are shared by the nonparametric derivative Padé estimations. Three examples are highlighted here as follows. Confirmation of our recent nonparametric derivative detection of an unassigned metabolite (a singlet peak) co-resonating with free choline near chemical shift 3.19 ppm (parts per million). Therein, with the nonderivative envelope, only one compound peak usually appears and is conventionally assigned to a free choline singlet. However, such an oversight would yield about twice larger value of the true concentration of this key cancer biomarker. The concentration level of another cancer biomarker (lactate) is also overestimated by any nonparametric nonderivative envelope. In sharp contrast, the parametric nonderivative Padé estimation unequivocally detects six usually invisible resonances (assignable to other metabolites) beneath the lactate doublet, around chemical shift 1.41 ppm. At least two of the strongest among these invisible six resonances can be also identified in the nonparametric fourth derivative Padé envelope. Regularization of the spectral compound for the water residual (4.71 ppm), which deforms the neighboring resonance lineshapes and impacts adversely on the concentration assessments of other nearby metabolites. This is accomplished by the fourth derivative envelope (coincident with the components) whose narrowing of the widths, cutting off the long tails and the background flattening generate a quantifiable singlet of water. This can serve as a reliable calibration reference resonance. After such a localization, no distortion appears around water, so that even very near 4.71 ppm, several smaller resonances are detected (assignable to a multiplet of nitrogen acetyl asparate), totally invisible in the nonparametric nonderivative envelope. [ABSTRACT FROM AUTHOR]

Tauc plots have been massively used to determine the band gap energy Eg\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\left( {E_{{\text{g}}} } \right)$$\end{document} of semiconductors, but its implementation still possibility of erroneous estimates, which can be attributed by the straight-line method that involving subjective analysis of the researcher's own judgment. Here, we have collaborated Kubelka–Munk, Taylor expansion, and density functional theory calculation as general method and fast Fourier transform (FFT) as a fresh technique for determining more accurately band gap. Based on UV–Vis spectra analysis and QE simulation, the band gap range of TiO2 from our calculation can be reported to be (3.26 ± 0.3) eV for a purity (~ 97.23%) with a crystallinity (~ 75%). It was found that FFT is a new viable comparison method to identify the suitable Eg\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$E_{{\text{g}}}$$\end{document} of semiconductors, which is crucial for optimizing material design and tailoring their functionality for various applications. [ABSTRACT FROM AUTHOR]

Consider a multivariate polynomial f∈K[x1,…,xn]\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$f \in K [x_1, \ldots , x_n]$$\end{document} over a field K, which is given through a black box capable of evaluating f at points in Kn\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$K^n$$\end{document}, or possibly at points in An\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$A^n$$\end{document} for any K-algebra A. The problem of sparse interpolation is to express f in its usual form with respect to the monomial basis. We analyze the complexity of various old and new algorithms for this task in terms of bounds D and T for the total degree of f and its number of terms. We mainly focus on the case when K is a finite field and explore possible speed-ups. [ABSTRACT FROM AUTHOR]

In this contribution, the time-domain harmonic state estimation is evaluated using the real-time digital simulation, Kalman filter, an optimal measurement algorithm and a physical scaled-down laboratory implementation. This methodology is implemented using MATLAB/Simulink® and runs on RT-LAB® platform in real time. The optimal placement algorithm of measurement devices is used to obtain full observability of the system. This measurement algorithm finds the optimal placement with a limited number of measurement devices, whose measurements may be contaminated with noise. The measurement model is implemented in the physical test power system. Besides, the state estimator assesses the system inputs (internal generator voltages, nonlinear electrical load variables) whose dynamics are totally unknown. The harmonic content of the waveforms is obtained through the fast Fourier transform. The estimated responses in the case studies using the RT-LAB® platform are validated through direct comparison against those obtained in the physical implementation of the electrical power system, obtaining satisfactory results. [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]

Cloudiness or formation is a concept routinely used in industry to address deviations from homogeneity in nonwovens and papers. Measuring a cloudiness index based on image data is a common task in industrial quality assurance. The two most popular ways of quantifying cloudiness are based on power spectrum or correlation function on the one hand or the Laplacian pyramid on the other hand. Here, we recall the mathematical basis of the first approach comprehensively, derive a cloudiness index, and demonstrate its practical estimation. We prove that the Laplacian pyramid as well as other quantities characterizing cloudiness like the range of interaction and the intensity of small-angle scattering are very closely related to the power spectrum. Finally, we show that the power spectrum can be measured easily by image analysis methods and carries more information than the alternatives. [ABSTRACT FROM AUTHOR]

Sentiment analysis or opinion mining has an extensive area in the field of research. Today we consider the huge amount of structured and unstructured data available in the web for a particular subject to get an opinion. The surplus data handling termed as big data requires some new technology to deal with. This paper considers the requirement of sentiment analysis of such huge data for fast processing. Based on fast Fourier transform on temporal intuitionistic fuzzy set generated from text, this algorithm (FFT–TIFS) expedites the sentiment classification. Fourier analysis converts a signal from its time domain to its representation in frequency domain. Such frequency domain algorithm on temporal intuitionistic fuzzy set is used in sentiment analysis for the first time. This algorithm is useful for short Twitter text, document-level as well as sentence-level binary sentiment classification. It is tested on aclImdb, Polarity, MR, Sentiment 140 and CR dataset which gives an average of 80% accuracy. The proposed method shows significant improvement in required time complexity where the method achieves 17 times faster processing in comparison with sequential fuzzy C-means (FCM) method, and again, it is at least 7 times faster than distributed FCM method present in the literature. The method presented in this paper has a novel approach towards fastest processing time and suitability of various sizes of the text sentiment analysis. [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]

The present study deals with two different kinds of time signals, encoded by in vitro proton magnetic resonance spectroscopy (MRS) with a high external static magnetic field, 14.1T (Bruker 600 MHz spectrometer). These time signals originate from the specific biofluid samples taken from two patients, one with benign and the other with malignant ovarian cysts. The latter two diagnoses have been made by histopathologic analyses of the samples. Histopathology is the diagnostic gold standard in medicine. The obtained results from signal processing by the nonparametric derivative fast Padé transform (dFPT) show that a number of resonances assignable to known metabolites are considerably more intense in the malignant than in the benign specimens. Such conclusions from the dFPT include the recognized cancer biomarkers, lactic acid and choline-containing compounds. For example, the peak height ratio for the malignant-to-benign samples is about 18 for lactate, Lac. This applies equally to doublet Lac(d) and quartet Lac(q) resonating near 1.41 and 4.36 ppm (parts per million), respectively. For the choline-containing conglomerate (3.19-3.23 ppm), the dFPT with already low-derivative orders (2nd, 3rd) succeeds in clearly separating the three singlet component resonances, free choline Cho(s), phosphocholine PC(s) and glycerophosphocholine GPC(s). These constituents of total choline, tCho, are of critical diagnostic relevance because the increased levels, particularly of PC(s) and GPC(s), are an indicator of a malignant transformation. It is gratifying that signal processing by the dFPT, as a shape estimator, coheres with the mentioned histopathology findings of the two samples. A very large number of resonances is identifiable and quantifiable by the nonparametric dFPT, including those associated with the diagnostically most important low molecular weight metabolites. This is expediently feasible by the automated sequential visualization and quantification that separate and isolate sharp resonances first and subsequently tackle broad macromolecular lineshape profiles. Such a stepwise workflow is not based on subtracting nor annulling any part of the spectrum, in sharp contrast to controversial customary practice in the MRS literature. Rather, sequential estimation exploits the chief derivative feature, which is a faster peak height increase of the thin than of the wide resonances. This is how the dFPT simultaneously improves resolution (linewidth narrowing) and reduces noise (background flattening). Such a twofold achievement makes the dFPT-based proton MRS a high throughput strategy in tumor diagnostics as hundreds of metabolites can be visualized/quantified to offer the opportunity for a possible expansion of the existing list of a handful of cancer biomarkers. [ABSTRACT FROM AUTHOR]

Due to the extensive use of Unmanned Aerial Vehicles (UAVs) and the co-evolution of current technology, a key introduction to fault detection has arisen in recent studies in order to prevent unfortunate consequences. In this study, vibration-based signals from a commercially available innovative quadcopter flying in hover mode are collected using a vibration accelerometer, a data acquisition device, and a laptop. An ADXL335 accelerometer is fixed on the center of the drone where the centerlines of the four blades intersect. The superposition of numerous vibration arrangements over identical spectra hinders the ability to analyze the spectral data in the manner required to locate any framework's discrete vibration. This work presents a technique for separating a synthesized vibration signal towards discrete vibrations and other extraneous vibrations of a structure utilizing the Discrete Wavelet Transform (DWT) integrated with the Fast Fourier Transform (FFT). The research article findings in this study demonstrate the reliability and applicability of specific categories of discrete vibrations that are sorted out during the structural change evaluation to develop the best feasible strategy for removing the undesired and unanticipated vibration components and noise. The methodology demonstrated in this paper has the potential for practical application to multirotor UAVs in general. [ABSTRACT FROM AUTHOR]

This paper describes the noise analysis of an electro-optic (EO) sensor system based on experimental and simulation results. We developed a polarization simulator of the EO sensor system using the Jones vector and matrix. The polarization simulator included not only the laser intensity noise but also the laser polarization noise. The polarization noise was converted into an intensity noise due to the polarization noise using a polarizer after the laser source. We proposed a method to adjust differential balance using phasor diagram. The method is used for analysis of the noise characteristics. We expected that the existence of the laser polarization noise can be demonstrated by our experimental setup with and without the polarizer after the laser source. The noise characteristics of experimental results more than 4 kHz agreed with the simulation results under considering the effect of a receiver noise. However, the noise characteristics less than 4 kHz did not agree with simulation results. It was found that the noise characteristics less than 4 kHz are caused by the light intensity unbalance between p- and s- polarized light in our system. [ABSTRACT FROM AUTHOR]

In this paper we present the first known deterministic algorithm for the construction of multiple rank-1 lattices for the approximation of periodic functions of many variables. The algorithm works by converting a potentially large reconstructing single rank-1 lattice for some d-dimensional frequency set I ⊂{0,…,N − 1}d into a collection of much smaller rank-1 lattices which allow for accurate and efficient reconstruction of trigonometric polynomials with coefficients in I (and, therefore, for the approximation of multivariate periodic functions). The total number of sampling points in the resulting multiple rank-1 lattices is theoretically shown to be less than O | I | log 2 (N | I |) with constants independent of d, and by performing one-dimensional fast Fourier transforms on samples of trigonometric polynomials with Fourier support in I at these points, we obtain exact reconstruction of all Fourier coefficients in fewer than O d | I | log 4 (N | I |) total operations. Additionally, we present a second multiple rank-1 lattice construction algorithm which constructs lattices with even fewer sampling points at the cost of only being able to reconstruct exact trigonometric polynomials rather than having additional theoretical approximation guarantees. Both algorithms are tested numerically and surpass the theoretical bounds. Notably, we observe that the oversampling factors #samples/|I| appear to grow only logarithmically in |I| for the first algorithm and appear near-optimally bounded by four in the second algorithm. [ABSTRACT FROM AUTHOR]

The propagation of acoustic waves in a porous medium whose skeleton consists of a gas hydrate with pores filled with water has been studied. A system of equations is written that describes the propagation of acoustic waves in such a porous medium. A dispersion equation is obtained, on the basis of which the phase velocity of sound and the decrement of attenuation of acoustic waves are analyzed. The coefficients of reflection and passage at the "liquid–porous medium" and "porous medium–liquid" interfaces have been derived and investigated. Based on the dispersion equation and corresponding reflection and passage coefficients, the propagation of the finite-duration pulses in the porous medium is investigated. The possibility of estimating the thickness of the gas hydrate bed with the aid of acoustic waves is shown. [ABSTRACT FROM AUTHOR]

Time signals are measured experimentally throughout sciences, technologies and industries. Of particular interest here is the focus on time signals encoded by means of magnetic resonance spectroscopy (MRS). The great majority of generic time signals are equivalent to auto-correlation functions from quantum physics. Therefore, a quantum-mechanical theory of measurements of encoded MRS time signals is achievable by performing quantum-mechanical spectral analysis. When time signals are measured, such an analysis becomes an inverse problem (harmonic inversion) with the task of reconstruction of the fundamental frequencies and the corresponding amplitudes. These complex-valued nodal parameters are the building blocks of the associated resonances in the frequency spectrum. Customarily, the MRS literature reports on fitting some ad hoc mathematical expressions to a set of resonances in a Fourier spectrum to extract their positions, widths and heights. Instead, an alternative would be to diagonalize the so-called data matrix with the signal points as its elements and to extract the resonance parameters without varying any adjusting, free constants as these would be absent altogether. Such a data matrix (the Hankel matrix) is from the category of the evolution matrix in the Schrödinger picture of quantum mechanics. Therefore, the spectrum of this matrix, i.e. the eigenvalues and the corresponding amplitudes, as the Cauchy residues (that are the squared projections of the full wave functions of the system onto the initial state) are equivalent to the sought resonance parameters, just mentioned. The lineshape profile of the frequency-dependent quantum-mechanical spectral envelope is given by the Heaviside partial fraction sum. Each term (i.e. every partial fraction) in this summation represents a component lineshape to be assigned to a given molecule (metabolite) in the tissue scanned by MRS. This is far reaching, since such a procedure allows reconstruction of the most basic quantum-mechanical entities, e.g. the total wave function of the investigated system and its 'Hamiltonian' (a generator of the dynamics), directly from the encoded time signals. Since quantum mechanics operates with abstract objects, it can be applied to any system including living species. For example, time signals measured from the brain of a human being can be analyzed along these lines, as has actually been done e.g. by own our research. In this way, one can arrive at a quantum-mechanical description of the dynamics of vital organs of the patient by retrieving the interactions as the most important parts of various pathways of the tissue functions and metabolism. Of practical importance is that the outlined quantum-mechanical prediction of the frequency spectrum coincides with the Padé approximant, which is in signal processing alternatively called the fast Padé transform (FPT) for nonderivative estimations. Further, there is a novelty called the derivative fast Padé transform (dFPT). The FPT and dFPT passed the test of time with three fundamentally different time signals, synthesized (noise-free, noise-contaminated) as well as encoded from phantoms and from patients. Such systematics are necessary as they permit robust and reliable benchmarkings of the theory in a manner which can build confidence of the physician, while interpreting the patient's data and making the appropriate diagnosis. In the present study, we pursue further this road paved earlier by applying the FPT and dFPT (both as shape and parameter estimators) to time signals encoded by in vivo proton MRS from an ovarian tumor. A clinical 3T scanner is used for encoding at a short echo time (30 ms) at which most resonances have not reached yet their decay mode and, as such, could be detected to assist with diagnostics. We have two goals, mathematical and clinical. First, we want to find out whether particularly the nonparametric dFPT, as a shape estimator, can accurately quantify. Secondly, we want to determine whether this processor can provide reliable information for evaluating an ovarian tumor. From the obtained results, it follows that both goals have met with success. The nonparametric dFPT, from its onset as a shape estimator, transformed itself into a parameter estimator. Its quantification capabilities are confirmed by reproducing the components reconstructed by the parametric dFPT. Thereby, fully quantified information is provided to such a precise extent that a large number of sharp resonances (more than 160) appear as being well isolated and, thus, assignable to the known metabolites with no ambiguities. Importantly, some of these metabolites are recognized cancer biomarkers (e.g. choline, phosphocholine, lactate). Also, broader resonances assigned to macromolecules are quantifiable by a sequential estimation (after subtracting the formerly quantified sharp resonances and processing the residual spectrum by the nonparametric dFPT). This is essential too as the presence of macromolecules in nonoderivative envelopes deceptively exaggerates the intensities of sharper resonances and, hence, can be misleading for diagnostics. The dFPT, as the quantification-equipped shape estimator, rules out such possibilities as wider resonances can be separately quantified. This, in turn, helps make adequate assessment of the true yield from sharp resonances assigned to metabolites of recognized diagnostic relevance. [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 theme of this study is derivative nuclear magnetic resonance (dNMR) spectroscopy. This versatile methodology of peering into the molecular structure of general matter is common to e.g. analytical chemistry and medical diagnostics. Theoretically, the potential of dNMR is huge and the art is putting it into practice. The implementation of dNMR (be it in vitro or in vivo) is wholly dependent on the manner in which the encoded time signals are analyzed. These acquired data contain the entire information which is, however, opaque in the original time domain. Their frequency-dependent dual representation, a spectrum, can be transparent, provided that the appropriate signal processors are used. In signal processing, there are shape and parameter estimators. The former processors are qualitative as they predict only the forms of the lineshape profiles of spectra. The latter processors are quantitative because they can give the peak parameters (positions, widths, heights, phases). Both estimators can produce total shape spectra or envelopes. Additionally, parameter estimators can yield the component spectra, based on the reconstructed peak quantifiers. In principle, only parameter estimators can solve the quantification problem (harmonic inversion) to determine the structure of the time signal and, hence, the quantitative content of the investigated matter. The derivative fast Fourier transform (dFFT) and the derivative fast Padé transform (dFPT) are the two obvious candidates to employ for dNMR spectroscopy. To make fair comparisons between the dFFT and dFPT, the latter should also be applied as a shape estimator. This is what is done in the present study, using the time signals encoded from a patient with brain tumor (glioma) using a 1.5T clinical scanner. Moreover, within the dFPT itself, the shape estimations are compared to the parameter estimations. The goal of these testings is to see whether, for in vivo dNMR spectroscopy, shape estimations by the dFPT could quantify (without fitting), similarly to parameter estimations. We check this key point in two successive steps. First, we compare the envelopes from the shape and parameter estimations in the dFPT. The second comparison is between the envelopes and components from the shape and parameter estimations, respectively, in the dFPT. This plan for benchmarking shape estimations by the dFPT is challenging both on the level of data acquisition and data analysis. The data acquisition reported here provides encoded time signals of short length, only 512 as compared to 2048, which is customarily employed. Moreover, the encoding echo time was long (272 ms) at which most of resonances assigned to metabolites with shorter spin-spin relaxations are likely to be obliterated from the frequency spectra. Yet, in face of such seemingly insurmountable obstacles, we are looking into the possibility to extract diagnostically relevant information, having particularly in focus the resonances for recognized cancer biomarkers, notably lactate, choline and phosphocholine. Further, we want to see how many of the remaining resonances in the spectra could accurately be identified with clinical reliability as some of them could also be diagnostically relevant. From the mathematical stance, we are here shaking the sharp border between shape and parameter estimators. That border stood around for a long time within nonderivative estimations. However, derivative shape estimations have a chance to tear the border down. Recently, shape estimations by the dFPT have been shown to lead such a trend as this processor could quantify using the time signals encoded from a phantom (a test sample of known content). Further, the present task encounters a number of additional challenges, including a low signal-to-noise ratio (SNR) and, of course, the unknown content of the scanned tissue. Nevertheless, we are determined to find out whether the nonparametric dFPT can deliver the unique quantification-equipped shape estimation and, thus, live up to the expectation of derivative processing: a long-sought simultaneous improvement of resolution and SNR. In every facet of in vivo dNMR, we found that shape estimations by the dFPT has successfully passed the outlined most stringent tests. It begins with transforming itself to a parameter estimator (already with the 3rd and 4th derivatives). It ends with reconstructing some 54 well-isolated resonances. These include the peaks assigned to recognized cancer biomarkers. In particular, a clear separation of choline from phosphocholine is evidenced for the first time by reliance upon the dFPT with its shape estimations alone. [ABSTRACT FROM AUTHOR]

A piston is the key component of the diesel engine, which is subjected to higher pressure and temperature inside the combustion chamber. The wear propagation on piston leads to an increase in engine vibrations, acoustic emissions, exhaust emissions, lubricant degradation, reduction in the total power output and thermal efficiency of the engine. Hence, it is necessary to consider fault diagnostic techniques to detect the faults developed in the piston during the in-service condition. In this experimental work, efforts were made to detect the piston scuffing fault using vibration and acoustic emission analyses. The fault-related features were extracted from vibro-acoustic signals using signal processing tools viz. fast Fourier transform and continuous wavelet transform. The performance parameters such as brake power, brake thermal efficiency, brake specific fuel consumption, fuel consumption and in-cylinder combustion pressure, emission parameters viz. carbon monoxide, carbon dioxide, hydrocarbon, and nitrogen oxide, and lubricant degradation analyses were also considered to analyze the effects of piston scuffing fault on these parameters. The results provide a good correlation between vibration and acoustic signals, performance, and lubricant parameters to detect and diagnose the scuffing fault that appeared on the piston of the diesel engine. [ABSTRACT FROM AUTHOR]

The article considers the problem of estimating the parameters of the autoregressive (AR) signal in the presence of background noise. Based on the frequency representation of the AR signal, a technique of calculating the likelihood function of the AR parameters is shown and the implementation of the Expectation-Maximization method for iterative evaluation of the AR parameters is considered. Analysis of different measures of distortion of speech signals shows that the proposed approaches in the frequency domain have the same accuracy as the corresponding approaches in the time domain, but are characterized by significantly lower computing costs. [ABSTRACT FROM AUTHOR]

Under the condition of a strong electric field, partial discharge often occurs when insulated wire is damaged. The recognition of partial discharge is an effective method for the fast and accurate detection of high voltage insulated wire faults. This paper proposes a PD recognition algorithm based on a convolutional neural network and long short-term memory (LSTM). In addition, attention mechanisms are introduced to give separate weights to LSTM hidden states through a mapping, weighting, and learning parameter matrix. This is done to reduce the loss of historical information and to strengthen the influence of important information. The complex relationship between the voltage signal change and the grid operation state response has been established. The proposed method is verified by the ENET data set published by VSB University. The recognition accuracy is 95.16% for no-PD and 94.44% for PD. Results from the proposed algorithm show that this method has a higher detection accuracy. [ABSTRACT FROM AUTHOR]

The tensile strength of welded joints subjected to thermal stresses degrades with age. Tensile strength is generally assessed using tensile test, which is a destructive technique. This degradation measurement using the nondestructive testing (NDT) method has merit as specimens are intact even after the test. In situ NDT offers another significant advantage that testing of material can be performed without removing the sample from its service. Ultrasonic testing (UT) is a widely used NDT technique for material characterization and flaws detection. Motivated by this, we aim to investigate the tensile strength of mild steel post-weld heat-treated samples through advanced signal processing of the acquired ultrasonic signals through UT of mild steel heat-treated welded specimens. To this end, mild steel welded specimens were prepared for this study using electric arc welding with E6013 electrodes. After welding, specimens were heat-treated at different temperatures and then normalized. Ultrasonic signals were acquired using the pulse-echo technique on different samples, heat-treated at different temperatures, and later ultrasonic signal's attenuation was measured. The acquired UT signals were then processed using advance signal processing techniques i.e., fast Fourier transform (FFT) and power spectral density (PSD). Measured attenuation of UT signals and discriminatory features computed through the application of signal processing techniques on acquired UT signals then correlated with the specimens' tensile strength. Analysis of results showed that the tensile strength, FFT power of UT signals, and UT signals' PSD energy decreases as UT signal attenuation, increases with an increase in heat treatment temperature. Results also revealed that there exists a relationship between FFT signals strength, PSD energy, and UT signals attenuation with respect to heat treatment temperatures. This study will help weld quality inspectors to use in situ UT for predicting the tensile strength of mild steel welded specimens using the relationship established through the proposed scheme. [ABSTRACT FROM AUTHOR]

Numerical artifacts in the form of spurious oscillations are among the critical issues of Fast Fourier Transfer (FFT) methods for solving multiphase elastic problems such as numerical homogenization, in spite of their computational simplicity and efficiency. In the first part of the present work, it is shown that the irregular discretization of the interface due to the use of a voxel-based discretization is the dominant cause of oscillations. The second part of the present work focuses on numerical artifacts reduction schemes, and in particular special treatments for dealing with the irregular discretization of the interface such as the composite voxel method and neighbor averaging methods. An improved composite voxel method by using the level-set technique is proposed, which alleviates the implementation difficulty of the composite voxel method. This improved method is particularly relevant for non-parametrized interface representations such as those obtained from three-dimensional experimental images. [ABSTRACT FROM AUTHOR]

The High Altitude Water Cherenkov (HAWC) gamma-ray observatory is located close to the equator (latitude 18 ∘ N), at an altitude of 4100 m above sea level. HAWC has 295 water Cherenkov detectors (WCD), each containing four photomultiplier tubes (PMT). The main purpose of HAWC is the determination of the energy and arrival direction of very high energy gamma rays produced by energetic processes in the universe, HAWC also has a scaler system which counts the arrival of secondary particles to the detector. In this work we show that the scaler system of HAWC is an ideal instrument for solar modulation and space-weather studies due to its large area and high sensitivity. In order to prepare the scaler system for low energy heliospheric studies, we model and correct the efficiency variation of each PMT of the array, which result in a capability to measure variations > 0.01 % with high accuracy. Using the singular value decomposition method, we correct the rate deviations of all PMTs of the array, due to changes in efficiency, gain and operational voltage. We isolate and remove the atmospheric modulations of the PMTs count rates measured by the TDC-scaler data acquisition system. In particular, the atmospheric pressure at the HAWC site exhibits an oscillating behavior with a period of ∼12 hours and we make use of this periodic property to estimate the pressure coefficients for the HAWC TDC-scaler system. These corrections performed on the TDC-scaler system make the HAWC TDC-scaler system an ideal instrument for solar modulation and space-weather studies. As examples of this capability, we present the preliminary analysis of the solar modulation of cosmic rays at three time scales observed by HAWC, with an unprecedented accuracy. [ABSTRACT FROM AUTHOR]

In this article, an improved fast Fourier transform (FFT)–based millimeter-wave imaging algorithm with range compensation is presented, which can be used to reconstruct 3D images for near-field multiple-input multiple-output synthetic aperture radar (MIMO-SAR). The frequency-domain interpolation is avoided and only one-step spherical-wave decomposition is employed in this algorithm. During the image reconstruction process, the amplitude factor is considered for the compensation of signal propagation loss, and the final target image can be obtained by FFT/IFFT and coherent accumulation steps. As demonstrated with numerical theoretical analysis and experimental results, the proposed method greatly reduces the computational load but ensures the quality of image reconstruction compared to the back-projection (BP) algorithm. Moreover, it is superior to the MIMO-range migration algorithm (MIMO-RMA) in compensating propagation loss and other performance indexes in the image reconstruction results. [ABSTRACT FROM AUTHOR]

Background: Metaconcrete is a new concept of concrete, showing marked attenuation properties under impact and blast loading, where traditional aggregates are partially replaced by resonant bi-material inclusions. In a departure from conventional mechanical metamaterials, the inclusions are dispersed randomly as cast in the material. The behavior of metaconcrete at supersonic frequencies has been investigated theoretically and numerically and confirmed experimentally. Objective: The feasibility of metaconcrete to achieve wave attenuation at low frequencies demands further experimental validation. The present study is directed at characterizing dynamically, in the range of the low sonic frequencies, the—possibly synergistic—effect of combinations of different types of inclusions on the attenuation properties of metaconcrete. Methods: Dynamic tests are conducted on cylindrical metaconcrete specimens cast with two types of spherical inclusions, made of a steel core and a polymeric coating. The two inclusions differ in terms of size and coating material: type 1 inclusions are 22 mm diameter with 1.35 mm PDMS coating; type 2 inclusions are 24 mm diameter with 2 mm layer natural rubber coating. Linear frequency sweeps in the low sonic range (< 10 kHz), tuned to numerically estimated inclusion eigenfrequencies, are applied to the specimens through a mechanical actuator. The transmitted waves are recorded by transducers and Fast-Fourier transformed (FFT) to bring the attenuation spectrum of the material into full display. Results: Amplitude reductions of transmitted signals are markedly visible for any metaconcrete specimens in the range of the inclusion resonant frequencies, namely, 3,400-3,500 Hz for the PDMS coating inclusions and near 3,200 Hz for the natural rubber coating inclusions. Specimens with mixed inclusions provide a rather uniform attenuation in a limited range of frequencies, independently of the inclusion density, while specimens with a single inclusion type are effective over larger frequency ranges. With respect to conventional concrete, metaconcrete reduces up to 90% the amplitude of the transmitted signal within the attenuation bands. Conclusions: Relative to conventional concrete, metaconcrete strongly attenuates waves over frequency bands determined by the resonant frequencies of the inclusions. The present dynamical tests conducted in the sonic range of frequencies quantify the attenuation properties of the metaconcrete cast with two types inclusions, providing location, range and intensity of the attenuation bands, which are dependent on the physical-geometric features of the inclusions. [ABSTRACT FROM AUTHOR]

In this paper, we consider solutions for discrete systems arising from multi-term time-fractional diffusion equations. Using discrete sine transform techniques, we find that all-at-once systems of such equations have a structure similar to that of diagonal-plus-Toeplitz matrices. We establish a generalized circulant approximate inverse preconditioner for the all-at-once systems. Through a detailed analysis of the preconditioned matrices, we show that the spectrum of the obtained preconditioned matrices is clustered around one. We give some numerical examples to demonstrate the effectiveness of the proposed preconditioner. [ABSTRACT FROM AUTHOR]

In ultra-high sampling rates, FFT is widely used for acoustic emission signals. In this manuscript, the effectual architecture of hardware is presented based on the execution of FFT due to radix-2 frequency decimation algorithm (R2DIF) and channeled method that allows data to be effectively shared through storage by shift registers. An optimal rotation method/design uses the modified digital coordinate rotation computer algorithm (m-CORDIC) as well as Radix- 2r depending on coding scheme to replace complex multiplier as FFT. The m-CORDIC algorithm enhances computing confluence, while Radix-2r allows the logarithmic reduction of the adder steps. The suggested design does not need large blocks of memory used to maintain the factor as twiddle. Experimental outcomes displays the presented design performs the existing methods by achieving high accuracy and throughput. Compared to the CSD as well as DBNS, novel radix-2r encoding desires an average of 23.12% and 3.07% fewer additions, respectively. The expansion of CSD is canonical signed-digit. [ABSTRACT FROM AUTHOR]

The seismic response of a highly heterogeneous hydraulic fill dam was evaluated by studying the natural frequencies of the first and second modes of vibration and analyzing the crest accelerations of different two-dimensional or 2D sections of the dam when subjected to two different earthquake excitations. The existing methods for determination of the natural frequency of earthen embankment structures can only be used to analyze the structural response at small strain levels. However, during seismic events, the natural frequency of an earthen dam is significantly affected by the nonlinear material behavior exhibited by the geomaterials at high strain levels. Hence, a novel method was devised to evaluate the strain-dependent natural frequency for plane strain 2D dam sections, using a synthesized multi-sine base excitation. The degradation of first and second natural frequencies of transverse vibration for all the 2D sections followed a linear trend when plotted against the respective crest's root mean square strain on a logarithmic scale. The slope of the degradation curve was found to depend on the constituent material properties prevalent in the individual sections. The observed variations in natural frequencies and crest accelerations of the 2D dam sections were also used to assess the suitability of using two-dimensional plane strain analyses for studying the response of a long earthen dam having variability in material properties. Results indicate that there is a considerable chance of erroneous estimation of the seismic response of such highly heterogeneous earthen dams that are conventionally analyzed using plane strain models. A 2D analysis was found to merely capture the seismic response of the individual sections of the dam as independent entities while ignoring the stiffening or weakening effect of the adjacent neighboring segments that may have different material properties. [ABSTRACT FROM AUTHOR]

The Iterative Filtering method is a technique developed recently for the decomposition and analysis of nonstationary and nonlinear signals. In this work, we propose two alternative formulations of the original algorithm which allows to transform the iterative filtering method into a direct technique, making the algorithm closer to an online algorithm. We present a few numerical examples to show the effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

The fast Fourier transform-moving average (FFT-MA) is an efficient method for the generation of geostatistical simulations. The method relies on the calculation of a filter operator based on the covariance function of interest and the convolution of the filter with a white noise, to generate multiple realizations of spatially correlated variables. In this work, a revisited mathematical formulation of the FFT-MA method, with the exact expression of the filter, is presented. The proposed derivation of the filter is based on the Wiener–Khinchin theorem and the application of the Fourier transform in a discrete domain. In the specific case of white noise, the proposed formulation leads to the same expression of the traditional algorithm. However, the method can be applied to other types of noise. The proposed technique allows the calculation of a specific filter that imposes an exact covariance function on the noise. Therefore, the experimental covariance function is exactly equal to the theoretical one, which is not the case for many common simulation techniques due to the limited sample size. Applications of the FFT-MA method to synthetic and real data sets, including exact interpolation, hard data conditioning and correlated simulations from cross-correlated noises, are also presented. [ABSTRACT FROM AUTHOR]

New type of shaft-inside-shaft friction high-speed power turbine coupling was investigated. Experimental test rig was developed to evaluate the new coupling (case C) and compare its performance with conventional bush couplings without absorber pads (case A) and with absorber pads (case B). Two accelerometers were used for the vibration analysis, and for each case, signals were recorded for the angular vibration on the alternator casing and for displacement axial vibration on the platform. Vibration signals were analysed through the fast Fourier-transform frequency spectrum in the range of 0–2.5 kHz. Higher shaft speed of 13,037 rpm was achieved with the new coupling compared to 6885 and 8056 rpm for cases A and B, respectively, indicating significant reduction in friction losses. Unbalance, looseness and misalignment faults were analysed through the harmonic frequencies 1X-5X for the three cases. The severity of misalignment was examined by the 2X/1X ratio on the alternator and the platform. The new coupling suffered from high misalignment at low rotating speeds, but showed superior performance above 4000 rpm. [ABSTRACT FROM AUTHOR]

An efficient micromechanical methodology is developed for tailoring elastic and thermal properties of random heterogeneous materials. The methodology involves three steps: (i) statistical reconstruction based on the two-point correlation function (TPCF), (ii) thermomechanical homogenization, and (iii) optimization. The method relies on the tailoring the state of anisotropy of the microstructure to achieve desired directional effective properties. This capability is demonstrated by designing heterogeneous microstructures with optimal elastic modulus and thermal conductivity in perpendicular directions. The study aims at presenting optimal computational algorithms for the reconstruction, homogenization and optimization steps. Several studies study are presented to demonstrate the feasibility of obtaining desired thermomechanical properties with a minimal set of design variables. These case studies highlight the advantages and limitations of the method, along with its computational cost. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the numerical solutions of the coupled fractional Klein-Gordon-Schrödinger equation. The numerical schemes are constructed by combining the Crank-Nicolson/leap-frog difference methods for the temporal discretization and the Galerkin finite element methods for the spatial discretization. We give a detailed analysis of the conservation properties in the senses of discrete mass and energy. Then the numerical solutions are shown to be unconditionally bounded in L2 −norm, H α 2 − semi-norm and L ∞ − norm, respectively. Based on the well-known Brouwer fixed-point theorem and the mathematical induction, the unique solvability of the discrete solutions is proved. Moreover, the schemes are proved to be unconditionally convergent with the optimal order O τ 2 + h r + 1 , where τ is the temporal step, h is the spatial grid size, and r is the order of the selected finite element space. Furthermore, by using the proposed decoupling and iterative algorithms, several numerical examples are included to support theoretical results and show the effectiveness of the schemes. Finally, the fast Krylov subspace solver with suitable circulant preconditioner is designed to effectively solve the Toeplitz-like linear systems. In each iterative step, this method can effectively reduce the memory requirement of above each finite element scheme from O M 2 to O(M), and the computational complexity from O M 3 to O (M log M) , where M is the number of grid nodes. Numerical tests are carried out to show that this fast algorithm is more practical than the traditional backslash and LU factorization/Cholesky decomposition methods, in terms of memory requirement and computational cost. [ABSTRACT FROM AUTHOR]