Search

A large-span steel–concrete composite beam with precast hollow core slabs (CBHCSs) is a relatively new floor structure that can be applied to various long-span structures. However, human-induced vibrations may present serviceability issues in such structures. To alleviate vibrations, both the walking forces excited by humans and the associated floor responses must be elucidated. In this study, 150 load–time histories of walking, excited by 25 test participants, are obtained using a force measuring plate. The dynamic loading factors and phase angles in the Fourier series functions for one-step walking are determined. Subsequently, walking tests are performed on seven CBHCS specimens to capture the essential dynamic properties of mode shapes, natural frequencies, damping ratios, and acceleration time histories. The CBHCS floor system generally exhibits a high frequency (> 10 Hz) and low damping (damping ratio

In order to improve the speed of passenger screening while preserving the effective capability to detect more sophisticated threats, airport security imaging systems must be able to accurately characterize concealed body-worn objects. In addition to improving the passenger experience, this system capability will enhance airport security for the traveling public. This paper presents a real-time, fully-automatic algorithm for the wideband millimeter-wave (mm-wave) radar reconstruction of the nominal human body contours, even in the presence of an affixed weak dielectric object or when a portion of the body cross-section is not captured by the imaging scanner. The algorithm extracts the main contours from a noisy collection of 3D reconstructed reflectivity and approximates the nominal human body cross-section via fitting a low order angular Fourier series. This important step is essential for precise characterization of concealed body-worn explosives. A ranking algorithm is developed as a metric for the nominal body reconstruction accuracy. We verify the developed algorithm by applying it to the actual images of the High Definition-Advanced Imaging Technology (HD-AIT) system, a laboratory prototype mm-wave scanning system developed recently by the US Department of Homeland Security (DHS). The reconstructed body contours may be used to estimate the electric permittivity of the concealed person-worn objects.

Nowadays, vibration serviceability criteria are becoming the governing factor in the design of most modern staircases, because their increasing susceptibility to human induced vibrations. Although more awareness have been raised to the dynamic design of new staircases, there are still few studies found in the literature that compare the different results of numerical methods for predicting vibrations with experimental data, in order to validate the same. Hence, this paper employs the main existing numerical methods to an actual staircase with known liveness, by comparing the predicted results with the experimental data, to evaluate their accuracy when designing flexible staircases. This paper is Part 2 of a set of two papers. In Part 1, the different numerical methods are presented and details are given of how to apply them. To accomplish this, an in-situ staircase dynamic characterisation and several walking tests are performed. The measured vibrations are initially compared with different proposed acceptable limits to confirm that the vibrations exceed the limits. The different numerical methods are then employed and the predicted results are compared with the experimental results. Lastly, the main findings of this work are discussed together with those of diverse researchers who also applied one of these procedures to estimate vibrations. The results obtained showed that, with two of the numerical procedures applied (footfall force time histories and simplified vibration evaluation), it was possible to effectively predict the vibrations, while with the remaining two (Fourier series walking models and steady-state analysis), in general, overestimated responses were predicted.

Recent trends towards slender construction with prominent and exigent architectural requirements often result in low frequency staircases that are significantly flexible and susceptible to unacceptable vibrations, which may promote safety concerns for their users. For structural engineers, however, there is still a lack of understanding, available information and specific design guides for predicting the dynamic behaviour of staircases due to human induced vibrations. To address this problem, this work reviews and applies the main existing numerical methods for predicting vibrations, to evaluate their precision and provide practical guidance when designing flexible staircases. The work developed is presented in a two-part paper. In Part 1, the actual paper, several numerical methods are introduced and a detailed description is given of how these can be employed in a design stage. The distinction between low and high frequency staircases is explained, since it directly influences the structure’s behaviour and, subsequently, the selected method. A description is given of how to simulate walking dynamic loads, which forms the basis of all methods. The group effect is also discussed because it tends to considerably amplify the staircase response. Finally, the different numerical procedures are applied to a practical case and compared. It was observed that, although the four numerical methods were employed with the same staircase, their results were different. The reasons for the higher results of Fourier series walking models are explained. In Part 2, the follow-up paper, the numerical methods are employed on a real staircase, comparing the estimated and experimental results.

We give explicit expressions for the Fourier coefficients of Eisenstein series twisted by Dirichlet characters and modular symbols on [Formula: see text] in the case where N is prime and equal to the conductor of the Dirichlet character. We obtain these expressions by computing the spectral decomposition of automorphic functions closely related to these Eisenstein series. As an application, we then evaluate certain sums of modular symbols in a way which parallels past work of Goldfeld, O’Sullivan, Petridis, and Risager. In one case we find less cancelation in this sum than would be predicted by the common phenomenon of “square root cancelation”, while in another case we find more cancelation.

Purpose The purpose of this paper is to analyze the unbalanced magnetic pull (UMP) of the rotor of traction motor and the influence of the UMP on thermal characteristics of traction motor bearing. Design/methodology/approach The unbalanced magnetic pull on the rotor with different eccentricity was calculated by Fourier series expansion method. A bearing thermal analysis finite element model considering both the vibration of high-speed train caused by track irregularity and the UMP of traction motor rotor was established. The validity of the model is verified by experimental data obtained from a service high-speed train. Findings The results show that thermal failure of bearing subassemblies most likely occurs at contact area between the inner ring and rollers. The UMP of rotor of traction motor has a significant effect on the temperature of the inner ring and roller of the bearing. When the eccentricity is 10%, the temperature can even be increased by about 12°C. Therefore, the UMP of rotor of traction motor must be considered in thermal analysis of traction motor bearing. Originality/value In the thermal analysis of the bearing of the traction motor of high-speed train, the UMP of the rotor of the traction motor is considered for the first time

At present, it is difficult to predict the operation accuracy of machine tools in the preliminary design stage. How to quantitatively reflect the contribution of tolerance on the position error of machine tool has a significant guidance for machine tool design stage. Thus, this paper presents a sensitivity analysis method based on components tolerance, which can clearly give the machine tool designer key the tolerances. Firstly, taking the translational axis as the research object, the operation accuracy model of Y-axis is established based on the homogeneous transform matrix (HTM) and multi-body system (MBS) theory. Meanwhile, the relationship between tolerances and geometric errors has been mapped by the Fourier expansion and the model of parameters have been identified by self-design simulation. As a basis, the tolerance sensitivity analysis (TSA) method based on the single-factor partial derivation is constructed to acquire the key tolerance parameters. Finally, the result of the experiment shows that the assembly tolerance of the Y-Z plane of the base, the manufacturing tolerance of the lead screw and the assembly tolerance of the X-Y plane of the carriage contribute a great deal to the position error, which needs to be strictly controlled in the future design to improve the accuracy of the machine tool.

In this paper, the effect of radiation pressure force on formation of the nominal halo orbit around the collinear point $$L_1$$ is estimated in the framework of Sun–Earth system. Using Lindstedt–Poincare technique, the periodic solutions up to third-order approximation are computed. Further, the Fourier series solutions of nominal halo orbit are also evaluated. With considering the radiation pressure force effect, the proposed analysis in this work can be used to design a trajectory for spacecraft moving in more realistic system.

In this paper, a rose-flower variety classification scheme, using color and shape features is presented. The first three statistical moments of the R, G, and B planes of the image were calculated to describe the color, while Fourier coefficients are used to describe the shape. For shape description, signatures (wave-forms) of the boundary contour of the binary images were extracted. Fourier coefficients that are used to describe the shape were estimated using the signatures generated. Depending on the Fourier coefficients, a representation of sums of angles formed along boundaries of the flowers was defined. Using these sums and the color features as input to an artificial neural network (ANN), the flowers were classified into their respective target classes. The eighteen flower varieties considered in this study were classified with an accuracy of 95.6%, 98.9%, and 100% using their shape, color, and combination of both shape and color features, respectively. Comparing these results, it was found that the combination of the two features is an efficient criterion for rose flower variety discrimination and classification.

Geometric error is one of the important errors that affect the machining of five-axis machine tools and how to identify th8e vital geometric error is effective for compensation. For this reason, the global sensitivity analysis of geometric errors for five-axis machine tools is an effective means to find the vital geometric error items that affect the machining accuracy of machine tools. However, it is difficult to deal with the higher order items of error parameter coupling in the global sensitivity analysis. In this paper, a novel global sensitivity analysis method for vital geometric error based on multi-body theory and truncated Fourier expansion is proposed. First, multi-body system (MBS) and homogeneous transformation matric (HTM) methods are used to establish the position error of the machine tool. Then, the output value of the error parameter is represented as the amplitude of the truncated Fourier series and the global sensitivity index is represented by the ratio of its amplitude variance to the total function variance through normalization processing. Moreover, the global sensitivity analysis method is presented to calculate the sensitivity index of each geometric error parameter and the vital geometric error parameters have been identified. Finally, an experiment on compensating for vital geometric error parameters is performed and the experimental results show that the proposed method is feasible and accurate.

A theoretical solution method for the in-plane vibration characteristics of the plate with cutouts is proposed in this paper. The energy principle in conjunction with the Rayleigh–Ritz solution technique is adopted for the theoretical modeling of the in-plane vibration of the structure. The energy functions for the plate with cutouts are established by subtracting the energies of the cutout domains from the total energies of the whole plate. To ensure continuity over the entire solution domain, the in-plane displacements are composed of two-dimensional standard Fourier series and supplementary functions. The in-plane eigenmodes of the plates with different square cutouts are compared with the results obtained from the finite element method (FEM), with good agreements. The influences of the cutouts on the in-plane vibration characteristics of the plates with cutouts are investigated by varying the number, size, and position of the cutouts.

A broadband constant beam pattern (CBP) array is an acoustic array whose beam patterns are independent of operating frequencies. In this article, the theoretical far-field acoustic beam pattern analytic formulations have been mathematically derived for a cylindrical array on an infinite rigid cylinder, after applying the Fourier series expansion, the Fourier sine or cosine transform, and the stationary phase method to the Helmholtz equation with boundary conditions. When the ratio of the array radius over the operating frequency wavelength was large, the horizontal (xoy) plane beam patterns demonstrated broadband CBP performances under the far-field conditions. The vertical (xoz) plane acoustic beam patterns are determined by the array vertical aperture shading's Fourier spectrum coupled with the residuals from the asymptotic approximations of the Hankel function and its derivative. The theoretical results matched with the results by Kirchhoff's integral numerical simulation with various horizontal shading examples for directional acoustic beams by the broadband CBP approach.

Surface electromyogram (sEMG) provides a non-invasive way to collect EMG signals. The sEMG signals acquired from the muscles of the forearm can be used to recognize the hand grasps and gestures. In this work, an automatic recognition algorithm to identify hand movements using sEMG signals has been proposed. The signals are decomposed into Fourier intrinsic band functions (FIBFs) using the Fourier decomposition method (FDM). The features like entropy, kurtosis, and L 1 norm are computed for each FIBF. Statistically relevant features are determined using the Kruskal Wallis test and used to train machine learning-based classifiers like support vector machine, k-nearest neighbor, ensemble bagged trees, and ensemble subspace discriminant. Two publicly available datasets are used to test the efficacy of the proposed algorithm. With an average accuracy of 99.49 % on the UCI dataset and 93.53 % on NinaPro DB5, the proposed method performs superior than the state-of-the-art algorithms. The performance of the proposed algorithm has also been analyzed in the presence of noise. The proposed method is based on Fourier theory, which makes it suitable for real-time implementation due to low computational complexity. It would help in the design of efficient and easy-to-use prosthetic hands.

Epilepsy is a disease recognized as the chronic neurological dysfunction of the human brain which is described by the sudden and excessive electrical discharges of the brain cells. Electroencephalogram (EEG) is a prime tool applied for the diagnosis of epilepsy. In this study, a novel and effective approach is introduced to decompose the non-stationary EEG signals using the Fourier decomposition method. The concept of position, velocity, and acceleration has been employed on the EEG signals for feature extraction using $$L^p$$ norms computed from Fourier intrinsic band functions (FIBFs). The proposed scheme comprises three main sections. In the first section, the EEG signal is decomposed into a finite number of FIBFs. In the second stage, the features are extracted from FIBFs and relevant features are selected by using the Kruskal–Wallis test. In the last stage, the significant features are passed on to the support vector machine (SVM) classifier. By applying 10-fold cross-validation, the proposed method provides better results in comparison to the state-of-the-art methods discussed in the literature, with an average classification accuracy of 99.96% and 99.94% for classification of EEG signals from the BONN dataset and the CHB-MIT dataset, respectively. It can be implemented using the computationally efficient fast Fourier transform (FFT) algorithm.

In the actual production, it is expected to find several sensitivity geometric errors which have great influence on machining accuracy, so as to provide references for the manufacturing, assembly, and other links of the machine tool, and fundamentally improve the working performance. To study this problem, a novel global sensitivity analysis (GSA) method is proposed. Based on the MBS theory, the spatial error model is established to analyze the local influence of geometric error on machining accuracy. An improved second-order partial correlation coefficient based on the Pearson product moment is proposed to analyze the correlation between geometric errors. In addition, the error parameters will change greatly in the stroke of the moving parts. However, the rapid fluctuation of geometric error value will have a dynamic impact on the machining accuracy of machine tools, which is rarely noticed in the previous sensitivity analysis. This change is defined as the fluctuation of error. The high fitting degree function of error-displacement is obtained by using the high order Fourier series and sine series. Then, the fluctuation of the error in the machining stroke is analyzed by using the derivative of the function to the displacement. Through geometric error characteristics (including the local influence, correlation, and fluctuation) are studied comprehensively, the GSA of error is carried out. Finally, taking a machining center as an example and combining the sensitivity analysis results, the improvement measures are proposed to verify the correctness of the method.

This paper contributes to the research of rhythmic behavior of a group of people, which, more or less synchronized, moves or jumps on a thin and elastic plate, thus performing a dynamically variable load. The analysis of the rhythmic behaviour of the crowd carried out on the basis of the experimental testing on the special steel test platform. The experiment consisted of sixteen measurements of live force and acceleration of the test platform. The dynamic loads caused by the mass of the human crowd and individuals had different intensities. The measurements of acceleration of the test platform were performed in order to estimate how the live human force influences on vibrations of machine structures. This research allows us to gain a picture of how serious the threats are from some human actions on the support structure of machines that are handled when performing works in industry, construction or mining. On the basis of these experiments, the mathematical models of the equivalent excitation forces were developed. The measured accelerations of the test platform tread surface and calculated dynamic coefficients of human force indicate that similar actions can seriously endanger balance of the support structure of some machine, and even, for example, can cause the main girder of the bridge crane to fall out. This and similar experiments allow us to formulate appropriate models of excitation loads by human force, which can then be used in simulation analyses in order to develop future systems of electronic protection of machines structures from adverse events.

The author gives numerical results on taking account of the influence of anisotropy of physicomechanical properties of free-edge cylindrical shell sleeves from orthotropic material on the stressed state in fuel assembles of the core of a nuclear rocket engine in their probable local radial interaction, which is important in designing.

Relevance. In design and calculation of civil engineering structures, several standard commercial software packages, which are successfully applied to solve everyday engineering problems, are traditionally used. However, when it is necessary to design the models of complex shape shell structures with defining surfaces based on parametric equations, such programs often have certain drawbacks. The aim of the work - analysis of existing types of commercial computational software packages in order to check which allow to design finite element models for shell structures with median surfaces of complex geometry given by parametric equations. Methods. The analysis of commercial computational software packages is carried out by studying the software manuals, and by building and calculating a model in the shape of a right helicoid as a test example. To evaluate the results of the stress-strain state of a shell with a middle surface in the form of a right helicoid, an analytical calculation method based on the Reissner’s equations and Fourier series expansion is used. Results. A review of modern commercial computational software packages as applied to models defined by parametric equations is carried out. A model for a shell structure with a median surface in the form of right helicoid is built. The numerical results of stress-strain behavior of the right helicoid are obtained and analyzed in comparison with the analytical solutions obtained using the Reissner’s equations with Fourier series expansion. The pros and cons of several popular means of software are presented.

This paper proposes an analytical model for the modular multilevel converter (MMC) based on the theory of harmonic balance, which removes the iteration process for traditional models. The proposed model considers dynamic harmonic interactions between the modulation of converters and passive elements in the MMC. By transferring the equations into frequency-domain as complex Fourier series, a steady-state harmonic model is created with singular coefficients matrix. Then, through the elimination of all DC components in dynamic model, the singular coefficient matrix can be derived to nonsingular one, and the order of it can be reduced. Finally, the typical open-loop analytical model with DC neutral grounded MMC is derived aim, and the time-domain simulations is used to validate the effectiveness of proposed model. The proposed model can be used to accelerate the simulation and analyze the influence of parameters to guide the design of MMC.

This study aims to take the compound planetary gear train as an example to investigate how the vibration isolator affects the dynamic characteristics of the gear system. The dynamic parameters are obtained from the finite element model of the gearbox case with the vibration isolators by the substructure method. The lumped mass method is used to construct the systematic coupled dynamic model of the compound planetary gear train with the marine twin-layer gearbox case. The dynamic response of the coupled system is calculated by the numerical calculation method of the Fourier series. The number of vibration isolators negatively affects the bearing forces of the input shaft, output shaft, and planets. The influence of the number of vibration isolators on LSCs is different in the differential stage and the encased stage. When the vibration isolators stiffness is less than 200 N/μm, the stiffness of the vibration isolator has a significant effect on the bearing forces of the input shaft, output shaft, and planets. The increase in the stiffness of the vibration isolator would increase the LSCs of the differential stage and decrease the LSCs of the encased stage. The number and stiffness of the vibration isolator have influences on the bearing forces and the LSCs. Compared with the LSCs in the differential stage, the LSCs in the encased stage are more sensitive to the number and stiffness of vibration isolators.

High-frequency parts of ocean wave spectra are strongly coupled to the local wind. Measurements of ocean wave spectra can be used to estimate sea surface winds. In this study, two deep neural networks (DNNs) were used to estimate the wind speed and direction from the first five Fourier coefficients from buoys. The DNNs were trained by wind and wave measurements from more than 100 meteorological buoys during 2014–2018. It is found that the wave measurements can best represent the wind information about 40 min previously because the high-frequency portion of the wave spectrum integrates preceding wind conditions. The overall root-mean-square error (RMSE) of estimated wind speed is ∼1.1 m s−1, and the RMSE of the wind direction is ∼ 14∘ when wind speed is 7–25 m s−1. This model can be used not only for the wind estimation for compact wave buoys but also for the quality control of wind and wave measurements from meteorological buoys.

We give congruences modulo powers of $p \in \{3, 5,7\}$ for the Fourier coefficients of certain modular functions in level $p$ with poles only at 0, answering a question posed by Andersen and the first author and continuing work done by the authors and Moss. The congruences involve a modulus that depends on the base $p$ expansion of the modular form's order of vanishing at $\infty$., Comment: arXiv admin note: text overlap with arXiv:1709.10189 Version 2: Corrected typos

This chapter helps the reader to understand the difference between periodic and nonperiodic signals and to become familiar with the Fourier transform. It explains how to apply the Fourier transform to the spectral analysis of nonperiodic signals. The chapter examines the main Fourier transform pairs and the main properties of the Fourier transform. It provides study examples of applications of the Fourier transform to the spectral analysis of various nonperiodic signals and systems. The chapter also discusses four types of signals – continuous periodic, continuous nonperiodic, discrete periodic, and discrete nonperiodic. It also discusses four types of the Fourier tools: continuous‐time Fourier series, continuous‐time Fourier transform, discrete Fourier transform (DFT), and discrete‐time Fourier transform. The chapter also why only DFT can be employed for digital signal processing and how DFT can be applied for the spectral analysis of both discrete periodic and discrete nonperiodic signals.

We study the computational hardness of recovering single bits of the private key in the supersingular isogeny Diffie–Hellman (SIDH) key exchange and similar schemes. Our objective is to give a polynomial-time reduction between the problem of computing the private key in SIDH to the problem of computing any of its bits. The parties in the SIDH protocol work over elliptic curve torsion groups of different order N . Our results depend on the parity of N . Our main result shows that if N is odd, then each of the top and lower O ( log log N ) bits of the private key is as hard to compute, with any noticeable advantage, as the entire key. A similar, but conditional, result holds for each of the middle bits. This condition can be checked, and heuristically holds almost always. The case of even N is a bit more challenging. We give several results, one of which is similar to the result for an odd N , under the assumption that one always succeeds to recover the designated bit. To achieve these results we extend the solution to the chosen-multiplier hidden number problem, for domains of a prime-power order, by studying the Fourier coefficients of single-bit functions over these domains.

Background Motion correction is mandatory for the functional Fourier decomposition magnetic resonance imaging (FD-MRI) of the lungs. Therefore, it is important to evaluate the quality of various image-registration algorithms for pulmonary FD-MRI and to determine their impact on FD-MRI outcome. Purpose To evaluate different image-registration algorithms for FD-MRI in functional lung imaging. Material and Methods Fifteen healthy volunteers were examined in a 1.5-T whole-body MR scanner (Magnetom Avanto, Siemens AG) with a non-contrast enhanced 2D TrueFISP pulse sequence in coronal view and free-breathing (acquisition time 45 s, 250 images). Three image-registration algorithms were used to compensate the spatial variation of the lungs (fMRLung 3.0, ANTs, and Elastix). Quality control for image registration was performed by edge detection (ED), quotient image criterion (QI), and dice similarity coefficient (DSC). Ventilation, perfusion, and a ventilation/perfusion quotient (V/Q) were calculated using the three registered datasets. Results Average computing times for the three image-registration algorithms were 1.0 ± 1.6 min, 38.0 ± 13.5 min, and 354 ± 78 min for fMRLung, ANTs, and Elastix, respectively. No significant difference in the quality of motion correction provided by different image-registration algorithms occurred. Significant differences were observed between fMRLung- and Elastix-based perfusion values ​​of the left lung as well as fMRLung- and ANTs-based V/Q quotient of the right and the entire lung ( P Conclusion The mandatory motion correction for functional FD-MRI of the lung can be achieved through different image-registration algorithms with consistent quality. However, a significantly difference in computing time between the image-registration algorithms still requires an optimization.

We give an asymptotic formula for traces of weak Maass forms at CM points with an effective bound on the error term. Upon specializing to the modular j-function, we deduce such a result for traces of singular moduli. Due to work of Zagier, and Bringmann and Ono, these traces of weak Maass forms at CM points appear as Fourier coefficients of half-integral weight weakly holomorphic modular forms. Hence, our results give effective upper bounds for these Fourier coefficients.

This article presents techniques into prediction and control of the radiated harmonic levels in time-modulated antenna arrays (TMAs). The effect of ramping on the controlling switching waveform, due to slew in the RF switches, is analyzed first. This is followed by a novel technique for controlling and reducing the fundamental carrier component (due to the Fourier series 0 Hz term) that is always produced by TMAs. A new bespoke, steerable, TMA RF hardware test platform is presented, using three gain states to pragmatically implement the proposed carrier reduction technique. The platform implementation utilizes binary logic control interfaces to the TMA, rather than analog control interfaces. Laboratory measurements using the test platform demonstrate a 16.5 dB reduction (limited by PCB emissions) in the level of the fundamental carrier component relative to the steered first harmonic, from a possible reduction of 21.3 dB. The array gain for the first harmonic beam is 2 dBi.

Time-of-flight (ToF) cameras are active imaging sensors able to capture the 3-D geometry of a scene. Objects can be then segmented and recognized from their 3-D geometry. Only very recently it has been shown that ToF cameras can also recognize the material on a per-pixel basis, as opposed to classical computer vision approaches, which rely on texture and operate per patches or regions. Differently, ToF-based material recognition takes profit of differences between the temporal impulse response function of different materials to distinguish them. Existing approaches use either raw data or processed depth measurements at different modulation frequencies to generate distinctive feature vectors for classification. In this letter we stress the importance of the bandlimited character of the material impulse response function (MIRF) and propose direct Fourier sampling. These Fourier coefficients are then used as set of features after appropriate complex scaling. Using orthogonal sensing functions enables classification with fewer but more informative measurements. Minimizing the number of measurements speeds up both acquisition, training, and classification. Moreover, 2-D superpixel segmentation in feature space allows for reliable classification with few queries per region. We demonstrate that the proposed approach allows for real-time simultaneous depth- and material-sensing ToF imaging.

Purpose: The subjective visual vertical (SVV) test is used to evaluate the otolith function in the inner ear. This study compared the differ ent balance ability according to the results of the SVV in healthy adults. Methods: This study recruited 30 normal healthy subjects who did not have neurological and musculoskeletal disorders. The subjects were divided into experimental and control groups based on the results of SVV: experimental group, >2°; control group

Medical image fusion helps in meaningfully combining, the information provided by various imaging sensors, targeting the clinical details of human organs. It is well known that the Magnetic Resonance Imaging (MRI) provides the structural content, whereas Positron Emission Tomography (PET) and Single Photon Emission Computed Tomography (SPECT) provides functional information. The structural and functional details are required in a single image, to accurately identify the abnormalities in the initial stages. We propose a combination of Fourier Decomposition Method (FDM), Principal Component Analysis (PCA) and maximum selection rule-based technique for generating MRI-PET and MRI-SPECT fused images. Here, FDM is used as an analysis tool, whereas PCA and maximum selection are used for generating the fusion mechanism. FDM helps to decompose the source images into meaningful layers called modes, based on the local features of the images. PCA a tool for dimensionality reduction preserves significant information from the image layers. Crucial details from the modes are properly combined using the rule of max selection. The proposed fusion methodology, when compared with the state-of-the-art fusion methods in terms of visual quality and objective metrics, exhibited promising performance.

Thermal infrared (TIR) imaging has been an indispensable tool in surveillance and remote sensing fields due to the characteristic of this spectrum that enables the sensing system to detect relatively warm targets, especially in low-light conditions. However, the acquired TIR images often suffer from observable stripe noise, which reduces the target detectability to some extent. To remove the noise and keep the image details, this letter proposes a novel method that combines the spectral processing technology with the image-guidance mechanism. Specifically, the frequency band contaminated by stripe noise is corrected with the corresponding Fourier coefficients of a guided image, which can be estimated by existing smoothing methods. Various experiments on the simulated and real TIR images show high performance and efficiency of the proposed method. In addition, in the application of small target detection, it is demonstrated that local contrast between the target and its background is well maintained and the signal-to-clutter ratio is increased when our method is performed.

For the investigation of the initial post-buckling of a column built in at one end, clamped in rotation with a flexible support at the other, the stability of the bifurcation point is studied using the Fourier series. The second-order variation of the potential energy is proved to be semi-positive-definite at the bifurcation point. When the disturbance matches the buckling mode, the fourth-order variation is positive for some flexible support stiffness, and negative for other flexible support stiffness. Based on the Koiter's initial post-buckling theory, the condition on the flexible support stiffness conducive to the unstable branch path is derived. The unstable branch paths indicate that the buckling load of the column will be sensitive to the imperfections

The classification of tomography images into non-healthy or healthy is a key pre-clinical state for patients. The training and feature extraction comprise the most time and memory consuming process...

This paper proposes a dynamic model for the first time in order to investigate nonlinear time-varying dynamic behavior of a drivetrain including parallel axis gears (such as spur and helical gears) and intersecting axis gears (such as spiral bevel gears). Flexibilities of shafts and bearings are included in the dynamic model by the use of finite element modeling. Finite element models of shafts are coupled with each other by the mesh models of gear pairs including backlash nonlinearity and fluctuating mesh stiffness. A system of nonlinear algebraic equations is established from the resulting nonlinear differential equations of motion by utilizing multi-harmonic harmonic balance method (HBM) in conjunction with continuous-time Fourier transform (CFT). Since the number of nonlinear equations is large, potential convergence problems are avoided by utilizing continuous-time Fourier transform, in contrast with gear dynamics studies that use discrete Fourier transform (DFT). Solutions obtained by utilizing CFT and DFT are compared, and the advantages of utilizing CFT are shown. Fourier coefficients are calculated by utilizing analytical integration rather than numerical integration for a further improvement in computational time. A new solution method, modal superposition method, is introduced for the first time to study nonlinear dynamics of drivetrains with multiple gear meshes, which is impractical if traditional solution methods are used due to the increased number of nonlinear equations. Using modal superposition method, the number of nonlinear equations becomes proportional to the number of modes employed which is significantly less than the number of degrees of freedom associated with nonlinearities, especially as the number of gear meshes in the drivetrain increases. Consequently, the proposed method decreases the computational effort drastically in the forced response analysis of multi-mesh, multi-stage gear systems and also makes it possible to model gear shafts by using finite element method. The resulting system of nonlinear algebraic equations is solved by utilizing Newton’s method with arc-length continuation. Solutions obtained by HBM are validated by the solutions obtained by direct numerical integration. Several parametric studies are carried out in order to investigate the effects of design parameters on the dynamics of the drivetrain. It is observed that nonlinear modeling of helical gear pairs is necessary if they are coupled with spur or spiral bevel gear pairs.

The geometric errors of rotary axes are crucial error sources of a five-axis machine tool. They directly affect the machining accuracy, and therefore become one of the most important items for accuracy design. In this paper, a prediction and identification method for the geometric errors of rotary axes on a five-axis machine tool is proposed. The prediction is realized by calculating the mapping relationship between tolerances and geometric errors of rotary axes, which is based on exploring rotary axes’ motion regulation and Fourier series fitting. Then in order to figure out the practical geometric errors of rotary axes, the identifying model is established based on homogeneous transform matrix (HTM). Double ball-bar (DBB) is adopted to test error motions of rotary axes. Finally, a demonstration experiment has been conducted for verifying the effectiveness and precision of the proposed prediction model. The experimental results show that the predicting model is able to reflect the motion principle of rotary axes’ kinematic errors. The SSE, which expresses residual sum of squares between estimated value and identified point, of ez(c),δx(c),ey(c),δz(c),ex(c), and δy(c), are 7.7716 × 10−11, 1.2064 × 10−4, 2.7838 × 10−10, 2.9639 × 10−7, 1.8966 × 10−10, and 2.7838 × 10−10, respectively. And R2, who represent fitting equation’s coefficient of determination, of abovementioned geometric errors, are 0.8978, 0.9876, 0.9978, 0.9453, 0.9985, and 0.9978, respectively. The computing results show that two kinds of curves are basically coincide, and the proposed method is proven to be feasibility.

In this letter, we focus on the trajectory design problem in wireless communications aided by unmanned aerial vehicles (UAVs), where a UAV serves multiple ground users for wireless transmission, to maximize the minimum transmission rate for all the ground users. A novel approach based on finite Fourier series (FFS) is proposed to reconstruct the trajectory with harmonics. Simulation results show that the FFS-based approach achieves similar max-min rate performance compared to the prevailing approach based on discrete waypoints (DW) while it is significantly less time-consuming due to a reduced number of variables.

The elastic stability of plates with simply supported edges (SSSS) and with two edges clamped and two simply supported (CSCS) under combination of bending, shear and patch load is investigated. General analytical approach for elastic buckling analysis of plates with different boundary conditions, subjected to any combination of in-plane loads, is presented. Exact solutions for pre-buckling stress distributions and double Fourier series for deflection functions within Ritz energy method guarantees accuracy of results and enabled very complex stability analysis. Combined in-plane loads action is very common during incremental bridge lunching and different stress conditions can occur in web girders. All analyses conducted so far regarding such problems are related to simply supported plate (SSSS). However, web girder is elastically restrained to the certain point depending on flanges rigidity and authors considered interesting to investigate behavior of plate with two opposite edges restrained and other two simply supported (CSCS) under same load conditions as simply supported plate. First part of the paper deals with patch load problem for plates with two different boundary conditions and evaluation of input data for bending-patch load (M-F), shear-patch load (V-F) and bending-shear-patch load (M-V-F) interaction curves and surfaces definition. Second part is dedicated to presentation, analysis and comparison of the interaction curves and surfaces for the cases of simply supported plate (SSSS) and plate with two clamped and two simply supported edges (CSCS), in order to obtain realistic bucking load ratios in accordance with boundary conditions.

In our previous work, a distributed moisture sensor based on the induced long-period fiber grating in the presence of moisture is proposed. The proposed structure is analyzed numerically (Opt Laser Technol 117:126–133, 2019). In this article, due to the axial symmetry and periodic structure of the proposed sensor, the Love’s potential and Fourier series are employed to obtain an analytical solution for the refractive index variation along the sensor versus moisture density. The analytical method reduces the computation time relative to our numerical calculation drastically. The analytical results are in good agreement with those that are obtained by numerical calculations. The analytical method is employed for the analysis and design of distributed moisture fiber sensor.

A non-cryogenic technology has been developed for the extraction of helium from natural gas in a membrane installation operating in an unsteady mode. The separating membrane in this setup consists of microcapsules – cenospheres. The microscopic dimensions of the walls of such capsules provide a high diffusion rate of helium, unattainable in installations with a stationary mode of operation. A wave technique for calculating membrane installations with an unsteady mode of operation has been developed. The calculation is carried out by expanding the input concentration signal in a Fourier series according to the eigenfrequencies of this periodic process. Moreover, each of its concentration eigenwaves, independently of the others, passes through a layer of microcapsules. At the output, all solutions for individual eigenwaves are added up. Using a specific example of the extraction of helium from natural gas, the capabilities of the new technology are demonstrated. It is shown that the transmission of natural gas through an installation with three apparatuses 10 m long filled with cenospheres makes it possible to achieve a helium recovery coefficient of 33%.

Nowadays, application of pulsed periodic fields in various technological devices is of interest, in particular for the influencing on a conductive media. In this paper solution of the problem of th...

The article is devoted to the improvement of the information technology previously developed by the authors for the analysis and forecasting of the number of new confirmed cases of the disease for the coronavirus COVID-19 caused by the SARS-CoV-2 infection, using the example of the daily total data of the current "wave" in Ukraine, taking into account various holidays and pseudo-holydays, which may have an abnormal effect. The previously created technology was operable only for the area of continuous growth of the values of one wave, and the improved one can already be used to analyze and predict data throughout the entire period, since it takes into account the multi-wave nature of this phenomenon. An algorithm for identifying the parameters of each wave is proposed. A number of mathematical relationships have been developed that allow, in a first approximation, to estimate the start, end and period of each wave, even in the case when one wave passes into another. A new empirical relationships is proposed to estimate the order of the Fourier series for describing the time process of each wave for only 10 % of its values at the top, since, as a rule, such data are available in an explicit form, otherwise the data will not be recognized as a separate wave. The ratios are derived separately for the case of only positive coefficients, when the peak is located to the left of the middle of the half-period, and separately - for the case of an alternating series, when the peak is located to the right of it. However, these approximate estimates are recommended to be refined within a certain range of possible values, since in the general case of different variants of the harmonic amplitude values, the proposed ratios can give underestimates. It is proposed to apply the model identified by this technology to predict the most pessimistic and most optimistic scenarios for the development of the phenomenon, that is, changes in the number of new confirmed cases of the disease for the coronavirus COVID-19 in the future in a given country. Python software was created based on the Kaggle platform, which is used both for Ukraine and for 69 other countries. Using the identified models, a number of important conclusions were obtained regarding understanding the patterns of the spread of coronavirus both in Ukraine and in other 69 countries of the world. The results were submitted to the Working Group on Mathematical Modeling of Problems Associated with the SARS-CoV-2 Coronavirus Epidemic in Ukraine.

This paper presents a detailed analysis of the electromagnetic force and vibration behavior of an axial flux permanent magnet synchronous machine (AFPMSM). First, the AFPMSM configuration and two types of dual three-phase winding are introduced. Subsequently, the electromagnetic force of the double-stator inner-rotor AFPMSM is investigated. Its spatial and temporal characteristics are derived analytically and validated through two-dimensional Fourier decomposition. A multiphysics model is established to calculate the vibration of the AFPMSM, which includes control, electromagnetic, structural, and vibration model. The accuracy of this multiphysics model is verified by the modal and vibration test. Furthermore, the vibration of the AFPMSM with three winding types considering current harmonics are calculated based on the multiphysics model. The vibration performance of the AFPMSM with three different winding types are compared and the mechanism of vibration is discussed. It was concluded that the novel detached winding could mitigate the vibration of dual three-phase AFPMSMs. Finally, the vibration test is carried out to validate the theoretical analysis and the experimental results agree well-with the simulation results. This paper provides an effective method for double-stator permanent magnet synchronous machine (PMSMs) to reduce vibration.

Electrocardiography (ECG) is the depiction of the hearts recorded electrical activity, obtained by attaching electrodes that are specifically designed to place at particular points of human body. The graphically represented signal has three main parts- P wave, QRS complex and thirdly T wave together giving normal ECG wave. Deviations in the normal graphical representation of ECG indicate types of cardiac disorders. An automatic system which involves MATLAB-based tool is being used to simulate synthetic ECG signals of cardiac pathology. The model of the pathological signals uses the real time clinical data of the pathologies and it is done with the help of Fourier series by mathematical modeling the ECG signal wave. This model is a useful tool that allows comparison with patient’s current ECG record collected by regular methods. Thus helps in the detection of pathologies that lead to serious cardiac arrhythmia.

This paper addresses a methodology to optimize PV panel cleaning schedule. PV system yield is impacted due to soiling on panel surface. This soiling changes during the system operation as a consequence of environmental conditions. In order to reduce the impact of soiling accumulation, the panel surface must be cleaned. However, cost and frequency of cleaning can affect plant revenue. Therefore, to enhance financial performance, an optimal cleaning strategy must be selected. This strategy depends mostly on energy cost, soiling rate, cleaning costs, and system efficiency. Hence, the model proposed in this work takes into account these variables in order to support the decisions during the assessment of PV yield. The methodology was evaluated through two irradiation profiles with different associated costs. As a result, the methodology made it possible to estimate a cleaning strategy optimizing the incomes under different scenarios.

A Fourier series is an expansion of a periodic function f(x) in terms of an infinite sum of sines and cosines. Fourier series make use of the orthogonality relationships of the sine and cosine functions. The computation and study of Fourier series are known as harmonic analysis. It is a useful way to break up an arbitrary periodic function into a set of simple terms that can be plugged in, solved individually, and then recombined to obtain the solution to the original problem or an approximation to it to whatever accuracy is desired or practical. This paper deals with the mathematical basics of Fourier series using trigonometric functions. This is the basic for a discrete Fourier transform. It al-lows transforms discrete data to frequency data or vice versa, transforming frequency data to discrete data. The most important part of the article is the application of the Fourier series and the Fourier transform to metrology - specifically on the roundness profile. There are mentioned mathematical relationships for the practical use of harmonic analysis and the detailed method of determining the actual phase. General relationships do not give accurate results, since the phase shift quadrant. The results of the harmonic analysis authors applied graphically on a concrete example of a roundness profile. The individual harmonic components are shown in the linear and polar graphs as well as the resulting roundness profile. Fourier analysis knowledge will contribute to a better analysis of the roundness profiles measured on the drawn tubes that will be investigated in the research project.

Electric solar wind sail (E-sail) is an innovative propulsion system, which can generate low and continuous thrust without any propellant by reflecting ions from the solar wind. Because the propulsive acceleration of E-sail is low and continuous, its trajectory is usually characterized by long flight time. In order to explore more flight plans, rapid trajectory design is useful for preliminary mission analysis and design. This paper presents a method for rapid generation of minimum-time, three-dimensional trajectories for an E-sail using the finite Fourier series shape-based method. Unlike the more conventional electric thruster, the thrust vector of an E-sail is constrained. In order to consider the characteristics of the E-sail thrust, inequality constraints of thrust acceleration are investigated based on a recent thrust model. The numerical simulation results show that the proposed method is useful to quickly design the flight trajectory of the E-sail by considering the actual characteristics of the thrust vector.