Journal articles on the topic 'Modal summation method'
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La Mura, C., T. B. Yanovskaya, F. Romanelli, and G. F. Panza. "Three-Dimensional Seismic Wave Propagation by Modal Summation: Method and Validation." Pure and Applied Geophysics 168, no. 1-2 (May 22, 2010): 201–16. http://dx.doi.org/10.1007/s00024-010-0165-2.
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Qiu, Ju, Wei Lian, Huaxiang Rao, Caiyun Wang, Tengteng Luo, and Jiali Tang. "Localization of Vibration Weak Position of Composites Based on Weighted Modal Strain Energy Summation." Journal of Composites Science 6, no. 11 (October 31, 2022): 324. http://dx.doi.org/10.3390/jcs6110324.
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In this paper, two typical examples are used to illustrate the weak position of aircraft structure in the process of vibration. Through the modal analysis of the typical composite plate and I-shaped beam, the first 20-order modal strain energy of the plate is extracted, which is difficult to locate the weak spot due to the highly scattered location of the higher modal strain energy. The modal participation factor is introduced as the weight factor of the summation of the modal strain energy. The modal participation factor is large, the weighting factor is large, and the high modal strain energy of the composite plate moves diagonally in the 45° direction of the composite plate and the high strain energy region is consistent with the previous modes of the plate. This is the result of the weak in-plane shear stiffness of the composite panel, which shows the effectiveness of the mode weighted summation method. The I-shaped composite beam uses the modal strain energy summation of the weight factor, and the higher modal strain energy is concentrated on the middle part of the beam and at 1/4 and 3/4 of it. Therefore, the weak part of the vibration can be clearly identified. The higher modal strain energy is extracted by the method proposed to this paper, which can be used as a reference to structural design and dynamic on-line monitoring.
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SILVA, R. L., L. M. TRAUTWEIN, C. S. BARBOSA, L. C. ALMEIDA, and G. H. SIQUEIRA. "Empirical method for structural damage location using dynamic analysis." Revista IBRACON de Estruturas e Materiais 13, no. 1 (February 2020): 19–31. http://dx.doi.org/10.1590/s1983-41952020000100003.
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Abstract This paper presents the use of numerical model techniques for identification and damage location adopting the Modal Curvature Difference (MCD) method as reference for the analysis of a simply supported concrete structure. Then, an empirical formulation to detect damages in this structure is proposed. In this method, called Acceleration Summation Difference (ASD), the difference of acceleration amplitude between intact and damaged structures are calculated for concrete plates simply supported on rubber bearings. During the analyses, the finite element models were developed using SAP2000® software. The results obtained depicted that it is possible to determine the approximate position of one or more damages in the structure, with some restrictions, and the proposed ASD method presented good correlation to localize the position of single or multiple damages.
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Dong, Chunguang, Ronghui Wang, Xiaoxia Zhen, and Haonan Ni. "Free vibration of summation and difference resonance of the vertical cable and other coupled structural members." Advances in Structural Engineering 21, no. 5 (October 6, 2017): 707–20. http://dx.doi.org/10.1177/1369433217729515.
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Free vibration of summation and difference resonance of the vertical cable and other coupled structural members were investigated in this article. A model of a vertical cable and two mass–springs was built, with the sling considered to be geometrically nonlinear, and the upper and lower connecting structural members were taken as two mass–springs. Assuming the displacement of the sling, modal superposition method and D’Alembert principle were used to derive the dynamic equilibrium equations of the coupled structure. The nonlinear dynamic equilibrium equations were studied by means of multiple scales method, and the second-order approximation solutions of single-modal motion of the system were obtained. Numerical examples were presented to discuss the amplitude responses as functions of time of free vibration, with and without damping, respectively. Additionally, fourth-order Runge–Kutta method was directly used for the nonlinear dynamic equilibrium equations to complement and verify the analytical solutions. The results show that the coupled system performs strongly nonlinear and coupled characteristics, which is useful for engineering design.
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Kaveh, A., H. Rahami, and Iman Shojaei. "An efficient method for seismic analysis of structures." Engineering Computations 32, no. 6 (August 3, 2015): 1708–21. http://dx.doi.org/10.1108/ec-07-2014-0159.
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Purpose – The purpose of this paper is to present an efficient method for dynamic analysis of structures utilizing a modal analysis with the main purpose of decreasing the computational complexity of the problem. In traditional methods, the solution of initial-value problems (IVPs) using numerical methods like finite difference method leads to step by step and time-consuming recursive solutions. Design/methodology/approach – The present method is based on converting the IVP into boundary-value problems (BVPs) and utilizing the features of the latter problems in efficient solution of the former ones. Finite difference formulation of BVPs leads to matrices with repetitive tri-diagonal and block tri-diagonal patterns wherein the eigensolution and matrix inversion are obtained using graph products rules. To get advantage of these efficient solutions for IVPs like the dynamic analysis of single DOF systems, IVPs are converted to boundary-value ones using mathematical manipulations. The obtained formulation is then generalized to the multi DOF systems by utilizing modal analysis. Findings – Applying the method to the modal analysis leads to a simple and efficient formulation. The laborious matrix inversion and eigensolution operations, of computational complexities of O(n2.373) and O(n3), respectively, are converted to a closed-form formulation with summation operations. Research limitations/implications – No limitation. Practical implications – Swift analysis has become possible. Originality/value – Suitability of solving IVPs and modal analysis using conversion and graph product rules is presented and applied to efficient seismic optimal analysis and preliminary design.
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Liu, Zhong-Sheng, Kun Wang, Cheng Huang, and Su-Huan Chen. "An extended hybrid method for contribution due to truncated lower- and higher-frequency modes in modal summation." Engineering Structures 18, no. 7 (July 1996): 558–63. http://dx.doi.org/10.1016/0141-0296(95)00123-9.
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Lee, Jongsuh. "Estimation Modal Parameter Variation with Respect to Internal Energy Variation Based on the Iwan Model." Applied Sciences 9, no. 20 (October 12, 2019): 4290. http://dx.doi.org/10.3390/app9204290.
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Typical factors that cause nonlinear behavior in structures are geometric nonlinearity, force and displacement boundary condition nonlinearities, and material nonlinearity. The nonlinearity caused by an increase of the internal energy in built-up structures is mostly due to the displacement boundary condition induced by the contact interface region. This study proposes an experimental mode analysis technique that predicts changes in natural frequencies and damping ratios when the external excitation force increases in a structure’s contact surfaces. Specifically, the nonlinearity of the dynamic characteristics induced by the contact region is described by the constitutive Iwan model. Next, an estimation method was developed for two parameters among the four of the Iwan model. This study used a modal analysis method. As an extension of a previous study, the approximate form of the harmonic excitation-induced force was determined in closed form. The configuration of the numerical model for the full structure was introduced from this resultant form. By using these numerical results, responses in the full structure, according to the harmonic excitation, have been represented in mode summation form. This research proposes an estimation method for two parameters among the four of the constitutive model. The proposed method was verified by simulations conducted with the lumped model and by experiments conducted on a partially connected double beam.
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Zhang, Tong, Ludi Kang, Xin Li, Hongbo Zhang, and Bilong Liu. "Sound Transmission Prediction of Sandwich Plates With Honeycomb and Foam Cores and an Emphatic Discussion on Radiation Terms." International Journal of Acoustics and Vibration 26, no. 1 (March 30, 2021): 70–79. http://dx.doi.org/10.20855/ijav.2020.25.11735.
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When applying the modal summation method to the sound transmission loss (STL) prediction of various plates, the assumption of the blocked sound pressure, or alternatively speaking, ignoring sound radiation terms, has obvious simplicity and is sometimes used for the single-layered panels, rib-stiffened plates or heavily damped sandwich plates. For light-weighted sandwich plates with honeycomb and foam cores, however, this assumption is somewhat in doubt and worth examining. Based on sixth-order differential equations governing the flexural vibration of sandwich plates, the prediction formula of STL is derived by the modal summation approach. Theoretical predictions were validated by measurement data. Next, the theoretical formula of STL under the assumption of the blocked sound pressure was examined. The STL discrepancies of sandwich plates caused by sound radiation terms are illustrated. It was found that the STL discrepancies of sandwich plates were closely related to frequency, reached their peak value at the coincidence frequency region. The results indicate that the sound radiation terms, or the couplings between the radiated sound pressure and the plate response, should not be ignored for the prediction of STL for sandwich plates with honeycomb and foam cores.
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Zhang, Zhiyi, Yong Chen, Hongguang Li, and Hongxing Hua. "Simulation and Experimental Study on Vibration and Sound Radiation Control with Piezoelectric Actuators." Shock and Vibration 18, no. 1-2 (2011): 343–54. http://dx.doi.org/10.1155/2011/509675.
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FEM/BEM is adopted to model the interaction between the fluid and structures. In the modeling, modal truncation and inertial coupling are applied to sufficiently reduce the coupled model order. This approach is adopted for the purpose of constructing a modal model in the time domain. Active vibration control is realized with piezoelectric actuators and an adaptive method. In the control, the summation of vibration responses is used as the control error since the integral of acceleration on the plate surface is approximately proportional to the far field sound pressure. A rigidly baffled plate connected with a mass through one piezoelectric actuator is simulated at first. In the experiment, the plate is excited by a rotating eccentric mass and controlled with four piezoelectric actuators. The results have shown that active vibration control with the piezoelectric actuators can lead to a noticeable attenuation in sound pressure.
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Shen, Runjie, Danqiong Hua, Yiying Wang, Ruimin Xing, and Min Ma. "Ultra-short-time prediction technology of wind power station output based on variational mode decomposition and particle swarm optimization least squares vector machine." E3S Web of Conferences 185 (2020): 01051. http://dx.doi.org/10.1051/e3sconf/202018501051.
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Wind power is developing rapidly in the context of sustainable development, and a series of problems such as wind curtailment and power curtailment have gradually emerged. The forecast of power generation output has become one of the hotspots of current research. This paper proposes a wind power plant output ultra-short-time prediction technology based on variational modal decomposition and particle swarm optimization least squares vector machine. Variational Modal Decomposition (VMD) method decomposes the historical output data of wind power plants at multiple levels. At the same time, it explores the impact of various decomposition methods such as EMD decomposition on the prediction accuracy, and uses the least squares support vector machine based on particle swarm optimization algorithm. Predictive summation is performed on each level of data separately to obtain a more accurate prediction effect, which has a certain improvement in prediction accuracy compared with traditional prediction algorithms.
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Tan, Guojin, Wensheng Wang, Yongchun Cheng, Haibin Wei, Zhigang Wei, and Hanbing Liu. "Dynamic Response of a Nonuniform Timoshenko Beam with Elastic Supports, Subjected to a Moving Spring-Mass System." International Journal of Structural Stability and Dynamics 18, no. 05 (May 2018): 1850066. http://dx.doi.org/10.1142/s0219455418500669.
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This paper is concerned with the dynamic response of a nonuniform Timoshenko beam with elastic supports subjected to a moving spring-mass system. The modal orthogonality of nonuniform Timoshenko beams and the corresponding overall matrix of undetermined coefficients are derived. Then the natural frequencies and mode shapes of nonuniform Timoshenko beams are obtained by the Runge–Kutta method and cubic spline interpolation method. By using the Newmark-[Formula: see text] method and the mode summation method, the vibration equation of Timoshenko beams subjected to a moving spring-mass system was established. A comparison of results between the proposed method and finite element method reveals that this method possesses favorable accuracy for dynamic response analysis. In numerical examples, the effects of the support spring and moving spring-mass system on Timoshenko beams have been examined in detail.
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Xi, Z. C., G. R. Liu, K. Y. Lam, and H. M. Shang. "A Strip Element Method for Analyzing Wave Scattering by a Crack in an Axisymmetric Cross-Ply Laminated Composite Cylinder." Journal of Applied Mechanics 67, no. 2 (December 7, 1999): 427–29. http://dx.doi.org/10.1115/1.1303800.
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A strip element method is presented for analyzing waves scattered by a crack in an axisymmetric cross-ply laminated composite cylinder. The cylinder is at the outset discretized as axisymmetric strip elements through the radial direction. The application of the Hamilton variational principle develops a set of governing ordinary differential equations. The particular solutions to the resulting equations are found using a modal analysis approach in conjunction with the Fourier transform technique. The complementary solutions are formulated by the superposition of eigenvectors, the unknown coefficients of which are determined from axial stress boundary conditions at the tips of the crack. The summation of the particular and complementary solutions gives the general solutions. Numerical examples are given for cross-ply laminated composite cylinders with radial cracks. The results show that the present method is effective and efficient. [S0021-8936(00)00202-6]
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LEE, JONGSUH, SEMYUNG WANG, PETER KINDT, BERT PLUYMERS, and WIM DESMET. "DAMPING ANALYSIS WITH RESPECT TO ROLLING SPEED BY ANALYTIC SOLUTION OF A FLEXIBLE RING MODEL AND ITS FREQUENCY RESPONSE FUNCTION DERIVATION BY MODAL SUMMATION METHOD." International Journal of Applied Mechanics 06, no. 05 (October 2014): 1450054. http://dx.doi.org/10.1142/s1758825114500549.
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In this research, a modal approach has been adopted to analyze the dynamic characteristics of the rolling tire by a ring model. Previously, most of the researchers focused on the changes in natural frequencies with respect to the rotational speed (in global coordinate) only. In this research, the change in the damping has also been taken into account by including a damping term in the ring model equations. The bi-orthogonal property which is used to obtain the Frequency Response Functions (FRFs) of a rotor/bearing system described in Cartesian coordinate has been applied to the ring model described in cylindrical coordinate to obtain the FRFs. The obtained damping values and FRFs from the analytic model are then compared with experimental results. Moreover, the physical meanings of the results are analyzed, based on experimental data of a stationary tire and a rolling tire at 60 km/h and 100 km/h.
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Yu, S. D., and F. Xi. "Free Vibration Analysis of Planar Flexible Mechanisms." Journal of Mechanical Design 125, no. 4 (December 1, 2003): 764–72. http://dx.doi.org/10.1115/1.1626130.
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This paper presents a methodology for accurate free vibration analysis of planar flexible mechanisms. Each flexible body is considered as a beam and modelled using higher-order beam elements for longitudinal and flexural deformations. The global equations of motion for a mechanism consisting of multiple flexible bodies are formulated using the augmented Lagrange equations. Free vibration analyses are conducted at desired fast Fourier configurations to determine instantaneous structural natural frequencies and structural mode shapes. Dynamical frequencies and dynamical mode shapes incorporating the gyroscopic effects and dynamic axial loads are obtained using the modal summation method. Numerical results and comparisons are given for a rotating beam and two four-bar crank-rocker mechanisms.
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Zhu, J., A. H. Shah, and S. K. Datta. "Transient Response of a Composite Plate With Delamination." Journal of Applied Mechanics 65, no. 3 (September 1, 1998): 664–70. http://dx.doi.org/10.1115/1.2789109.
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Transient response of a composite plate with a near-surface delamination has been studied in this paper. A new technique developed by the authors to evaluate the Cauchy Principal Value integrals and the weakly singular integrals involved in the boundary integral equations has been employed and modifided to treat the corner points on the boundary. The time harmonic Green’s functions appearing in the boundary integral equation are evaluated by combining a stiffness method and the modal summation technique. To circumvent the difficulties associated with the evaluation of hypersingular integrals for cracks, the multidomain technique is employed. The accuracy and efficiency of the method are checked by comparing the displacements in a uniaxial graphite-epoxy plate containing a delamination with results obtained by a hybrid method. It is shown that the presence of the delamination significantly alters the surface response spectra of the plate. Results are presented in both time and frequency domains. The results show that the technique would be useful for ultrasonic nondestructive evaluation of defects in composite and anisotropic plates, and for studying dynamic response of such plates to impact.
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ZHANG, YAN-LEI, and LI-QUN CHEN. "STEADY-STATE RESPONSE OF PIPES CONVEYING PULSATING FLUID NEAR A 2:1 INTERNAL RESONANCE IN THE SUPERCRITICAL REGIME." International Journal of Applied Mechanics 06, no. 05 (October 2014): 1450056. http://dx.doi.org/10.1142/s1758825114500562.
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The work investigates steady-state responses of a pipe conveying fluid with a harmonic component of flow speed superposed on a constant mean value in the supercritical regime. If the flow speed exceeds a critical value, the straight configuration of the pipe becomes unstable and bifurcates into two stable curved configurations. The transverse motion measured from each of the curved equilibrium configurations is governed by a nonlinear integro-partial-differential equation. The Galerkin method is employed to discretize the governing equation into a set of coupled nonlinear ordinary differential equations with gyroscopic terms. For the pipes in the supercritical regime, the method of multiple scales is used to determine the steady-state in the vicinity of two-to-one resonance. In the presence of the internal resonance, the subharmonic, the superharmonic and the summation, and the difference resonances exist due to the pulsating fluid. The amplitude–frequency relationships are established with the emphasis on the effects of the viscosity, the pulsating amplitude, the nonlinearity, and the mean flow speed. Some nonlinear phenomena such as the appearance of the peak or jumps pertaining to modal interaction are demonstrated. The numerical integration results are in agreement with the analytical predictions.
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BOUCHAGE, GERALDINE, and MICHAEL I. TAROUDAKIS. "FLUCTUATIONS OF THE MODAL ARRIVAL TIMES DUE TO LINEAR INTERNAL WAVES: APPLICATION TO INVERSION." Journal of Computational Acoustics 14, no. 04 (December 2006): 469–87. http://dx.doi.org/10.1142/s0218396x06003104.
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It is well known that internal waves in the ocean are an important source of environmental variability which has serious effects in the structure of an acoustic field due to a known source. When measurements of the acoustic field form the input data for an inversion procedure aiming at the recovery of the environmental parameters, the information they carry on includes the internal wave effects. It is therefore natural to assume that neglecting the effects of the internal waves in an inversion procedure based on acoustic field measurements, errors are induced in the inversion. The paper deals with this problem and addresses the case of inversion schemes using travel time information of an acoustic signal. Using a statistical 2D model of the internal waves, based on the Garrett and Munk spectrum, the spatial and temporal evolution of the internal waves field as well as the fluctuations of the sound speed profile is estimated for a characteristic shallow-water environment. Considering a sound speed anomaly in the water column as the oceanographic feature to be recovered, the paper studies the influence of the internal waves field on the modal travel time information obtained through the propagation of a tomographic signal through this environment. The sound speed anomaly denoted as "current" is described by a suitable Gaussian function. Using an analytical expression based on a perturbation approach, the difference in the modal arrival times calculated for a background environment and a perturbed one (considering that the sound speed perturbations are due either to a current or to the summation of a current and of the internal waves field) was calculated for each propagating mode of the waveguide. These calculations led to the conclusion that the internal waves have a non-negligible impact on the arrival times and that the maximum amplitude of a current can be under- or overestimated of several meters per second when these waves are not taken into account in the inversion method, whereas they are present in the oceanic medium.
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Sun, Cheng, Zailin Yang, and Guanxixi Jiang. "Stable Symmetric Matrix Form Framework for the Elastic Wave Equation Combined with Perfectly Matched Layer and Discretized in the Curve Domain." Symmetry 12, no. 2 (February 1, 2020): 202. http://dx.doi.org/10.3390/sym12020202.
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In this paper, we present a stable and accurate high-order methodology for the symmetric matrix form (SMF) of the elastic wave equation. We use an accurate high-order upwind finite difference method to define spatial discretization. Then, an efficient complex frequency-shifted (CFS) unsplit multi-axis perfectly matched layer (MPML) is implemented using the auxiliary differential equation (ADE) that is used to build higher-order time schemes for elastodynamics in the unbounded curve domain. It is derived to be compatible with SMF. The SMF framework has a general form of a hyperbolic partial differential equation (PDE) that can be expanded to different dimensions (2D, 3D) or different wave modal (SH, P-SV) without requiring significant modifications owing to a simplified process of derivation and programming. Subsequently, an energy analysis on the framework combined with initial boundary value problems is conducted, and the stability analysis can be extended to a semi-discrete approximation similarly. Thus, we propose a semi-discrete approximation based on ADE CFS-MPML in which the curve domain is discretized using the upwind summation-by-parts (SBP) operators, and where the boundary conditions are enforced weakly using the simultaneous approximation terms (SAT). The proposed method’s robustness and adequacy are illustrated by conducting several numerical simulations.
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Triantafyllidis, Petros, Panagiotis M. Hatzidimitriou, Nikos Theodulidis, Peter Suhadolc, Costas Papazachos, Dimitris Raptakis, and Kostas Lontzetidis. "Site effects in the city of Thessaloniki (Greece) estimated from acceleration data and 1D local soil profiles." Bulletin of the Seismological Society of America 89, no. 2 (April 1, 1999): 521–37. http://dx.doi.org/10.1785/bssa0890020521.
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Abstract In this study, the site effects on seismic ground motion in the city of Thessaloniki (Greece) are estimated by applying experimental methods on acceleration data and theoretical modeling. The technique of standard spectral ratio (SSR) is applied to a reference station located on rock, while the horizontal-to-vertical spectral ratio (HVSR) technique is applied to earthquake records (entire record length including P and S waves) as well as on noise recordings. In addition, the SSR method is also applied to the vertical components. The results from all methods are compared in terms of resonant frequencies and amplification levels. The fundamental resonant frequency is identified by all methods, while the average amplification level is generally underestimated when the HVSR technique is used. An attempt is made to correlate the site amplifications computed in this study with the observed macroseismic intensities reported at the same sites for the 20 June 1978 earthquake. A relation of the form, δI=α+b⋅log[SSℛ¯(f)] is derived, where δI is the intensity increment with respect to the intensity of the reference station and SSR(ƒ) is the mean amplification factor obtained at each station using the SSR technique for a certain frequency band. In the numerical approach, we construct complete strong-motion synthetics using the modal summation method for the P-SV waves up to frequencies of 10 Hz. As input, four point sources are used, located at different distances and azimuths from the stations. Ratios of response spectra of the local 1D over the regional 1D synthetic seismograms are calculated. The obtained mean spectral amplifications are compared with those derived from experimental data, and the two sets are found to be consistent at most stations.
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Leger, P., and E. L. Wilson. "Modal summation methods for structural dynamic computations." Earthquake Engineering & Structural Dynamics 16, no. 1 (January 1988): 23–27. http://dx.doi.org/10.1002/eqe.4290160103.
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Weatherly, Jessie, Piero Macchi, and Anatoliy Volkov. "On the calculation of the electrostatic potential, electric field and electric field gradient from the aspherical pseudoatom model. II. Evaluation of the properties in an infinite crystal." Acta Crystallographica Section A Foundations and Advances 77, no. 5 (July 29, 2021): 399–419. http://dx.doi.org/10.1107/s2053273321005532.
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The previously reported exact potential and multipole moment (EP/MM) method for fast and precise evaluation of the intermolecular electrostatic interaction energies in molecular crystals using the pseudoatom representation of the electron density [Nguyen, Macchi & Volkov (2020), Acta Cryst. A76, 630–651] has been extended to the calculation of the electrostatic potential (ESP), electric field (EF) and electric field gradient (EFG) in an infinite crystal. The presented approach combines an efficient Ewald-type summation (ES) of atomic multipoles up to the hexadecapolar level in direct and reciprocal spaces with corrections for (i) the net polarization of the sample (the `surface term') due to a net dipole moment of the crystallographic unit cell (if present) and (ii) the short-range electron-density penetration effects. The rederived and reported closed-form expressions for all terms in the ES algorithm have been augmented by the expressions for the surface term available in the literature [Stenhammar, Trulsson & Linse (2011), J. Chem. Phys. 134, 224104] and the exact potential expressions reported in a previous study [Volkov, King, Coppens & Farrugia (2006), Acta Cryst. A62, 400–408]. The resulting algorithm, coded using Fortran in the XDPROP module of the software package XD, was tested on several small molecular crystal systems (formamide, benzene, L-dopa, paracetamol, amino acids etc.) and compared with a series of EP/MM-based direct-space summations (DS) performed within a certain number of unit cells generated along both the positive and negative crystallographic directions. The EP/MM-based ES technique allows for a noticeably more precise determination of the EF and EFG and significantly better precision of the evaluated ESP when compared with the DS calculations, even when the latter include contributions from an array of symmetry-equivalent atoms generated within four additional unit cells along each crystallographic direction. In terms of computational performance, the ES/EP/MM method is significantly faster than the DS calculations performed within the extended unit-cell limits but trails the DS calculations within the reduced summation ranges. Nonetheless, the described EP/MM-based ES algorithm is superior to the direct-space summations as it does not require the user to monitor continuously the convergence of the evaluated properties as a function of the summation limits and offers a better precision–performance balance.
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Miles, M. D., and E. R. Funke. "A Comparison of Methods for Synthesis of Directional Seas." Journal of Offshore Mechanics and Arctic Engineering 111, no. 1 (February 1, 1989): 43–48. http://dx.doi.org/10.1115/1.3257137.
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Numerical models for synthesis of directional seas are evaluated. Several authors have recently reported limitations associated with the commonly used double summation model which is neither ergodic nor spatially homogeneous for a finite number of terms. In order to overcome these problems, a modified double summation model is presented which uses unidirectional, narrow-band random wave trains as the fundamental components rather than plane sinusoidal waves. Various alternatives for generating the fundamental wave trains are investigated by numerical simulation and results are also compared to a simpler single summation wave model.
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Hamdan, Hamdan, Nikos Economou, Antonis Vafidis, Maksim Bano, and Jose Ortega-Ramirez. "A New Approach for Adaptive GPR Diffraction Focusing." Remote Sensing 14, no. 11 (May 26, 2022): 2547. http://dx.doi.org/10.3390/rs14112547.
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Several researchers have utilized multipath summation to manage the common problem of scattered energy within GPR sections. Such energy results in degrading the lateral resolution and continuity of reflectors. If detailed velocity models are known, then it is fairly easy to focus the scattered energy by means of conventional migration methods. However, this is rarely the case in GPR sections, as the common-offset antenna array is mostly used, and therefore cannot provide velocity models. This gives an important advantage for the multipath summation method, which has proved to be successful in focusing such diffractions, without the need to build a detailed migration velocity field model. This multipath summation method is based on stacking (summation) of constant velocity migrated sections (weighted or not) over a predefined velocity range. The main drawback of this technique is the high computational cost and the need for user interference to select the appropriate stacking weights. We developed an improved implementation of the weighted multipath summation method that reduces both the computational cost, and the user interference in stacking weights selections. This data adaptive methodology can expedite the migration process, suppress the need for a detailed velocity model, and reduce the user subjectivity. Moreover, a data adaptive spectral scaling scheme was developed. This is applied on the output of the multipath summation process to reduce the expected blurriness in the resulting GPR sections.
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Harlow, D. G., and T. J. Delph. "A Probabilistic Model for Creep-Fatigue Failure." Journal of Pressure Vessel Technology 119, no. 1 (February 1, 1997): 45–51. http://dx.doi.org/10.1115/1.2842265.
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We outline here a method for incorporating the scatter observed in creep rupture times and fatigue cycles-to-failure into a probabilistic model for creep-fatigue failure. We do this within the context of the well-known damage fraction summation rule. Various numerical methods for calculating the probability of failure for given creep-fatigue loading cycles are discussed.
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Popov, Mikhail M., Nikolay M. Semtchenok, Peter M. Popov, and Arie R. Verdel. "Depth migration by the Gaussian beam summation method." GEOPHYSICS 75, no. 2 (March 2010): S81—S93. http://dx.doi.org/10.1190/1.3361651.
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Seismic depth migration aims to produce an image of seismic reflection interfaces. Ray methods are suitable for subsurface target-oriented imaging and are less costly compared to two-way wave-equation-based migration, but break down in cases when a complex velocity structure gives rise to the appearance of caustics. Ray methods also have difficulties in correctly handling the different branches of the wavefront that result from wave propagation through a caustic. On the other hand, migration methods based on the two-way wave equation, referred to as reverse-time migration, are known to be capable of dealing with these problems. However, they are very expensive, especially in the 3D case. It can be prohibitive if many iterations are needed, such as for velocity-model building. Our method relies on the calculation of the Green functions for the classical wave equation by per-forming a summation of Gaussian beams for the direct and back-propagated wavefields. The subsurface image is obtained by cal-culating the coherence between the direct and backpropagated wavefields. To a large extent, our method combines the advantages of the high computational speed of ray-based migration with the high accuracy of reverse-time wave-equation migration because it can overcome problems with caustics, handle all arrivals, yield good images of steep flanks, and is readily extendible to target-oriented implementation. We have demonstrated the quality of our method with several state-of-the-art benchmark subsurface models, which have velocity variations up to a high degree of complexity. Our algorithm is especially suited for efficient imaging of selected subsurface subdomains, which is a large advantage particularly for 3D imaging and velocity-model refinement applications such as subsalt velocity-model improvement. Because our method is also capable of providing highly accurate migration results in structurally complex subsurface settings, we have also included the concept of true-amplitude imaging in our migration technique.
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Merzlikin, Dmitrii, and Sergey Fomel. "Analytical path-summation imaging of seismic diffractions." GEOPHYSICS 82, no. 1 (January 1, 2017): S51—S59. http://dx.doi.org/10.1190/geo2016-0140.1.
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Diffraction imaging aims to emphasize small subsurface objects, such as faults, fracture swarms, and channels. Similar to classical reflection imaging, velocity analysis is crucially important for accurate diffraction imaging. Path-summation migration provides an imaging method that produces an image of the subsurface without picking a velocity model. Previous methods of path-summation imaging involve a discrete summation of the images corresponding to all possible migration velocity distributions within a predefined integration range and thus involve a significant computational cost. We have developed a direct analytical formula for path-summation imaging based on the continuous integration of the images along the velocity dimension, which reduces the cost to that of only two fast Fourier transforms. The analytic approach also enabled automatic migration velocity extraction from diffractions using a double path-summation migration framework. Synthetic and field data examples confirm the efficiency of the proposed techniques.
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Ma, Binhui, Zhiyong Hu, Zhuo Li, Kai Cai, Minghua Zhao, Chengbin He, Qiunan Chen, Bingchu Chen, and Xiaocheng Huang. "A Three-Section-Settlement Calculation Method for Composite Foundation Reinforced by Geogrid-Encased Stone Columns." Advances in Civil Engineering 2021 (April 22, 2021): 1–10. http://dx.doi.org/10.1155/2021/5576713.
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The analysis of the bearing characteristics and deformation mechanism of composite foundation reinforced with geogrid-encased stone columns is presented in order to obtain its settlement calculation method. The settlement of composite foundation is divided into three sections which are the reinforced section, unreinforced section, and underlying stratum. Based on Hooke’s law of space problem and the thoughts of the layer-wise summation method, the relative slip displacement between pile and soil of reinforced section without plastic zone is analyzed. The settlement of reinforced section is calculated by the layered iteration method based on the pile element model. The compatibility of vertical and radial deformations of unreinforced section is analyzed based on the pile-soil element model. The settlement of underlying stratum is still calculated by the layer-wise summation method. Finally, two engineering examples are analyzed and the results show that the settlement calculated by the presented method is close to the measured one. The method overcomes the defect that the calculated results by the other existing methods are more dangerous and it is more feasible and can be applied in engineering practice.
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Jang, Kyung-In, Jongwon Seok, Byung-Kwon Min, and Sang Jo Lee. "Behavioral model for magnetorheological fluid under a magnetic field using Lekner summation method." Journal of Magnetism and Magnetic Materials 321, no. 9 (May 2009): 1167–76. http://dx.doi.org/10.1016/j.jmmm.2008.10.046.
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Powell, Colin, and Yuri Lawryshyn. "A method for determining the optimal discretization of UV lamps for emission-based fluence rate models." Water Science and Technology 71, no. 12 (March 30, 2015): 1768–74. http://dx.doi.org/10.2166/wst.2015.101.
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A method for optimizing the number of segment sources needed to discretize UV lamps for fluence rate modeling and dose calculations when using the multiple segment source summation (MSSS) fluence rate model (FRM) is presented. An ideal location for determining the optimal number of point or segment sources was found using the multiple point source summation (MPSS) method with no reflection and refraction. This location was then used to conduct a fast discretization study for the MSSS FRM. A lower than previously used number of segment sources was required. This method reduced the time needed to perform a discretization study and thus for fluence rate and dose distribution calculations in UV reactors.
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Ma, Yan Jun, Bin Yan, and Jing Zhang. "Study on a New Foundation Stiffness Calculation Model." Applied Mechanics and Materials 166-169 (May 2012): 1258–61. http://dx.doi.org/10.4028/www.scientific.net/amm.166-169.1258.
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This paper combined the feature of Winkler foundation model and base model of limited compressible layer based on the layer-wise summation method, on condition that considering the feature of foundation soil, to derived from a newly foundation stiffness calculation model and to verify it.
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George, Th, J. Virieux, and R. Madariaga. "Seismic wave synthesis by Gaussian beam summation: A comparison with finite differences." GEOPHYSICS 52, no. 8 (August 1987): 1065–73. http://dx.doi.org/10.1190/1.1442372.
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We apply Gaussian beam summation to the calculation of seismic reflections from complex interfaces, introducing several modifications of the original method. First, we use local geographical coordinates for the representation of paraxial rays in the vicinity of the recording surface. In this way we avoid the time‐consuming evaluation of the ray‐centered coordinates of the observation points. Second, we propose a method for selecting the beams that ensures numerical stability of the synthetic seismograms. Third, we introduce a simple source wave packet that simplifies and stabilizes the calculations of inverse Fourier transforms. We compare reflection seismograms computed using the Gaussian beam‐summation method with those calculated by finite differences. Two simple models are used. The first is a continuous curved interface separating an elastic layer from a free half‐space. A double caustic, or degenerate focal point, appears due to the crossing of reflected rays. In this instance the finite‐difference simulation and the Gaussian beam summation are in excellent agreement. Both phase and amplitude are modeled correctly for both the direct and reverse branches. When compared to geometrical ray theory, Gaussian beam summation provides a good approximation of the field near the caustics while geometrical ray theory does not. The second, more complex, model we consider is a trapezoidal dome with sharp corners in the interface. The corners of the dome in this model produce rather strong diffractions. Also, creeping head waves propagate along the interface. The results compare well with the finite‐difference simulation except for the diffracted branches, where the traveltime of diffracted waves is poorly approximated by the Gaussian beam‐summation method.
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Heidarieh, S. M., M. Jahed, and A. Ghazizadeh. "A New Nonlinear Sparse Component Analysis for a Biologically Plausible Model of Neurons." Neural Computation 31, no. 9 (September 2019): 1853–73. http://dx.doi.org/10.1162/neco_a_01214.
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It is known that brain can create a sparse representation of the environment in both sensory and mnemonic forms (Olshausen & Field, 2004 ). Such sparse representation can be combined in downstream areas to create rich multisensory responses to support various cognitive and motor functions. Determining the components present in neuronal responses in a given region is key to deciphering its functional role and connection with upstream areas. One approach for parsing out various sources of information in a single neuron is by using linear blind source separation (BSS) techniques. However, applying linear techniques to neuronal spiking activity is likely to be suboptimal due to inherent and unknown nonlinearity of neuronal responses to inputs. This letter proposes a nonlinear sparse component analysis (SCA) method to separate jointly sparse inputs to neurons with post summation nonlinearity, or SCA for post-nonlinear neurons (SCAPL). Specifically, a linear clustering approach followed by principal curve regression (PCR) and a nonlinear curve fitting are used to separate sources. Analysis using simulated data shows that SCAPL accuracy outperforms ones obtained by linear SCA, as well as other separating methods, including linear independent and principal component analyses. In SCAPL, the number of derived sparse components is not limited by the number of neurons, unlike most BSS methods. Furthermore, this method allows for a broad range of post-summation nonlinearities that could differ among neurons. The sensitivity of our method to noise, joint sparseness, degree, and shape of nonlinearity and mixing ill conditions is discussed and compared to existing methods. Our results show that the proposed method can successfully separate input components in a population of neurons provided that they are temporally sparse to some degree. Application of SCAPL should facilitate comparison of functional roles across regions by parsing various elements present in a region.
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Yuniar Istiqomah, Erfiani Erfiani, and Utami Dyah Syafitri. "Klasifikasi Kadar Glukosa Darah Keluaran Alat Non-invasif Menggunakan Regresi Logistik Ordinal dengan Peringkasan Luas." Xplore: Journal of Statistics 12, no. 1 (January 15, 2023): 110–21. http://dx.doi.org/10.29244/xplore.v12i1.1078.
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Diabetes Mellitus (DM) is the silent killer because its symptoms tend to go unnoticed. Blood glucose level checks must be performed periodically to control blood glucose levels for DM and non-sufferers. The IPB Non-Invasive Biomarking Team developed a non-invasive monitoring device to check blood. The tool uses the spectroscopy principle and produces an output in the form of a residual value of light intensity. A method is needed to predict the category of blood glucose levels based on the measurement results of non-invasive tools. Classification modeling is one of the methods that can be used to analyze the relationship between the blood glucose level class of invasive measurement results and the residual value of the intensity of non-invasive measurement results. One of the commonly used classification methods is ordinal logistic regression. This method generates the final model of a cumulative opportunity logit function with an opportunity value for each class as a differentiator between classes. Light spectrum-based data used as predictor X changes often provide changes that correlate with each other. The principal component analysis reduces its dimensions to become a new set of changes that do not correlate. A good data summarization approach at the preprocessing stage is also necessary to provide good modeling. Several summarization methods have been carried out in previous studies. Graph area summation in the period is the best summarization method because it can take advantage of the general data information. This study uses the ordinal logistic regression method as a modeling method by applying principal component analysis and graph area summation applied to 2017 data and 2019 data. Classification modeling in the 2017 data had a balanced accuracy value of 64,64%. Classification modeling in the 2019 data produced a balanced accuracy value of 57,57%. The design used in the 2017 tool and the 2019 tool is different, causing the residual intensity graph of the non-invasive measurement results to be read differently. The 2017 data model is better applied to homogeneous data and the 2019 data model is better applied to heterogeneous data.
Keywords: blood glucose levels, non-invasive tool, graph area summation, ordinal logistic regression, principal component
analysis.
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Rather, Akhter Mohiuddin. "A Hybrid Intelligent Method of Predicting Stock Returns." Advances in Artificial Neural Systems 2014 (September 7, 2014): 1–7. http://dx.doi.org/10.1155/2014/246487.
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This paper proposes a novel method for predicting stock returns by means of a hybrid intelligent model. Initially predictions are obtained by a linear model, and thereby prediction errors are collected and fed into a recurrent neural network which is actually an autoregressive moving reference neural network. Recurrent neural network results in minimized prediction errors because of nonlinear processing and also because of its configuration. These prediction errors are used to obtain final predictions by summation method as well as by multiplication method. The proposed model is thus hybrid of both a linear and a nonlinear model. The model has been tested on stock data obtained from National Stock Exchange of India. The results indicate that the proposed model can be a promising approach in predicting future stock movements.
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Zhang, Si Quan, Chuan Qi, and Gang Chen. "Fast Calculation Method for the Magnetic Field of Coil above Conductive Plate." Advanced Materials Research 945-949 (June 2014): 2141–44. http://dx.doi.org/10.4028/www.scientific.net/amr.945-949.2141.
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A series expansion calculation model was proposed to compute the change of magnetic induction intensity at the coil center above a conductive plate, based on the Maxwell equations, the magnetic vector potential and solution region truncation. When the truncated solution region radius and the summation terms are chosen properly, the computation time can be reduced considerably and preserve the computational accuracy. The model was compared with finite element method and the results agreed very well, and it confirms the suitability of the proposed model and its application prospect in electromagnetic non-destructive testing.
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MILTON, K. A., I. L. SOLOVTSOV, and O. P. SOLOVTSOVA. "AN ANALYTIC METHOD OF DESCRIBING R-RELATED QUANTITIES IN QCD." Modern Physics Letters A 21, no. 17 (June 7, 2006): 1355–68. http://dx.doi.org/10.1142/s0217732306020767.
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A model based on the analytic approach to QCD, involving a summation of threshold singularities and taking into account the nonperturbative character of the light quark masses, is applied to find hadronic contributions to different physical quantities. It is shown that the suggested model allows us to describe well such objects as the hadronic contribution to the anomalous magnetic moment of the muon, the ratio of hadronic to leptonic τ-decay widths in the vector channel, the Adler D-function, the smeared RΔ-function, and the hadronic contribution to the evolution of the fine structure constant.
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Rasmussen, Vibe Maria, Catarina Ellehuus-Hilmersson, Per Rotbøll-Nielsen, and Mads Utke Werner. "Spatial summation of thermal stimuli assessed by a standardized, randomized, single-blinded technique." Scandinavian Journal of Pain 9, no. 1 (October 1, 2015): 81–86. http://dx.doi.org/10.1016/j.sjpain.2014.12.001.
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AbstractBackground and aimsQuantitative sensory testing of thermal perception (QTT) is a valuable method in clinical and experimental assessment of the function of small nerve fibres. Previous studies have indicated existence of spatial summation for warmth, cool and heat pain stimulation, but study designs and assessment methods have not always been mutually consistent. The aims of this study were, first, to examine spatial summation of QTT by differently sized contact thermodes, and, second, to evaluate if these differences are significant from a clinical and scientific perspective.MethodsSixteen healthy subjects were included. Warmth detection (WDT), cool detection (CDT) and heat pain (HPT) thresholds were assessed in random order, with the stimulation areas of the contact thermodes of 3.0, 6.3 and 12.5 cm2, blinded to the subjects. Assessments were made bilaterally at volar part of the distal arm and medial part of the lower leg. Data analyses were by a mixed model with random effect for subject and fixed-effects for the variables, site (arm/leg), thermode area (ln thermode area) and side (dominant/non-dominant), in addition to conventional pairwise non-parametric comparisons.ResultsData from 2 subjects were excluded. In the remaining 14 subjects only 4 subjects were able to identify the correct sequence of thermode sizes. The model demonstrated highly statistical significant relationships regarding main effects: thermode area (P < 0.0001) and stimulation site (P < 0.0001; except for CDT P = 0.011). The only significant interaction was between thermode area*site (P = 0.005) for CDT. The study demonstrated in 17 of 18 possible comparisons between thermode size and stimulation site, a significant spatial summation for WDT, CDT and HPT.ConclusionThis randomized, single-blind study of thermal thresholds demonstrated spatial summation and that considerable deviations may occur if values obtained with differing thermode sizes are used uncritically.ImplicationsData from the present study enable interpolation of thermal thresholds with differing thermode sizes, facilitating comparisons across studies.
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Schuster, Gerard T., and Min Zhou. "A theoretical overview of model-based and correlation-based redatuming methods." GEOPHYSICS 71, no. 4 (July 2006): SI103—SI110. http://dx.doi.org/10.1190/1.2208967.
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We review the equations for correlation-based redatuming methods. A correlation-based redatuming method uses natural-phase information in the data to time shift the weighted traces so they appear to be generated by sources (or recorded by geophones) shifted to a new location. This compares to model-based redatuming, which effectively time shifts the traces using traveltimes computed from a prior velocity model. For wavefield redatuming, the daylight imaging, interferometric imaging, reverse-time acoustics (RTA), and virtual-source methods all require weighted correlation of the traces with one another, followed by summation over all sources (and sometimes receivers). These methods differ from one another by their choice of weights. The least-squares interferometry and virtual-source imaging methods are potentially the most powerful because they account for the limited source and receiver aperture of the recording geometry. Interferometry, on the other hand, has the flexibility to select imaging conditions that target almost any type of event. Stationary-phase principles lead to a Fermat-based redatuming method known as redatuming by a seminatural Green’s function. No crosscorrelation is needed, so it is less expensive than the other methods. Finally, Fermat’s principle can be used to redatum traveltimes.
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LEVENDORSKIĬ, SERGEI. "EFFICIENT PRICING AND RELIABLE CALIBRATION IN THE HESTON MODEL." International Journal of Theoretical and Applied Finance 15, no. 07 (November 2012): 1250050. http://dx.doi.org/10.1142/s0219024912500501.
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We suggest a general scheme for improvement of FT-pricing formulas for European options and give efficient recommendations for the choice of the parameters of the numerical scheme, which allow for very accurate and fast calculations. The efficiency of the method stems from the properties of functions analytical in a strip, which were introduced to finance by Feng and Linetsky (2008). We demonstrate that an indiscriminate choice of parameters of a numerical scheme leads to an inaccurate pricing and calibration. As applications, we consider the Heston model and its generalization. For many parameter sets documented in empirical studies of financial markets, relative accuracy better than 0.01% can be achieved by summation of less than 10-20 terms even in the situations in which the standard approach requires more than 200. In some cases, the one-term formula produces an error of several percent, and the summation of two terms — less than 0.5%. Typically, 10 terms and fewer suffice to achieve the error tolerance of several percent and smaller.
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Fazli Malidareh, Babak, Seyed Abbas Hosseini, and Ebrahim Jabbari. "Discrete mixed subdomain least squares (DMSLS) meshless method with collocation points for modeling dam-break induced flows." Journal of Hydroinformatics 18, no. 4 (February 11, 2016): 702–23. http://dx.doi.org/10.2166/hydro.2016.116.
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This paper presents a new meshless numerical scheme to overcome the problem of shock waves and to apply boundary conditions in cases of dam-break flows in channels with constant and variable widths. The numerical program solves shallow water equations based on the discrete mixed subdomain least squares (DMSLS) meshless method with collocation points. The DMSLS meshless method is based on the minimization of a least squares functional defined as the weighted summation of the squared residuals of the governing equations over the entire domain and requiring the summation of residual function to be zero at collocation points in boundary subdomains. The collocated discrete subdomain meshless method is applied on the boundary, whereas the collocated discrete least squares meshless technique is applied to the interior domain. The meshless scheme extends for dam-break formulation of shallow water equations. The model is verified by comparing computed results with analytical and experimental data for constant and varying width channels. The developed model is also used to study one-dimensional dam-break problems involving different flow situations by considering changes to the channel width, a bumpy channel with various downstream boundary conditions, and the effects of bed friction and bed slope as source terms on wave propagation. The accuracy of the results is acceptable.
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Wen, Yong, Guanghua Yang, and Zhihui Zhong. "Study on Calculation Method of Foundation Nonlinear Settlement Based on In Situ Loading Test." Geofluids 2023 (February 2, 2023): 1–9. http://dx.doi.org/10.1155/2023/7845944.
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In this paper, a nonlinear deformation modulus method is proposed for foundation settlement calculation. In the proposed method, the nonlinear deformation modulus under different stress levels is obtained from the load-settlement curve of in situ loading test, which are then applied to the layerwise summation method for calculating foundation settlement. On this basis and referring to the Duncan-Chang model, a variable modulus constitutive model suitable for numerical calculation of foundation settlement is further proposed. The required parameters of this model are the same as those of the nonlinear deformation modulus method and can be determined by the in situ loading test. The validity of the proposed calculation methods of foundation settlement is verified by the in situ loading tests under different plate sizes. The results illustrate that both the nonlinear deformation modulus method and the variable modulus constitutive model compare quite well with the test results, and the deduced results can better reflect the nonlinearity of foundation settlement.
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Dong, Jiu-Ying, and Shu-Ping Wan. "Max-Min and Min-Max Gray Association Degree-Based Method for Multiattribute Decision Making." Journal of Intelligent Systems 24, no. 4 (December 1, 2015): 525–31. http://dx.doi.org/10.1515/jisys-2014-0091.
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AbstractA new method of multiattribute decision making is proposed based on the max-min and min-max gray association degree. The gray association coefficients between the alternative, positive ideal solution and negative ideal solution are defined. Here, we construct a bi-objective programming model that maximizes the minimum gray association degree and minimizes the maximum gray association degree simultaneously. By using the linear weighted summation method, the bi-objective programming model is transformed into a linear programming model. Thus, we can obtain the weight vector of attributes by solving the linear programming model. The ranking order of alternatives is generated according to the relative closeness. A numerical example is examined to demonstrate the applicability and implementation process of the decision method proposed in this paper.
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An, Xinyu, Baowei Song, Zhaoyong Mao, and Congcong Ma. "Layout Optimization Design of Two Vortex Induced Piezoelectric Energy Converters (VIPECs) Using the Combined Kriging Surrogate Model and Particle Swarm Optimization Method." Energies 11, no. 8 (August 8, 2018): 2069. http://dx.doi.org/10.3390/en11082069.
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The layout configuration of Vortex Induced Piezoelectric Energy Converters (VIPECs) is essential to improve its overall performance. Based on the formations of migrating geese, the configuration is characterized by two nondimensionalized layout parameters. A number of sampled points for different configurations are simulated with the two-dimensional Computation Fluid Dynamics (CFD) method. The influence of layout configurations on VIPECs’ lift force and wake structure is investigated and the generated open circuit output voltage is obtained through the derived output voltage equation. The response surface model of the output voltage of both the leading VIPEC and the following VIPEC and their summation are established using the Kriging surrogate model based on the obtained simulation results. Then, optimal layout parameters are found through the Particle Swarm Optimization (PSO) algorithm, and its predicted result is compared with that of the CFD simulation. The simulation and optimization results reveal that the output voltage is not always consistent with the lift force on the plate. When VIPECs are placed in parallel with a certain spacing, their overall performance increases. The summation of output voltage is predicted to improve by approximately 63.7% compared to two single VIPECs when they are placed at the optimal layout parameters.
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Gasymov, Oktay K., Adil R. Abduragimov, and Ben J. Glasgow. "A Simple Model-Free Method for Direct Assessment of Fluorescent Ligand Binding by Linear Spectral Summation." Journal of Fluorescence 24, no. 1 (September 18, 2013): 231–38. http://dx.doi.org/10.1007/s10895-013-1290-y.
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Wang, Wenqi, Yuhong Sun, and Jing Wu. "Environmental Warning System Based on the DPSIR Model: A Practical and Concise Method for Environmental Assessment." Sustainability 10, no. 6 (May 25, 2018): 1728. http://dx.doi.org/10.3390/su10061728.
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Though we are in urgent need of environmental warnings to slow environmental deterioration, currently, there is no internationally concise method for environmental warnings. In addition, the existing approaches do not combine the three aspects of ecology, resources, and environment. At the same time, the three elements of the environment (air, water, and soil) are separated in most environmental warning systems. Thus, the method this paper gives is an innovative attempt and aims to make environmental assessment more practical. This paper establishes the index system of an environmental early warning based on the Driving–Pressure–State–Influence–Response (DPSIR) model. The Analytic Hierarchy Process (AHP) method was used to determine the weights. Next, single and integrated index methods further assess the environmental warning state, in which the weighted summation method is used to summarize the data and results. The case of Tianjin is used to confirm the applicability of this method. In conclusion, the method in this paper is more well-behaved and, therefore, more suitable to assist cities in their environmental assessment.
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Zhang, Xin. "Analysis of financial market trend based on autoregressive conditional heteroscedastic model and BP neural network prediction." Journal of Intelligent & Fuzzy Systems 39, no. 4 (October 21, 2020): 5845–57. http://dx.doi.org/10.3233/jifs-189060.
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High-frequency data such as stock prices are aggregated into low-frequency monthly data for modeling. However, the summation method only applies to high frequency data in the form of flow, and the summation method reduces the sample size. Based on this, this paper uses the mixing model to construct the financial status index, which can model the data of different frequencies and compensate for the defects of the same frequency data modeling to some extent. Moreover, based on principal component analysis and text mining technology, this paper constructs two kinds of sentiment indexes, and studies the influence and prediction of two sentiment indexes on the closing price of stock market. In addition, in the empirical analysis, this paper establishes the GARCH model and BP neural network prediction model and predicts the closing price. Finally, this paper compares the pros and cons of predictive models and sentiment indices. The research shows that the BP neural network model established by using the lag variable of the Web text sentiment index as the input layer variable is more reliable and can be widely used in the stock market.
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Economou, Nikos, Antonis Vafidis, Maksim Bano, Hamdan Hamdan, and Jose Ortega-Ramirez. "Ground-penetrating radar data diffraction focusing without a velocity model." GEOPHYSICS 85, no. 3 (May 1, 2020): H13—H24. http://dx.doi.org/10.1190/geo2019-0101.1.
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Ground-penetrating Radar (GPR) sections commonly suffer from strong scattered energy and weak reflectors with distorted lateral continuity. This is mainly due to the gradual variation of moisture with depth, dense lateral sampling of common-offset GPR traces (which are considered as zero-offset data), along with the small wavelength of the electromagnetic waves that is comparable to the size of the shallow subsurface dielectric heterogeneities. Focusing of the diffractions requires efficient migration that, in the presence of highly heterogeneous subsurface formations, can be improved by a detailed migration velocity model. Such a velocity model is difficult to develop because the common-offset antenna array is mostly used for its reduced time and cost in the data acquisition and processing stages. In such cases, migration processes are based on limited information from velocity analysis of clear diffractions, cores, or other ground truth knowledge, often leading to insufficient imaging. We have developed a methodology to obtain GPR sections with focused diffractions that is based on multipath summation, using weighted stacking (summation) of constant-velocity migrated sections over a predefined velocity range. The success of this method depends on the assignment of an appropriate weight, for each constant-velocity migrated section to contribute to the final stack, and the optimal width of the velocity range used. Additionally, we develop a postmultipath summation processing step, which consists of time-varying spectral whitening, to deal with the decrease of the dominant frequency due to attenuation effects and the additional degraded resolution expected by the constant migration summed images. This imaging strategy leads to GPR sections with sufficiently focused diffractions, enhancing the lateral and the temporal resolution, without the need to explicitly build a migration velocity model.
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Tkachenko, Roman, Ivan Izonin, Natalia Kryvinska, Ivanna Dronyuk, and Khrystyna Zub. "An Approach towards Increasing Prediction Accuracy for the Recovery of Missing IoT Data based on the GRNN-SGTM Ensemble." Sensors 20, no. 9 (May 4, 2020): 2625. http://dx.doi.org/10.3390/s20092625.
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The purpose of this paper is to improve the accuracy of solving prediction tasks of the missing IoT data recovery. To achieve this, the authors have developed a new ensemble of neural network tools. It consists of two successive General Regression Neural Network (GRNN) networks and one neural-like structure of the Successive Geometric Transformation Model (SGTM). The principle of ensemble topology construction on two successively connected general regression neural networks, supplemented with an SGTM neural-like structure, is mathematically substantiated, which improves the accuracy of prediction results. The effectiveness of the method is based on the replacement of the summation of the results of the two GRNNs with a weighted summation, which improves the accuracy of the ensemble operation in general. A detailed algorithmic implementation of the ensemble method as well as a flowchart of its operation is presented. The parameters of the ensemble operation are determined by optimization using the brute-force method. Based on the developed ensemble method, the solution of the task of completing the partially missing values in the real monitoring dataset of the air environment collected by the IoT device is presented. By comparing the performance of the developed ensemble with the existing methods, the highest accuracy of its performance (by the parameters of Mean Absolute Percentage Error (MAPE) and Root Mean Squared Error (RMSE) accuracy) among the most similar in this class has been proved.
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Keane, A. J. "A Note on Modal Summations and Averaging Methods As Applied to Statistical Energy Analysis (S.E.A.)." Journal of Sound and Vibration 164, no. 1 (June 1993): 143–56. http://dx.doi.org/10.1006/jsvi.1993.1200.
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Ikram, Zul Jalali Wal, and Najmawati Azis. "Pengembangan Model dan Penggunaan Konteks dalam Mendukung Pemahaman Siswa pada Topik Penjumlahan yang Melibatkan Bilangan Negatif." Idealmathedu: Indonesian Digital Journal of Mathematics and Education 9, no. 1 (July 13, 2022): 63–69. http://dx.doi.org/10.53717/idealmathedu.v9i1.330.
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This study aims to develop learning activities to contribute to the theory based on empirical activities in learning the topic of summation involving negative numbers. This research also develops learning activities that combine context and models that students can apply to understand the topic. The type of research used to attain the objectives in this study is design research, each cycle consists of three steps, namely preliminary study, classroom experiment and retrospective method. The subjects of the study were grade 4 students and teachers at SD Islam Athirah Makassar. The results showed that to help students understand the concept of summation involving negative numbers, students must understand the concept of negative numbers and use the number line model to count. This can be supported by the context of equilibrium and the number line as a representation of the negative numbers. In classroom learning, the use of context stimulates students to think informally, furthermore, by indicating a state using numbers and with the help of a number line model, students can solve mathematical problems at a formal level.