Narrow Results

A hybrid method is developed based on the spectral and finite-difference methods for solving the inhomogeneous Zerilli equation in time-domain. The developed hybrid method decomposes the domain into the spectral and finite-difference domains. The singular source term is located in the spectral domain while the solution in the region without the singular term is approximated by the higher-order finite-difference method.

The spectral domain is also split into multi-domains and the finite-difference domain is placed as the boundary domain. Due to the global nature of the spectral method, a multi-domain method composed of the spectral domain only does not yield the proper power-law decay unless the range of the computational domain is large. The finite-difference domain helps reduce boundary effects due to the truncation of the computational domain. The multi-domain approach with the finite-difference boundary domain method reduces the computational cost significantly and also yields the proper power-law decay.

Stable and accurate interface conditions between the finite-difference and spectral domains and the spectral and spectral domains are derived. For the singular source term, we use both the Gaussian model with various values of full width at half-maximum and a localized discrete δ-function. The discrete δ-function was generalized to adopt the Gauss–Lobatto collocation points of the spectral domain.

The gravitational waveforms are measured. Numerical results show that the developed hybrid method accurately yields the quasi-normal modes and the power-law decay profile. The numerical results also show that the power-law decay profile is less sensitive to the shape of the regularized δ-function for the Gaussian model than expected. The Gaussian model also yields better results than the localized discrete δ-function.

To effectively improve the power dispatching, the prediction accuracy of wind power has been the concern of many scholars for many years. The wind power prediction problem is actually equivalent to the wind speed prediction problem. Based on linear regression (LR) and variational mode decomposition (VMD), in this paper, we proposed an efficient hybrid method to predict wind speed. In the proposed method, the VMD is used to decompose the signal of wind speed into several sub-signal. Compared with the original wind-speed series, each sub-signal is a more stable subsequence signal. Then, we used the LR method to predict each subsequence signal. Eventually, we obtain the final prediction results of the original wind speed series merged the forecasting values of all subsequences signal. We selected two data to test our proposed method in our experiment. Compared with several comparison methods, we found that our proposed methods has better prediction performance than other methods from the experimental results.

Predicting the response of a complex structural-acoustic system across a broad frequency range presents a number of challenges to an analyst. It is quite common to find that the uncertainty associated with the local dynamic properties of various subsystems of a system can vary greatly across the system. It is also common to find that the modal density and wavenumber content of the various subsystems can vary greatly across the system. Typically, this results in a mixture of strongly phase correlated (long wavelength) motion which spans many subsystems, superimposed with weakly phase correlated local motion that is confined to individual subsystems. This mismatch in the local statistical and dynamic properties of a system is often referred to as the mid-frequency problem. This paper provides a qualitative definition of the mid-frequency problem and suggests that a statistical description of the local dynamic properties of a system is an essential element of any mid-frequency prediction method. A hybrid approach to the mid-frequency problem is then described which employs a statistical description of the local modal properties of various subsystems in a system. The spatial statistics of the local modes are of particular interest and the way in which these statistics are encompassed in the hybrid analysis is discussed. Experimental investigations of the spatial statistics of a frame-panel structure are then presented and measurements of the acoustic power radiated by the structure are compared with numerical predictions.

The longer the input sentences, the worse the syntactic parsing results. Therefore, a long sentence is first divided into several clauses, and the syntactic analysis for each clause is performed. Finally, all the analysis results are merged into one. In the merging process, it is difficult to determine the dependency among clauses. To handle such syntactic ambiguity in determining inter-clause dependency, this paper proposes a hybrid method using restriction rules and Decision Trees-based machine learning. Based on restriction rules, clauses that cannot be the governor of a dependent clause are excluded from the governor candidates. Next, using Decision Trees machine learning algorithm, one clause is selected as the governor of a dependent clause. We extract various features from a clause, and analyze the effect of each feature on the performance. Experimental results show that our hybrid method outperformed both methods of using restriction rules and using Decision Trees.

This paper presents a new formulation combining the nonlinear theory of Novozhilov with the classical finite element method for the purpose of evaluating the vibratory characteristics of thin, closed and isotropic cylindrical shells. The theory developed in this paper is able to include the shell curvature effect in the circumferential direction of the orthogonal displacements and considers the impact of initial geometric imperfections on the dynamic response of the system. The formulation first takes a general form by expressing the shell displacements as an alliance between the generalized coordinates and spatial functions. Nonlinear kinematic relationships are inferred from Novozhilov’s theory. The equations of motion as well as the expressions of the mass, linear and nonlinear stiffness matrices are derived through the Lagrange method by considering the coupling between the different modes. An application of this model is illustrated in a further step, by adopting the displacement functions derived from exact solutions of linear Sanders’ theory equilibrium equations for thin cylindrical shells. The governing equations of motion are solved with the help of a direct iterative method. Linear and nonlinear frequencies are validated by comparison with the results in the literature. The relative nonlinear frequencies are determined as a function of vibration amplitudes and then compared with published results for several cases of shells. Excellent agreement is observed between the results derived from this theory and those found in the literature. The effect of different parameters including axial and circumferential wave number, length-to-radius ratio, thickness-to-radius ratio and various boundary conditions, on the nonlinear frequencies of cylindrical shells is investigated.

To investigate the dynamics of the wind–vehicle–bridge (WVB) system in the multi-body dynamics framework, which avoids the large computation cost of programming the motion equation of complex vehicle models and improves the calculation efficiency, an advanced hybrid method is proposed to optimize the WVB system coupling vibration analysis model. The dummy body coupling (DBC) method is integrated to build the connection between the MBS and the FE model, which cannot change the mechanical characteristics of the MBS vehicle model and the bridge FE model. The proposed method makes full use of the high efficiency of the established structure modeling, the powerful wheel–rail analysis function, and vehicle modeling in the multi-body dynamics framework. The complex bridge is modeled by a number of elements to reflect the actual dynamic characteristics of structure, which cannot satisfy the requirement of calculation in the multi-body dynamics framework. Thus, to avoid forming the wheel–rail relationship function, the bridge modeling as a finite element model would be transferred into multi-body dynamics coupling model of the WVB system as a flexible body. The verification of the relationship among the sub-systems of the multi-body model of the WVB system is investigated by analysis of the wind–vehicle, wind–bridge, and vehicle–bridge sub-systems. Finally, a dynamic analysis of the WVB system based on the proposed method is carried out for a double-track railway continuous bridge, in which the effects of different vehicle speeds and the incoming wind directions are studied. The simulation of the WVB system by the hybrid method has a high computational efficiency and strong practicability.

Support vector machine (SVM) is a machine learning method widely used in solving binary data classification problems due to its performance. Nevertheless, in practical problems of classification, there are often cases of the presence of more than two classes of objects in the original dataset. The paper considers a solution to the problem of SVM multiclass with the aim to increase the data classification quality based on a new way of hybridisation between SVM and $k$-nearest neighbour (KNN) algorithms. The first phase of the approach is called the filtering phase. At this level, the feature space is split into two classes separated by a hyperplane. In the next step called review, we generate a second hyperplane, then we calculate the distance between each test pattern and the second hyperplane in the feature space using e.g. the KNN function. The result of the two phases is three classes instead of two produced by the conventional SVM. For evaluation purposes, dataset experiments are conducted on seven benchmark datasets that have high dimensionality and large size. Numerical experiments show that the 3SVM approach can improve not only the accuracy compared to other multiclass SVM approaches, but also the precision, recall, and $F_1$-score.

Reducing the general problem of computing three-dimensional Green's function in a transversely isotropic plate to a finite summation of contributions from a series of planar problems can efficiently yield an accurate solution. Hence, solving the planar scattering problem, of the Pressure-Shear-Vertical (PSV) type or the Shear-Horizontal (SH) type, was performed by three different techniques: The boundary element method; the hybrid method; and the perfectly matched layer method. In the pursuit of these methods, the objective was to highlight their pros and cons in terms of accuracy and efficiency.

Both functionally graded materials (FGMs) and fluid-conveying pipes have wide applications in engineering communities. In this paper, the transverse vibration and stability of multi-span viscoelastic FGM pipes conveying fluid are investigated. Volume fraction laws including power law, sigmoid law and exponential law are introduced to describe the variations of material properties in FGM pipes. A hybrid method which combines reverberation-ray matrix method and wave propagation method is developed to calculate the natural frequencies, and the results determined by present method are compared with the existing results in literature. Then, a comparative study is performed to investigate the effects of fluid velocity, volume fraction laws and internal damping on transverse vibration and stability of the FGM pipes conveying fluid. The results demonstrate that the present method has high precision in dynamic analysis of multi-span pipes conveying fluid. It is also found that natural frequencies of FGM pipes can be adjusted by devising the volume fractions laws. This particular feature can be tailored to fulfill the special applications in engineering.

Seismic wave propagation in localized regions plays an important role in the study of seismology and earthquake engineering. However, modeling 3D broadband wavefield of heterogeneous media is computationally expensive and thus has been always a key challenge. In this paper, a frequency wavenumber-spectral element (FK-SEM) hybrid method for modeling broadband seismic wavefield of 3D localized regions is proposed, which obeys the framework of domain reduction, i.e., a finite region is intercepted from a semi-infinite space as the computational domain. To this end, the FK method (based upon the exact stiffness matrix) is first used to calculate the equivalent input of truncated boundaries to incident P, SV, and SH waves with arbitrary angles, and then the SEM is employed to finely simulate the wave propagation process in 3D localized regions. Meanwhile, a viscoelastic artificial boundary is developed in the SEM to realize the absorption of diffracted wavefields generated by internal irregularities. The hybrid method allows the engineering-sensitive high-frequency bands (10–20Hz) to be tackled without extra calculations, thereby significant savings computational resources. The correctness and accuracy of the method is verified by four models: a 3D flat stratified site (compared with the FK method), and three typical local sites including 3D canyon, basin and hill topographies (compared with the boundary element method (BEM)). Finally, the method is applied to a realistic case at Zigong Mountain, southwestern China, which suffered extensive topography-induced damages in 2008 Wenchuan earthquake. The results elucidate that the spectral ratio amplification factors predicted by the hybrid modeling are in good accordance with those obtained from strong earthquake data, which further validates the application potential of our method in assisting broadband ground motion research.

A hybrid method was developed in this study for fatigue life prediction (FLP) of lead-free solder (LFS) joints in ball grid array package under the coupled electrical–thermal–mechanical (ETM) fields. A modified constitutive model for lead-free solder joints under coupled ETM fields was proposed to describe the mechanical and fatigue behavior of solder joints under coupled ETM fields. A modified damage model under coupled ETM fields was then developed to obtain the fatigue life of LFS joints under coupled ETM fields. Uniaxial tension tests of an Sn–3.0Ag–0.5Cu (SAC305) solders and coupled multifields fatigue experiments were performed to verify the accuracy, applicability and validity by the modified constitutive model and fatigue damage model under coupled ETM fields. Based on the modified constitutive model and fatigue damage model, a hybrid method, including current, temperature and mechanics parameters, was proposed for the FLP of the LFS joints, which was demonstrated to be able to predict the results well. A hybrid method provides an idea for investigating the fatigue life of lead-free solder joints in coupled fields.

Heat exchangers with small-diameter multi-path tubes have been recently used to improve the efficiency of air conditioners. The difficulty in using tubes with small diameters and multi-paths is the nonuniformity of refrigerant distribution in refrigerant distributors, which results in lower heat-exchange efficiency. Grid methods, such as the volume of fluid method, are now widely used to simulate detailed motions of gas–liquid interfaces. A weak point of grid methods is the numerical diffusion of interfaces that occurs if the scale of interfaces becomes close to the computational grid sizes. We previously developed a particle/grid hybrid method for simulating multi-scale free surfaces. For this study, we modified the hybrid method and applied it to gas–liquid flow simulations in a distributor. The liquid film behaviors in both the distributor and a bend pipe placed in the upstream of the distributor were simulated mainly using the particle method, and gas flows were simulated using the grid method. The predicted liquid film near the outer circumference of the curvature in the bend pipe was thicker than that of near inner circumference of the curvature, which qualitatively agreed with the measurement. The simulated distribution ratio under a steady-flow condition agreed well with the measurement; the predicted distribution ratio was 0.63 and the measured distribution ratio was 0.6.

Stochastic effect in cellular systems has been an important topic in systems biology. Stochastic modeling and simulation methods are important tools to study stochastic effect. Given the low efficiency of stochastic simulation algorithms, the hybrid method, which combines an ordinary differential equation (ODE) system with a stochastic chemically reacting system, shows its unique advantages in the modeling and simulation of biochemical systems. The efficiency of the hybrid method is usually limited by reactions in the stochastic subsystem, which are modeled and simulated using Gillespie’s framework and frequently interrupt the integration of the ODE subsystem. In this paper, we develop an efficient implementation approach for the hybrid method coupled with traditional ODE solvers. We also compare the efficiency of the hybrid methods with three widely used ODE solvers RADAU5, DASSL, and DLSODAR. Numerical experiments with three biochemical models are presented. A detailed discussion is presented for the performances of three ODE solvers.