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Mathematical Problems in Engineering is a broad-based journal publishes results of rigorous engineering research across all disciplines, carried out using mathematical tools.
Chief Editor, Professor Guangming Xie, is currently a full professor of dynamics and control with the College of Engineering, Peking University. His research interests include complex system dynamics and control and intelligent and biomimetic robots.
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Multivariate Joint Probability Function of Earthquake Ground Motion Prediction Equations Based on Vine Copula Approach
In the structural earthquake engineering, a single parameter is often not sufficient enough to depict the severity of ground motions, and it is thus necessary to use multiple ones. In this sense, the correlation among multiple parameters is generally considered as an importance issue. The conventional approach for developing the correlation is based on regression analysis, along with simple pair copula approaches proposed in recent years. In this study, an innovative mathematical technique—vine copula—is firstly introduced to develop the empirical model for the multivariate dependence of pseudospectral accelerations (PSAs), which are the most commonly used earthquake ground motion parameters. This advancement not only offers a more flexible way of describing nonlinear dependence among multivariate PSAs from the marginal distribution functions but also highlights the extreme dependence. The results can be conventionally acquired in the ground motion selection and seismic risk and loss assessment based on multivariate parameters.
Modified Atom Search Optimization Based on Immunologic Mechanism and Reinforcement Learning
Atom search optimization algorithm has good searching ability and has been successfully applied to calculate hydrogeological parameters and groundwater dispersion coefficient. Since the atom search optimization algorithm is only based on the atom force motion model in molecular dynamics, it has some shortcomings such as slow search speed and low precision during the later stage of iteration. A modified atom search optimization based on the immunologic mechanism and reinforcement learning is proposed to overcome the abovementioned shortcomings in this paper. The proposed algorithm introduces a vaccine operator to better utilize the dominant position in the current atom population so that the speed, accuracy, and domain search ability of the atom search optimization algorithm can be strengthened. The reinforcement learning operator is applied to dynamically adjust the vaccination probability to balance the global exploration ability and local exploitation ability. The test results of 21 benchmark functions confirm that the performance of the proposed algorithm is superior to seven contrast algorithms in search accuracy, convergence speed, and robustness. The proposed algorithm is used to optimize the permutation flow shop scheduling problem. The experimental results indicate that the proposed algorithm can achieve better optimization results than the seven comparative algorithms, so the proposed algorithm has good practical application value.
Effects and Correction of Atmospheric Pressure Loading Deformation on GNSS Reference Stations in Mainland China
Atmospheric pressure loading (APL) deformation is one component of nontectonic deformation for Global Navigation Satellite System (GNSS) time series and is a kind of deformation response caused by a redistribution of atmospheric pressure. In this paper, we present an atmospheric data processing strategy to compute the APL based on a spherical harmonic expansion of the global atmosphere pressure changes. We also provide a sample model to describe the relativity between the global atmosphere pressure changes and APL vertical deformation. The results show that the variation of air mass has a major impact on the north-eastern area of East China, the eastern area of North China, and Northeast China, and the vertical crustal displacement caused by the atmosphere changes in these regions can reach about 20 mm. The correction of APL for vertical time series of GNSS reference stations in different regions indicates that the arid area of the Northwest China, Northeast China, Central China, and North China are greatly affected by APL. While for the station located in Sichuan-Yunnan region, the amplitude and period change are small after correction of APL for vertical time series of GNSS reference stations, which reveals that the area is seriously affected by tectonic movement and water migration loading. The correlation between atmospheric pressure changes and crustal deformation is analyzed, which shows that APL has a serious impact on the north-eastern area of North China, the Northeast China, and the eastern area of Central China when the variations in atmospheric pressure in mainland China are the same. The research results of this paper will provide some reference value for the study of crustal structural deformation and the establishment of geodetic datum.
Correction Method for Hydraulic Conductivity Measurements Made Using a Fixed Wall Permeameter
Hydraulic conductivity measurement through a fixed wall permeameter is a common practice to obtain the fluid transmissibility characteristics of soil matrix; however, sidewall leakage due to rigid wall effect may significantly influence the observed values for coarse-grained soils. In this study, the boundary flow error was identified through characterizing the geometrical properties of voids adjacent to the sidewall, and a parameter known as the boundary void ratio () was proposed to account for this effect. The findings suggest that a fixed wall cell containing coarse soils would unavoidably generate extra voids at the interface between soil grains and inner rigid wall, contributing to a larger at the wall than void ratio within the soil bed; the measured hydraulic conductivity is increased primarily due to the apparatus-induced error. A two-dimensional geometric model was then established to estimate the value for uniformly sized coarse soils confined by a rigid permeameter wall, based on which a method was obtained for eliminating the boundary flow error from a fixed wall cell. The mathematical method was finally validated against experimental data from existing literature. It can be concluded that the boundary condition at sidewall featuring unwanted gaps lead to overestimation of the coefficient of permeability; however, the proposed correction method could adequately eliminate the boundary flow error for uniformly sized coarse-grained soils tested within a rigid wall cell.
A Mixed Stress/Displacement Approach Model of Homogeneous Shells for Elastodynamic Problems
This paper presents the development of a model of homogeneous, moderately thick shells for elastodynamic problems. The model is obtained by adapting and modifying SAM-H model (stress approach model of homogeneous shells) developed by Domínguez Alvarado and Díaz in (2018) for static problems. In the dynamic version of SAM-H presented herein, displacements and stresses are approximated by polynomials of the out-of-plane coordinate. The stress approximation coincides with the static version of SAM-H when dynamic effects are neglected. The generalized forces and displacements appearing in the approximations are the same as those involved in a classical, moderately thick shell model (CS model) but the stress approximation adopted herein is more complex: the 3D motion equations and the stress boundary conditions at the faces of the shell are verified. The generalized motion and constitutive equations of dynamic SAM-H model are obtained by applying a variant of Euler–Lagrange equation which includes pertinently Hellinger–Reissner functional. In the constitutive equations, Poisson’s effect of out-of-plane normal stresses on in-plane strains is not ignored; this is one important feature of SAM-H. To test the accuracy of dynamic SAM-H model, the following structures were considered: a hollow sphere and a catenoid. In each case, eigenfrequencies are first calculated and then a frequency analysis is performed applying a harmonic load. The results are compared to those of a CS model, MITC6 (mixed interpolation of tensorial components with 6 nodes per element) shell element calculations, and solid finite element computations. In the two problems, CS, MITC6, and dynamic SAM-H models yield accurate eigenfrequencies and eigenmodes. Nevertheless, the frequency analysis performed in each case showed that dynamic SAM-H provides much more accurate amplitudes of stresses and displacements than the CS model and the MITC6 shell finite element technique.
Establishment of an Aggregation Model Associated with Instrument Interface Design Based on Kansei Factors of Electric Vehicle Drivers
In traditional Miryoku engineering, the construction of product Kansei factors is only based on the qualitative analysis method. The traditional Miryoku engineering cannot effectively reflect the complex and changeable Kansei factors of users. Therefore, the research path of the Kansei factors needs to be expanded. In this paper, we proposed an evaluation-fuzzy-quantification model based on users’ Kansei, and the evaluation analysis, the fuzzy computing, and the quantitative analysis were combined to quantify the importance of design considerations for the instrument interface of electric vehicles. The characteristic of the proposed method is that the qualitative analysis and quantitative analysis are combined to overcome their respective drawbacks. The results of the experiment verified that the proposed method could quantitatively analyze the design consideration factors, and the proposed approach could improve the usability and appeal of the instrument information interface.