Bootstrap approximation of wavelet estimates in a semiparametric regression model

The inference for the parameters in a semiparametric regression model is studied by using the wavelet and the bootstrap methods. The bootstrap statistics are constructed by using Efron＇s resampling technique, and the strong uniform convergence of the bootstrap approximation is proved. Our results can be used to construct the large sample confidence intervals for the parameters of interest. A simulation study is conducted to evaluate the finite-sample performance of the bootstrap method and to compare it with the normal approximation-based method.     

Prediction of Gas-Liquid Pressurization Performances of Multistage Multiphase Pumps Based on Similarity Laws and Neural Networks北大核心CSCD

It is very important to accurately predict the gas-liquid pressurization performance of multiphase pumps for the economy and safety of oil-gas production. Existent prediction models and methods are limited by narrow parameter ranges and low pump stages. A gas-liquid experimental platform at the industrial level was built, and the gas-liquid pressurization performances of a 25-stage centrifugal multiphase pump were obtained. A prediction method for gas-liquid pressurization performances was proposed for multiphase pumps with high stages at variable rotational speeds. Firstly, the artificial neural network of gas-liquid boosting pressure in the pump with low stages at a constant rotational speed, was constructed. Then, the boosting pressures at variable rotational speeds were converted to the designed condition by the 2-phase similarity law. Finally, based on the isothermal compression hypothesis, the inter-stage flow parameters were updated and the boosting pressures in pumps with high stages were acquired. The relative errors of prediction results of gas-liquid pressurization were less than 15% in pumps with different stage numbers (3~25 stages) and rotational speeds (2 500~3 500 r·min-1). The proposed method can be applied to other types of multiphase pumps, to determine the stage numbers of multiphase pumps and make production evaluation in oil-gas industry. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Numerical Simulation of Hydraulic Fractures Intersecting Natural Fractures in Shale With Plastic Deformation北大核心CSCD

The plastic deformation and numerous natural joints of shale pose a great challenge for the predic⁃ tion of the hydraulic fracture geometry extension. Based on the finite element method, a fully coupled numeri⁃ cal model for elastoplastic hydraulic fractures was established with natural fractures and bedding planes consid⁃ ered. The numerical model was validated with the KGD analytical solution and Blanton’s curve. The numerical results show that, compared with the numerical model solution of linear elasticity, the hydraulic fractures are prone to enter the natural weak interface due to the rock plastic deformation. The rock plastic deformation area mainly lies in the reservoir layer during the fracture propagation. In the case of rock ductile damage, the hy⁃ draulic fracture is more likely to penetrate the bedding plane. Hydraulic fractures can directly penetrate natural fractures and bedding planes at high injection rates due to large driving forces. The study provides new insights in terms of hydraulic fracture extension in elastoplastic formations. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

三参数Weibull分布参数和其它可靠性指标的区间估计方法

This paper discusses the interval estimations method for the parameters and other reliability characters of a three-poxameter Weibull distribution. According to the fiducial distrlbution theory of the parameter, the author presents the confidence intervals of the porameters, the reliability and the reliable life. An example mad simulation results are given. It is shown that the method presented in this paper is practicable and worth noticing.     

Surface Acoustic Wave Characterization of Equivalent Young's Moduli for Patterned Films北大核心CSCD

Based on the equivalent elasticity theory for layered materials, the micro-mechanics equivalent models for single and dual damascene structures were established. The equivalent elastic constant of the patterned structure was introduced, to establish the propagation model for the surface acoustic waves propagating in the layered structure of the patterned film/ substrate, and the theoretical dispersion curves of the surface acoustic waves were calculated with Green’s function and the matrix method. The finite element method was used to calculate 24 numerical examples of damascene structures with different volume ratios, and the results were compared with those of the strain energy method. The results show that, the average relative errors of the equivalent Young’s moduli of the 300 nm-thick dual damascene film and the 100 nm-thick single damascene film are 2.06% and 2.27%, respectively. The research verifies the correctness of the equivalent patterned structure model and the feasibility of the surface acoustic wave method to characterize the mechanical properties of patterned films, and provides a reference for the development of suitable chemico-mechanical polishing technologies for patterned films under low pressure. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

A Spatial Geometric Nonlinearity Spline Beam Element With Nodal Parameters Containing Strains北大核心CSCD

Many slender rods in engineering can be modeled as Euler-Bernoulli beams. For the analysis of their dynamic behaviors, it is necessary to establish the dynamic models for the flexible multi-body systems. Geometric nonlinear elements with absolute nodal coordinates help solve a large number of dynamic problems of flexible beams, but they still face such problems as shear locking, nodal stress discontinuity and low computation efficiency. Based on the theory of large deformation beams’ virtual power equations, the functional formulas between displacements and rotation angles at the nodes were established, which can satisfy the deformation coupling relationships. The generalized strains to describe geometric nonlinear effects in this case were derived. Some parameters of boundary nodes were replaced by axial strains and sectional curvatures to obtain a more accurate and concise constraint method for applying external forces. To improve the numerical efficiency and stability of the system’s motion equations, a model-smoothing method was used to filter high frequencies out of the model. The numerical examples verify the rationality and effectiveness of the proposed element. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

COMPUTATIONAL MULTISCALE METHODS FOR LINEAR HETEROGENEOUS POROELASTICITY

We consider a strongly heterogeneous medium saturated by an incompressible viscous fluid as it appears in geomechanical modeling.This poroelasticity problem suffers from rapidly oscillating material parameters,which calls for a thorough numerical treatment.In this paper,we propose a method based on the local orthogonal decomposition technique and motivated by a similar approach used for linear thermoelasticity.Therein,local corrector problems are constructed in line with the static equations,whereas we propose to consider the full system.This allows to benefit from the given saddle point structure and results in two decoupled corrector problems for the displacement and the pressure.We prove the optimal first-order convergence of this method and verify the result by numerical experiments.     

HYBRID REGULARIZED CONE-BEAM RECONSTRUCTION FOR AXIALLY SYMMETRIC OBJECT TOMOGRAPHY

In this paper,we consider 3 D tomographic reconstruction for axially symmetric objects from a single radiograph formed by cone-beam X-rays.All contemporary density reconstruction methods in high-energy X-ray radiography are based on the assumption that the cone beam can be treated as fan beams located at parallel planes perpendicular to the symmetric axis,so that the density of the whole object can be recovered layer by layer.Considering the relationship between different layers,we undertake the cone-beam global reconstruction to solve the ambiguity effect at the material interfaces of the reconstruction results.In view of the anisotropy of classical discrete total variations,a new discretization of total variation which yields sharp edges and has better isotropy is introduced in our reconstruction model.Furthermore,considering that the object density consists of continually changing parts and jumps,a high-order regularization term is introduced.The final hybrid regularization model is solved using the alternating proximal gradient method,which was recently applied in image processing.Density reconstruction results are presented for simulated radiographs,which shows that the proposed method has led to an improvement in terms of the preservation of edge location.     

HYBRID REGULARIZED CONE-BEAM RECONSTRUCTION FOR AXIALLY SYMMETRIC OBJECT TOMOGRAPHY

In this paper,we consider 3 D tomographic reconstruction for axially symmetric objects from a single radiograph formed by cone-beam X-rays.All contemporary density reconstruction methods in high-energy X-ray radiography are based on the assumption that the cone beam can be treated as fan beams located at parallel planes perpendicular to the symmetric axis,so that the density of the whole object can be recovered layer by layer.Considering the relationship between different layers,we undertake the cone-beam global reconstruction to solve the ambiguity effect at the material interfaces of the reconstruction results.In view of the anisotropy of classical discrete total variations,a new discretization of total variation which yields sharp edges and has better isotropy is introduced in our reconstruction model.Furthermore,considering that the object density consists of continually changing parts and jumps,a high-order regularization term is introduced.The final hybrid regularization model is solved using the alternating proximal gradient method,which was recently applied in image processing.Density reconstruction results are presented for simulated radiographs,which shows that the proposed method has led to an improvement in terms of the preservation of edge location.     

A Pseudo-Kinetic Approach for Helmholtz Equation

A lattice Boltzmann type pseudo-kinetic model for a non-homogeneous Helmholtz equation is derived in this paper. Numerical results for some model problems show the robustness and efficiency of this lattice Boltzmann type pseudo-kinetic scheme. The computation at each site is determined only by local parameters, and can be easily adapted to solve multiple scattering problems with many scatterers or wave propagation in non-homogeneous medium without increasing the computational cost.     

Correlation propagation for uncertainty analysis of structures based on a non-probabilistic ellipsoidal model

Traditional non-probabilistic methods for uncertainty propagation problems evaluate only the lower and upper bounds of structural responses, lacking any analysis of the correlations among the structural multi-responses. In this paper, a new non-probabilistic correlation propagation method is proposed to effectively evaluate the intervals and non-probabilistic correlation matrix of the structural responses. The uncertainty propagation process with correlated parameters is first decomposed into an interval propagation problem and a correlation propagation problem. The ellipsoidal model is then utilized to describe the uncertainty domain of the correlated parameters. For the interval propagation problem, a subinterval decomposition analysis method is developed based on the ellipsoidal model to efficiently evaluate the intervals of responses with a low computational cost. More importantly, the non-probabilistic correlation propagation equations are newly derived for theoretically predicting the correlations among the uncertain responses. Finally, the multi-dimensional ellipsoidal model is adopted again to represent both uncertainties and correlations of multi-responses. Three examples are presented to examine the accuracy and effectiveness of the proposed method both numerically and experimentally.     

Computation of material forces for the thermo-mechanical response of dynamically loaded elastomers

Elastomers are widely used in today's life. The material is characterized by large deformability upon failure, elastic and time dependent as well as non-time dependent effects which can be also a function of temperature. In addition, cyclically loaded components show heat build-up which is due to dissipation. As a result, the temperature evolution of an elastomeric component can strongly influence the material properties and durability characteristics. Representing best the real thermo-mechanical behaviour of an elastomeric component in its design process is one motivation for the use of sophisticated, coupled material approaches within numerical simulations. In order to assess the durability characteristics, for example regarding crack propagation, material forces (configurational forces) are one possible approach to be applied. In the present contribution, the implementation of material forces for a thermo-mechanically coupled material model including a continuum mechanical damage (CMD) approach is demonstrated in the context of the Finite Element Method (FEM). Special emphasis is given to material forces resulting from internal variables (viscosity and damage variables), temperature field evolution and dynamic loading. Using the example of an elastomeric component, for which the material model parameters have been previously identified by a uniaxial extension test, material forces are evaluated quantitatively. The influence of each contribution (internal variables, temperature field and dynamics) is illustrated and compared to the overall material force response. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the Sensitiveness of Absorption Coefficient to Changes in Material Parameters

An essential property of porous absorbers is the resistance to the incident sound wave, resulting in a damping effect. Damping results from the friction between air molecules and absorber pore-walls. In practice, the known dependencies of the sound absorption coefficient are used in the design of absorbers. But not every material can be characterized by a one-parameter model. The reliability of prediction can be improved by using detailed material models. Hence, additional material parameters, especially the pore geometry are needed. Since in practice the effort for determining material parameters must be minimized, this paper discusses the sensitivity of prediction of absorbers' performance depending on the influence of material parameters that are input for the prediction model chosen. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

串联系统多参数广义不确定度传递模式与多反馈控制

将多参数广义不确定度的概念引入串联系统参数不确定度的传递问题中,建立了串联系统多参数广义不确定度传递模型,该模型不仅揭示了参数不确定度在传递过程中的变化情况,传递细节表明传递矩阵元素对最后的传递结果有重要影响.文中阐述了传递矩阵的特征以及各个子系统在串联系统中的主次作用.针对串联系统建立了多参数广义不确定度多反馈控制模型,提出了针对单个系统、两个子系统、多个子系统多个层次的反馈控制模型.模型的提出从理论上说明了当对子系统传递矩阵进行修正时,输出参数不确定度的变化及其上界的面积范数,为工程实际提供了一个良好的理论模型支撑.     

基于GA-SVM的太原市空气质量指数预测

针对大气环境的复杂多变性和不确定性,采用太原市2014年至2016年的空气污染物监测数据,分别将改进的粒子群算法(IPSO)和遗传算法(GA)与支持向量机(SVM)相结合,通过参数寻优构建新模型完成对空气质量指数(AQI)的预测.实验结果表明,GA-SVM在预测精度、误差率和可靠性方面均优于IPSO-SVM与SVM.因此GA-SVM模型更适用于AQI的预测,为大气污染防治提供了科学合理的理论依据和新的预测方法.     

On Configurational-Force-Driven Crack Propagation and Adaptive Mesh Refinement in Finite Inelasticity

We introduce a consistent variational framework for inelasticity at finite strains, yielding dual balances in physical and material space as the Euler equations. The formulation is employed for the simultaneous usage of configurational forces as both driving forces for crack propagation as well as h-adaptive mesh refinement. The theoretical basis builds upon a global balance of internal and external power, where the mechanical response is exclusively governed by two scalar functions, the free energy function and a dissipation potential. The resulting variational structure is exploited in the context of fracture mechanics and yields evolution equations for internal variables. In the discrete setting, we present a geometry model fully separated from the finite element mesh structure that represents structural changes of the material configuration due to crack propagation. Advanced meshing algorithms provide an optimal discretization at the crack tip. Local and global criteria are obtained via error estimators based on configurational forces being interpreted as indicators of an energetic misfit due to an insufficient discretization. The numerical handling is decomposed into a staggered algorithm scheme for the dual set of equilibrium equations in material and physical space and efficient mesh generation tools. Exemplary numerical examples are considered to illustrate the method and to underline the effects of inelastic material behaviour in the presented context. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Diamond折纸管状结构轴向冲击性能分析

为了降低薄壁管状结构受轴向冲击时的初始峰值载荷,将diamond刚性折纸模型引入到薄壁管状结构的设计中.利用有限元分析方法,以方形截面为例,分析了diamond折纸管状结构的轴向冲击性能.结果表明:相比于传统方形薄壁管,diamond折纸管状结构具有较低的初始峰值载荷和更加平稳的变形过程.得出了diamond折纸管状结构按折纸预折形式变形的临界条件.分析了diamond折纸管状结构在轴向冲击载荷作用下,底角对初始峰值载荷和平均冲击载荷的影响.     

Novel reliability-based optimization method for thermal structure with hybrid random,interval and fuzzy parameters

In this paper, novel reliability-based optimization model and method are proposed for thermal structure design with random, interval and fuzzy uncertainties in material properties, external loads and boundary conditions. Random variables are used to quantify the probabilistic uncertainty with sufficient sample data; whereas, interval variables and fuzzy variables are adopted to model the non-probabilistic uncertainty associated with objective limited information and subjective expert opinions, respectively. Using the interval ranking strategy, the level-cut limit state function is precisely quantified to represent the safety state. The eventual safety possibility is derived based on multiple integral, where the cut levels of different fuzzy variables are considered to be independent. Then a hybrid reliability-based optimization model is established with considerable computational cost caused by three-layer nested loop. To improve the computational efficiency, a subinterval vertex method is presented to replace the inner-loop and middle-loop. Comparing numerical results with traditional reliability model, a mono-objective example and a multi-objective example are provided to demonstrate the feasibility of proposed method for hybrid reliability analysis and optimization in practical engineering.     

The Elastodynamics of Embryonic Epidermal Wound Closure

This paper is concerned with the elastodynamics of embryonic epidermal wound closing. Underlying the recovery process for this type of wounds is a mechanism of wound recognition through directed cell-to-cell signaling. The observed actin filament realignment induced by the biological signals leads to a purse-string effect and the resulting (unknown) "active stresses." The circumferential contraction of the epidermis surrounding the wound is then determined by the laws of mechanics and propagation properties of the relevant cell–cell signaling that decays with distance. With the wound known to retract for a short period immediately after infliction, the quasi-equilibrium configuration reached during this initial phase serves as the initial condition for the dynamic wound closing phase. A small strain variation of the Murray–Sherratt model of the quasi-equilibrium problem will be formulated for speedy computation of this initial state at the inception of the wound closure phase, with the latter problem being the main concern of this paper. Some theoretical developments are found to be instrumental to an efficient algorithm for the otherwise time-consuming task of calculating the effect of the biological signals generated by the presence of a wound. Application of our elastodynamic model to the case of a circular wound suggests that the propagation range of our choice of cell–cell signaling mechanism must be above a certain minimum fraction of the wound radius for wound closure. As expected, stress concentration occurs adjacent to the edge of the remaining small wound near the end of the wound closing process. At that point, the present model is not expected to be adequate and more appropriate expressions of elastic strain and active stress induced by actin filaments may be in order. Other biological processes such as cell proliferation and differentiation may be involved.     

Hyperbolastic modeling of wound healing

A new mathematical model for wound healing is introduced and applied to three sets of experimental data. The model is easy to implement but can accommodate a wide range of factors affecting the wound healing process. The data sets represent the areas of trace elements, diabetic wounds, growth factors, and nutrition within the field of wound healing. The model produces an explicit function accurately representing the time course of healing wounds from a given data set. Such a function is used to study variations in the healing velocity among different types of wounds and at different stages in the healing process. A new multivariable model of wound healing capable of analyzing the effects of several variables on accelerating the wound healing process is also introduced. Such a model can help to formulate appropriate strategies to treat wounds. It also would enable us to evaluate the efficacy of different treatment modalities during the inflammatory, proliferative, and tissue remodeling phases.