疲劳性能数据处理中的微分建模方法

考虑疲劳问题由微分方程控制的实质,直接应用微分方程模型处理疲劳性能数据。为此,引用灰色建模思想,认为一般的疲劳试验数据序列经过按矩形面积累加生成或按梯形面积累加生成后,其随机部分减弱,确定性信息得到加强,从而可用微分方程描述,微分方程的系数可通过微分近似公式由最小二乘法来直接辩识。由此导出线性微分方程DM(n,1)模型和非线性动态微分方程Verhulst模型的相关公式,并用于疲劳性能数据处理中的高周疲劳性能S—N曲线拟合、低周疲劳特性曲线拟合、疲劳裂纹扩展a—N曲线拟合与dadn—ΔK曲线拟合等问题,取得较好的效果,为疲劳性能数据处理提供新工具,对工程中建模和数据分析问题也有参考价值。

骨折端CT扫描参数个性化微分建模仿真目标骨段的准确性

背景:利用CT扫描骨折端,而后进行微分建模分析,是判断骨愈合程度一种行之有效的方法。为获得微分建模仿真的高精度,如何选择最优的CT扫描参数则需要进一步研究分析。目的:在个性化微分建模分析法中,对比不同CT扫描参数对建模精度的影响,验证个性化微分建模法对仿真目标骨段还原的准确性和有效性,探索该方法在判断下肢长管骨骨愈合程度中的研究价值。方法:用猪股骨建立内固定模型,分别采用80 kV-300 mA(A组-低剂量组)、120 kV-335 mA(B组-自动管电流调控系统组)、140 kV-300 mA(C组-手动设置对比组)、140 kV-80 mA(D组-高千伏低毫安组)4组不同曝光条件,进行相同螺距、层厚及环境的扫描,采用相同CT值范围,应用微分建模分析法分别进行目标骨段建模。对CT扫描图像中金属伪影的平均面积、最大面积,微分建模分析后的平均CT值、体积和最大壁厚峰值,以及4组扫描条件下辐射量进行比较,判断减小金属伪影、建模准确度及辐射情况,从而选出最优CT扫描参数。结果与结论:①伪影测量方法结果:A组金属伪影较多,对骨组织遮挡明显,存在漏诊可能;D组金属伪影最少,骨组织周围遮挡少,但图像对比度欠佳,灰雾度较大;而B、C组区别在于图像清晰度,对诊断的准确性基本一致,所以伪影大小排序为:A组>B组>C组>D组;②微分建模分析法结果:B组由于伪影较小,CT值丢失较少,所以仿真出的模型更加接近真实,而且B组采用自动管电流调控系统后,可以明显看出辐射量较小,更加保护患者;③提示B组条件下的CT扫描,可以有效减少金属伪影带来的干扰,更好地保留CT灰度值的原始信息,最大程度地保留目标骨段的密度信息。所以在建立微分建模时,CT自动管电流调控系统为最优的CT扫描参数,不仅可提高个性化微分建模的仿真精度,也增加了计算的准确性。

加权微分建模的初步研究

加权建模是必要的,微分建模是重要的,把二者结合起来,进行加权微分建模既必要也重要.给出了常用模型的微分建模结果,讨论了加权建模中的计算和权重选择问题,探讨了加权微分建模的思路和方法,并结合典型数据验证了该方法的有效性和稳定性.象加权建模一样,加权微分建模的精度、实用价值等,是和权重确定得合理与否紧密相联;应先进行模拟,以与近期实际值或典型样本相差最小的参数所对应的模型为准.

微分建模法及其在疲劳可靠性研究中的应用

很多工程问题可用微分方程描述,由此导出了微分建模方法.该方法的实质是直接用微分方程来描述客观物理现象,同时通过微分近似公式来直接辩识微分方程的系数.该方法用于三参数威布尔分布的参数估计和疲劳性能S N曲线拟合、低周疲劳特性曲线拟合、疲劳裂纹扩展a-N曲线拟合等问题,取得了较好的效果,为疲劳可靠性研究提供了新工具,对工程中建模和数据分析问题也有相当参考价值.

基于思维进化算法的常微分方程组演化建模

在基本的思维进化算法(Mind Evolutionary Computation, 原名Mind-Evolution-Based Machine Learning)框架[1]的基础上,吸取遗传规划(GP)中的树形编码思想,提出了利用树结构进行信息抽取的方法,进而实现了用于常微分方程组演化建模的趋同、异化算子,并获取了优良的效果,使MEC在非数值优化领域中得到了进一步应用。最后的仿真实例的结果表明,同GP方法[2]比较,MEC方法具有计算速度快、建模结果优和全局搜索性能好等明显优点。

Matlab软件在微分方程建模教学中的案例分析

本文通过精心收集整理的案例,演示了微分方程模型的建立过程,以及微分方程建立起来之后,如何利用Matlab软件通过拟合相关数据获得未知参数的具体数值。最后通过残差的向量2范数和计算树高与实际树高的对比图验证了本方法的有效性。

论即时战略游戏动态模型建立的教学应用

本文主要阐述了怎样把即时战略游戏这样一个游戏类型应用到数学微分方程建模的教学中去。并以一个具体的游戏为例。

导弹攻防对抗中追逃对策模型与配点求解法

未来的来袭导弹可能具备较强的机动性,其弹道不可预测,针对拦截弹追击此类目标的追逃问题,基于微分对策(differential game,DG)理论建立追逃博弈模型并给出求解方法。模型在分析两者相对运动的基础上,考虑地球重力和自转的影响,以推力角为控制变量,离地高度、速度和经度角为状态变量,建立微分方程组。然后将追逃DG模型转化为单边最优对策问题;并给出改进的高精度五阶Gauss-Lobatto多项式配点法来近似状态变量对时间的导数,将微分方程组转换为代数约束,降低非线性规划问题复杂程度。最后给出了本文研究的仿真实例。

偏微分高程图环境蚁群算法的三维路径规划

针对在三维空间路径规划中建模与避障问题,提出了一种新的在偏微分高程建模环境下蚁群算法的三维路径规划方法。首先,利用抽象建模和高程建模方法分别构建三维空间环境,并用偏微分对高程环境进行最优数据提取,在此基础上利用高程数学建模方法进行三维空间重建,最终形成偏微分高程环境。其次,首次将种群对于环境的最佳适应度值作为目标函数评判蚁群寻找最优路径的决策能力。最后,在不同的建模环境中应用蚁群算法进行路径寻优,输出最优路径。通过对仿真结果和实验数据分析,验证了所提方法的有效性和正确性。

森林救火模型改进

文献[1][2][3]解决了无风情况下的森林救火问题。当刮风时势必会加大火势,那么消防队如何根据风力做出判断,派出多少人救援会使得森林烧毁损失费和救援费总费用最小。考虑风力n级情况下,风力越大火势越大。文章把文献[1][2][3]中的图形建模转化为微分方程模型,用微分法对燃烧速度建立了新的模型,最后建立总费用模型,得出结论:风力越大,需要派出的救援人数越多,这一结论符合常理。

两类锂离子电池电化学机理模型的数值分析

在新能源锂离子电池领域,已有研究学者构造了若干种电池的电化学机理模型。为了分析相关物理化学过程,得到电池相关有效性质,基于DFN模型讨论电池的物理化学机制,使用了降阶简化后的单颗粒模型进行模拟研究。先采用不同的参数对单颗粒模型进行模拟,之后分析各个相关物理量,与DFN模型进行比较,得出精度控制良好一致性的范围,分析了模型预测的差异性。通过电池机理模型的研究,可获得电池的状态估计,这能够更好地认识电池。

电磁脉冲易损性分析方法

针对电磁脉冲易损性试验的两种情况,分别采取了不同的评估方法进行分析。对于成败型单元,分布参数的Bayes点估计为其验后分布的数学期望,并通过实例说明了其合理性;对于Weibull型单元,采用相关系数法或微分建模法进行参数估计,并用K-S检验了其合理性。

Logistic曲线预测沉降一种改进的求解方法

地基的全过程沉降量与时间的关系呈S形曲线,可用Logistic生长模型来描述。对模型参数的求解常用的三段法方法存在方法本身的缺陷,为此我们提出了非线性回归微分建模方法来求解模型参数,该方法具有一定的实用价值。

Modeling and solving for transverse vibration of gear with variational thickness

A analyzed model of gear with wheel hub, web and rim was derived from the Mindlin moderate plate theory. The gear was divided into three annular segments along the locations of the step variations. Traverse displacement, rotation angle, shear force and fiexural moment were equal to ensure the continuity along the interface of the wheel hub, web and rim segments. The governing differential equations for harmonic vibration of annular segments were derived to solve the gear vibration problem. The influence of hole to diameter ratios, segment thickness ratios, segment location ratios, Poisson ratio on the vibration behavior of stepped circular Mindlin disk were calculated, tabletted and plotted. Comparisons were made with the frequencies arising from the presented method, finite elements method, and structure modal experiment. The result correlation among these three ways is very good. The largest error for all frequencies is 5.46%, and less than 5% for most frequencies.

Modeling of radiative properties of metallic microscale rough surface

The radiative properties of a gold surface with one-dimensional Gaussian random roughness distribution were obtained with the finite-difference time-domain （FDTD） method and the recursive convolution treatment of the Drude Model. The bi-directional reflection distribution function （BRDF） for both TM mode and TE mode were obtained and compared with the highly accurate experimental data from the earlier work. The incident wavelength varies from 1.152 μm to 3.392 μm and incident angle is at 300-70°, respectively. The results show that, the predicted values and experimental results are in good agreement. The highly specular peak in the BRDF is reproduced in the numerical simulations, and the increase of the TM mode BRDF is found to be attributed to the effect of a variation in the optical constant at the incident wavelength period.

Application of differential equations in mathematical modeling

This paper introduces the main methods and steps of modeling principle by ordinary differential equations, and is used to explore the differential equation model to solve some practical problems, some features of the related problems. With the development of science and technology and production practice, differential equation is more closely connected with other subjects, and a mathematical model for some practical problems of good.

Groundwater Flow Modelling of Galma Basin, Nigeria： Using Finite Element Method

The groundwater flow characteristics of the Galma River Basin were simulated numerically by using the finite element method. The two-dimensional partial differential equation governing transient flow in an unconfined aquifer was modified to incorporate the effect of precipitation as a measurable source as it affects groundwater flow, such that for a given amount of precipitation over the basin, the flow of groundwater can be predicted at any point in the basin. With appropriate initial and boundary conditions, the modified equation was solved and the solution programmed for computer run. After calibration and verification, the borehole hydraulic data for the basin was used to predict flow due to groundwater hydraulic heads for 20 years. Findings revealed that there is a direct correlation of 0.79 and a strong linear relationship between simulated and observed hydraulic heads, and that data availability and choice of appropriate initial and boundary conditions are significant for good numerical modelling results. The contour plot of the hydraulic heads showed variation of heads from higher values at the upstream to lower values downstream, and groundwater flow follows the natural topography of the land from the upstream end of the basin towards the main streams and Galma River.

Damage and progressive failure of concrete structures using non-local peridynamic modeling

Peridynamics (PD), a recently developed theory of solid mechanics, which employs a non-local model of force interaction and makes use of integral formulation rather than the spatial partial differential equations used in the classical continuum mechanics theory, has shown effectiveness and promise in solving discontinuous problems at both macro and micro scales. In this paper, the peridynamics theory is used to analyze damage and progressive failure of concrete structures. A non-local peridynamic model for a rectangular concrete plate is developed, and a central pairwise force function is introduced to describe the interior interactions between particles within some definite distance. Damage initiation, evolution and crack propagation in the concrete model subject to in-plane uni-axial tension, in-plane uni-axial compression and out-of-plane impact load are investigated respectively. The numerical results show that discontinuities appear and grow spontaneously as part of the solution to the peridynamic equations of motion, and no special failure criteria or re-meshing techniques are required, which proves the potential of peridynamic modeling as a promising technique for analyzing the progressive failure of concrete materials and structures.

A method to estimate crop effects at higher frequencies by modeling and microwave radiometric data

To use the 0th-order τ-ω model to retrieve soil moisture from radiometric data at frequencies higher than the C band, the characteristics of the effective single scattering albedo ω and the opacity rof vegetation must be studied. In this paper, the co and r values of corn for the C, X, and Ku bands were retrieved by matching the simulations of a high-order matrix-doubling model to the τ-ω model. First, the brightness temperature of the matrix-doubling was validated by a truck-mounted radiometer in a field experiment, where the vegetation emission contributions were validated with aluminum foil to mask the soil emission. Then an emissivity database of corn fields for different growing seasons was established for a variety of soil conditions. With the transmissivity of corn determined from the database, the effective single scattering albedos of corn for different heights at the C, X, and Ku bands and at a 55° viewing angle were derived. To verify the accuracy of the derived co and τ values, we used SMEX02/PSR aircraft data and the Qp model to retrieve the soil moisture; the RMSE between the retrieval and the measurements was 4.76% at the C band and 5.36% at the X band.

Coupled 3D discrete-continuum numerical modeling of pile penetration in sand

A coupled discrete-continuum simulation incorporating a 3D aspect and non-circular particles was performed to analyze soil-pile interactions during pile penetration in sand.A self-developed non-circular particle numerical simulation program was used which considered sand near the pile as interacted particles using a discrete element method;the sand away from the pile was simulated as a continuous medium exhibiting linear elastic behaviors.The domain analyzed was divided into two zones.Contact forces at the interface between the two zones were obtained from a discrete zone and applied to the continuum boundaries as nodal forces,while the interface velocities were obtained from the continuum zone and applied to the discrete boundaries.We show that the coupled discrete-continuum simulation can give a microscopic description of the pile penetration process without losing the discrete nature of the zone concerned,and may significantly improve computational efficiency.