Model reduction for nonlinear multiscale parabolic problems using dynamic mode decomposition

In this article, a model reduction technique is presented to solve nonlinear multiscale parabolic problems using dynamic mode decomposition. The multiple scales and nonlinearity bring great challenges for simulating the problems. To overcome this difficulty, we develop a model reduction method for the nonlinear multiscale dynamic problems by integrating constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) with dynamic mode decomposition (DMD). CEM-GMsFEM has shown great efficiency to solve linear multiscale problems in a coarse space. However, using CEM-GMsFEM to directly solve multiscale nonlinear parabolic models involves dynamically computing the residual and the Jacobian on a fine grid. This may be very computationally expensive because the evaluation of the nonlinear term is implemented in a high-dimensional fine scale space. As a data-driven method, DMD can use observation data and give an explicit expression to accurately describe the underlying nonlinear dynamic system. To efficiently compute the multiscale nonlinear parabolic problems, we propose a CEM-DMD model reduction by combing CEM-GMsFEM and DMD. The CEM-DMD reduced model is a coarsen linear model, which avoids the nonlinear solver in the fine space. It is crucial to judiciously choose observation in DMD. Only proper observation can render an accurate DMD model. In the context of CEM-DMD, we introduce two different observations: fine scale observation and coarse scale observation. In the construction of DMD model, the coarse scale observation requires much less computation than the fine scale observation. The CEM-DMD model using the coarse scale observation gives a complete coarse model for the nonlinear multiscale dynamic systems and significantly improves the computation efficiency. To show the performance of the CEM-DMD using the different observations, we present a few numerical results for the nonlinear multiscale parabolic problems in heterogeneous porous media.     

Novel method of constructing generalized Hoberman sphere mechanisms based on deployment axes

This study proposes a method of constructing type II generalized angulated elements (GAEs II) Hoberman sphere mechanisms on the basis of deployment axes that intersect at one point. First, the constraint conditions for inserting n GAEs II into n deployment axes to form a loop are given. The angle constraint conditions of the deployment axes are obtained through a series of linear equations. Second, the connection conditions of two GAEs II loops that share a common deployable center are discussed. Third, a flowchart of constructing the generalized Hoberman sphere mechanism on the basis of deployment axes is provided. Finally, four generalized Hoberman sphere mechanisms based on a fully enclosed regular hexahedron, arithmetic sequence axes, orthonormal arithmetic sequence axes, and spiral-like axes are constructed in accordance with the given arrangement of deployment axes that satisfy the constraint conditions to verify the feasibility of the proposed method.     

Actuator fault estimation based on generalized learning observer for quasi-linear parameter varying systems

This article presents a generalized learning observer (GLO) design for the simultaneous estimation of states and actuator faults for polytopic quasi-linear parameter varying systems. The proposed approach is based on the use of a GLO, which generalized the existing results on the proportional-integral observers. Conditions of existence and stability of the observer are given through the stability analysis in the sense of Lyapunov. Its design is obtained in terms of a set of linear matrix inequalities. The performance of the proposed method is evaluated by simulation in a one-link-flexible joint robot system.     

基于PSO-GRNN模型的埋地管道腐蚀剩余寿命预测

目的 构建埋地管道腐蚀深度预测模型,预测腐蚀管道的剩余使用寿命。方法 依据ASME B31G剩余强度评价标准,给出管道的最大允许腐蚀深度计算方法,引入广义回归神经网络（GRNN）,构建埋地管道腐蚀深度预测模型,采用粒子群算法（PSO）优化GRNN的网络参数,结合管道腐蚀发展趋势预测方法,对埋地薄弱管道进行腐蚀剩余寿命预测。以陕西省某埋地输油管道为例,选取8个主要外腐蚀因素,构建外腐蚀指标体系,借助Pycharm编程仿真,结合埋片试验,对该模型预测结果进行验证分析,并预测各腐蚀管段剩余使用寿命。结果 与BP模型相比,PSO-GRNN模型的管道腐蚀深度预测结果最大相对误差控制在13.77%以内,平均相对误差仅为6.63%。寿命预测结果显示,部分管段的剩余使用寿命未能达到其预期服役寿命。结论 所建模型预测性能要明显优于BP模型,预测精度更高,能够较好地预测埋地管道的最大腐蚀深度和未来的腐蚀发展规律,剩余寿命预测结果贴近实际,为管道的维修和更换提供了指导依据,在实际工程中,具有一定的应用价值。     

利用ANSYS程序分析软岩冲击矿压及广义应力(应变)率准则

利用ANSYS程序分析了权台煤矿软岩冲击矿压。通过对所得数据的处理。总结出一种用于判断冲击矿压的广义应力(应变)率准则。即冲击矿压发生时。冲击点附近的应力(应变)变化比其他时刻同地的变化和其他位置同时刻的变化都为剧烈。并将这一准则用于工作面回采时的冲击矿压预测。结果是合理的。     

灰元、灰代数及广义概率空间

把灰数结构理论推广到一般被认识对象,得到了灰元、灰事件及灰代数,在认知结构上建立了允许概率动态变化的广义概率空间;分析了A·H·Kолмогоров概率空间的局限性,讨论了广义概率空间的可能应用前景。     

一种估计结构面迹长的新方法及其工程应用

为了研究结构面迹长与其产状之间的概率关系。根据结构面交切测量窗口的几何条件与交切频度之间的概率关系，拓展了H-H迹长估计方法。建立了结构面平均迹长与其在测量窗口中视倾角的关系表达式。在此基础上,结合Laslett迹长估计方法，提出了广义H-H迹长估计方法，进一步完善了H-H方法，并通过工程实例证明了其正确性。该方法使用简单方便，有很高的推广价值。     

开挖处理的虚拟单元广义初应力法及应用

结合岩土工程有限元分析软件开发的需要,提出单元开挖问题处理的虚拟单元广义初应力法,并基于该方法设计分步开挖问题数值分析算法,应用该方法编制的程序对一分步开挖问题进行了数值模拟分析,提出了虚拟单元广义初应力方法在岩土工程有限元分析软件设计及编程等方面的特点。     

北京地区非饱和土土压力初步研究

根据朗肯土压力理论,北京地区土压力计算值远大于实测土压力值。针对这个急需解决的问题进行了探讨,引入广义朗肯土压力公式,结合北京地铁13号线东直门车站基坑支护工程,对理论计算土压力和实测土压力进行了详细的分析,给出了该地区非饱和土土压力计算的基于试验指标的广义朗肯土压力表达式。     

用广义协调Coons混合曲面元分析中厚板的振动

利用文献[1]的厚薄板通用广义协调元Coons混合曲面法分析了中厚板的振动,其优点是自由度少、精度高、程序简便、收敛快。算例计算出了四边简支方板的前几阶频率,其结果与文献[2]的结果符合良好。