Nonlinear modal analysis via non‐parametric machine learning tools

Modal analysis is an important tool in the structural dynamics community; it is widely utilised to understand and investigate the dynamical characteristics of linear structures. Many methods have been proposed in recent years regarding the extension to nonlinear analysis, such as nonlinear normal modes or the method of normal forms, with the main objective being to formulate a mathematical model of a nonlinear dynamical structure based on observations of input/output data from the dynamical system. In fact, for the majority of structures where the effect of nonlinearity becomes significant, nonlinear modal analysis is a necessity. The objective of the current paper is to demonstrate a machine learning approach to output‐only nonlinear modal decomposition using kernel independent component analysis and locally linear‐embedding analysis. The key element is to demonstrate a pattern recognition approach which exploits the idea of independence of principal components from the linear theory by learning the nonlinear manifold between the variables. In this work, the importance of output‐only modal analysis via “blind source” separation tools is highlighted as the excitation input/force is not needed and the method can be implemented directly via experimental data signals without worrying about the presence or not of specific nonlinearities in the structure.     

深水水下管汇的结构设计概述

以南海某油气田的深水水下管汇为例,结合管汇的功能需求、结构组成、结构计算等,对深水水下管汇的结构设计进行了概述。     

Inverted pendulum stabilization: Characterization of codimension-three triple zero bifurcation via multiple delayed proportional gains

The paper considers the problem of stabilization of systems possessing a multiple zero eigenvalue at the origin. The controller that we propose, uses multiple delayed measurements instead of derivative terms. Doing so, we increase the performances of the closed loop in presence of system uncertainties and/or noisy measurements. The problem formulation and the analysis is presented through a classical engineering problem which is the stabilization of an inverted pendulum on a cart moving horizontally. On one hand, we perform a nonlinear analysis of the center dynamics described by a three dimensional system of ordinary differential equations with a codimension-three triple zero bifurcation. On the other hand, we present the complementary stability analysis of the corresponding linear time invariant system with two delays describing the behavior around the equilibrium. The aim of this analysis is to characterize the possible local bifurcations. Finally, the proposed control scheme is numerically illustrated and discussed.     

An overview of particle-based numerical manifold method and its application to dynamic rock fracturing

This review summarizes the development of particle-based numerical manifold method (PNMM) and its applications to rock dynamics. The fundamental principle of numerical manifold method (NMM) is first briefly introduced. Then, the history of the newly developed PNMM is given. Basic idea of PNMM and its simulation procedure are presented. Considering that PNMM could be regarded as an NMM-based model, a comparison of PNMM and NMM is discussed from several points of view in this paper. Besides, accomplished applications of PNMM to the dynamic rock fracturing are also reviewed. Finally, some recommendations are provided for the future work of PNMM.     

工件表面缺陷图像检测中的自适应聚类

目的 针对工件表面形态复杂、干涉交叠缺陷难以实现自动分离、分类图像检测的情况,提出一种工件表面交叠缺陷自适应图像聚类方法。方法 首先提取工件表面缺陷二值图像,采用混合概率主成分分析器估计缺陷位置各像素点局部切空间信息,并改进局部切空间之间的相似性矩阵;然后通过改进局部密度峰值自适应方法,基于相似性矩阵确定聚类中心点和数目;最后通过谱多流形聚类,将各分析器所包含的像素点分配至不同缺陷流形结构中,实现多个交叠缺陷分离、检测。结果 首先通过比较计算与实际测量的长度、宽度来验证该方法对相互交叠结构缺陷良好、准确的分离效果,平均相对误差分别为0.957%和0.650%。其次为了体现该方法对于分离工件表面相互交叠缺陷的有效性及优越性,使用k-means聚类、谱聚类与该方法进行对比实验,证明了该方法良好的聚类效果。最后对所设计方法的稳定性进行测试,统计检测结果的平均ME值均在6%以下,正确聚类数目率高达99%~100%。结论 该方法能够较为准确地自动识别工件表面图像中存在相互干涉的不同缺陷,并进行分离。     

岩石冲击破坏的数值流形方法模拟(英文)

岩石冲击破坏是一种典型的动力学问题。为了更好地利用数值流形方法对动力学问题进行分析,本文在对原数值流形方法中的动力学问题求解思想进行分析的基础上,采用动力有限元方法中的Newmark法对该算法进行了改进。改进后的数值流形方法与原来相比具有3个明显的优势:①当选择合适的参数后,该方法能够保证解的无条件收敛;②可以采用比原算法大的多的时间步长;③充分地考虑了动力学问题中的阻尼效应。最后通过一个算例说明了改进后的数值流形方法能够很好地模拟岩石在冲击载荷作用下破坏的全过程,克服了有限元法不能模拟岩石破坏后块体运动情况的不足。     

数值流形方法中的几点改进

简述了岩石力学中的数值流形方法及其分析过程，并就流形方法的具体实施作了几点改进，给出了相应的公式和算例。     

四面体有限单元覆盖的三维数值流形方法

构造三维流形单元的覆盖函数和总体位移函数，基于最小势能原理建立四面体有限单元覆盖的三维数值流形方法分析格式，详细推导了三维流形单元的刚度矩阵、初应力矩阵、荷载矩阵、惯性矩阵、位移约束矩阵和接触矩阵，并给出了相应的公式和算例。     

势问题的数值流形方法

以往的数值流形方法都是以最小势能原理或变分原理为基础来建立求解方程的。但在实际工程中有些实际问题,无法应用变分方法来建立数值流形方法的求解方程,必须寻找较一般的方法来推导数值流形方法的求解方程。本文研究了如何从加权残数法出发建立拉普拉斯方程数值流形方法的求解方程。通过建立拉普拉斯方程的数值流形方法,充实了数值流形方法的数学基础,并拓宽了其应用领域。最后以热传导和渗流为例,验证了本文方法的正确性。     

数值流形法在地壳形变场分析中的可行性研究

阐述了数值流形方法是综合传统有限元和非连续变形分析的一种新的数值分析方法，对该方法的基本思想和地壳变形的力学特征进行了分析，讨论了该方法在地壳形变场的分析中的可行性，具有广泛的研究应用前景。