Hierarchical deep learning for data-driven identification of reduced-order models of nonlinear dynamical systems

Nonlinear Dynamics - Identifying reduced-order models (ROMs) of nonlinear dynamical systems is difficult, especially when the system equation is unknown with only measurement data available. In...     

基于深度学习的跨分辨率结构拓扑优化设计方法

在传统拓扑优化设计中,随着结构单元增加,迭代计算过程消耗了大量的时间.本文提出了一种基于深度学习的方法来加速拓扑优化设计过程,缩短了结构拓扑优化设计的迭代过程,并生成了高分辨率拓扑优化结构.利用深度学习方法,在低分辨率中间构型与高分辨率拓扑构型之间创建高维映射关系,利用独立、连续和映射(ICM)方法建立深度学习网络所需...     

基于深度学习和近场动力学的层合板冲击工况识别

在冲击荷载作用下复合材料会产生断裂和分层等损伤。基于损伤数据对冲击工况进行识别，对改善复合材料的设计和确保其安全使用具有重要意义。基于此，本文提出一种基于深度学习和近场动力学（PD）理论的层合板冲击工况识别方法。首先使用改进的表面修正系数PD理论建立复合材料层合板刚体冲击损伤演化分析PD模型，PD模型数值模拟结果结合噪声数据增强技术构建层合板的冲击工况数据库；基于深度学习-卷积神经网络（CNN），对不同工况下的冲击损伤演化数据进行训练，实现对未知冲击工况的识别。结果显示，对于钢球冲击速度和角度的识别准确率均高于90%。     

基于拓扑优化和深度学习的新型结构生成方法

计算机辅助设计已广泛应用于结构计算和分析,但如何利用计算机智能生成最佳的新型结构还面临巨大挑战。针对这一问题,提出了一种基于拓扑优化和深度学习的新型结构智能生成方法。该方法首先通过结构拓扑优化分析获得不同参数下的优化结果制作训练集图片,并将训练集标签定义为相应的工况类型,然后应用最小二乘生成对抗网络(LSGAN)深度学习算法进行训练并生成大量的新型结构,最后建立评价指标和评估体系对生成的模型进行评价比较,根据需求选择最佳结构设计方案。结合一个铸钢支座节点底板设计的工程案例,详细阐述了上述方法的应用过程,并借助三维重构技术和增材制造技术实现结构模型的一体化制造。研究结果表明,基于拓扑优化和深度学习的新型结构智能生成方法不仅可以自动生成新的结构,而且可以进一步优化结构的材料用量和力学性能。     

基于自适应神经模糊推理系统的陀螺建模方法

系统地介绍了近年来陀螺信号处理中出现的各种主要的滤波方法,并分析了各自的优缺点.针对陀螺输出信号自身的特点,提出了一种基于自适应神经模糊推理系统的陀螺滤波方法,建立了陀螺误差模型.提出的滤波方法同时具有神经网络与模糊逻辑推理的优点,从而有效地减小了建模误差.分别探讨了陀螺静态时的零偏信号估计模型与敏感动态信号时的滤波方案.由仿真结果可以看出,该方法可以有效地估计陀螺的零偏,并能抑制陀螺输出信号中的噪声.     

在哈密顿体系下分析非线性动力学问题

首先将ｎ维未知向量ｑ的二阶非线性力系统Ｍｑ＋Ｇｑ＋Ｋｑ＝Ｆ（ｑ,ｑ,ｔ）转化为与其等价的２ｎ维未知向量ｖ的一阶微分方程ｖ＝Ｈｖ＋ｆ（ｖ,ｔ）,其中非线性部分ｊｉ（ｖ,ｔ）＝０（ｉ＝１,．．．ｎ）,ｆｉ（ｖ,ｔ）＝Ｆｉ－ｎ（ｑ,ｑ,ｔ）（ｉ＝ｎ＋１,．．．２ｎ）;然后给出一种求解ｖ的逐步积分公式,从而将精细积分法进一步推广应用到非线性动力学问题。算例表明本方法的计算量较小且结果合理可靠。     

一类非线性磁流变系统局部分岔特性研究

讨论了一类基于磁流变阻尼器非线性系统的局部分岔与控制问题,建立了该系统的动力学模型,运用中心流形定理和范式理论,得到该系统双零特征值问题的规范形及其普适开折,进而探讨了此系统的分岔行为和稳定性;给出了分岔曲线、转迁集;并给出了此类非线性系统的数值仿真结果.     

State reconstruction in a nonlinear vehicle suspension system using deep neural networks

Nonlinear Dynamics - In this paper, the optimal formation and optimal matching of a multi-robot system are investigated with a projection-based algorithm designed to get the optimal formation...     

A time-domain nonlinear system identification method based on multiscale dynamic partitions

Based on a theoretical foundation for empirical mode decomposition, which dictates the correspondence between the analytical and empirical slow-flow analyses, we develop a time-domain nonlinear system identification (NSI) technique. This NSI method is based on multiscale dynamic partitions and direct analysis of measured time series, and makes no presumptions regarding the type and strength of the system nonlinearity. Hence, the method is expected to be applicable to broad classes of applications involving time-variant/time-invariant, linear/nonlinear, and smooth/non-smooth dynamical systems. The method leads to nonparametric reduced order models of simple form; i.e., in the form of coupled or uncoupled oscillators with time-varying or time-invariant coefficients forced by nonhomogeneous terms representing nonlinear modal interactions. Key to our method is a slow/fast partition of transient dynamics which leads to the identification of the basic fast frequencies of the dynamics, and the subsequent development of slow-flow models governing the essential dynamics of the system. We provide examples of application of the NSI method by analyzing strongly nonlinear modal interactions in two dynamical systems with essentially nonlinear attachments.     

Spline adaptive filters based on real-time over-sampling strategy for nonlinear system identification

Nonlinear Dynamics - In this paper, a new spline adaptive filter (SAF) used for identifying the nonlinear systems is presented, in which a real-time over-sampling (RTOS) strategy is proposed in...     

GEOMETRIC FRAMEWORK AND MINIMAL REALIZATIONS OF NONLINEAR SYSTEMS ON FIBRE BUNDLE

ＧＥＯＭＥＴＲＩＣＦＲＡＭＥＷＯＲＫＡＮＤＭＩＮＩＭＡＬＲＥＡＬＩＺＡＴＩＯＮＳＯＦＮＯＮＬＩＮＥＡＲＳＹＳＴＥＭＳＯＮＦＩＢＲＥＢＵＮＤＬＥＭｕＸｉａｏｗｕ（慕小武）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＺｈｅｎｇｚｈｏｕＵｎｉｖｅｒｓ...     

Modeling and analysis of a piezoelectric transducer embedded in a nonlinear damped dynamical system

This paper focuses on the dynamical analysis of the motion of a new three-degree-of-freedom (DOF) system consisting of two segments that are attached together. External harmonic forces energize this system. The equations of motion (EOM) are derived utilizing Lagrangian equations, and the approximate solutions up to the third order are investigated using the methodology of multiple scales. A comparison between these solutions and numerical ones is constructed to confirm the validity of the analytic solutions. The modulation equations (ME) are acquired from the investigation of the resonance cases and the solvability conditions. The bifurcation diagrams and spectrums of Lyapunov exponent are presented to reveal the different types of the system’s motion and to represent Poincaré maps. The piezoelectric transducer is connected to the dynamical system to convert the vibrational motion into electricity; it is one of the energy harvesting devices which have various applications in our practical life like environmental and structural monitoring, medical remote sensing, military applications, and aerospace. The influences of excitation amplitude, natural frequency, coupling coefficient, damping coefficient, capacitance, and load resistance on the output voltage and power are performed graphically. The steady-state solutions and stability analysis are discussed through the resonance curves.

     

基于Caputo导数的分数阶非线性振动系统响应计算

研究了含分数阶Caputo导数的非线性振动系统响应的数值计算方法。首先,由Caputo分数阶导数算子的叠加关系,得到含分数阶导数项非线性振动系统状态方程的标准形式。其次,基于Caputo导数与Riemann-Liouville导数和Grunwald-Letnikov导数间的关系,推导计算了Caputo导数的一般数值迭代格式。本文方法不要求状态方程中各分数阶导数阶数相等,弱化了已有算法中对分数阶导数阶数的限制,并可推广到多自由度的情形。随后,选择若干有解析解的算例验证了本文方法的正确性。最后,以多吸引子共存的分数阶Duffing振子系统为例,比较Caputo和GL两种算法所得结果,说明了用GL算法求解存在的问题。     

基于开放式结构有限元系统SiPESC.FEMS的动力时程分析通用算法构架

基于开放式结构有限元分析软件系统SiPESC.FEMS,针对动力时程分析算法共性,采用C++面向对象程序设计方法和软件设计模式,研发了一种结构动力分析通用算法构架。构架的核心思想是算法与数据模型相分离,从而实现算法通用性,整个构架由四个基本类及子类构成。本文重点阐述了基本类的抽象过程和通用接口的设计思想,给出了利用插件技术实现算法构架的步骤。利用该构架已实现了Newmark法、Wilson-θ法、中心差分法及改进中心差分法,并进行数值验证。研究工作表明,算法构架适用于通用时程积分算法,可方便地进行动态扩展,具备良好的开放性和重用性。     

Physics-informed deep learning for digital materials

In this work, a physics-informed neural network(PINN) designed specifically for analyzing digital materials is introduced. This proposed machine learning(ML) model can be trained free of ground truth data by adopting the minimum energy criteria as its loss function. Results show that our energy-based PINN reaches similar accuracy as supervised ML models. Adding a hinge loss on the Jacobian can constrain the model to avoid erroneous deformation gradient caused by the nonlinear logarithmic strain. Lastly, we discuss how the strain energy of each material element at each numerical integration point can be calculated parallelly on a GPU. The algorithm is tested on different mesh densities to evaluate its computational efficiency which scales linearly with respect to the number of nodes in the system. This work provides a foundation for encoding physical behaviors of digital materials directly into neural networks, enabling label-free learning for the design of next-generation composites.     

非线性学习方法与非线性科学

本文立足于中国传统文化提出非线性学习方法, 使数学物理中国化、简单化、个性化. 从八卦的角度统一看待非线性科学中的孤子、混沌、分形和机器学习, 以诗联网引领学科之间的对话, 实现学科之间的乾坤大挪移.     

A novel Z-function-based completely model-free reinforcement learning method to finite-horizon zero-sum game of nonlinear system

Nonlinear Dynamics - This work demonstrates that non-parity-time-symmetric complex potentials can support continuous soliton families in competing cubic–quintic nonlinearities. We fix the...     

Modeling and control of a nonlinear half-vehicle suspension system: a hybrid fuzzy logic approach

Modeling and control of vehicle suspension system are high noteworthy from safety to comfort. In this paper, an analytical nonlinear half-vehicle model which is included quadratic tire stiffness, cubic suspension stiffness, and coulomb friction is derived based on fundamental physics. A hybrid fuzzy logic approach which combines fuzzy logic and PID controllers is designed for reducing the vibration levels of passenger seat and vehicle body. Performances of designed controllers have been evaluated by numerical simulations. Comparisons with classical PID control, Fuzzy Logic Control (FLC) and Hybrid Fuzzy-PID control (HFPID) have also been provided. Results of numerical simulations are evaluated in terms of time histories of displacement and acceleration responses and ride index comparison. A good performance for the Hybrid Fuzzy-PID controller with coupled rules (HFPIDCR) is achieved in simulation studies despite the nonlinearities.