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A new insight on balanced augmented Lagrangian method

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arXiv

arXiv 2021年

作者： Bai, Jianchao School of Mathematics and Statistics The MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi'an710129 China

Motivated by the recent work [He-Yuan, Balanced Augmented Lagrangian Method for Convex Programming, arXiv: 2108.08554v1, 19 Aug 2021], a novel Augmented Lagrangian Method (ALM) has been proposed for solving a family of convex optimization problem subject to equality or inequality constraint. This new method is also extended to solve the multi-block convex optimization problem. Preliminary and some new convergence results are established with the aid of variational analysis for the saddle point of the problem and the first-order optimality conditions of involved subproblems. © 2021, CC BY.

关键词： Convex optimization

Intermittency mitigation of an aeroelastic airfoil system in randomly fluctuating flows via linear augmentation

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Intermittency mitigation of an aeroelastic airfoil system in...

第八届国际振动工程会议

作者： Qi Liu Yong Xu School of Mathematics and Statistics Northwestern Polytechnical University MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University

Intermittency, as an undesired behavior in typical airfoil systems, must be suppressed because which can lead to flutter and structural damage of the aircraft. Therefore, in this work, we are devoted to exploring the intermittency mitigation of a two-dimensional airfoil model subjected to randomly fluctuating flows. A recently developed method is introduced to achieve suppression of the intermittency behavior by augmentation of the nonlinear aeroelastic airfoil model with a linear control system. Several numerical results are implemented to test effectiveness of the employed method. We uncover that the undesired intermittency behavior can be mitigated for a proper choice of the control function. The introduced strategy has some superior performances for the aeroelastic airfoil system in comparison with the existing methods, which needn't to change the internal parameters of the system. This work will provide guidance to controlling problems of the engineering applications.

关键词： Intermittency mitigation of an aeroelastic airfoil system in randomly fluctuating flows via linear augmentation

Adaptive Backward Stepwise Selection-Based Sparse Identification of Nonlinear dynamics

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SSRN 2024年

作者： Jiang, Feng Du, Lin Xue, Qing Grebogi, Celso Deng, Zichen MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi’an710072 China School of Mechanics Civil Engineering and Architecture Northwestern Polytechnical University Xi’an710072 China School of Mathematics and Statics Northwestern Polytechnical University Xi’an710072 China MOE Key Laboratory for Complexity Science in Aerospace Northwestern Polytechnical University Xi’an710072 China Institute for Complex Systems and Mathematical Biology University of Aberdeen AberdeenAB24 3UE United Kingdom

Sparse identification of nonlinear dynamics (SINDy) has seen significant advancements in recent years, whereas determining hyperparameters within the SINDy remains challenging. In this study, we propose the Adaptive Backward Stepwise Selection of SINDy (ABSS-SINDy) to directly address the above issue, offering insight into the conditions under which SINDy excels and potential areas of failure from the perspective of backward stepwise selection. We validate the improved approach through a series of numerical experiments encompassing planar dynamic and three-dimensional chaotic systems, thereby illustrating the efficacy of the ABSS-SINDy. The findings underscore the capability of ABSS-SINDy to autonomously determine optimal hyperparameters within the SINDy framework, transcending a previously implicit and limiting assumption, thus extending the application capabilities of SINDy. © 2024, The Authors. All rights reserved.

关键词： dynamics

Combined Extension and Torsion of Hydrogels with Chemo-Mechanical Coupling: Revealing Negative Poynting Effect

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SSRN 2024年

作者： Zheng, Chengxiang Hu, Minghui Wu, Tao Pasquale, Ciarletta Li, Qian Deng, Zichen School of Mechanics Civil Engineering and Architecture Northwestern Polytechnical University Xi'An710072 China MIIT Key Laboratory of Dynamics and Control of Complex Systems Xi'An710072 China MOX Department di Mathematica Polytechnic di Milano piazza Leonardo da Vinci 32 Milano20133 Italy China Electronic Product Reliability and Environmental Testing Research Institute China Guangdong Provincial Key Laboratory of Electronic Information Products Reliability Technology China

In this paper, combined extension and torsion of hydrogel subject to a chemo-mechanical coupled loading is described in the framework of continuum mechanics, where the free energy density consists of the elastic, mixing and chemical contributions. A simplified, closed-form and exactly analytical solution to the mechanical response is obtained, which accounts for the coupling effect of external loading, chemical potential and microstructural parameters, such as crosslinking degree, Flory parameter, etc. In particular, the effect of free swelling and microscopic diffusion on deformation of the hydrogel is discussed, reaching some fundamental conclusions. The classic negative Poynting effect is revealed that the cylinder tends to shorten on twisting, and an inhomogeneous deformation, induced by torsion, along the radial direction is demonstrated. Furthermore, the dynamic competition between external loading and solvent environment is revealed and investigated, where the direct connection between internal micro-physical parameters and macroscopic deformation is demonstrated. The theoretical results presented in this paper may provide predictions and guidance for the mechanical analysis and design of hydrogel cylinder subject to extension and torsion in a solvent. © 2024, The Authors. All rights reserved.

关键词： Torsional stress

Patterns transition in a Subthalamopallidal Network under magnetic field effect

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Patterns transition in a Subthalamopallidal Network under ma...

第八届国际振动工程会议

作者： Zilu Cao Lin Du Honghui Zhang Zichen Deng Kangning An School of Mathematics and Statistics Northwestern Polytechnical University MIIT Key Laboratory of Dynamics and Control of Complex Systems School of Aeronautics Northwestern Polytechnical University

Subthalamic nucleus(STN) in basal ganglia is regarded as the role of origin of abnormal oscillation in Parkinson's Disease(PD). Synchronous and tremor-like activity of STN are the major features in PD. In this paper, we investigate the firing patterns of a subthalamopallidal model under magnetic field. Firstly, we study the effect of electromagnetic coefficient by timeseries, bifurcation analysis of interspike interval and synchronous coefficient. Results show that with the increasement of electromagnetic coefficient, the pattern of subthalamopallidal network could transfer from sparse irregular spiking to continue spiking with a stronger synchrony. It also finds that with a weaker input of globus pallidus, the network could transfer from asynchronous continue wave to synchronous continue spiking with stronger electromagnetic coefficient. Then, we research the effect of electromagnetic noise. Results indicate that noise could inhibit continue spiking, and the pattern of network transfers to episode wave. Conversely, it could induce episode wave from sparse spiking in the network. Finally, we characterize the cooperation of electromagnetic coefficient and electromagnetic noise by the statistical results of pattern transitions and synchrony, otherwise, we also give the area where two factors could adjust the abnormal oscillation of the network. This work helps to understand the activity of subthalamopallidal network under magnetic field and provide insights into the mechanisms behind the magnetic effect.

关键词： subthalamopallidal network magnetic field patterns transiton abnormal scillation

Inverse Design of a Nurbs-Based Chiral Metamaterial Via Machine Learning for Programmable Mechanical Deformation

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SSRN 2023年

作者： Hou, Xiuhui Zhao, Wenhao Zhang, Kai Deng, Zichen School of Mechanics Civil Engineering and Architecture Northwestern Polytechnical University Xi’an710072 China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi’an710072 China School of Aeronautics Northwestern Polytechnical University Xi’an710072 China State Key Laboratory of Structural Analysis Optimization and CAE Software for Industrial Equipment Dalian University of Technology Liaoning Dalian116024 China

Chiral metamaterials are manmade structures with extraordinary mechanical properties derived from their special geometrical design instead of the chemical composition. To make the mechanical deformation programmable, the Non-Uniform Rational B-Spline (NURBS) curves are taken to replace the traditional ligament boundaries of the chiral structure. The Neural Networks are innovatively inserted into the calculation of mechanical properties of the chiral structure instead of finite element methods to improve computational efficiency. For the general problem of structure configuration determination with specified mechanical properties, such as Young’s modulus, Poisson’s ratio or deformation, an inverse design method using the Neural Network-based surrogate model is proposed to build the relationship between local geometric configuration and overall deformation. To satisfy some more complex deformation requirements, a non-homogeneous inverse design method is proposed and verified through simulation and experiments. Numerical and test results reveal the high computational efficiency and accuracy of the proposed method in the device design of chiral metamaterials. © 2023, The Authors. All rights reserved.

关键词： Numerical methods

On the Notch Sensitivity of Nacre: A Large-Scale Numerical Investigation

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SSRN 2024年

作者： Yan, Yi Chen, Xiao Gao, Yuan Deng, Zi-Chen Feng, Xi-Qiao Department of Engineering Mechanics MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi’an710072 China Department of Materials Science and Technology National University of Singapore 117575 Singapore School of Mechanical Engineering Hebei University of Technology Tianjin300401 China Institute of Biomechanics and Medical Engineering AML Department of Engineering Mechanics Tsinghua University Beijing100084 China

The brick–mortar microstructure of nacre endows it with remarkable strength and fracture toughness. Notably, nacre demonstrates robustness against flaws and minor cracks, although its microstructural mechanisms remain elusive. A significant challenge is that the fracture behavior of nacre spans a wide range of length scales, from the mineral platelet less than 1 μm to a damage process zone extending several millimeters. In this study, we employ a multiscale tension-shear-chain (TSC) network model to simulate the large-scale fracture process of nacre's brick-and-mortar structure. In particular, we investigate how the fracture behavior of nacre is influenced by notches of varying sizes. Our large-scale simulations show that with the decrease in the preexisting-crack length, an independent crack initiation gradually replaces the precrack propagation during the fracture of nacre. This observation confirms the critical transition of fracture from the process dominated by fracture toughness to the one by strength, namely from notch sensitivity to insensitivity. Further investigations are carried out on the dependence of this fracture transition on constituent and microstructural parameters, including the interfacial cohesive strength and microstructural randomness. We also propose a scaling law formulating the relationship between these parameters and the notch sensitivity, which provides insight into nacre’s tolerance to flaws at a microscale level. Our findings could guide the design of nacre-inspired artificial materials for fracture prevention. © 2024, The Authors. All rights reserved.

关键词： Fracture toughness

Reusable Energy-Absorbers Design Harnessing Snapping-Through Buckling of Multistable Metamaterials of Hierarchical Double-Curved Beam

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SSRN 2023年

作者： Jin, Mingzhu Hou, Xiuhui Zhao, Wenhao Deng, Zichen School of Aeronautics Northwestern Polytechnical University Xi’an710072 China Institute of Extreme Mechanics Northwestern Polytechnical University Xi’an710072 China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi’an710072 China School of Mechanics Civil Engineering and Architecture Northwestern Polytechnical University Xi’an710072 China

We exploit the snapping-through buckling phenomenon exhibited by hierarchical DCB structures to devise a mechanical metamaterial with a unique deformation mode, encompassing multi-stability, multi-path, multi-platform, and multi-step characteristics, hence referred to as a 4M mechanical metamaterial. By employing DCB as fundamental building block elements, hierarchical metamaterials with two-dimensional series or parallel lattices are successfully constructed, as well as three-dimensional (3D) tubular geometries, denoted as DCB-n-m-C and DCB-n-m-M metamaterials, respectively. These metamaterials exhibit reversible energy absorption characteristics and the stiffness can be transformed from positive to negative under both small and large elastic deformations. Consequently, novel properties such as multistability, programmability, and reusable energy absorption characteristics are achieved. To comprehensively understand the mechanical response of the metamaterials, a thorough investigation into the influence of geometric parameters is conducted, including the number of polygonal edges, the number of the layers, the aspect ratio Q and material properties. This investigation involves a combination of theoretical analyses, numerical simulations, and experimental verifications. Notably, the force-displacement curves obtained during both loading and unloading process overlap almost completely, indicating the almost perfect recovery of the proposed structure after unloading. Furthermore, the effective crushing distance and energy absorption efficiency increase with the increase of geometric parameter Q. © 2023, The Authors. All rights reserved.

关键词： Energy absorption

Quantifying the parameter dependent basin of the unsafe regime of asymmetric Lévy-noise-induced critical transitions

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Applied Mathematics and Mechanics(English Edition) 2021年第1期42卷 65-84页

作者： Jinzhong MA Yong XU Yongge LI Ruilan TIAN Shao juan MA J.KURTHS School of Mathematical Sciences Shanxi UniversityTaiyuan 030000China Department of Applied Mathematics Northwestern Polytechnical UniversityXi’an 710072China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical UniversityXi’an 710072China Department of Engineering Mechanics Shijiazhuang Tiedao UniversityShijiazhuang 050043China School of Mathematics&Information Science North Minzu UniversityYinchuan 750021China Potsdam Institute for Climate Impact Research Potsdam 14412Germany Department of Physics Humboldt University at BerlinBerlin 12489Germany

In real systems,the unpredictable jump changes of the random environment can induce the critical transitions(CTs)between two non-adjacent states,which are more *** an asymmetric Lévy-noise-induced tri-stable model with desirable,sub-desirable,and undesirable states as a prototype class of real systems,a prediction of the noise-induced CTs from the desirable state directly to the undesirable one is carried *** first calculate the region that the current state of the given model is absorbed into the undesirable state based on the escape probability,which is named as the absorbed ***,a new concept of the parameter dependent basin of the unsafe regime(PDBUR)under the asymmetric Lévy noise is *** is an efficient tool for approximately quantifying the ranges of the parameters,where the noise-induced CTs from the desirable state directly to the undesirable one may *** importantly,it may provide theoretical guidance for us to adopt some measures to avert a noise-induced catastrophic CT.

关键词： tri-stable model asymmetric Lévy noise critical transition(CT) escape probability absorbed region parameter dependent basin of unsafe regime(PDBUR)