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Identification of partial differential equations from noisy data with integrated knowledge discovery and embedding using evolutionary neural networks

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Theoretical & Applied Mechanics Letters 2024年第2期14卷 90-97页

作者： Hanyu Zhou Haochen Li Yaomin Zhao HEDPS Center for Applied Physics and Technologyand College of EngineeringPeking UniversityBeijing 100871China State Key Laboratory for turbulence and Complex Systems College of EngineeringPeking UniversityBeijing 100871China

Identification of underlying partial differential equations(PDEs)for complex systems remains a formidable challenge.In the present study,a robust PDE identification method is proposed,demonstrating the ability to extract accurate governing equations under noisy conditions without prior knowledge.Specifically,the proposed method combines gene expression programming,one type of evolutionary algorithm capable of generating unseen terms based solely on basic operators and functional terms,with symbolic regression neural networks.These networks are designed to represent explicit functional expressions and optimize them with data gradients.In particular,the specifically designed neural networks can be easily transformed to physical constraints for the training data,embedding the discovered PDEs to further optimize the metadata used for iterative PDE identification.The proposed method has been tested in four canonical PDE cases,validating its effectiveness without preliminary information and confirming its suitability for practical applications across various noise levels.

关键词： PDE discovery Gene Expression Programming Deep Learning Knowledge embedding

A novel triple periodic minimal surface-like plate lattice and its data-driven optimization method for superior mechanical properties

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Applied Mathematics and Mechanics(English Edition) 2024年第2期45卷 217-238页

作者： Yanda WANG Yanping LIAN Zhidong WANG Chunpeng WANG Daining FANG State Key Laboratory for turbulence and Complex Systems&center for Applied Physics and Technology College of EngineeringPeking UniversityBeijing 100871China Institute of Advanced Structure Technology Beijing Institute of TechnologyBeijing 100081China

Lattice structures can be designed to achieve unique mechanical properties and have attracted increasing attention for applications in high-end industrial equipment,along with the advances in additive manufacturing(AM)technologies.In this work,a novel design of plate lattice structures described by a parametric model is proposed to enrich the design space of plate lattice structures with high connectivity suitable for AM processes.The parametric model takes the basic unit of the triple periodic minimal surface(TPMS)lattice as a skeleton and adopts a set of generation parameters to determine the plate lattice structure with different topologies,which takes the advantages of both plate lattices for superior specific mechanical properties and TPMS lattices for high connectivity,and therefore is referred to as a TPMS-like plate lattice(TLPL).Furthermore,a data-driven shape optimization method is proposed to optimize the TLPL structure for maximum mechanical properties with or without the isotropic constraints.In this method,the genetic algorithm for the optimization is utilized for global search capability,and an artificial neural network(ANN)model for individual fitness estimation is integrated for high efficiency.A set of optimized TLPLs at different relative densities are experimentally validated by the selective laser melting(SLM)fabricated samples.It is confirmed that the optimized TLPLs could achieve elastic isotropy and have superior stiffness over other isotropic lattice structures.

关键词： lattice structure triple periodic minimal surface(TPMS) plate lattice structural optimization machine learning

Influence of Bottom Inclination on the Flow Structure in a Rotating Convective Layer

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Fluid Dynamics & Materials Processing 2024年第4期20卷 739-748页

作者： Andrei Vasiliev Andrei Sukhanovskii Elena Popova Laboratory of turbulence Institute of Continuous Media Mechanics UB RASPerm614013Russia

The formation of convective flows in a rotating cylindrical layer with an inclined bottom and free surface is studied.Convection is driven by localized cooling at the center of the upper free surface and by rim heating at the bottom near the sidewall.The horizontal temperature difference in a rotating layer leads to the formation of a convective flow with a complex structure.The mean meridional circulation,consisting of three cells,provides a strongly non-uniform differential rotation.As a result of the instability of the main cyclonic zonal flow,the train of baroclinic waves appears in the upper layer.The baroclinic waves provide most of the heat transfer in the middle radii and are responsible for strong temperature and velocity fluctuations.It is shown that the inclination of the bottom is a crucial factor for the structure of the convective cells and the dynamics of the baroclinic waves.The increase in the inclination angle leads to a significant increase in the energy of the waves.The obtained results may be important for heat and mass transfer in various geophysical and industrial systems,including transport of various additives and impurities in rotating crucibles,and crystallization processes.

关键词： Laboratory modeling global atmospheric circulation baroclinic waves beta-effect

Observation of Doppler shift f_(D) modulated by the internal kink mode using conventional reflectometry in the EAST tokamak

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plasma Science and Technology 2024年第3期26卷 1-9页

作者：李恭顺张涛耿康宁文斐叶凯萱徐立清朱翔张学习钟富彬周振杨书琪周子强喻琳兰婷王守信提昂张寿彪刘海庆李国强高翔 the EAST Team Institute of plasma Physics Chinese Academy of SciencesHefei 230031People's Republic of China Advanced Energy research center Shenzhen UniversityShenzhen 518060People's Republic of China University of Science and Technology of China Hefei 230026People's Republic of China

In this paper we present a new experimental observation using a conventional reflectometry technique,poloidal correlation reflectometry(PCR),in the Experimental Advanced Superconducting Tokamak(EAST).The turbulence spectrum detected by the PCR system exhibits an asymmetry and induced Doppler shift f_(D)during the internal kink mode(IKM)rotation phase.This Doppler shift f_(D)is the target measurement of Doppler reflectometry,but captured by conventional reflectometry.Results show that the Doppler shift f_(D)is modulated by the periodic changes in the effective angle between the probing wave and cutoff layer normal,but not by plasma turbulence.The fishbone mode and saturated long-lived mode are typical IKMs,and this modulation phenomenon is observed in both cases.Moreover,the value of the Doppler shift f_(D)is positively correlated with the amplitude of the IKM,even when the latter is small.However,the positive and negative frequency components of the Doppler shift f_(D)can be asymmetric,which is related to the plasma configuration.A simulated analysis is performed by ray tracing to verify these observations.These results establish a clear link between f_(D)and IKM rotation,and are helpful for studying the characteristics of IKM and related physical phenomena.

关键词： microwave reflectometry Doppler shift internal kink mode

Numerical study of flow and thermal characteristics of pulsed impinging jet on a dimpled surface

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Theoretical & Applied Mechanics Letters 2024年第2期14卷 106-117页

作者： Amin Bagheri Kazem Esmailpour Morteza Heydari Renewable Energy research center Damavand BranchIslamic Azad UniversityDamavandIran

This research comprehensively investigates the flow and thermal characteristics of a pulsating impinging jet over a dimpled surface.It analyzes the impact of key parameters(e.g.,inlet velocity pulsation functions,pulsation frequency,amplitude,dimple pitch,dimple depth,Reynolds number)on flow patterns and heat transfer.Validated computational fluid dynamics and the Re-normalization group turbulence model are employed to accurately simulate complex turbulent flow behavior.Local and average heat transfer coefficients are calculated and compared to steady impingement cases,revealing the potential benefits of pulsation for heat transfer enhancement.The study also examines how pulsation-induced flow modulation and thermal mixing affect heat transfer mechanisms.Results indicate that combining fluctuating flow with a dimpled surface can improve heat transfer rates.In summary,increasing pulsation amplitude consistently enhances heat transfer,while the effect of frequency varies between impinging and wall jet zones.

关键词： Pulsating impinging jet Dimpled surface Heat transfer enhancement Pulsation frequency and amplitude Coherent structures

The Boundary Element Method for Ordinary State-Based Peridynamics

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Computer Modeling in Engineering & Sciences 2024年第6期139卷 2807-2834页

作者： Xue Liang Linjuan Wang State Key Laboratory for turbulence and Complex Systems Department of Mechanics and Engineering ScienceCollege of EngineeringPeking UniversityBeijing100871China CAPT-HEDPS and IFSA Collaborative Innovation Center of MoECollege of EngineeringPeking UniversityBeijing100871China School of Astronautics Beihang UniversityBeijing100191China

The peridynamics(PD),as a promising nonlocal continuum mechanics theory,shines in solving discontinuous problems.Up to now,various numerical methods,such as the peridynamic mesh-free particlemethod(PD-MPM),peridynamic finite element method(PD-FEM),and peridynamic boundary element method(PD-BEM),have been proposed.PD-BEM,in particular,outperforms other methods by eliminating spurious boundary softening,efficiently handling infinite problems,and ensuring high computational accuracy.However,the existing PD-BEM is constructed exclusively for bond-based peridynamics(BBPD)with fixed Poisson’s ratio,limiting its applicability to crack propagation problems and scenarios involving infinite or semi-infinite problems.In this paper,we address these limitations by introducing the boundary element method(BEM)for ordinary state-based peridynamics(OSPD-BEM).Additionally,we present a crack propagationmodel embeddedwithin the framework ofOSPD-BEM to simulate crack propagations.To validate the effectiveness of OSPD-BEM,we conduct four numerical examples:deformation under uniaxial loading,crack initiation in a double-notched specimen,wedge-splitting test,and threepoint bending test.The results demonstrate the accuracy and efficiency of OSPD-BEM,highlighting its capability to successfully eliminate spurious boundary softening phenomena under varying Poisson’s ratios.Moreover,OSPDBEMsignificantly reduces computational time and exhibits greater consistencywith experimental results compared to PD-MPM.

关键词： Ordinary state-based peridynamics boundary element method crack propagation fracture toughness

Energy Harvesting in the Wake of An Inverted C-Shaped Bluff Body

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China Ocean Engineering 2024年第1期38卷 68-80页

作者： WANG Jun-lei LI Shen-fang Md.Mahbub ALAM ZHU Hong-jun HU Guo-biao School of Mechanical and Power Engineering Zhengzhou UniversityZhengzhou 450000China center for turbulence Control Harbin Institute of Technology(Shenzhen)Shenzhen 518055China State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation Southwest Petroleum UniversityChengdu 610500China Internet of Things Thrust The Hong Kong University of Science and Technology(Guangzhou)Guangzhou 511400China

This paper proposes a novel wake-induced vibration(WIV)-based energy harvesting system consisting of two bluff bodies.An inverted C-shaped bluff body is stationary installed at the upstream position to generate an interference wake street,and a cylinder bluff body equipped with a transducer is elastically suspended at the downstream position to harness WIV energy.The hydrodynamics and energy harvesting(EH)performance of the proposed system are investigated via experimental studies.The reduced velocity(U*)ranging from 2 to 14(the corresponding Reynolds number ranging from 15100 to 106200)is considered in the present study.It is found that the wake generated by the inverted C-shaped bluff body significantly affects the EH performance.Enlarging the opening angle(α)of the C-shaped bluff body increases the vibration amplitude of the downstream cylinder,thereby increasing the harvested power.When the spacing(L)between two bluff bodies is two times the cylinder diameter(D),the wake-induced vibration(WIV)mode is observed,while the combined WIV and wake galloping(WG)mode occurs whenαis 150°,and L equals 3D or 4D.The average drag coefficient becomes negative when L is 2D,3D,or 4D.By carefully configuring a C-shaped bluff body,the wake generated by it can bring an augmenting effect on the vibration of the downstream EH cylinder.For example,the RMS power output of the proposed EH system reaches a maximum of 0.31 W at U*=8 and L=4D,which is 300%greater than that of its traditional counterpart.Furthermore,after a number of case stud-ies,it is identified that the proposed EH system can achieve the best performance whenαis 150°and L=2D.

关键词： wake-induced vibration vortex-induced vibration galloping energy harvesting bluff body

Robust autofocusing propagation in turbulence

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Chinese Physics B 2024年第6期33卷 370-375页

作者：刘娜娜谭柳陈凯健洪佩龙莫小明邹炳锁任煜轩梁毅 Guangxi Key Laboratory for Relativistic Astrophysics Center on Nanoenergy ResearchSchool of Physical Science and TechnologyGuangxi UniversityNanning 530004China School of Mathematics and Physics Anqing Normal UniversityAnqing 246133China Institute for Translational Brain research MOE Frontiers Center for Brain ScienceFudan UniversityShanghai 200032China

turbulence in complex environments such as the atmosphere and biological media has always been a great challenge to the application of beam propagation in optical communication, optical trapping and manipulation. To overcome this challenge, this study comprehensively investigates the robust propagation of traditional Gaussian and autofocusing beams in turbulent environments. In order to select stable beams that exhibit high intensity and high field gradient at the focal position in complex environments, Kolmogorov turbulence theory is used to simulate the propagation of beams in atmospheric turbulence based on the multi-phase screen method. We systematically analyze the intensity fluctuations, the variation of the coherence factor and the change in the scintillation index with propagation distance. The analysis reveals that the intensity fluctuations of autofocusing beams are significantly smaller than those of Gaussian beams, and the coherence of autofocusing beams is better than that of Gaussian beams under turbulence. Moreover, autofocusing beams exhibit less oscillation than Gaussian beams, indicating that autofocusing beams propagate in complex environments with less distortion and intensity fluctuation. Overall, this work clearly demonstrates that autofocusing beams exhibit higher stability in propagation compared with Gaussian beams, showing great promise for applications such as optical trapping and manipulation in complex environments.

关键词： propagation beams autofocusing turbulence

Development of a 2D spatial displacement estimation method for turbulence velocimetry of the gas puff imaging system on EAST

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plasma Science and Technology 2024年第3期26卷 17-24页

作者：李乐天刘少承颜宁刘晓菊高翔 Anhui University Hefei 230039People's Republic of China Institute of plasma Physics Chinese Academy of SciencesHefei 230031People's Republic of China

A gas puff imaging(GPI)diagnostic has been developed and operated on EAST since 2012,and the time-delay estimation(TDE)method is used to derive the propagation velocity of fluctuations from the two-dimensional GPI data.However,with the TDE method it is difficult to analyze the data with fast transient events,such as edge-localized mode(ELM).Consequently,a method called the spatial displacement estimation(SDE)algorithm is developed to estimate the turbulence velocity with high temporal resolution.Based on the SDE algorithm,we make some improvements,including an adaptive median filter and super-resolution technology.After the development of the algorithm,a straight-line movement and a curved-line movement are used to test the accuracy of the algorithm,and the calculated speed agrees well with preset speed.This SDE algorithm is applied to the EAST GPI data analysis,and the derived propagation velocity of turbulence is consistent with that from the TDE method,but with much higher temporal resolution.

关键词： gas puff imaging spatial displacement estimation SDE edge turbulence velocity TDE EAST tokamak