连接界面上存在的跨尺度、多物理场和非线性行为是引起结构复杂非线性动力学的主要原因.由于连接界面的力学行为的复杂性,以及难以对连接界面进行直接试验观测,连接界面的力学建模一直是非常具有挑战性的科学问题.本文首先从分析结合面...连接界面上存在的跨尺度、多物理场和非线性行为是引起结构复杂非线性动力学的主要原因.由于连接界面的力学行为的复杂性,以及难以对连接界面进行直接试验观测,连接界面的力学建模一直是非常具有挑战性的科学问题.本文首先从分析结合面的跨尺度物理机理入手,将名义的光滑平面视作凹凸不平的粗糙面,考虑单个微凸体的黏滑摩擦行为,建立接触载荷与变形的非线性关系,然后采用GW(Greenwood and Williamson)模型数理统计方法建立整个粗糙界面的跨尺度力学模型,并与公开文献中试验结果进行对比.考虑连接界面具有典型非线性特征,提出一种改进的Iwan唯象模型,利用精细有限元方法获得非线性特征结果,采用系统辨识理论建立连接结构的降阶力学模型,并利用有限元结果进行模型验证.结果表明,本文提出的粗糙界面跨尺度模型在法向载荷较小时与试验结果吻合较好,改进的Iwan模型能够较好描述连接界面的非线性特征,并与有限元结果吻合较好.展开更多
The hydraulic fracturing is a nonlinear,fluid-solid coupling and transient problem,in most cases it is always time-consuming to simulate this process numerically.In recent years,although many numerical methods were pr...The hydraulic fracturing is a nonlinear,fluid-solid coupling and transient problem,in most cases it is always time-consuming to simulate this process numerically.In recent years,although many numerical methods were proposed to settle this problem,most of them still require a large amount of computer resources.Thus it is a high demand to develop more efficient numerical approaches to achieve the real-time monitoring of the fracture geometry during the hydraulic fracturing treatment.In this study,a reduced order modeling technique namely Proper Generalized Decomposition(PGD),is applied to accelerate the simulations of the transient,non-linear coupled system of hydraulic fracturing problem,to match this extremely tight response time constraint.The separability of the solution in space and time dimensions is studied for a simplified model problem.The solid and fluid equations are coupled explicitly by inverting the solid discrete problem,and a simple iterative procedure to handle the non-linear characteristic of the hydraulic fracturing problem is proposed in this work.Numeral validation illustrates that the results of PGD match well with these of standard finite element method in terms o f fracture opening and fluid pressure in the hydro-fracture.Moreover,after the off-line calculations,the numerical results can be obtained in real time.展开更多
The fast and accurate reduced-order modeling of fluidized beds is a challenging task in the field of fluid dynamics,owing to their high dimensionality and nonlinear dynamic behavior.In this study,a nonintrusive reduce...The fast and accurate reduced-order modeling of fluidized beds is a challenging task in the field of fluid dynamics,owing to their high dimensionality and nonlinear dynamic behavior.In this study,a nonintrusive reduced order modeling method,the reduced order model based on principal component analysis and bidirectional long short-term memory networks(PBLSTM ROM),was developed to capture complex spatio-temporal dynamics of fluidized beds.By combining principal component analysis and Bidirectional long-short-term memory networks,the PBLSTM ROM effectively extracted dynamic evolution information without any prior knowledge of governing equations,enabling reduced-order modeling of unsteady flow fields.The PBLSTM ROM was validated using the solid volume fraction and gas velocity flow fields of a fluidized bed with immersed tubes,showing superior performance over both the PLSTM and PANN ROMs in accurately capturing temporal changes in the fluidization fields,especially in the region near immersed tubes where severe fluctuations appear.Moreover,the PBLSTM ROM improved the simulation speed by five orders of magnitude compared to traditional computational fluid dynamics simulations.These findings suggest that the PBLSTM ROM presents a promising approach for analyzing the complex fluid flows in engineering practice.展开更多
对于熔盐堆全堆高保真流体动力学计算,即使借助超级计算机的并行计算能力在面对快速甚至实时求解的问题仍然面临效率的巨大挑战,引入和采用模型降阶(Reduced Order Modeling,ROM)方法,将能够有效解决这类问题。基于本征正交分解(Proper ...对于熔盐堆全堆高保真流体动力学计算,即使借助超级计算机的并行计算能力在面对快速甚至实时求解的问题仍然面临效率的巨大挑战,引入和采用模型降阶(Reduced Order Modeling,ROM)方法,将能够有效解决这类问题。基于本征正交分解(Proper Orthogonal Decomposition,POD)方法与Galerkin投影法,引入基于有限体积的模型降阶(ROM based on Finite Volume approximation,FV-ROM)方法和上确界稳定模型降阶(ROM with supremizer stabilization,SUP-ROM)方法,针对液态燃料熔盐堆(Liquid Fuel Molten Salt Reactor,LFMSR)层流和湍流瞬态工况开展适用性分析。结果表明:FV-ROM方法在速度误差和计算效率方面占有明显优势,层流和湍流瞬态速度平均L^(2)相对误差低于0.5%和0.6%,且单步长的加速比分别为1500和1000倍左右;相比之下,SUP-ROM方法在压力预测方面表现出显著的优势,层流和湍流瞬态压力平均L^(2)相对误差低至0.20%和0.38%。因此,通过FV-ROM和SUP-ROM两种方法相结合的方式进行熔盐堆流体动力学速度场和压力场预测,能够更加有效地提高流体动力学仿真的效率,并确保瞬态模拟过程计算可靠性和精确度。展开更多
Many important problems in science and engineering require solving the so-called parametric partial differential equations(PDEs),i.e.,PDEs with different physical parameters,boundary conditions,shapes of computational...Many important problems in science and engineering require solving the so-called parametric partial differential equations(PDEs),i.e.,PDEs with different physical parameters,boundary conditions,shapes of computational domains,etc.Typical reduced order modeling techniques accelerate the solution of the parametric PDEs by projecting them onto a linear trial manifold constructed in the ofline stage.These methods often need a predefined mesh as well as a series of precomputed solution snapshots,and may struggle to balance between the efficiency and accuracy due to the limitation of the linear ansatz.Utilizing the nonlinear representation of neural networks(NNs),we propose the Meta-Auto-Decoder(MAD)to construct a nonlinear trial manifold,whose best possible performance is measured theoretically by the decoder width.Based on the meta-learning concept,the trial manifold can be learned in a mesh-free and unsupervised way during the pre-training stage.Fast adaptation to new(possibly heterogeneous)PDE parameters is enabled by searching on this trial manifold,and optionally fine-tuning the trial manifold at the same time.Extensive numerical experiments show that the MAD method exhibits a faster convergence speed without losing the accuracy than other deep learning-based methods.展开更多
The efficient dynamic modeling and vibration transfer analysis of a fluid-delivering branch pipeline(FDBP)are essential for analyzing vibration coupling effects and implementing vibration reduction optimization.Theref...The efficient dynamic modeling and vibration transfer analysis of a fluid-delivering branch pipeline(FDBP)are essential for analyzing vibration coupling effects and implementing vibration reduction optimization.Therefore,this study proposes a reduced-order dynamic modeling method suitable for FDBPs and then analyzes the vibration transfer characteristics.For the modeling method,the finite element method and absorbing transfer matrix method(ATMM)are integrated,considering the fluid–structure coupling effect and fluid disturbances.The dual-domain dynamic substructure method is developed to perform the reduced-order modeling of FDBP,and ATMM is adopted to reduce the matrix order when solving fluid disturbances.Furthermore,the modeling method is validated by experiments on an H-shaped branch pipeline.Finally,transient and steady-state vibration transfer analyses of FDBP are performed,and the effects of branch locations on natural characteristics and vibration transfer behavior are analyzed.Results show that transient vibration transfer represents the transfer and conversion of the kinematic,strain,and damping energies,while steady-state vibration transfer characteristics are related to the vibration mode.In addition,multiple-order mode exchanges are triggered when branch locations vary in frequency-shift regions,and the mode-exchange regions are also the transformation ones for vibration transfer patterns.展开更多
This paper considers the problem of simulating the humidity distributions of a grain storage system. The distributions are described by partial differential equations(PDE). It is quite difficult to obtain the humidity...This paper considers the problem of simulating the humidity distributions of a grain storage system. The distributions are described by partial differential equations(PDE). It is quite difficult to obtain the humidity profiles from the PDE model. Hence, a discretization method is applied to obtain an equivalent ordinary differential equation model. However, after applying the discretization technique, the cost of solving the system increases as the size increases to a few thousands. It may be noted that after discretization,the degree of freedom of the system remain the same while the order increases. The large dynamic model is reduced using a proper orthogonal decomposition based technique and an equivalent model but of much reduced size is obtained. A controller based on optimal control theory is designed to obtain an input such that the output humidity reaches a desired profile and also its stability is analyzed.Numerical results are presented to show the validity of the reduced model and possible further extensions are identified.展开更多
文摘连接界面上存在的跨尺度、多物理场和非线性行为是引起结构复杂非线性动力学的主要原因.由于连接界面的力学行为的复杂性,以及难以对连接界面进行直接试验观测,连接界面的力学建模一直是非常具有挑战性的科学问题.本文首先从分析结合面的跨尺度物理机理入手,将名义的光滑平面视作凹凸不平的粗糙面,考虑单个微凸体的黏滑摩擦行为,建立接触载荷与变形的非线性关系,然后采用GW(Greenwood and Williamson)模型数理统计方法建立整个粗糙界面的跨尺度力学模型,并与公开文献中试验结果进行对比.考虑连接界面具有典型非线性特征,提出一种改进的Iwan唯象模型,利用精细有限元方法获得非线性特征结果,采用系统辨识理论建立连接结构的降阶力学模型,并利用有限元结果进行模型验证.结果表明,本文提出的粗糙界面跨尺度模型在法向载荷较小时与试验结果吻合较好,改进的Iwan模型能够较好描述连接界面的非线性特征,并与有限元结果吻合较好.
基金Research Grants Council of Hong Kong under General Research Fund(15249316,15214418)PolyU Departmental General Research Fund(G-YBXQ)+1 种基金国家自然科学基金重大研究计划培育项目(91952107)国家自然科学基金青年项目(11902269)。
文摘为满足锅炉优化气固流场以防止受热面磨损对炉内三维速度场数据实时获取的需求,建立了一种基于计算流体力学(CFD)和本征正交分解(POD)的煤粉锅炉三维速度场快速预测模型.通过建立数值模型对一台330 MW四角切圆煤粉锅炉大量变工况条件下的三维速度场数据进行了模拟计算并建立数据集,采用POD方法对数据集进行了模态与模态系数提取,通过机器学习方法构建了工况参数与模态系数间的映射关系,实现了任意工况参数下锅炉速度场的快速预测.结果表明,所提模型可以通过少量模态重构出锅炉速度场的主要特征.模型泛化性和计算结果准确率较高,计算结果平均相对误差为1.80%,均方根误差小于0.35 m/s.模型计算速度快,获取锅炉速度场的平均计算时间由CFD模拟所需的约2819 min减小至约3 min.
基金the National Science Foundation of China(Grant Nos.51804033 and 51936001)China Postdoctoral Science and Foundation(Grant No.2018M641254)+3 种基金Beijing Postdoctoral Research Foundation(2018-ZZ-045)the Project of Construction of Innovative Teams and Teacher Career Development for Universities and Colleges Under Beijing Municipality(Grant No.IDHT20170507)Program of Great Wall Scholar(Grant No.CIT&TCD20180313)Jointly Projects of Beijing Natural Science Foundation and Beijing Municipal Education Commission(Grant No.KZ201810017023).
文摘The hydraulic fracturing is a nonlinear,fluid-solid coupling and transient problem,in most cases it is always time-consuming to simulate this process numerically.In recent years,although many numerical methods were proposed to settle this problem,most of them still require a large amount of computer resources.Thus it is a high demand to develop more efficient numerical approaches to achieve the real-time monitoring of the fracture geometry during the hydraulic fracturing treatment.In this study,a reduced order modeling technique namely Proper Generalized Decomposition(PGD),is applied to accelerate the simulations of the transient,non-linear coupled system of hydraulic fracturing problem,to match this extremely tight response time constraint.The separability of the solution in space and time dimensions is studied for a simplified model problem.The solid and fluid equations are coupled explicitly by inverting the solid discrete problem,and a simple iterative procedure to handle the non-linear characteristic of the hydraulic fracturing problem is proposed in this work.Numeral validation illustrates that the results of PGD match well with these of standard finite element method in terms o f fracture opening and fluid pressure in the hydro-fracture.Moreover,after the off-line calculations,the numerical results can be obtained in real time.
基金supported by the National Key R&D Program of China(grant No.2021YFF0500400)Key Research Program of Shaanxi Province(grant No.2022GXLH-01-08)+2 种基金National Key R&D Program of China(grant No.2018YFB1501003)Shaanxi Province Qin Chuangyuan“Scientist+Engineer”Team(grant No.2022KXJ-179)Targeted Funding Program of Power Construction Corporation of China(grant No.DJ-PTZX-2021-03).
文摘The fast and accurate reduced-order modeling of fluidized beds is a challenging task in the field of fluid dynamics,owing to their high dimensionality and nonlinear dynamic behavior.In this study,a nonintrusive reduced order modeling method,the reduced order model based on principal component analysis and bidirectional long short-term memory networks(PBLSTM ROM),was developed to capture complex spatio-temporal dynamics of fluidized beds.By combining principal component analysis and Bidirectional long-short-term memory networks,the PBLSTM ROM effectively extracted dynamic evolution information without any prior knowledge of governing equations,enabling reduced-order modeling of unsteady flow fields.The PBLSTM ROM was validated using the solid volume fraction and gas velocity flow fields of a fluidized bed with immersed tubes,showing superior performance over both the PLSTM and PANN ROMs in accurately capturing temporal changes in the fluidization fields,especially in the region near immersed tubes where severe fluctuations appear.Moreover,the PBLSTM ROM improved the simulation speed by five orders of magnitude compared to traditional computational fluid dynamics simulations.These findings suggest that the PBLSTM ROM presents a promising approach for analyzing the complex fluid flows in engineering practice.
文摘对于熔盐堆全堆高保真流体动力学计算,即使借助超级计算机的并行计算能力在面对快速甚至实时求解的问题仍然面临效率的巨大挑战,引入和采用模型降阶(Reduced Order Modeling,ROM)方法,将能够有效解决这类问题。基于本征正交分解(Proper Orthogonal Decomposition,POD)方法与Galerkin投影法,引入基于有限体积的模型降阶(ROM based on Finite Volume approximation,FV-ROM)方法和上确界稳定模型降阶(ROM with supremizer stabilization,SUP-ROM)方法,针对液态燃料熔盐堆(Liquid Fuel Molten Salt Reactor,LFMSR)层流和湍流瞬态工况开展适用性分析。结果表明:FV-ROM方法在速度误差和计算效率方面占有明显优势,层流和湍流瞬态速度平均L^(2)相对误差低于0.5%和0.6%,且单步长的加速比分别为1500和1000倍左右;相比之下,SUP-ROM方法在压力预测方面表现出显著的优势,层流和湍流瞬态压力平均L^(2)相对误差低至0.20%和0.38%。因此,通过FV-ROM和SUP-ROM两种方法相结合的方式进行熔盐堆流体动力学速度场和压力场预测,能够更加有效地提高流体动力学仿真的效率,并确保瞬态模拟过程计算可靠性和精确度。
基金supported by the National Key R&D Program of China under Grant No.2021ZD0110400.
文摘Many important problems in science and engineering require solving the so-called parametric partial differential equations(PDEs),i.e.,PDEs with different physical parameters,boundary conditions,shapes of computational domains,etc.Typical reduced order modeling techniques accelerate the solution of the parametric PDEs by projecting them onto a linear trial manifold constructed in the ofline stage.These methods often need a predefined mesh as well as a series of precomputed solution snapshots,and may struggle to balance between the efficiency and accuracy due to the limitation of the linear ansatz.Utilizing the nonlinear representation of neural networks(NNs),we propose the Meta-Auto-Decoder(MAD)to construct a nonlinear trial manifold,whose best possible performance is measured theoretically by the decoder width.Based on the meta-learning concept,the trial manifold can be learned in a mesh-free and unsupervised way during the pre-training stage.Fast adaptation to new(possibly heterogeneous)PDE parameters is enabled by searching on this trial manifold,and optionally fine-tuning the trial manifold at the same time.Extensive numerical experiments show that the MAD method exhibits a faster convergence speed without losing the accuracy than other deep learning-based methods.
基金supported by the Fundamental Research Funds for the Central Universities(Grant No.N2403006)the National Science and Technology Major Project,China(Grant No.J2019-I-0008-0008).
文摘The efficient dynamic modeling and vibration transfer analysis of a fluid-delivering branch pipeline(FDBP)are essential for analyzing vibration coupling effects and implementing vibration reduction optimization.Therefore,this study proposes a reduced-order dynamic modeling method suitable for FDBPs and then analyzes the vibration transfer characteristics.For the modeling method,the finite element method and absorbing transfer matrix method(ATMM)are integrated,considering the fluid–structure coupling effect and fluid disturbances.The dual-domain dynamic substructure method is developed to perform the reduced-order modeling of FDBP,and ATMM is adopted to reduce the matrix order when solving fluid disturbances.Furthermore,the modeling method is validated by experiments on an H-shaped branch pipeline.Finally,transient and steady-state vibration transfer analyses of FDBP are performed,and the effects of branch locations on natural characteristics and vibration transfer behavior are analyzed.Results show that transient vibration transfer represents the transfer and conversion of the kinematic,strain,and damping energies,while steady-state vibration transfer characteristics are related to the vibration mode.In addition,multiple-order mode exchanges are triggered when branch locations vary in frequency-shift regions,and the mode-exchange regions are also the transformation ones for vibration transfer patterns.
文摘This paper considers the problem of simulating the humidity distributions of a grain storage system. The distributions are described by partial differential equations(PDE). It is quite difficult to obtain the humidity profiles from the PDE model. Hence, a discretization method is applied to obtain an equivalent ordinary differential equation model. However, after applying the discretization technique, the cost of solving the system increases as the size increases to a few thousands. It may be noted that after discretization,the degree of freedom of the system remain the same while the order increases. The large dynamic model is reduced using a proper orthogonal decomposition based technique and an equivalent model but of much reduced size is obtained. A controller based on optimal control theory is designed to obtain an input such that the output humidity reaches a desired profile and also its stability is analyzed.Numerical results are presented to show the validity of the reduced model and possible further extensions are identified.
