The purpose of this article is to develop and analyze least-squares approximations for the incompressible magnetohydrodynamic equations. The major advantage of the least-squares finite element method is that it is not...The purpose of this article is to develop and analyze least-squares approximations for the incompressible magnetohydrodynamic equations. The major advantage of the least-squares finite element method is that it is not subjected to the so-called Ladyzhenskaya-Babuska-Brezzi （LBB） condition. The authors employ least-squares functionals which involve a discrete inner product which is related to the inner product in H^-1（Ω）.展开更多
The Galerkin and least-squares methods are two classes of the most popular Krylov subspace methOds for solving large linear systems of equations. Unfortunately, both the methods may suffer from serious breakdowns of t...The Galerkin and least-squares methods are two classes of the most popular Krylov subspace methOds for solving large linear systems of equations. Unfortunately, both the methods may suffer from serious breakdowns of the same type: In a breakdown situation the Galerkin method is unable to calculate an approximate solution, while the least-squares method, although does not really break down, is unsucessful in reducing the norm of its residual. In this paper we first establish a unified theorem which gives a relationship between breakdowns in the two methods. We further illustrate theoretically and experimentally that if the coefficient matrix of a lienar system is of high defectiveness with the associated eigenvalues less than 1, then the restarted Galerkin and least-squares methods will be in great risks of complete breakdowns. It appears that our findings may help to understand phenomena observed practically and to derive treatments for breakdowns of this type.展开更多
This article explores the comparison between the probability method and the least squares method in the design of linear predictive models. It points out that these two approaches have distinct theoretical foundations...This article explores the comparison between the probability method and the least squares method in the design of linear predictive models. It points out that these two approaches have distinct theoretical foundations and can lead to varied or similar results in terms of precision and performance under certain assumptions. The article underlines the importance of comparing these two approaches to choose the one best suited to the context, available data and modeling objectives.展开更多
As a novel class of purely organic fluores-cent materials,multiple resonance thermal-ly activated delayed fluorescence(MR-TADF)compounds hold significant promise for next-generation display technologies.The efficiency...As a novel class of purely organic fluores-cent materials,multiple resonance thermal-ly activated delayed fluorescence(MR-TADF)compounds hold significant promise for next-generation display technologies.The efficiency of exciton utilization and the overall performance of organic light-emit-ting devices are closely linked to the singlet-triplet energy gap(ΔE_(ST))of MR-TADF emitters.Identifying an economic and accu-rate theoretical approach to predictΔE_(ST)would be beneficial for high-throughput screening and facilitate the inverse design of MR-TADF molecules.In this study,we evaluated the S_(1)state energy(E(S_(1))),T_(1)state ener-gy(E(T_(1))),andΔE_(ST)using three different physical interpretations:adiabatic excitation ener-gy,vertical absorption energy,and vertical emission energy.We employed the time-depen-dent density functional theory(TDDFT)and delta self-consistent field(ΔSCF)methods to calculate E(S_(1)),E(T_(1)),andΔE_(ST)for 20 MR-TADF molecules reported in the literature.We compared these calculated values with experimental data obtained from fluorescence spec-troscopy at room-temperature(or 77 K)and phosphorescence spectroscopy conducted at 77 K.Our findings indicate that the vertical absorption energy at the S0 state minimum,deter-mined by theΔSCF method,accurately predicts the S_(1)state energy.Similarly,the vertical absorption energy at the S0 state minimum,calculated using the TDDFT method,effectively predicts the T_(1)state energy.TheΔE_(ST)derived from the difference between these two excita-tion energies exhibited the smallest mean absolute error of only 0.039 eV compared to the ex-perimental values.This combination represents the most accurate and cost-effective method reported to date for predicting theΔE_(ST)of MR-TADF molecules,and can be integrated into AI-driven inverse design workflows for new emitters.展开更多
This mixed-methods study investigated how AI-enhanced English as a Foreign Language(EFL)learning environments influence students’psychological well-being through the mediating roles of motivation and language learnin...This mixed-methods study investigated how AI-enhanced English as a Foreign Language(EFL)learning environments influence students’psychological well-being through the mediating roles of motivation and language learning anxiety and the moderating role of trust.Participants were Chinese university students(N=310,62%female,mean age=18.9,SD=0.8),of whom 15 completed interviews to both add to and to clarify the evidence from the surveys.Structural equation modeling results revealed that AI use had significant indirect effects on well-being through increased motivation and reduced language learning anxiety.Trust in AI significantly moderated both paths,amplifying the motivational benefits and anxiety reduction associated with AI use.Thematic analysis supported these results,identifying three experiential themes:(1)motivational empowerment through personalization,(2)anxiety regulation through safe practice and feedback,and(3)trust as the emotional bridge between AI and well-being.The study extends AI psychology applications by empirically linking technology engagement with affective outcomes and underscores the need for human-centered and trust-enhancing design in AI-supported education.From these findings,we conclude that adaptive,transparent,and autonomy-supportive AI systems promote self-determined motivation,emotional safety,and overall psychological health among EFL learners.展开更多
The numerical dispersion phenomenon in the finite-difference forward modeling simulations of the wave equation significantly affects the imaging accuracy in acoustic reflection logging.This issue is particularly prono...The numerical dispersion phenomenon in the finite-difference forward modeling simulations of the wave equation significantly affects the imaging accuracy in acoustic reflection logging.This issue is particularly pronounced in the reverse time migration(RTM)method used for shear-wave(S-wave)logging imaging.This not only affects imaging accuracy but also introduces ambiguities in the interpretation of logging results.To address this challenge,this study proposes the use of a least-squares difference coefficient optimization algorithm aiming to suppress the numerical dispersion phenomenon in the RTM of S-wave reflection imaging logging.By optimizing the difference coefficients,the high-precision finite-difference algorithm serves as an effective operator for both forward and backward RTM processes.This approach is instrumental in eliminating migration illusions,which are often caused by numerical dispersion.The effectiveness of this optimized algorithm is demonstrated through numerical results,which indicate that it can achieve more accurate forward imaging results across various conditions,including high-and low-velocity strata,and is effective in both large and small spatial grids.The results of processing real data demonstrate that numerical dispersion optimization effectively reduces migration artifacts and diminishes ambiguities in logging interpretations.This optimization offers crucial technical support to the RTM method,enhancing its capability for accurately modeling and imaging S-wave reflections.展开更多
This article deals with a first-order least-squares approach to the solution of an optimal control problem governed by Stokes equations.As with our earlier work on a velocity control by the Stokes flow in[S.Ryu,H.-C.L...This article deals with a first-order least-squares approach to the solution of an optimal control problem governed by Stokes equations.As with our earlier work on a velocity control by the Stokes flow in[S.Ryu,H.-C.Lee and S.D.Kim,SIAM J.Numer.Anal.,47(2009),pp.1524-1545],we recast the objective functional as a H1 seminorm in the velocity control term.By introducing a velocity-flux variable and using the Lagrange multiplier rule,a first-order optimality system is obtained.We show that the least-squares principle based on L2 norms applied to this system yields the optimal discretization error estimates for each variable in H1 norm,including the velocity flux.For numerical tests,multigrid method is employed to the discrete algebraic system,so that the velocity and flux controls are obtained.展开更多
Many science and engineering applications involve solvinga linear least-squares system formed from some field measurements. In the distributed cyber-physical systems(CPS),each sensor node used for measurement often on...Many science and engineering applications involve solvinga linear least-squares system formed from some field measurements. In the distributed cyber-physical systems(CPS),each sensor node used for measurement often only knowspartial independent rows of the least-squares system. To solve the least-squares all the measurements must be gathered at a centralized location and then perform the computa-tion. Such data collection and computation are inefficient because of bandwidth and time constraints and sometimes areinfeasible because of data privacy concerns. Iterative methods are natural candidates for solving the aforementionedproblem and there are many studies regarding this. However,most of the proposed solutions are related to centralized/parallel computations while only a few have the potential to beapplied in distributed networks. Thus distributed computations are strongly preferred or demanded in many of the realworld applications, e.g. smart-grid, target tracking, etc. Thispaper surveys the representative iterative methods for distributed least-squares in networks.展开更多
The main purpose of reverse engineering is to convert discrete data pointsinto piecewise smooth, continuous surface models. Before carrying out model reconstruction it issignificant to extract geometric features becau...The main purpose of reverse engineering is to convert discrete data pointsinto piecewise smooth, continuous surface models. Before carrying out model reconstruction it issignificant to extract geometric features because the quality of modeling greatly depends on therepresentation of features. Some fitting techniques of natural quadric surfaces with least-squaresmethod are described. And these techniques can be directly used to extract quadric surfaces featuresduring the process of segmentation for point cloud.展开更多
A least-squares finite-element method （LSFEM） for the non-conservative shallow-water equations is presented. The model is capable of handling complex topography, steady and unsteady flows, subcritical and supercriti...A least-squares finite-element method （LSFEM） for the non-conservative shallow-water equations is presented. The model is capable of handling complex topography, steady and unsteady flows, subcritical and supercritical flows, and flows with smooth and sharp gradient changes. Advantages of the model include： （1） sources terms, such as the bottom slope, surface stresses and bed frictions, can be treated easily without any special treatment; （2） upwind scheme is no needed; （3） a single approximating space can be used for all variables, and its choice of approximating space is not subject to the Ladyzhenskaya-Babuska-Brezzi （LBB） condition; and （4） the resulting system of equations is symmetric and positive-definite （SPD） which can be solved efficiently with the preconditioned conjugate gradient method. The model is verified with flow over a bump, tide induced flow, and dam-break. Computed results are compared with analytic solutions or other numerical results, and show the model is conservative and accurate. The model is then used to simulate flow past a circular cylinder. Important flow charac-teristics, such as variation of water surface around the cylinder and vortex shedding behind the cylinder are investigated. Computed results compare well with experiment data and other numerical results.展开更多
Numerical solution of shallow-water equations （SWE） has been a challenging task because of its nonlinear hyperbolic nature, admitting discontinuous solution, and the need to satisfy the C-property. The presence of s...Numerical solution of shallow-water equations （SWE） has been a challenging task because of its nonlinear hyperbolic nature, admitting discontinuous solution, and the need to satisfy the C-property. The presence of source terms in momentum equations, such as the bottom slope and friction of bed, compounds the difficulties further. In this paper, a least-squares finite-element method for the space discretization and θ-method for the time integration is developed for the 2D non-conservative SWE including the source terms. Advantages of the method include： the source terms can be approximated easily with interpolation functions, no upwind scheme is needed, as well as the resulting system equations is symmetric and positive-definite, therefore, can be solved efficiently with the conjugate gradient method. The method is applied to steady and unsteady flows, subcritical and transcritical flow over a bump, 1D and 2D circular dam-break, wave past a circular cylinder, as well as wave past a hump. Computed results show good C-property, conservation property and compare well with exact solutions and other numerical results for flows with weak and mild gradient changes, but lead to inaccurate predictions for flows with strong gradient changes and discontinuities.展开更多
For the second-order finite volume method,implicit schemes and reconstruction methods are two main algorithms which influence the robustness and efficiency of the numerical simulations of compressible turbulent flows....For the second-order finite volume method,implicit schemes and reconstruction methods are two main algorithms which influence the robustness and efficiency of the numerical simulations of compressible turbulent flows.In this paper,a compact least-squares reconstruction method is proposed to calculate the gradients for the distribution of flow field variables approximation.The compactness of the new reconstruction method is reflected in the gradient calculation process.The geometries of the face-neighboring elements are no longer utilized,and the weighted average values at the centroid of the interfaces are used to calculate the gradients instead of the values at the centroid of the face-neighboring elements.Meanwhile,an exact Jacobian solving strategy is developed for implicit temporal discretization.The accurate processing of Jacobian matrix can extensively improve the invertibility of the Jacobian matrix and avoid introducing extra numerical errors.In addition,a modified Venkatakrishnan limiter is applied to deal with the shock which may appear in transonic flows and the applicability of the mentioned methods is enhanced further.The combination of the proposed methods makes the numerical simulations of turbulent flow converge rapidly and steadily with an adaptive increasing CFL number.The numerical results of several benchmarks indicate that the proposed methods perform well in terms of robustness,efficiency and accuracy,and have good application potential in turbulent flow simulations of complex configurations.展开更多
Modal parameters can accurately characterize the structural dynamic properties and assess the physical state of the structure.Therefore,it is particularly significant to identify the structural modal parameters accordi...Modal parameters can accurately characterize the structural dynamic properties and assess the physical state of the structure.Therefore,it is particularly significant to identify the structural modal parameters according to the monitoring data information in the structural health monitoring(SHM)system,so as to provide a scientific basis for structural damage identification and dynamic model modification.In view of this,this paper reviews methods for identifying structural modal parameters under environmental excitation and briefly describes how to identify structural damages based on the derived modal parameters.The paper primarily introduces data-driven modal parameter recognition methods(e.g.,time-domain,frequency-domain,and time-frequency-domain methods,etc.),briefly describes damage identification methods based on the variations of modal parameters(e.g.,natural frequency,modal shapes,and curvature modal shapes,etc.)and modal validation methods(e.g.,Stability Diagram and Modal Assurance Criterion,etc.).The current status of the application of artificial intelligence(AI)methods in the direction of modal parameter recognition and damage identification is further discussed.Based on the pre-vious analysis,the main development trends of structural modal parameter recognition and damage identification methods are given to provide scientific references for the optimized design and functional upgrading of SHM systems.展开更多
With the development of computational power, there has been an increased focus on data-fitting related seismic inversion techniques for high fidelity seismic velocity model and image, such as full-waveform inversion a...With the development of computational power, there has been an increased focus on data-fitting related seismic inversion techniques for high fidelity seismic velocity model and image, such as full-waveform inversion and least squares migration. However, though more advanced than conventional methods, these data fitting methods can be very expensive in terms of computational cost. Recently, various techniques to optimize these data-fitting seismic inversion problems have been implemented to cater for the industrial need for much improved efficiency. In this study, we propose a general stochastic conjugate gradient method for these data-fitting related inverse problems. We first prescribe the basic theory of our method and then give synthetic examples. Our numerical experiments illustrate the potential of this method for large-size seismic inversion application.展开更多
It is well known that the Two-step Weighted Least-Squares(TWLS) is a widely used method for source localization and sensor position refinement. For this reason, we propose a unified framework of the TWLS method for jo...It is well known that the Two-step Weighted Least-Squares(TWLS) is a widely used method for source localization and sensor position refinement. For this reason, we propose a unified framework of the TWLS method for joint estimation of multiple disjoint sources and sensor locations in this paper. Unlike some existing works, the presented method is based on more general measurement model, and therefore it can be applied to many different localization scenarios.Besides, it does not have the initialization and local convergence problem. The closed-form expression for the covariance matrix of the proposed TWLS estimator is also derived by exploiting the first-order perturbation analysis. Moreover, the estimation accuracy of the TWLS method is shown analytically to achieve the Cramér-Rao Bound(CRB) before the threshold effect takes place. The theoretical analysis is also performed in a common mathematical framework, rather than aiming at some specific signal metrics. Finally, two numerical experiments are performed to support the theoretical development in this paper.展开更多
As pivotal supporting technologies for smart manufacturing and digital engineering,model-based and data-driven methods have been widely applied in many industrial fields,such as product design,process monitoring,and s...As pivotal supporting technologies for smart manufacturing and digital engineering,model-based and data-driven methods have been widely applied in many industrial fields,such as product design,process monitoring,and smart maintenance.While promising,both methods have issues that need to be addressed.For example,model-based methods are limited by low computational accuracy and a high computational burden,and data-driven methods always suffer from poor interpretability and redundant features.To address these issues,the concept of data-model fusion(DMF)emerges as a promising solution.DMF involves integrating model-based methods with data-driven methods by incorporating big data into model-based methods or embedding relevant domain knowledge into data-driven methods.Despite growing efforts in the field of DMF,a unanimous definition of DMF remains elusive,and a general framework of DMF has been rarely discussed.This paper aims to address this gap by providing a thorough overview and categorization of both data-driven methods and model-based methods.Subsequently,this paper also presents the definition and categorization of DMF and discusses the general framework of DMF.Moreover,the primary seven applications of DMF are reviewed within the context of smart manufacturing and digital engineering.Finally,this paper directs the future directions of DMF.展开更多
Soil improvement is one of the most important issues in geotechnical engineering practice.The wide application of traditional improvement techniques(cement/chemical materials)are limited due to damage ecological en-vi...Soil improvement is one of the most important issues in geotechnical engineering practice.The wide application of traditional improvement techniques(cement/chemical materials)are limited due to damage ecological en-vironment and intensify carbon emissions.However,the use of microbially induced calcium carbonate pre-cipitation(MICP)to obtain bio-cement is a novel technique with the potential to induce soil stability,providing a low-carbon,environment-friendly,and sustainable integrated solution for some geotechnical engineering pro-blems in the environment.This paper presents a comprehensive review of the latest progress in soil improvement based on the MICP strategy.It systematically summarizes and overviews the mineralization mechanism,influ-encing factors,improved methods,engineering characteristics,and current field application status of the MICP.Additionally,it also explores the limitations and correspondingly proposes prospective applications via the MICP approach for soil improvement.This review indicates that the utilization of different environmental calcium-based wastes in MICP and combination of materials and MICP are conducive to meeting engineering and market demand.Furthermore,we recommend and encourage global collaborative study and practice with a view to commercializing MICP technique in the future.The current review purports to provide insights for engineers and interdisciplinary researchers,and guidance for future engineering applications.展开更多
The separation-of-variable(SOV)methods,such as the improved SOV method,the variational SOV method,and the extended SOV method,have been proposed by the present authors and coworkers to obtain the closed-form analytica...The separation-of-variable(SOV)methods,such as the improved SOV method,the variational SOV method,and the extended SOV method,have been proposed by the present authors and coworkers to obtain the closed-form analytical solutions for free vibration and eigenbuckling of rectangular plates and circular cylindrical shells.By taking the free vibration of rectangular thin plates as an example,this work presents the theoretical framework of the SOV methods in an instructive way,and the bisection–based solution procedures for a group of nonlinear eigenvalue equations.Besides,the explicit equations of nodal lines of the SOV methods are presented,and the relations of nodal line patterns and frequency orders are investigated.It is concluded that the highly accurate SOV methods have the same accuracy for all frequencies,the mode shapes about repeated frequencies can also be precisely captured,and the SOV methods do not have the problem of missing roots as well.展开更多
In this paper,we present a novel initial costates solver for initializing time-optimal trajectory problems in relative motion with continuous low thrust.The proposed solver consists of two primary components:training ...In this paper,we present a novel initial costates solver for initializing time-optimal trajectory problems in relative motion with continuous low thrust.The proposed solver consists of two primary components:training a Multilayer Perceptron(MLP)for generating reference sequence and Time of Flight(TOF)to the target,and deriving a system of linear algebraic equations for obtaining the initial costates.To overcome the challenge of generating training samples for the MLP,the backward generation method is proposed to obtain five different training databases.The training database and sample form are determined by analyzing the input and output correlation using the Pearson correlation coefficient.The best-performing MLP is obtained by analyzing the training results with various hyper-parameter combinations.A reference sequence starting from the initial states is obtained by integrating forward with the near-optimal control vector from the output of MLP.Finally,a system of linear algebraic equations for estimating the initial costates is derived using the reference sequence and the necessary conditions for optimality.Simulation results demonstrate that the proposed initial costates solver improves the convergence ratio and reduce the function calls of the shooting function.Furthermore,Monte-Carlo simulation illustrates that the initial costates solver is applicable to different initial velocities,demonstrating excellent generalization ability.展开更多
The microstructures of pharmaceutical preparations play a pivotal role in determining their critical quality attributes(CQAs),such as drug release,content uniformity,and stability,which greatly impact the safety and e...The microstructures of pharmaceutical preparations play a pivotal role in determining their critical quality attributes(CQAs),such as drug release,content uniformity,and stability,which greatly impact the safety and efficacy of drugs.Unlike the inherent molecular structures of active pharmaceutical ingredients(APIs)and excipients,the microstructures of pharmaceutical preparations are developed during the formulation process,presenting unique analytical challenges.In this review,we primarily focus on presenting the research methods used to elucidate the microstructures of pharmaceutical preparations,including X-ray imaging(XRI),scanning electron microscopy(SEM),atomic force microscopy(AFM),Raman spectroscopy,infrared(IR)spectroscopy,and rheometer technology.Subsequently,we highlight the applications,advantages,and limitations of these methods.Finally,we discuss the current challenges and future perspectives in this field.This review aims to provide a comprehensive reference for understanding the microstructures of pharmaceutical preparations,offering new insights and potential advancements in their development.展开更多
基金supported by the National Basic Research Program of China (2005CB321701)NSF of mathematics research special fund of Hebei Province(08M005)
文摘The purpose of this article is to develop and analyze least-squares approximations for the incompressible magnetohydrodynamic equations. The major advantage of the least-squares finite element method is that it is not subjected to the so-called Ladyzhenskaya-Babuska-Brezzi （LBB） condition. The authors employ least-squares functionals which involve a discrete inner product which is related to the inner product in H^-1（Ω）.
文摘The Galerkin and least-squares methods are two classes of the most popular Krylov subspace methOds for solving large linear systems of equations. Unfortunately, both the methods may suffer from serious breakdowns of the same type: In a breakdown situation the Galerkin method is unable to calculate an approximate solution, while the least-squares method, although does not really break down, is unsucessful in reducing the norm of its residual. In this paper we first establish a unified theorem which gives a relationship between breakdowns in the two methods. We further illustrate theoretically and experimentally that if the coefficient matrix of a lienar system is of high defectiveness with the associated eigenvalues less than 1, then the restarted Galerkin and least-squares methods will be in great risks of complete breakdowns. It appears that our findings may help to understand phenomena observed practically and to derive treatments for breakdowns of this type.
文摘This article explores the comparison between the probability method and the least squares method in the design of linear predictive models. It points out that these two approaches have distinct theoretical foundations and can lead to varied or similar results in terms of precision and performance under certain assumptions. The article underlines the importance of comparing these two approaches to choose the one best suited to the context, available data and modeling objectives.
基金support provided by the National Natural Science Foundation of China(No.22273043).
文摘As a novel class of purely organic fluores-cent materials,multiple resonance thermal-ly activated delayed fluorescence(MR-TADF)compounds hold significant promise for next-generation display technologies.The efficiency of exciton utilization and the overall performance of organic light-emit-ting devices are closely linked to the singlet-triplet energy gap(ΔE_(ST))of MR-TADF emitters.Identifying an economic and accu-rate theoretical approach to predictΔE_(ST)would be beneficial for high-throughput screening and facilitate the inverse design of MR-TADF molecules.In this study,we evaluated the S_(1)state energy(E(S_(1))),T_(1)state ener-gy(E(T_(1))),andΔE_(ST)using three different physical interpretations:adiabatic excitation ener-gy,vertical absorption energy,and vertical emission energy.We employed the time-depen-dent density functional theory(TDDFT)and delta self-consistent field(ΔSCF)methods to calculate E(S_(1)),E(T_(1)),andΔE_(ST)for 20 MR-TADF molecules reported in the literature.We compared these calculated values with experimental data obtained from fluorescence spec-troscopy at room-temperature(or 77 K)and phosphorescence spectroscopy conducted at 77 K.Our findings indicate that the vertical absorption energy at the S0 state minimum,deter-mined by theΔSCF method,accurately predicts the S_(1)state energy.Similarly,the vertical absorption energy at the S0 state minimum,calculated using the TDDFT method,effectively predicts the T_(1)state energy.TheΔE_(ST)derived from the difference between these two excita-tion energies exhibited the smallest mean absolute error of only 0.039 eV compared to the ex-perimental values.This combination represents the most accurate and cost-effective method reported to date for predicting theΔE_(ST)of MR-TADF molecules,and can be integrated into AI-driven inverse design workflows for new emitters.
文摘This mixed-methods study investigated how AI-enhanced English as a Foreign Language(EFL)learning environments influence students’psychological well-being through the mediating roles of motivation and language learning anxiety and the moderating role of trust.Participants were Chinese university students(N=310,62%female,mean age=18.9,SD=0.8),of whom 15 completed interviews to both add to and to clarify the evidence from the surveys.Structural equation modeling results revealed that AI use had significant indirect effects on well-being through increased motivation and reduced language learning anxiety.Trust in AI significantly moderated both paths,amplifying the motivational benefits and anxiety reduction associated with AI use.Thematic analysis supported these results,identifying three experiential themes:(1)motivational empowerment through personalization,(2)anxiety regulation through safe practice and feedback,and(3)trust as the emotional bridge between AI and well-being.The study extends AI psychology applications by empirically linking technology engagement with affective outcomes and underscores the need for human-centered and trust-enhancing design in AI-supported education.From these findings,we conclude that adaptive,transparent,and autonomy-supportive AI systems promote self-determined motivation,emotional safety,and overall psychological health among EFL learners.
基金supported by Scientific Research and Technology Development Project of CNPC(2021DJ4002,2022DJ3908).
文摘The numerical dispersion phenomenon in the finite-difference forward modeling simulations of the wave equation significantly affects the imaging accuracy in acoustic reflection logging.This issue is particularly pronounced in the reverse time migration(RTM)method used for shear-wave(S-wave)logging imaging.This not only affects imaging accuracy but also introduces ambiguities in the interpretation of logging results.To address this challenge,this study proposes the use of a least-squares difference coefficient optimization algorithm aiming to suppress the numerical dispersion phenomenon in the RTM of S-wave reflection imaging logging.By optimizing the difference coefficients,the high-precision finite-difference algorithm serves as an effective operator for both forward and backward RTM processes.This approach is instrumental in eliminating migration illusions,which are often caused by numerical dispersion.The effectiveness of this optimized algorithm is demonstrated through numerical results,which indicate that it can achieve more accurate forward imaging results across various conditions,including high-and low-velocity strata,and is effective in both large and small spatial grids.The results of processing real data demonstrate that numerical dispersion optimization effectively reduces migration artifacts and diminishes ambiguities in logging interpretations.This optimization offers crucial technical support to the RTM method,enhancing its capability for accurately modeling and imaging S-wave reflections.
基金This work was supported by Korea Research Foundation under grant KRF-2005-070-C00017.
文摘This article deals with a first-order least-squares approach to the solution of an optimal control problem governed by Stokes equations.As with our earlier work on a velocity control by the Stokes flow in[S.Ryu,H.-C.Lee and S.D.Kim,SIAM J.Numer.Anal.,47(2009),pp.1524-1545],we recast the objective functional as a H1 seminorm in the velocity control term.By introducing a velocity-flux variable and using the Lagrange multiplier rule,a first-order optimality system is obtained.We show that the least-squares principle based on L2 norms applied to this system yields the optimal discretization error estimates for each variable in H1 norm,including the velocity flux.For numerical tests,multigrid method is employed to the discrete algebraic system,so that the velocity and flux controls are obtained.
基金partially supported by US NSF under Grant No.NSF-CNS-1066391and No.NSF-CNS-0914371,NSF-CPS-1135814 and NSF-CDI-1125165
文摘Many science and engineering applications involve solvinga linear least-squares system formed from some field measurements. In the distributed cyber-physical systems(CPS),each sensor node used for measurement often only knowspartial independent rows of the least-squares system. To solve the least-squares all the measurements must be gathered at a centralized location and then perform the computa-tion. Such data collection and computation are inefficient because of bandwidth and time constraints and sometimes areinfeasible because of data privacy concerns. Iterative methods are natural candidates for solving the aforementionedproblem and there are many studies regarding this. However,most of the proposed solutions are related to centralized/parallel computations while only a few have the potential to beapplied in distributed networks. Thus distributed computations are strongly preferred or demanded in many of the realworld applications, e.g. smart-grid, target tracking, etc. Thispaper surveys the representative iterative methods for distributed least-squares in networks.
基金This project is supported by Research Foundation for Doctoral Program of Higher Education, China (No.98033532)
文摘The main purpose of reverse engineering is to convert discrete data pointsinto piecewise smooth, continuous surface models. Before carrying out model reconstruction it issignificant to extract geometric features because the quality of modeling greatly depends on therepresentation of features. Some fitting techniques of natural quadric surfaces with least-squaresmethod are described. And these techniques can be directly used to extract quadric surfaces featuresduring the process of segmentation for point cloud.
基金the National Science Council ot Taiwan,China for funding this research(Project no.:NSC 94-2218-E-035-011)
文摘A least-squares finite-element method （LSFEM） for the non-conservative shallow-water equations is presented. The model is capable of handling complex topography, steady and unsteady flows, subcritical and supercritical flows, and flows with smooth and sharp gradient changes. Advantages of the model include： （1） sources terms, such as the bottom slope, surface stresses and bed frictions, can be treated easily without any special treatment; （2） upwind scheme is no needed; （3） a single approximating space can be used for all variables, and its choice of approximating space is not subject to the Ladyzhenskaya-Babuska-Brezzi （LBB） condition; and （4） the resulting system of equations is symmetric and positive-definite （SPD） which can be solved efficiently with the preconditioned conjugate gradient method. The model is verified with flow over a bump, tide induced flow, and dam-break. Computed results are compared with analytic solutions or other numerical results, and show the model is conservative and accurate. The model is then used to simulate flow past a circular cylinder. Important flow charac-teristics, such as variation of water surface around the cylinder and vortex shedding behind the cylinder are investigated. Computed results compare well with experiment data and other numerical results.
基金the National Science Council of Taiwan for funding this research (NSC 96-2221-E-019-061).
文摘Numerical solution of shallow-water equations （SWE） has been a challenging task because of its nonlinear hyperbolic nature, admitting discontinuous solution, and the need to satisfy the C-property. The presence of source terms in momentum equations, such as the bottom slope and friction of bed, compounds the difficulties further. In this paper, a least-squares finite-element method for the space discretization and θ-method for the time integration is developed for the 2D non-conservative SWE including the source terms. Advantages of the method include： the source terms can be approximated easily with interpolation functions, no upwind scheme is needed, as well as the resulting system equations is symmetric and positive-definite, therefore, can be solved efficiently with the conjugate gradient method. The method is applied to steady and unsteady flows, subcritical and transcritical flow over a bump, 1D and 2D circular dam-break, wave past a circular cylinder, as well as wave past a hump. Computed results show good C-property, conservation property and compare well with exact solutions and other numerical results for flows with weak and mild gradient changes, but lead to inaccurate predictions for flows with strong gradient changes and discontinuities.
基金supported by the National Natural Science Foundation of China(Nos.11702329,12102247)the Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management Systems,China(No.VATLAB-2021-01)。
文摘For the second-order finite volume method,implicit schemes and reconstruction methods are two main algorithms which influence the robustness and efficiency of the numerical simulations of compressible turbulent flows.In this paper,a compact least-squares reconstruction method is proposed to calculate the gradients for the distribution of flow field variables approximation.The compactness of the new reconstruction method is reflected in the gradient calculation process.The geometries of the face-neighboring elements are no longer utilized,and the weighted average values at the centroid of the interfaces are used to calculate the gradients instead of the values at the centroid of the face-neighboring elements.Meanwhile,an exact Jacobian solving strategy is developed for implicit temporal discretization.The accurate processing of Jacobian matrix can extensively improve the invertibility of the Jacobian matrix and avoid introducing extra numerical errors.In addition,a modified Venkatakrishnan limiter is applied to deal with the shock which may appear in transonic flows and the applicability of the mentioned methods is enhanced further.The combination of the proposed methods makes the numerical simulations of turbulent flow converge rapidly and steadily with an adaptive increasing CFL number.The numerical results of several benchmarks indicate that the proposed methods perform well in terms of robustness,efficiency and accuracy,and have good application potential in turbulent flow simulations of complex configurations.
基金supported by the Innovation Foundation of Provincial Education Department of Gansu(2024B-005)the Gansu Province National Science Foundation(22YF7GA182)the Fundamental Research Funds for the Central Universities(No.lzujbky2022-kb01)。
文摘Modal parameters can accurately characterize the structural dynamic properties and assess the physical state of the structure.Therefore,it is particularly significant to identify the structural modal parameters according to the monitoring data information in the structural health monitoring(SHM)system,so as to provide a scientific basis for structural damage identification and dynamic model modification.In view of this,this paper reviews methods for identifying structural modal parameters under environmental excitation and briefly describes how to identify structural damages based on the derived modal parameters.The paper primarily introduces data-driven modal parameter recognition methods(e.g.,time-domain,frequency-domain,and time-frequency-domain methods,etc.),briefly describes damage identification methods based on the variations of modal parameters(e.g.,natural frequency,modal shapes,and curvature modal shapes,etc.)and modal validation methods(e.g.,Stability Diagram and Modal Assurance Criterion,etc.).The current status of the application of artificial intelligence(AI)methods in the direction of modal parameter recognition and damage identification is further discussed.Based on the pre-vious analysis,the main development trends of structural modal parameter recognition and damage identification methods are given to provide scientific references for the optimized design and functional upgrading of SHM systems.
基金partially supported by the National Natural Science Foundation of China (No.41230318)
文摘With the development of computational power, there has been an increased focus on data-fitting related seismic inversion techniques for high fidelity seismic velocity model and image, such as full-waveform inversion and least squares migration. However, though more advanced than conventional methods, these data fitting methods can be very expensive in terms of computational cost. Recently, various techniques to optimize these data-fitting seismic inversion problems have been implemented to cater for the industrial need for much improved efficiency. In this study, we propose a general stochastic conjugate gradient method for these data-fitting related inverse problems. We first prescribe the basic theory of our method and then give synthetic examples. Our numerical experiments illustrate the potential of this method for large-size seismic inversion application.
基金co-supported by the National Natural Science Foundation of China (Nos. 61201381, 61401513 and 61772548)the China Postdoctoral Science Foundation (No. 2016M592989)+1 种基金the Self-Topic Foundation of Information Engineering University, China (No. 2016600701)the Outstanding Youth Foundation of Information Engineering University, China (No. 2016603201)
文摘It is well known that the Two-step Weighted Least-Squares(TWLS) is a widely used method for source localization and sensor position refinement. For this reason, we propose a unified framework of the TWLS method for joint estimation of multiple disjoint sources and sensor locations in this paper. Unlike some existing works, the presented method is based on more general measurement model, and therefore it can be applied to many different localization scenarios.Besides, it does not have the initialization and local convergence problem. The closed-form expression for the covariance matrix of the proposed TWLS estimator is also derived by exploiting the first-order perturbation analysis. Moreover, the estimation accuracy of the TWLS method is shown analytically to achieve the Cramér-Rao Bound(CRB) before the threshold effect takes place. The theoretical analysis is also performed in a common mathematical framework, rather than aiming at some specific signal metrics. Finally, two numerical experiments are performed to support the theoretical development in this paper.
基金supported in part by the National Natural Science Foundation of China(NSFC)under Grants(52275471 and 52120105008)the Beijing Outstanding Young Scientist Program,and the New Cornerstone Science Foundation through the XPLORER PRIZE.
文摘As pivotal supporting technologies for smart manufacturing and digital engineering,model-based and data-driven methods have been widely applied in many industrial fields,such as product design,process monitoring,and smart maintenance.While promising,both methods have issues that need to be addressed.For example,model-based methods are limited by low computational accuracy and a high computational burden,and data-driven methods always suffer from poor interpretability and redundant features.To address these issues,the concept of data-model fusion(DMF)emerges as a promising solution.DMF involves integrating model-based methods with data-driven methods by incorporating big data into model-based methods or embedding relevant domain knowledge into data-driven methods.Despite growing efforts in the field of DMF,a unanimous definition of DMF remains elusive,and a general framework of DMF has been rarely discussed.This paper aims to address this gap by providing a thorough overview and categorization of both data-driven methods and model-based methods.Subsequently,this paper also presents the definition and categorization of DMF and discusses the general framework of DMF.Moreover,the primary seven applications of DMF are reviewed within the context of smart manufacturing and digital engineering.Finally,this paper directs the future directions of DMF.
基金funded by the National Natural Science Foundation of China(No.41962016)the Natural Science Foundation of NingXia(Nos.2023AAC02023,2023A1218,and 2021AAC02006).
文摘Soil improvement is one of the most important issues in geotechnical engineering practice.The wide application of traditional improvement techniques(cement/chemical materials)are limited due to damage ecological en-vironment and intensify carbon emissions.However,the use of microbially induced calcium carbonate pre-cipitation(MICP)to obtain bio-cement is a novel technique with the potential to induce soil stability,providing a low-carbon,environment-friendly,and sustainable integrated solution for some geotechnical engineering pro-blems in the environment.This paper presents a comprehensive review of the latest progress in soil improvement based on the MICP strategy.It systematically summarizes and overviews the mineralization mechanism,influ-encing factors,improved methods,engineering characteristics,and current field application status of the MICP.Additionally,it also explores the limitations and correspondingly proposes prospective applications via the MICP approach for soil improvement.This review indicates that the utilization of different environmental calcium-based wastes in MICP and combination of materials and MICP are conducive to meeting engineering and market demand.Furthermore,we recommend and encourage global collaborative study and practice with a view to commercializing MICP technique in the future.The current review purports to provide insights for engineers and interdisciplinary researchers,and guidance for future engineering applications.
基金supported by the National Natural Science Foundation of China(12172023).
文摘The separation-of-variable(SOV)methods,such as the improved SOV method,the variational SOV method,and the extended SOV method,have been proposed by the present authors and coworkers to obtain the closed-form analytical solutions for free vibration and eigenbuckling of rectangular plates and circular cylindrical shells.By taking the free vibration of rectangular thin plates as an example,this work presents the theoretical framework of the SOV methods in an instructive way,and the bisection–based solution procedures for a group of nonlinear eigenvalue equations.Besides,the explicit equations of nodal lines of the SOV methods are presented,and the relations of nodal line patterns and frequency orders are investigated.It is concluded that the highly accurate SOV methods have the same accuracy for all frequencies,the mode shapes about repeated frequencies can also be precisely captured,and the SOV methods do not have the problem of missing roots as well.
基金This study was funded by the National Natural Science Foundation of China(Nos.11972077 and 12272039).
文摘In this paper,we present a novel initial costates solver for initializing time-optimal trajectory problems in relative motion with continuous low thrust.The proposed solver consists of two primary components:training a Multilayer Perceptron(MLP)for generating reference sequence and Time of Flight(TOF)to the target,and deriving a system of linear algebraic equations for obtaining the initial costates.To overcome the challenge of generating training samples for the MLP,the backward generation method is proposed to obtain five different training databases.The training database and sample form are determined by analyzing the input and output correlation using the Pearson correlation coefficient.The best-performing MLP is obtained by analyzing the training results with various hyper-parameter combinations.A reference sequence starting from the initial states is obtained by integrating forward with the near-optimal control vector from the output of MLP.Finally,a system of linear algebraic equations for estimating the initial costates is derived using the reference sequence and the necessary conditions for optimality.Simulation results demonstrate that the proposed initial costates solver improves the convergence ratio and reduce the function calls of the shooting function.Furthermore,Monte-Carlo simulation illustrates that the initial costates solver is applicable to different initial velocities,demonstrating excellent generalization ability.
文摘The microstructures of pharmaceutical preparations play a pivotal role in determining their critical quality attributes(CQAs),such as drug release,content uniformity,and stability,which greatly impact the safety and efficacy of drugs.Unlike the inherent molecular structures of active pharmaceutical ingredients(APIs)and excipients,the microstructures of pharmaceutical preparations are developed during the formulation process,presenting unique analytical challenges.In this review,we primarily focus on presenting the research methods used to elucidate the microstructures of pharmaceutical preparations,including X-ray imaging(XRI),scanning electron microscopy(SEM),atomic force microscopy(AFM),Raman spectroscopy,infrared(IR)spectroscopy,and rheometer technology.Subsequently,we highlight the applications,advantages,and limitations of these methods.Finally,we discuss the current challenges and future perspectives in this field.This review aims to provide a comprehensive reference for understanding the microstructures of pharmaceutical preparations,offering new insights and potential advancements in their development.
