In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to ...In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.展开更多
In this paper,a novel method for investigating the particle-crushing behavior of breeding particles in a fusion blanket is proposed.The fractal theory and Weibull distribution are combined to establish a theoretical m...In this paper,a novel method for investigating the particle-crushing behavior of breeding particles in a fusion blanket is proposed.The fractal theory and Weibull distribution are combined to establish a theoretical model,and its validity was verified using a simple impact test.A crushable discrete element method(DEM)framework is built based on the previously established theoretical model.The tensile strength,which considers the fractal theory,size effect,and Weibull variation,was assigned to each generated particle.The assigned strength is then used for crush detection by comparing it with its maximum tensile stress.Mass conservation is ensured by inserting a series of sub-particles whose total mass was equal to the quality loss.Based on the crushable DEM framework,a numerical simulation of the crushing behavior of a pebble bed with hollow cylindrical geometry under a uniaxial compression test was performed.The results of this investigation showed that the particle withstands the external load by contact and sliding at the beginning of the compression process,and the results confirmed that crushing can be considered an important method of resisting the increasing external load.A relatively regular particle arrangement aids in resisting the load and reduces the occurrence of particle crushing.However,a limit exists to the promotion of resistance.When the strain increases beyond this limit,the distribution of the crushing position tends to be isotropic over the entire pebble bed.The theoretical model and crushable DEM framework provide a new method for exploring the pebble bed in a fusion reactor,considering particle crushing.展开更多
Effective partitioning is crucial for enabling parallel restoration of power systems after blackouts.This paper proposes a novel partitioning method based on deep reinforcement learning.First,the partitioning decision...Effective partitioning is crucial for enabling parallel restoration of power systems after blackouts.This paper proposes a novel partitioning method based on deep reinforcement learning.First,the partitioning decision process is formulated as a Markov decision process(MDP)model to maximize the modularity.Corresponding key partitioning constraints on parallel restoration are considered.Second,based on the partitioning objective and constraints,the reward function of the partitioning MDP model is set by adopting a relative deviation normalization scheme to reduce mutual interference between the reward and penalty in the reward function.The soft bonus scaling mechanism is introduced to mitigate overestimation caused by abrupt jumps in the reward.Then,the deep Q network method is applied to solve the partitioning MDP model and generate partitioning schemes.Two experience replay buffers are employed to speed up the training process of the method.Finally,case studies on the IEEE 39-bus test system demonstrate that the proposed method can generate a high-modularity partitioning result that meets all key partitioning constraints,thereby improving the parallelism and reliability of the restoration process.Moreover,simulation results demonstrate that an appropriate discount factor is crucial for ensuring both the convergence speed and the stability of the partitioning training.展开更多
The application of nitrogen fertilizers in agricultural fields can lead to the release of nitrogen-containing gases(NCGs),such as NO_(x),NH_(3) and N_(2)O,which can significantly impact regional atmospheric environmen...The application of nitrogen fertilizers in agricultural fields can lead to the release of nitrogen-containing gases(NCGs),such as NO_(x),NH_(3) and N_(2)O,which can significantly impact regional atmospheric environment and con-tribute to global climate change.However,there remain considerable research gaps in the accurate measurement of NCGs emissions from agricultural fields,hindering the development of effective emission reduction strategies.We improved an open-top dynamic chambers(OTDCs)system and evaluated the performance by comparing the measured and given fluxes of the NCGs.The results showed that the measured fluxes of NO,N_(2)O and NH_(3)were 1%,2%and 7%lower than the given fluxes,respectively.For the determination of NH_(3) concentration,we employed a stripping coil-ion chromatograph(SC-IC)analytical technique,which demonstrated an absorption efficiency for atmospheric NH_(3) exceeding 96.1%across sampling durations of 6 to 60 min.In the summer maize season,we utilized the OTDCs system to measure the exchange fluxes of NO,NH_(3),and N_(2)O from the soil in the North China Plain.Substantial emissions of NO,NH_(3) and N_(2)O were recorded following fertilization,with peaks of 107,309,1239 ng N/(m^(2)·s),respectively.Notably,significant NCGs emissions were observed following sus-tained heavy rainfall one month after fertilization,particularly with NH_(3) peak being 4.5 times higher than that observed immediately after fertilization.Our results demonstrate that the OTDCs system accurately reflects the emission characteristics of soil NCGs and meets the requirements for long-term and continuous flux observation.展开更多
Marine thin plates are susceptible to welding deformation owing to their low structural stiffness.Therefore,the efficient and accurate prediction of welding deformation is essential for improving welding quality.The t...Marine thin plates are susceptible to welding deformation owing to their low structural stiffness.Therefore,the efficient and accurate prediction of welding deformation is essential for improving welding quality.The traditional thermal elastic-plastic finite element method(TEP-FEM)can accurately predict welding deformation.However,its efficiency is low because of the complex nonlinear transient computation,making it difficult to meet the needs of rapid engineering evaluation.To address this challenge,this study proposes an efficient prediction method for welding deformation in marine thin plate butt welds.This method is based on the coupled temperature gradient-thermal strain method(TG-TSM)that integrates inherent strain theory with a shell element finite element model.The proposed method first extracts the distribution pattern and characteristic value of welding-induced inherent strain through TEP-FEM analysis.This strain is then converted into the equivalent thermal load applied to the shell element model for rapid computation.The proposed method-particularly,the gradual temperature gradient-thermal strain method(GTG-TSM)-achieved improved computational efficiency and consistent precision.Furthermore,the proposed method required much less computation time than the traditional TEP-FEM.Thus,this study lays the foundation for future prediction of welding deformation in more complex marine thin plates.展开更多
At present,there is currently a lack of unified standard methods for the determination of antimony content in groundwater in China.The precision and trueness of related detection technologies have not yet been systema...At present,there is currently a lack of unified standard methods for the determination of antimony content in groundwater in China.The precision and trueness of related detection technologies have not yet been systematically and quantitatively evaluated,which limits the effective implementation of environmental monitoring.In response to this key technical gap,this study aimed to establish a standardized method for determining antimony in groundwater using Hydride Generation–Atomic Fluorescence Spectrometry(HG-AFS).Ten laboratories participated in inter-laboratory collaborative tests,and the statistical analysis of the test data was carried out in strict accordance with the technical specifications of GB/T 6379.2—2004 and GB/T 6379.4—2006.The consistency and outliers of the data were tested by Mandel's h and k statistics,the Grubbs test and the Cochran test,and the outliers were removed to optimize the data,thereby significantly improving the reliability and accuracy.Based on the optimized data,parameters such as the repeatability limit(r),reproducibility limit(R),and method bias value(δ)were determined,and the trueness of the method was statistically evaluated.At the same time,precision-function relationships were established,and all results met the requirements.The results show that the lower the antimony content,the lower the repeatability limit(r)and reproducibility limit(R),indicating that the measurement error mainly originates from the detection limit of the method and instrument sensitivity.Therefore,improving the instrument sensitivity and reducing the detection limit are the keys to controlling the analytical error and improving precision.This study provides reliable data support and a solid technical foundation for the establishment and evaluation of standardized methods for the determination of antimony content in groundwater.展开更多
Recent years have witnessed growing interests in solving partial differential equations by deep neural networks,especially in the high-dimensional case.Unlike classical numerical methods,such as finite difference meth...Recent years have witnessed growing interests in solving partial differential equations by deep neural networks,especially in the high-dimensional case.Unlike classical numerical methods,such as finite difference method and finite element method,the enforcement of boundary conditions in deep neural networks is highly nontrivial.One general strategy is to use the penalty method.In the work,we conduct a comparison study for elliptic problems with four different boundary conditions,i.e.,Dirichlet,Neumann,Robin,and periodic boundary conditions,using two representative methods:deep Galerkin method and deep Ritz method.In the former,the PDE residual is minimized in the least-squares sense while the corresponding variational problem is minimized in the latter.Therefore,it is reasonably expected that deep Galerkin method works better for smooth solutions while deep Ritz method works better for low-regularity solutions.However,by a number of examples,we observe that deep Ritz method can outperform deep Galerkin method with a clear dependence of dimensionality even for smooth solutions and deep Galerkin method can also outperform deep Ritz method for low-regularity solutions.Besides,in some cases,when the boundary condition can be implemented in an exact manner,we find that such a strategy not only provides a better approximate solution but also facilitates the training process.展开更多
In this paper, the jacket platform is simulated by a non-uniform cantilever beam subjected to axial force. Based on the Hamilton theory, the equation of bending motion is developed and solved by the classical Ritz met...In this paper, the jacket platform is simulated by a non-uniform cantilever beam subjected to axial force. Based on the Hamilton theory, the equation of bending motion is developed and solved by the classical Ritz method combined with the pseudo-excitation method for random responses with non-classical damping. Usually, random responses of this continuous structure are obtained by orthogonality of modes, and some normal modes of the structure are needed, causing inconvenience for the analysis of the non-uniform beam whose normal modes are not easy to be obtained. However, if the pseudo-excitation method is extended to calculate random responses by combining it with the classical Ritz method, the responses of a non-uniform beam, such as auto-PSD function, cross-PSD and higher spectral moments, can be solved directly avoiding the calculation of normal modes. The numerical results show that the present method is effective and useful in aseismic design of platforms.展开更多
This study presents the Chebyshev polynomials-based Ritz method to examine the thermal buckling and free vibration characteristics of metal foam beams.The analyses include three models for porosity distribution and tw...This study presents the Chebyshev polynomials-based Ritz method to examine the thermal buckling and free vibration characteristics of metal foam beams.The analyses include three models for porosity distribution and two scenarios for thermal distribution.The material properties are assessed under two conditions,i.e.,temperature dependence and temperature independence.The theoretical framework for the beams is based on the higher-order shear deformation theory,which incorporates shear deformations with higher-order polynomials.The governing equations are established from the Lagrange equations,and the beam displacement fields are approximated by the Chebyshev polynomials.Numerical simulations are performed to evaluate the effects of thermal load,slenderness,boundary condition(BC),and porosity distribution on the buckling and vibration behaviors of metal foam beams.The findings highlight the significant influence of temperature-dependent(TD)material properties on metal foam beams'buckling and vibration responses.展开更多
The stress field in granular soils heap(including piled coal) will have a non-negligible impact on the settlement of the underlying soils. It is usually obtained by measurements and numerical simulations.Because the f...The stress field in granular soils heap(including piled coal) will have a non-negligible impact on the settlement of the underlying soils. It is usually obtained by measurements and numerical simulations.Because the former method is not reliable as pressure cells instrumented on the interface between piled coal and the underlying soft soil do not work well, results from numerical methods alone are necessary to be doubly checked with one more method before they are extended to more complex cases. The generalized stress field in granular soils heap is analyzed with Rayleighe Ritz method. The problem is divided into two cases: case A without horizontal constraint on the base and case B with horizontal constraint on the base. In both cases, the displacement functions u(x, y) and v(x, y) are assumed to be cubic polynomials with 12 undetermined parameters, which will satisfy the Cauchy’s partial differential equations, generalized Hooke’s law and boundary equations. A function is built with the Rayleighe Ritz method according to the principle of minimum potential energy, and the problem is converted into solving two undetermined parameters through the variation of the function, while the other parameters are expressed in terms of these two parameters. By comparison of results from the Rayleighe Ritz method and numerical simulations, it is demonstrated that the Rayleighe Ritz method is feasible to study the generalized stress field in granular soils heap. Solutions from numerical methods are verified before being extended to more complicated cases.展开更多
In this paper,we analyse the equal width（EW） wave equation by using the mesh-free reproducing kernel particle Ritz（kp-Ritz） method.The mesh-free kernel particle estimate is employed to approximate the displacement...In this paper,we analyse the equal width（EW） wave equation by using the mesh-free reproducing kernel particle Ritz（kp-Ritz） method.The mesh-free kernel particle estimate is employed to approximate the displacement field.A system of discrete equations is obtained through the application of the Ritz minimization procedure to the energy expressions.The effectiveness of the kp-Ritz method for the EW wave equation is investigated by numerical examples in this paper.展开更多
The doubly curved shell(DCS)is a common structure in the engineering field.In a thermal environment,the vibration characteristics of the DCS will be affected by the thermal effect.The research on the vibration charact...The doubly curved shell(DCS)is a common structure in the engineering field.In a thermal environment,the vibration characteristics of the DCS will be affected by the thermal effect.The research on the vibration characteristics of DCS in thermal environment is relatively limited.In this paper,the thermal strain and the change of Young’s modulus caused by the changing of temperature are studied,and the DCS energy equation is established systematically.The displacement tolerance function of the DCS is constructed by the spectral geometry method,and the natural frequencies and mode shapes of the DCS with different structural parameters,such as thicknesses,ratios of R_(a)/R_(b) and a/b,at different temperatures are solved by the Rayleigh-Ritz method.The results show that the natural frequency of the DCS decreases with the increasing temperature,R_(a)/R_(b) and a/b ratios,and increases with the increasing thickness.展开更多
A rotor manipulation mechanism for micro unmanned helicopter utilizing the inertia and the elasticity of the rotor is introduced. The lagging motion equation of the rotor blades is established, and then the natural fr...A rotor manipulation mechanism for micro unmanned helicopter utilizing the inertia and the elasticity of the rotor is introduced. The lagging motion equation of the rotor blades is established, and then the natural frequencies and mode shapes of the blade for the helicopter are studied by using beam characteristic orthogonal polynomials by the Rayleigh-Ritz method. The variation of natural frequencies with the speed of rotation and the mode shapes at different rotational speeds are plotted. The using of orthogonal polynomials for the bending shapes enables the computation of higher natural frequencies of any order to be accomplished without facing any difficulties.展开更多
Free vibration analysis of non-homogeneous orthotropic plates resting on a Pasternak type of elastic foundation is investigated. A set of admissible orthogonal polynomials are generated with Gram-Schmidt orthogonaliza...Free vibration analysis of non-homogeneous orthotropic plates resting on a Pasternak type of elastic foundation is investigated. A set of admissible orthogonal polynomials are generated with Gram-Schmidt orthogonalization procedure and adopted in the Rayleigh-Ritz method. Accuracy and applicability of the method are examined by comparison of the results for different boundary conditions and material types with those available in literature. It is found that this method has good accuracy regardless of type of boundary condition and yields very accurate results even with low number of terms of orthogonal polynomials for the first mode of vibration. For higher modes of vibration, higher terms of orthogonal polynomials should be used. The effects of foundation parameter, density and non-homogeneity parameters on natural frequency are examined. It is concluded that natural frequency of plates are more sensitive to shearing layer coefficient rather than Winkler coefficient and density parameter has weakening effect on natural frequency.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
To analyze the differences in the transport and distribution of different types of proppants and to address issues such as the short effective support of proppant and poor placement in hydraulically intersecting fract...To analyze the differences in the transport and distribution of different types of proppants and to address issues such as the short effective support of proppant and poor placement in hydraulically intersecting fractures,this study considered the combined impact of geological-engineering factors on conductivity.Using reservoir production parameters and the discrete elementmethod,multispherical proppants were constructed.Additionally,a 3D fracture model,based on the specified conditions of the L block,employed coupled(Computational Fluid Dynamics)CFD-DEM(Discrete ElementMethod)for joint simulations to quantitatively analyze the transport and placement patterns of multispherical proppants in intersecting fractures.Results indicate that turbulent kinetic energy is an intrinsic factor affecting proppant transport.Moreover,the efficiency of placement and migration distance of low-sphericity quartz sand constructed by the DEM in the main fracture are significantly reduced compared to spherical ceramic proppants,with a 27.7%decrease in the volume fraction of the fracture surface,subsequently affecting the placement concentration and damaging fracture conductivity.Compared to small-angle fractures,controlling artificial and natural fractures to expand at angles of 45°to 60°increases the effective support length by approximately 20.6%.During hydraulic fracturing of gas wells,ensuring the fracture support area and post-closure conductivity can be achieved by controlling the sphericity of proppants and adjusting the perforation direction to control the direction of artificial fractures.展开更多
基金Supported in part by Natural Science Foundation of Guangxi(2023GXNSFAA026246)in part by the Central Government's Guide to Local Science and Technology Development Fund(GuikeZY23055044)in part by the National Natural Science Foundation of China(62363003)。
文摘In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.
基金supported by Anhui Provincial Natural Science Foundation(2408085QA030)Natural Science Research Project of Anhui Educational Committee,China(2022AH050825)+3 种基金Medical Special Cultivation Project of Anhui University of Science and Technology(YZ2023H2C008)the Excellent Research and Innovation Team of Anhui Province,China(2022AH010052)the Scientific Research Foundation for High-level Talents of Anhui University of Science and Technology,China(2021yjrc51)Collaborative Innovation Program of Hefei Science Center,CAS,China(2019HSC-CIP006).
文摘In this paper,a novel method for investigating the particle-crushing behavior of breeding particles in a fusion blanket is proposed.The fractal theory and Weibull distribution are combined to establish a theoretical model,and its validity was verified using a simple impact test.A crushable discrete element method(DEM)framework is built based on the previously established theoretical model.The tensile strength,which considers the fractal theory,size effect,and Weibull variation,was assigned to each generated particle.The assigned strength is then used for crush detection by comparing it with its maximum tensile stress.Mass conservation is ensured by inserting a series of sub-particles whose total mass was equal to the quality loss.Based on the crushable DEM framework,a numerical simulation of the crushing behavior of a pebble bed with hollow cylindrical geometry under a uniaxial compression test was performed.The results of this investigation showed that the particle withstands the external load by contact and sliding at the beginning of the compression process,and the results confirmed that crushing can be considered an important method of resisting the increasing external load.A relatively regular particle arrangement aids in resisting the load and reduces the occurrence of particle crushing.However,a limit exists to the promotion of resistance.When the strain increases beyond this limit,the distribution of the crushing position tends to be isotropic over the entire pebble bed.The theoretical model and crushable DEM framework provide a new method for exploring the pebble bed in a fusion reactor,considering particle crushing.
基金funded by the Beijing Engineering Research Center of Electric Rail Transportation.
文摘Effective partitioning is crucial for enabling parallel restoration of power systems after blackouts.This paper proposes a novel partitioning method based on deep reinforcement learning.First,the partitioning decision process is formulated as a Markov decision process(MDP)model to maximize the modularity.Corresponding key partitioning constraints on parallel restoration are considered.Second,based on the partitioning objective and constraints,the reward function of the partitioning MDP model is set by adopting a relative deviation normalization scheme to reduce mutual interference between the reward and penalty in the reward function.The soft bonus scaling mechanism is introduced to mitigate overestimation caused by abrupt jumps in the reward.Then,the deep Q network method is applied to solve the partitioning MDP model and generate partitioning schemes.Two experience replay buffers are employed to speed up the training process of the method.Finally,case studies on the IEEE 39-bus test system demonstrate that the proposed method can generate a high-modularity partitioning result that meets all key partitioning constraints,thereby improving the parallelism and reliability of the restoration process.Moreover,simulation results demonstrate that an appropriate discount factor is crucial for ensuring both the convergence speed and the stability of the partitioning training.
基金supported by the National Key Research and Develop-ment Program(No.2022YFC3701103)the National Natural Science Foundation of China(Nos.42130714 and 41931287).
文摘The application of nitrogen fertilizers in agricultural fields can lead to the release of nitrogen-containing gases(NCGs),such as NO_(x),NH_(3) and N_(2)O,which can significantly impact regional atmospheric environment and con-tribute to global climate change.However,there remain considerable research gaps in the accurate measurement of NCGs emissions from agricultural fields,hindering the development of effective emission reduction strategies.We improved an open-top dynamic chambers(OTDCs)system and evaluated the performance by comparing the measured and given fluxes of the NCGs.The results showed that the measured fluxes of NO,N_(2)O and NH_(3)were 1%,2%and 7%lower than the given fluxes,respectively.For the determination of NH_(3) concentration,we employed a stripping coil-ion chromatograph(SC-IC)analytical technique,which demonstrated an absorption efficiency for atmospheric NH_(3) exceeding 96.1%across sampling durations of 6 to 60 min.In the summer maize season,we utilized the OTDCs system to measure the exchange fluxes of NO,NH_(3),and N_(2)O from the soil in the North China Plain.Substantial emissions of NO,NH_(3) and N_(2)O were recorded following fertilization,with peaks of 107,309,1239 ng N/(m^(2)·s),respectively.Notably,significant NCGs emissions were observed following sus-tained heavy rainfall one month after fertilization,particularly with NH_(3) peak being 4.5 times higher than that observed immediately after fertilization.Our results demonstrate that the OTDCs system accurately reflects the emission characteristics of soil NCGs and meets the requirements for long-term and continuous flux observation.
基金Supported by the National Natural Science Foundation of China under Grant No.51975138the High-Tech Ship Scientific Research Project from the Ministry of Industry and Information Technology under Grant No.CJ05N20the National Defense Basic Research Project under Grant No.JCKY2023604C006.
文摘Marine thin plates are susceptible to welding deformation owing to their low structural stiffness.Therefore,the efficient and accurate prediction of welding deformation is essential for improving welding quality.The traditional thermal elastic-plastic finite element method(TEP-FEM)can accurately predict welding deformation.However,its efficiency is low because of the complex nonlinear transient computation,making it difficult to meet the needs of rapid engineering evaluation.To address this challenge,this study proposes an efficient prediction method for welding deformation in marine thin plate butt welds.This method is based on the coupled temperature gradient-thermal strain method(TG-TSM)that integrates inherent strain theory with a shell element finite element model.The proposed method first extracts the distribution pattern and characteristic value of welding-induced inherent strain through TEP-FEM analysis.This strain is then converted into the equivalent thermal load applied to the shell element model for rapid computation.The proposed method-particularly,the gradual temperature gradient-thermal strain method(GTG-TSM)-achieved improved computational efficiency and consistent precision.Furthermore,the proposed method required much less computation time than the traditional TEP-FEM.Thus,this study lays the foundation for future prediction of welding deformation in more complex marine thin plates.
基金supported by the National Natural Science Foundation of China(Project No.42307555).
文摘At present,there is currently a lack of unified standard methods for the determination of antimony content in groundwater in China.The precision and trueness of related detection technologies have not yet been systematically and quantitatively evaluated,which limits the effective implementation of environmental monitoring.In response to this key technical gap,this study aimed to establish a standardized method for determining antimony in groundwater using Hydride Generation–Atomic Fluorescence Spectrometry(HG-AFS).Ten laboratories participated in inter-laboratory collaborative tests,and the statistical analysis of the test data was carried out in strict accordance with the technical specifications of GB/T 6379.2—2004 and GB/T 6379.4—2006.The consistency and outliers of the data were tested by Mandel's h and k statistics,the Grubbs test and the Cochran test,and the outliers were removed to optimize the data,thereby significantly improving the reliability and accuracy.Based on the optimized data,parameters such as the repeatability limit(r),reproducibility limit(R),and method bias value(δ)were determined,and the trueness of the method was statistically evaluated.At the same time,precision-function relationships were established,and all results met the requirements.The results show that the lower the antimony content,the lower the repeatability limit(r)and reproducibility limit(R),indicating that the measurement error mainly originates from the detection limit of the method and instrument sensitivity.Therefore,improving the instrument sensitivity and reducing the detection limit are the keys to controlling the analytical error and improving precision.This study provides reliable data support and a solid technical foundation for the establishment and evaluation of standardized methods for the determination of antimony content in groundwater.
基金the grants NSFC 11971021National Key R&D Program of China(No.2018YF645B0204404)NSFC 11501399(R.Du)。
文摘Recent years have witnessed growing interests in solving partial differential equations by deep neural networks,especially in the high-dimensional case.Unlike classical numerical methods,such as finite difference method and finite element method,the enforcement of boundary conditions in deep neural networks is highly nontrivial.One general strategy is to use the penalty method.In the work,we conduct a comparison study for elliptic problems with four different boundary conditions,i.e.,Dirichlet,Neumann,Robin,and periodic boundary conditions,using two representative methods:deep Galerkin method and deep Ritz method.In the former,the PDE residual is minimized in the least-squares sense while the corresponding variational problem is minimized in the latter.Therefore,it is reasonably expected that deep Galerkin method works better for smooth solutions while deep Ritz method works better for low-regularity solutions.However,by a number of examples,we observe that deep Ritz method can outperform deep Galerkin method with a clear dependence of dimensionality even for smooth solutions and deep Galerkin method can also outperform deep Ritz method for low-regularity solutions.Besides,in some cases,when the boundary condition can be implemented in an exact manner,we find that such a strategy not only provides a better approximate solution but also facilitates the training process.
文摘In this paper, the jacket platform is simulated by a non-uniform cantilever beam subjected to axial force. Based on the Hamilton theory, the equation of bending motion is developed and solved by the classical Ritz method combined with the pseudo-excitation method for random responses with non-classical damping. Usually, random responses of this continuous structure are obtained by orthogonality of modes, and some normal modes of the structure are needed, causing inconvenience for the analysis of the non-uniform beam whose normal modes are not easy to be obtained. However, if the pseudo-excitation method is extended to calculate random responses by combining it with the classical Ritz method, the responses of a non-uniform beam, such as auto-PSD function, cross-PSD and higher spectral moments, can be solved directly avoiding the calculation of normal modes. The numerical results show that the present method is effective and useful in aseismic design of platforms.
文摘This study presents the Chebyshev polynomials-based Ritz method to examine the thermal buckling and free vibration characteristics of metal foam beams.The analyses include three models for porosity distribution and two scenarios for thermal distribution.The material properties are assessed under two conditions,i.e.,temperature dependence and temperature independence.The theoretical framework for the beams is based on the higher-order shear deformation theory,which incorporates shear deformations with higher-order polynomials.The governing equations are established from the Lagrange equations,and the beam displacement fields are approximated by the Chebyshev polynomials.Numerical simulations are performed to evaluate the effects of thermal load,slenderness,boundary condition(BC),and porosity distribution on the buckling and vibration behaviors of metal foam beams.The findings highlight the significant influence of temperature-dependent(TD)material properties on metal foam beams'buckling and vibration responses.
文摘The stress field in granular soils heap(including piled coal) will have a non-negligible impact on the settlement of the underlying soils. It is usually obtained by measurements and numerical simulations.Because the former method is not reliable as pressure cells instrumented on the interface between piled coal and the underlying soft soil do not work well, results from numerical methods alone are necessary to be doubly checked with one more method before they are extended to more complex cases. The generalized stress field in granular soils heap is analyzed with Rayleighe Ritz method. The problem is divided into two cases: case A without horizontal constraint on the base and case B with horizontal constraint on the base. In both cases, the displacement functions u(x, y) and v(x, y) are assumed to be cubic polynomials with 12 undetermined parameters, which will satisfy the Cauchy’s partial differential equations, generalized Hooke’s law and boundary equations. A function is built with the Rayleighe Ritz method according to the principle of minimum potential energy, and the problem is converted into solving two undetermined parameters through the variation of the function, while the other parameters are expressed in terms of these two parameters. By comparison of results from the Rayleighe Ritz method and numerical simulations, it is demonstrated that the Rayleighe Ritz method is feasible to study the generalized stress field in granular soils heap. Solutions from numerical methods are verified before being extended to more complicated cases.
基金Project supported by the Natural Science Foundation of Zhejiang Province,China (Grant No. Y6110007)
文摘In this paper,we analyse the equal width（EW） wave equation by using the mesh-free reproducing kernel particle Ritz（kp-Ritz） method.The mesh-free kernel particle estimate is employed to approximate the displacement field.A system of discrete equations is obtained through the application of the Ritz minimization procedure to the energy expressions.The effectiveness of the kp-Ritz method for the EW wave equation is investigated by numerical examples in this paper.
基金supported by the National Natural Science Foundation of China(No.51805341)the Natural Science Foundation of Jiangsu Province(No.BK20180843).
文摘The doubly curved shell(DCS)is a common structure in the engineering field.In a thermal environment,the vibration characteristics of the DCS will be affected by the thermal effect.The research on the vibration characteristics of DCS in thermal environment is relatively limited.In this paper,the thermal strain and the change of Young’s modulus caused by the changing of temperature are studied,and the DCS energy equation is established systematically.The displacement tolerance function of the DCS is constructed by the spectral geometry method,and the natural frequencies and mode shapes of the DCS with different structural parameters,such as thicknesses,ratios of R_(a)/R_(b) and a/b,at different temperatures are solved by the Rayleigh-Ritz method.The results show that the natural frequency of the DCS decreases with the increasing temperature,R_(a)/R_(b) and a/b ratios,and increases with the increasing thickness.
基金This work was supported by the "985"foundation of China(No.082200102).
文摘A rotor manipulation mechanism for micro unmanned helicopter utilizing the inertia and the elasticity of the rotor is introduced. The lagging motion equation of the rotor blades is established, and then the natural frequencies and mode shapes of the blade for the helicopter are studied by using beam characteristic orthogonal polynomials by the Rayleigh-Ritz method. The variation of natural frequencies with the speed of rotation and the mode shapes at different rotational speeds are plotted. The using of orthogonal polynomials for the bending shapes enables the computation of higher natural frequencies of any order to be accomplished without facing any difficulties.
文摘Free vibration analysis of non-homogeneous orthotropic plates resting on a Pasternak type of elastic foundation is investigated. A set of admissible orthogonal polynomials are generated with Gram-Schmidt orthogonalization procedure and adopted in the Rayleigh-Ritz method. Accuracy and applicability of the method are examined by comparison of the results for different boundary conditions and material types with those available in literature. It is found that this method has good accuracy regardless of type of boundary condition and yields very accurate results even with low number of terms of orthogonal polynomials for the first mode of vibration. For higher modes of vibration, higher terms of orthogonal polynomials should be used. The effects of foundation parameter, density and non-homogeneity parameters on natural frequency are examined. It is concluded that natural frequency of plates are more sensitive to shearing layer coefficient rather than Winkler coefficient and density parameter has weakening effect on natural frequency.
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funded by the project of the Major Scientific and Technological Projects of CNOOC in the 14th Five-Year Plan(No.KJGG2022-0701)the CNOOC Research Institute(No.2020PFS-03).
文摘To analyze the differences in the transport and distribution of different types of proppants and to address issues such as the short effective support of proppant and poor placement in hydraulically intersecting fractures,this study considered the combined impact of geological-engineering factors on conductivity.Using reservoir production parameters and the discrete elementmethod,multispherical proppants were constructed.Additionally,a 3D fracture model,based on the specified conditions of the L block,employed coupled(Computational Fluid Dynamics)CFD-DEM(Discrete ElementMethod)for joint simulations to quantitatively analyze the transport and placement patterns of multispherical proppants in intersecting fractures.Results indicate that turbulent kinetic energy is an intrinsic factor affecting proppant transport.Moreover,the efficiency of placement and migration distance of low-sphericity quartz sand constructed by the DEM in the main fracture are significantly reduced compared to spherical ceramic proppants,with a 27.7%decrease in the volume fraction of the fracture surface,subsequently affecting the placement concentration and damaging fracture conductivity.Compared to small-angle fractures,controlling artificial and natural fractures to expand at angles of 45°to 60°increases the effective support length by approximately 20.6%.During hydraulic fracturing of gas wells,ensuring the fracture support area and post-closure conductivity can be achieved by controlling the sphericity of proppants and adjusting the perforation direction to control the direction of artificial fractures.
