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
Convex feasibility problems are widely used in image reconstruction,sparse signal recovery,and other areas.This paper is devoted to considering a class of convex feasibility problem arising from sparse signal recovery...Convex feasibility problems are widely used in image reconstruction,sparse signal recovery,and other areas.This paper is devoted to considering a class of convex feasibility problem arising from sparse signal recovery.We rst derive the projection formulas for a vector onto the feasible sets.The centralized circumcentered-reection method is designed to solve the convex feasibility problem.Some numerical experiments demonstrate the feasibility and e ectiveness of the proposed algorithm,showing superior performance compared to conventional alternating projection methods.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
A three-dimensional （3D） predictor-corrector finite difference method for standing wave is developed. It is applied to solve the 3D nonlinear potential flow equa- tions with a free surface. The 3D irregular tank is ...A three-dimensional （3D） predictor-corrector finite difference method for standing wave is developed. It is applied to solve the 3D nonlinear potential flow equa- tions with a free surface. The 3D irregular tank is mapped onto a fixed cubic tank through the proper coordinate transform schemes. The cubic tank is distributed by the staggered meshgrid, and the staggered meshgrid is used to denote the variables of the flow field. The predictor-corrector finite difference method is given to develop the difference equa- tions of the dynamic boundary equation and kinematic boundary equation. Experimental results show that, using the finite difference method of the predictor-corrector scheme, the numerical solutions agree well with the published results. The wave profiles of the standing wave with different amplitudes and wave lengths are studied. The numerical solutions are also analyzed and presented graphically.展开更多
A finite volume element predictor-corrector method for a class of nonlinear parabolic system of equations is presented and analyzed. Suboptimal L^2 error estimate for the finite volume element predictor-corrector meth...A finite volume element predictor-corrector method for a class of nonlinear parabolic system of equations is presented and analyzed. Suboptimal L^2 error estimate for the finite volume element predictor-corrector method is derived. A numerical experiment shows that the numerical results are consistent with theoretical analysis.展开更多
We present the new predictor-corrector methods for systems of nonlinear differential equations, based on the method of exponential time differencing. We compare the present schemes with the explicit multistep exponent...We present the new predictor-corrector methods for systems of nonlinear differential equations, based on the method of exponential time differencing. We compare the present schemes with the explicit multistep exponential time differencing and Adams–Bashforth–Moulton method. The numerical results show that the schemes are more accurate and more efficient than Adams predictor-corrector method. The exponential time differencing method has been developed and perfected by the present studies.展开更多
In this paper, we present and analyze modified families of predictor-corrector iterative methods for finding simple zeros of univariate nonlinear equations, permitting near the root. The main advantage of our methods ...In this paper, we present and analyze modified families of predictor-corrector iterative methods for finding simple zeros of univariate nonlinear equations, permitting near the root. The main advantage of our methods is that they perform better and moreover, have the same efficiency indices as that of existing multipoint iterative methods. Furthermore, the convergence analysis of the new methods is discussed and several examples are given to illustrate their efficiency.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
Although predictor-corrector methods have been extensively applied,they might not meet the requirements of practical applications and engineering tasks,particularly when high accuracy and efficiency are necessary.A no...Although predictor-corrector methods have been extensively applied,they might not meet the requirements of practical applications and engineering tasks,particularly when high accuracy and efficiency are necessary.A novel class of correctors based on feedback-accelerated Picard iteration(FAPI)is proposed to further enhance computational performance.With optimal feedback terms that do not require inversion of matrices,significantly faster convergence speed and higher numerical accuracy are achieved by these correctors compared with their counterparts;however,the computational complexities are comparably low.These advantages enable nonlinear engineering problems to be solved quickly and accurately,even with rough initial guesses from elementary predictors.The proposed method offers flexibility,enabling the use of the generated correctors for either bulk processing of collocation nodes in a domain or successive corrections of a single node in a finite difference approach.In our method,the functional formulas of FAPI are discretized into numerical forms using the collocation approach.These collocated iteration formulas can directly solve nonlinear problems,but they may require significant computational resources because of the manipulation of high-dimensionalmatrices.To address this,the collocated iteration formulas are further converted into finite difference forms,enabling the design of lightweight predictor-corrector algorithms for real-time computation.The generality of the proposed method is illustrated by deriving new correctors for three commonly employed finite-difference approaches:the modified Euler approach,the Adams-Bashforth-Moulton approach,and the implicit Runge-Kutta approach.Subsequently,the updated approaches are tested in solving strongly nonlinear problems,including the Matthieu equation,the Duffing equation,and the low-earth-orbit tracking problem.The numerical findings confirm the computational accuracy and efficiency of the derived predictor-corrector algorithms.展开更多
This study investigated the physicochemical properties,enzyme activities,volatile flavor components,microbial communities,and sensory evaluation of high-temperature Daqu(HTD)during the maturation process,and a standar...This study investigated the physicochemical properties,enzyme activities,volatile flavor components,microbial communities,and sensory evaluation of high-temperature Daqu(HTD)during the maturation process,and a standard system was established for comprehensive quality evaluation of HTD.There were obvious changes in the physicochemical properties,enzyme activities,and volatile flavor components at different storage periods,which affected the sensory evaluation of HTD to a certain extent.The results of high-throughput sequencing revealed significant microbial diversity,and showed that the bacterial community changed significantly more than did the fungal community.During the storage process,the dominant bacterial genera were Kroppenstedtia and Thermoascus.The correlation between dominant microorganisms and quality indicators highlighted their role in HTD quality.Lactococcus,Candida,Pichia,Paecilomyces,and protease activity played a crucial role in the formation of isovaleraldehyde.Acidic protease activity had the greatest impact on the microbial community.Moisture promoted isobutyric acid generation.Furthermore,the comprehensive quality evaluation standard system was established by the entropy weight method combined with multi-factor fuzzy mathematics.Consequently,this study provides innovative insights for comprehensive quality evaluation of HTD during storage and establishes a groundwork for scientific and rational storage of HTD and quality control of sauce-flavor Baijiu.展开更多
We develop the three-step explicit and implicit schemes of exponential fitting methods. We use the three- step explicit exponential fitting scheme to predict an approximation, then use the three-step implicit exponent...We develop the three-step explicit and implicit schemes of exponential fitting methods. We use the three- step explicit exponential fitting scheme to predict an approximation, then use the three-step implicit exponential fitting scheme to correct this prediction. This combination is called the three-step predictor-corrector of exponential fitting method. The three-step predictor-corrector of exponential fitting method is applied to numerically compute the coupled nonlinear Schroedinger equation and the nonlinear Schroedinger equation with varying coefficients. The numerical results show that the scheme is highly accurate.展开更多
Due to the heterogeneity of rock masses and the variability of in situ stress,the traditional linear inversion method is insufficiently accurate to achieve high accuracy of the in situ stress field.To address this cha...Due to the heterogeneity of rock masses and the variability of in situ stress,the traditional linear inversion method is insufficiently accurate to achieve high accuracy of the in situ stress field.To address this challenge,nonlinear stress boundaries for a numerical model are determined through regression analysis of a series of nonlinear coefficient matrices,which are derived from the bubbling method.Considering the randomness and flexibility of the bubbling method,a parametric study is conducted to determine recommended ranges for these parameters,including the standard deviation(σb)of bubble radii,the non-uniform coefficient matrix number(λ)for nonlinear stress boundaries,and the number(m)and positions of in situ stress measurement points.A model case study provides a reference for the selection of these parameters.Additionally,when the nonlinear in situ stress inversion method is employed,stress distortion inevitably occurs near model boundaries,aligning with the Saint Venant's principle.Two strategies are proposed accordingly:employing a systematic reduction of nonlinear coefficients to achieve high inversion accuracy while minimizing significant stress distortion,and excluding regions with severe stress distortion near the model edges while utilizing the central part of the model for subsequent simulations.These two strategies have been successfully implemented in the nonlinear in situ stress inversion of the Xincheng Gold Mine and have achieved higher inversion accuracy than the linear method.Specifically,the linear and nonlinear inversion methods yield root mean square errors(RMSE)of 4.15 and 3.2,and inversion relative errors(δAve)of 22.08%and 17.55%,respectively.Therefore,the nonlinear inversion method outperforms the traditional multiple linear regression method,even in the presence of a systematic reduction in the nonlinear stress boundaries.展开更多
A split-step second-order predictor-corrector method for space-fractional reaction-diffusion equations with nonhomogeneous boundary conditions is presented and analyzed for the stability and convergence.The matrix tra...A split-step second-order predictor-corrector method for space-fractional reaction-diffusion equations with nonhomogeneous boundary conditions is presented and analyzed for the stability and convergence.The matrix transfer technique is used for spatial discretization of the problem.The method is shown to be unconditionally stable and second-order convergent.Numerical experiments are performed to confirm the stability and secondorder convergence of the method.The split-step predictor-corrector method is also compared with an IMEX predictor-corrector method which is found to incur oscillatory behavior for some time steps.Our method is seen to produce reliable and oscillatioresults for any time step when implemented on numerical examples with nonsmooth initial data.We also present a priori reliability constraint for the IMEX predictor-corrector method to avoid unwanted oscillations and show its validity numerically.展开更多
The energy norm convergence rate of the finite element solution of the heat equation is reduced by the time-regularity of the exact solution. This paper presents an adaptive finite element treatment of time-dependent ...The energy norm convergence rate of the finite element solution of the heat equation is reduced by the time-regularity of the exact solution. This paper presents an adaptive finite element treatment of time-dependent singularities on the one-dimensional heat equation. The method is based on a Fourier decomposition of the solution and an extraction formula of the coefficients of the singularities coupled with a predictor-corrector algorithm. The method recovers the optimal convergence rate of the finite element method on a quasi-uniform mesh refinement. Numerical results are carried out to show the efficiency of the method.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
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
Bearing is an indispensable key component in mechanical equipment,and its working state is directly related to the stability and safety of the whole equipment.In recent years,with the rapid development of artificial i...Bearing is an indispensable key component in mechanical equipment,and its working state is directly related to the stability and safety of the whole equipment.In recent years,with the rapid development of artificial intelligence technology,especially the breakthrough of deep learning technology,it provides a new idea for bearing fault diagnosis.Deep learning can automatically learn features from a large amount of data,has a strong nonlinear modeling ability,and can effectively solve the problems existing in traditional methods.Aiming at the key problems in bearing fault diagnosis,this paper studies the fault diagnosis method based on deep learning,which not only provides a new solution for bearing fault diagnosis but also provides a reference for the application of deep learning in other mechanical fault diagnosis fields.展开更多
The visual noise of each light intensity area is different when the image is drawn by Monte Carlo method.However,the existing denoising algorithms have limited denoising performance under complex lighting conditions a...The visual noise of each light intensity area is different when the image is drawn by Monte Carlo method.However,the existing denoising algorithms have limited denoising performance under complex lighting conditions and are easy to lose detailed information.So we propose a rendered image denoising method with filtering guided by lighting information.First,we design an image segmentation algorithm based on lighting information to segment the image into different illumination areas.Then,we establish the parameter prediction model guided by lighting information for filtering(PGLF)to predict the filtering parameters of different illumination areas.For different illumination areas,we use these filtering parameters to construct area filters,and the filters are guided by the lighting information to perform sub-area filtering.Finally,the filtering results are fused with auxiliary features to output denoised images for improving the overall denoising effect of the image.Under the physically based rendering tool(PBRT)scene and Tungsten dataset,the experimental results show that compared with other guided filtering denoising methods,our method improves the peak signal-to-noise ratio(PSNR)metrics by 4.2164 dB on average and the structural similarity index(SSIM)metrics by 7.8%on average.This shows that our method can better reduce the noise in complex lighting scenesand improvethe imagequality.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 the Natural Science Foundation of Guangxi Province(Grant Nos.2023GXNSFAA026067,2024GXN SFAA010521)the National Natural Science Foundation of China(Nos.12361079,12201149,12261026).
文摘Convex feasibility problems are widely used in image reconstruction,sparse signal recovery,and other areas.This paper is devoted to considering a class of convex feasibility problem arising from sparse signal recovery.We rst derive the projection formulas for a vector onto the feasible sets.The centralized circumcentered-reection method is designed to solve the convex feasibility problem.Some numerical experiments demonstrate the feasibility and e ectiveness of the proposed algorithm,showing superior performance compared to conventional alternating projection methods.
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 Yunnan Provincial Applied Basic Research Program of China(No. KKSY201207019)
文摘A three-dimensional （3D） predictor-corrector finite difference method for standing wave is developed. It is applied to solve the 3D nonlinear potential flow equa- tions with a free surface. The 3D irregular tank is mapped onto a fixed cubic tank through the proper coordinate transform schemes. The cubic tank is distributed by the staggered meshgrid, and the staggered meshgrid is used to denote the variables of the flow field. The predictor-corrector finite difference method is given to develop the difference equa- tions of the dynamic boundary equation and kinematic boundary equation. Experimental results show that, using the finite difference method of the predictor-corrector scheme, the numerical solutions agree well with the published results. The wave profiles of the standing wave with different amplitudes and wave lengths are studied. The numerical solutions are also analyzed and presented graphically.
基金The Major State Research Program (G1999030803) of China and the NNSF (G10271066, 19972023) of China.
文摘A finite volume element predictor-corrector method for a class of nonlinear parabolic system of equations is presented and analyzed. Suboptimal L^2 error estimate for the finite volume element predictor-corrector method is derived. A numerical experiment shows that the numerical results are consistent with theoretical analysis.
基金The project supported by National Natural Science Foundation of China under Grant No.19902002
文摘We present the new predictor-corrector methods for systems of nonlinear differential equations, based on the method of exponential time differencing. We compare the present schemes with the explicit multistep exponential time differencing and Adams–Bashforth–Moulton method. The numerical results show that the schemes are more accurate and more efficient than Adams predictor-corrector method. The exponential time differencing method has been developed and perfected by the present studies.
文摘In this paper, we present and analyze modified families of predictor-corrector iterative methods for finding simple zeros of univariate nonlinear equations, permitting near the root. The main advantage of our methods is that they perform better and moreover, have the same efficiency indices as that of existing multipoint iterative methods. Furthermore, the convergence analysis of the new methods is discussed and several examples are given to illustrate their efficiency.
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.
基金work is supported by the Fundamental Research Funds for the Central Universities(No.3102019HTQD014)of Northwestern Polytechnical UniversityFunding of National Key Laboratory of Astronautical Flight DynamicsYoung Talent Support Project of Shaanxi State.
文摘Although predictor-corrector methods have been extensively applied,they might not meet the requirements of practical applications and engineering tasks,particularly when high accuracy and efficiency are necessary.A novel class of correctors based on feedback-accelerated Picard iteration(FAPI)is proposed to further enhance computational performance.With optimal feedback terms that do not require inversion of matrices,significantly faster convergence speed and higher numerical accuracy are achieved by these correctors compared with their counterparts;however,the computational complexities are comparably low.These advantages enable nonlinear engineering problems to be solved quickly and accurately,even with rough initial guesses from elementary predictors.The proposed method offers flexibility,enabling the use of the generated correctors for either bulk processing of collocation nodes in a domain or successive corrections of a single node in a finite difference approach.In our method,the functional formulas of FAPI are discretized into numerical forms using the collocation approach.These collocated iteration formulas can directly solve nonlinear problems,but they may require significant computational resources because of the manipulation of high-dimensionalmatrices.To address this,the collocated iteration formulas are further converted into finite difference forms,enabling the design of lightweight predictor-corrector algorithms for real-time computation.The generality of the proposed method is illustrated by deriving new correctors for three commonly employed finite-difference approaches:the modified Euler approach,the Adams-Bashforth-Moulton approach,and the implicit Runge-Kutta approach.Subsequently,the updated approaches are tested in solving strongly nonlinear problems,including the Matthieu equation,the Duffing equation,and the low-earth-orbit tracking problem.The numerical findings confirm the computational accuracy and efficiency of the derived predictor-corrector algorithms.
文摘This study investigated the physicochemical properties,enzyme activities,volatile flavor components,microbial communities,and sensory evaluation of high-temperature Daqu(HTD)during the maturation process,and a standard system was established for comprehensive quality evaluation of HTD.There were obvious changes in the physicochemical properties,enzyme activities,and volatile flavor components at different storage periods,which affected the sensory evaluation of HTD to a certain extent.The results of high-throughput sequencing revealed significant microbial diversity,and showed that the bacterial community changed significantly more than did the fungal community.During the storage process,the dominant bacterial genera were Kroppenstedtia and Thermoascus.The correlation between dominant microorganisms and quality indicators highlighted their role in HTD quality.Lactococcus,Candida,Pichia,Paecilomyces,and protease activity played a crucial role in the formation of isovaleraldehyde.Acidic protease activity had the greatest impact on the microbial community.Moisture promoted isobutyric acid generation.Furthermore,the comprehensive quality evaluation standard system was established by the entropy weight method combined with multi-factor fuzzy mathematics.Consequently,this study provides innovative insights for comprehensive quality evaluation of HTD during storage and establishes a groundwork for scientific and rational storage of HTD and quality control of sauce-flavor Baijiu.
基金The project supported by Liu Hui Applied Mathematics Center of Nankai University and 985 Education Development Plan of Tianjin University
文摘We develop the three-step explicit and implicit schemes of exponential fitting methods. We use the three- step explicit exponential fitting scheme to predict an approximation, then use the three-step implicit exponential fitting scheme to correct this prediction. This combination is called the three-step predictor-corrector of exponential fitting method. The three-step predictor-corrector of exponential fitting method is applied to numerically compute the coupled nonlinear Schroedinger equation and the nonlinear Schroedinger equation with varying coefficients. The numerical results show that the scheme is highly accurate.
基金funded by the National Key R&D Program of China(Grant No.2022YFC2903904)the National Natural Science Foundation of China(Grant Nos.51904057 and U1906208).
文摘Due to the heterogeneity of rock masses and the variability of in situ stress,the traditional linear inversion method is insufficiently accurate to achieve high accuracy of the in situ stress field.To address this challenge,nonlinear stress boundaries for a numerical model are determined through regression analysis of a series of nonlinear coefficient matrices,which are derived from the bubbling method.Considering the randomness and flexibility of the bubbling method,a parametric study is conducted to determine recommended ranges for these parameters,including the standard deviation(σb)of bubble radii,the non-uniform coefficient matrix number(λ)for nonlinear stress boundaries,and the number(m)and positions of in situ stress measurement points.A model case study provides a reference for the selection of these parameters.Additionally,when the nonlinear in situ stress inversion method is employed,stress distortion inevitably occurs near model boundaries,aligning with the Saint Venant's principle.Two strategies are proposed accordingly:employing a systematic reduction of nonlinear coefficients to achieve high inversion accuracy while minimizing significant stress distortion,and excluding regions with severe stress distortion near the model edges while utilizing the central part of the model for subsequent simulations.These two strategies have been successfully implemented in the nonlinear in situ stress inversion of the Xincheng Gold Mine and have achieved higher inversion accuracy than the linear method.Specifically,the linear and nonlinear inversion methods yield root mean square errors(RMSE)of 4.15 and 3.2,and inversion relative errors(δAve)of 22.08%and 17.55%,respectively.Therefore,the nonlinear inversion method outperforms the traditional multiple linear regression method,even in the presence of a systematic reduction in the nonlinear stress boundaries.
文摘A split-step second-order predictor-corrector method for space-fractional reaction-diffusion equations with nonhomogeneous boundary conditions is presented and analyzed for the stability and convergence.The matrix transfer technique is used for spatial discretization of the problem.The method is shown to be unconditionally stable and second-order convergent.Numerical experiments are performed to confirm the stability and secondorder convergence of the method.The split-step predictor-corrector method is also compared with an IMEX predictor-corrector method which is found to incur oscillatory behavior for some time steps.Our method is seen to produce reliable and oscillatioresults for any time step when implemented on numerical examples with nonsmooth initial data.We also present a priori reliability constraint for the IMEX predictor-corrector method to avoid unwanted oscillations and show its validity numerically.
文摘The energy norm convergence rate of the finite element solution of the heat equation is reduced by the time-regularity of the exact solution. This paper presents an adaptive finite element treatment of time-dependent singularities on the one-dimensional heat equation. The method is based on a Fourier decomposition of the solution and an extraction formula of the coefficients of the singularities coupled with a predictor-corrector algorithm. The method recovers the optimal convergence rate of the finite element method on a quasi-uniform mesh refinement. Numerical results are carried out to show the efficiency of the method.
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.
文摘Bearing is an indispensable key component in mechanical equipment,and its working state is directly related to the stability and safety of the whole equipment.In recent years,with the rapid development of artificial intelligence technology,especially the breakthrough of deep learning technology,it provides a new idea for bearing fault diagnosis.Deep learning can automatically learn features from a large amount of data,has a strong nonlinear modeling ability,and can effectively solve the problems existing in traditional methods.Aiming at the key problems in bearing fault diagnosis,this paper studies the fault diagnosis method based on deep learning,which not only provides a new solution for bearing fault diagnosis but also provides a reference for the application of deep learning in other mechanical fault diagnosis fields.
基金supported by the National Natural Science(No.U19A2063)the Jilin Provincial Development Program of Science and Technology (No.20230201080GX)the Jilin Province Education Department Scientific Research Project (No.JJKH20230851KJ)。
文摘The visual noise of each light intensity area is different when the image is drawn by Monte Carlo method.However,the existing denoising algorithms have limited denoising performance under complex lighting conditions and are easy to lose detailed information.So we propose a rendered image denoising method with filtering guided by lighting information.First,we design an image segmentation algorithm based on lighting information to segment the image into different illumination areas.Then,we establish the parameter prediction model guided by lighting information for filtering(PGLF)to predict the filtering parameters of different illumination areas.For different illumination areas,we use these filtering parameters to construct area filters,and the filters are guided by the lighting information to perform sub-area filtering.Finally,the filtering results are fused with auxiliary features to output denoised images for improving the overall denoising effect of the image.Under the physically based rendering tool(PBRT)scene and Tungsten dataset,the experimental results show that compared with other guided filtering denoising methods,our method improves the peak signal-to-noise ratio(PSNR)metrics by 4.2164 dB on average and the structural similarity index(SSIM)metrics by 7.8%on average.This shows that our method can better reduce the noise in complex lighting scenesand improvethe imagequality.
