To meet the requirements of quick positioning of mobile terminals from base stations(BSs)or third-party devices,as well as to improve the convergence speed and reduce the steady state maladjustment of the least mean s...To meet the requirements of quick positioning of mobile terminals from base stations(BSs)or third-party devices,as well as to improve the convergence speed and reduce the steady state maladjustment of the least mean square(LMS)method,a new logarithmic-sigmoid variable step-size LMS(LG-SVSLMS)was proposed and applied to estimate the direction of arrival(DOA)of orthogonal frequency division multiple access(OFDMA)signals.Based on the proposed LG-SVSLMS,a non-blind DOA estimation system for OFDMA signals was constructed.The proposed LG-SVSLMS adopts a new multi-parameter step-size update function which combines the sigmoid function and the logarithmic function.It controls the adjustment magnitude of step-size during the initial and steady state phases of the LMS method to achieve both a high convergence speed and low steady state maladjustment.Finally,simulation was conducted to verify the performance of the LG-SVSLMS.The simulation results show that the non-blind DOA estimation system based on the LG-SVSLMS can accurately estimate the DOA of the target signal in the scenario where interference signals from multi-source and multi-path fading signals arrive at the third-party devices asynchronously with the target signal,and the estimation deviation is within±3°.The non-blind DOA estimation for OFDMA signals with the proposed LG-SVSLMS is of great significance for the instant positioning technology of mobile terminals based on the adaptive antenna array.展开更多
Path planning is crucial for autonomous flight of fixed-wing Unmanned Aerial Vehicles(UAVs).However,due to the high-speed flight and complex control of fixed-wing UAVs,ensuring the feasibility and safety of planned pa...Path planning is crucial for autonomous flight of fixed-wing Unmanned Aerial Vehicles(UAVs).However,due to the high-speed flight and complex control of fixed-wing UAVs,ensuring the feasibility and safety of planned paths in complex environments is challenging.This paper proposes a feasible path planning algorithm named Closed-loop Radial Ray A^(*)(CL-RaA^(*)).The core components of the CL-RaA^(*)include an adaptive variable-step-size path search and a just-in-time expansion primitive.The former enables fast path search in complex environments,while the latter ensures the feasibility of the generated paths.By integrating these two components and conducting safety checks on the trajectories to be expanded,the CL-RaA^(*)can rapidly generate safe and feasible paths that satisfy the differential constraints that comprehensively consider the dynamics and control characteristics of six-degree-of-freedom fixed-wing UAVs.The final performance tests and simulation validations demonstrate that the CL-RaA^(*)can generate safe and feasible paths in various environments.Compared to feasible path planning algorithms that use the rapidlyexploring random trees,the CL-RaA^(*)not only ensures deterministic planning results in the same scenarios but also generates smoother feasible paths for fixed-wing UAVs more efficiently.In environments with dense grid obstacles,the feasible paths generated by the CL-RaA^(*)are more conducive to UAV tracking compared to those planned using Dubins curves.展开更多
To solve the contradiction between convergence rate and steady-state error in least mean square (LMS) algorithm, basing on independence assumption, this paper proposes and proves the optimal step-size theorem from the...To solve the contradiction between convergence rate and steady-state error in least mean square (LMS) algorithm, basing on independence assumption, this paper proposes and proves the optimal step-size theorem from the view of minimizing mean squared error (MSE). The theorem reveals the one-to-one mapping between the optimal step-size and MSE. Following the theorem, optimal variable step-size LMS (OVS-LMS) model, describing the theoretical bound of the convergence rate of LMS algorithm, is constructed. Then we discuss the selection of initial optimal step-size and updating of optimal step-size at the time of unknown system changing. At last an optimal step-size LMS algorithm is proposed and tested in various environments. Simulation results show the proposed algorithm is very close to the theoretical bound.展开更多
Implicit-explicit （IMEX） linear multistep methods are popular techniques for solving partial differential equations （PDEs） with terms of different types. While fixed timestep versions of such schemes have been dev...Implicit-explicit （IMEX） linear multistep methods are popular techniques for solving partial differential equations （PDEs） with terms of different types. While fixed timestep versions of such schemes have been developed and studied, implicit-explicit schemes also naturally arise in general situations where the temporal smoothness of the solution changes. In this paper we consider easily implementable variable step-size implicit-explicit （VSIMEX） linear multistep methods for time-dependent PDEs. Families of order-p, pstep VSIMEX schemes are constructed and analyzed, where p ranges from 1 to 4. The corresponding schemes are simple to implement and have the property that they reduce to the classical IMEX schemes whenever constant time step-sizes are imposed. The methods are validated on the Burgers＇ equation. These results demonstrate that by varying the time step-size, VSIMEX methods can outperform their fixed time step counterparts while still maintaining good numerical behavior.展开更多
In this work,we analyze the three-step backward differentiation formula(BDF3)method for solving the Allen-Cahn equation on variable grids.For BDF2 method,the discrete orthogonal convolution(DOC)kernels are positive,th...In this work,we analyze the three-step backward differentiation formula(BDF3)method for solving the Allen-Cahn equation on variable grids.For BDF2 method,the discrete orthogonal convolution(DOC)kernels are positive,the stability and convergence analysis are well established in[Liao and Zhang,Math.Comp.,90(2021),1207–1226]and[Chen,Yu,and Zhang,arXiv:2108.02910,2021].However,the numerical analysis for BDF3 method with variable steps seems to be highly nontrivial due to the additional degrees of freedom and the non-positivity of DOC kernels.By developing a novel spectral norm inequality,the unconditional stability and convergence are rigorously proved under the updated step ratio restriction rk:=τk/τk−1≤1.405 for BDF3 method.Finally,numerical experiments are performed to illustrate the theoretical results.To the best of our knowledge,this is the first theoretical analysis of variable steps BDF3 method for the Allen-Cahn equation.展开更多
With independence assumption, this paper proposes and proves the superior step-size theorem on least mean square (LMS) algorithm, from the view of minimizing mean squared error (MSE). Following the theorem we construc...With independence assumption, this paper proposes and proves the superior step-size theorem on least mean square (LMS) algorithm, from the view of minimizing mean squared error (MSE). Following the theorem we construct a parallel variable step-size LMS filters algorithm. The theoretical model of the proposed algorithm is analyzed in detail. Simulations show the proposed theoretical model is quite close to the optimal variable step-size LMS (OVS-LMS) model. The experimental learning curves of the proposed algorithm also show the fastest convergence and fine tracking performance. The proposed algorithm is therefore a good realization of the OVS-LMS model.展开更多
In this paper,we establish some strong laws of large numbers,which are for nonindependent random variables under the framework of sublinear expectations.One of our main results is for blockwise m-dependent random vari...In this paper,we establish some strong laws of large numbers,which are for nonindependent random variables under the framework of sublinear expectations.One of our main results is for blockwise m-dependent random variables,and another is for sub-orthogonal random variables.Both extend the strong law of large numbers for independent random variables under sublinear expectations to the non-independent case.展开更多
In this paper,we consider the fourth-order parabolic equation with p(x)Laplacian and variable exponent source ut+∆^(2)u−div(|■u|^(p(x)−2■u))=|u|^(q(x))−1u.By applying potential well method,we obtain global existence...In this paper,we consider the fourth-order parabolic equation with p(x)Laplacian and variable exponent source ut+∆^(2)u−div(|■u|^(p(x)−2■u))=|u|^(q(x))−1u.By applying potential well method,we obtain global existence,asymptotic behavior and blow-up of solutions with initial energy J(u_(0))≤d.Moreover,we estimate the upper bound of the blow-up time for J(u_(0))≤0.展开更多
Thermal-mechanical damage and deformation at the interface between shotcrete linings and the surrounding rock of tunnels under high-temperature and variable-temperature conditions are critical to the safe construction...Thermal-mechanical damage and deformation at the interface between shotcrete linings and the surrounding rock of tunnels under high-temperature and variable-temperature conditions are critical to the safe construction and operation of tunnel engineering.This study investigated the thermo-mechanical damage behavior of the composite interface between alkali-resistant glass fiber-reinforced concrete(ARGFRC)and granite,focusing on a plateau railway tunnel.Laboratory triaxial tests,laser scanning,XRD analysis,numerical simulations,and theoretical analyses were employed to investigate how different initial curing temperatures and joint roughness coefficient(JRC)influence interfacial damage behavior.The results indicate that an increase in interface roughness exacerbates the structural damage at the interface.At a JRC of 19.9 and a temperature of 70℃,crack initiation in granite was notably restrained when the confining pressure rose from 7 MPa to 10 MPa.Roughness-induced stress distribution at the interface was notably altered,although this effect became less pronounced under high confining pressure conditions.Additionally,during high-temperature curing,thermal stress concentration at the tips of micro-convex protrusions on the granite surface induced microcracks in the adjacent ARGFRC matrix,followed by deformation.These findings provide practical guidelines for designing concrete support systems to ensure tunnel structural safety in high-altitude regions with harsh thermal environments.展开更多
Marine forecasting is critical for navigation safety and disaster prevention.However,traditional ocean numerical forecasting models are often limited by substantial errors and inadequate capture of temporal-spatial fe...Marine forecasting is critical for navigation safety and disaster prevention.However,traditional ocean numerical forecasting models are often limited by substantial errors and inadequate capture of temporal-spatial features.To address the limitations,the paper proposes a TimeXer-based numerical forecast correction model optimized by an exogenous-variable attention mechanism.The model treats target forecast values as internal variables,and incorporates historical temporal-spatial data and seven-day numerical forecast results from traditional models as external variables based on the embedding strategy of TimeXer.Using a self-attention structure,the model captures correlations between exogenous variables and target sequences,explores intrinsic multi-dimensional relationships,and subsequently corrects endogenous variables with the mined exogenous features.The model’s performance is evaluated using metrics including MSE(Mean Squared Error),MAE(Mean Absolute Error),RMSE(Root Mean Square Error),MAPE(Mean Absolute Percentage Error),MSPE(Mean Square Percentage Error),and computational time,with TimeXer and PatchTST models serving as benchmarks.Experiment results show that the proposed model achieves lower errors and higher correction accuracy for both one-day and seven-day forecasts.展开更多
Sustained and spatially explicit monitoring of the United Nations 2030 Agenda for Sustainable Development is critical for effectively tracking progress toward the global Sustainable Development Goals(SDGs).Although la...Sustained and spatially explicit monitoring of the United Nations 2030 Agenda for Sustainable Development is critical for effectively tracking progress toward the global Sustainable Development Goals(SDGs).Although land cover information has long been recognized as an essential component for monitoring SDGs,a standardized scientific framework for identifying and prioritizing land cover related essential variables does not exist.Therefore,we propose a novel expert-and data-driven framework for identifying,refining,and selecting a priority list of Essential Land cover-related Variables for SDGs(ELcV4SDGs).This framework integrates methods including expert knowledge-based analysis,clustering of variables with similar attributes,and quantified index calculation to establish the priority list.Applying the framework to 15 specific SDG indicators,we found that the ELcV4SDGs priority list comprises three main categories,type and structure,pattern and intensity,and process and evolution of land cover,which are further divided into 19 subcategories and ultimately encompass 50 general variables.The ELcV4SDGs will support detailed spatial monitoring and enhance their scientific applications for SDG monitoring and assessment,thereby guiding future SDG priority actions and informing decision-making to advance the 2030 SDGs agenda at local,national,and global levels.展开更多
Energy shortage has become one of themost concerning issues in the world today,and improving energy utilization efficiency is a key area of research for experts and scholars worldwide.Small-diameter heat exchangers of...Energy shortage has become one of themost concerning issues in the world today,and improving energy utilization efficiency is a key area of research for experts and scholars worldwide.Small-diameter heat exchangers offer advantages such as reduced material usage,lower refrigerant charge,and compact structure.However,they also face challenges,including increased refrigerant pressure drop and smaller heat transfer area inside the tubes.This paper combines the advantages and disadvantages of both small and large-diameter tubes and proposes a combined-diameter heat exchanger,consisting of large and small diameters,for use in the indoor units of split-type air conditioners.There are relatively few studies in this area.In this paper,A theoretical and numerical computation method is employed to establish a theoretical-numerical calculation model,and its reliability is verified through experiments.Using this model,the optimal combined diameters and flow path design for a combined-diameter heat exchanger using R32 as the working fluid are derived.The results show that the heat transfer performance of all combined diameter configurations improves by 2.79%to 8.26%compared to the baseline design,with the coefficient of performance(COP)increasing from 4.15 to 4.27~4.5.These designs can save copper material,but at the cost of an increase in pressure drop by 66.86%to 131.84%.The scheme IIIH,using R32,is the optimal combined-diameter and flow path configuration that balances both heat transfer performance and economic cost.展开更多
Acoustic echo cancellation is often applied in communication and video call system to reduce unnecessary echoes generated between speakers and microphones.In these systems,the speech input signal of the adaptive filte...Acoustic echo cancellation is often applied in communication and video call system to reduce unnecessary echoes generated between speakers and microphones.In these systems,the speech input signal of the adaptive filter is often colored and unstable,which decays the convergence rate of the adaptive filter if the NLMS algorithm is used.In this paper,an improved nonparametric variable step-size subband(NPVSS-NSAF)algorithm is proposed to address the problem.The variable step-size is derived by minimizing the sum of the square Euclidean norm of the difference between the optimal weight vectors to be updated and the past estimated weight vectors.Then the parameters are eliminated by using the power of subband signal noise equal to the power of subband posteriori error.The performance of the proposed algorithm is simulated in the aspects of misalignment and return loss enhancement.Experiment results show a fast convergence rate and low misalignment of the proposed algorithm in system identification.展开更多
This paper proposes a robust adaptive filter based on the exponent sin cost to improve the capability against Gaussian or multiple types of non-Gaussian noises of the adaptive filtering algorithm when dealing with tim...This paper proposes a robust adaptive filter based on the exponent sin cost to improve the capability against Gaussian or multiple types of non-Gaussian noises of the adaptive filtering algorithm when dealing with time-varying/time-invariant linear systems function exponent sin(ExpSin).Then a variable step-size(VSS)-ExpSin algorithm is extended further.Besides,the stepsize,the convergence,and the steady-state performance of the proposed algorithm are validated experimentally.The Monte Carlo simulation results of linear system identification illustrate the principle and efficiency of this proposed adaptive filtering algorithm.Results suggest that the proposed adaptive filtering algorithm has superior performance when estimating the unknown linear systems under multiple-types measurement noises.展开更多
An internal state variable(ISV)model was established according to the experimental results of hot plane strain compression(PSC)to predict the microstructure evolution during hot spinning of ZK61 alloy.The effects of t...An internal state variable(ISV)model was established according to the experimental results of hot plane strain compression(PSC)to predict the microstructure evolution during hot spinning of ZK61 alloy.The effects of the internal variables were considered in this ISV model,and the parameters were optimized by genetic algorithm.After validation,the ISV model was used to simulate the evolution of grain size(GS)and dynamic recrystallization(DRX)fraction during hot spinning via Abaqus and its subroutine Vumat.By comparing the simulated results with the experimental results,the application of the ISV model was proven to be reliable.Meanwhile,the strength of the thin-walled spun ZK61 tube increased from 303 to 334 MPa due to grain refinement by DRX and texture strengthening.Besides,some ultrafine grains(0.5μm)that played an important role in mechanical properties were formed due to the proliferation,movement,and entanglement of dislocations during the spinning process.展开更多
In order to solve the problem of the variable coefficient ordinary differen-tial equation on the bounded domain,the Lagrange interpolation method is used to approximate the exact solution of the equation,and the error...In order to solve the problem of the variable coefficient ordinary differen-tial equation on the bounded domain,the Lagrange interpolation method is used to approximate the exact solution of the equation,and the error between the numerical solution and the exact solution is obtained,and then compared with the error formed by the difference method,it is concluded that the Lagrange interpolation method is more effective in solving the variable coefficient ordinary differential equation.展开更多
The optimization of the waverider is constrained by the reversely designed leading edge and the constant shock angle distribution. This paper proposes a design method called the variable Leading-Edge Cone (vLEC) metho...The optimization of the waverider is constrained by the reversely designed leading edge and the constant shock angle distribution. This paper proposes a design method called the variable Leading-Edge Cone (vLEC) method to address these limitations. In the vLEC method, the waverider is directly designed from the preassigned leading edge and the variable shock angle distribution based on the Leading-Edge Cone (LEC) concept. Since the vLEC method is an approximate method, two test waveriders are designed and evaluated using numerical simulations to validate the shock design accuracy and the effectiveness of the vLEC method. The results show that the shocks of the test waveriders coincide well with the preassigned positions. Furthermore, four specifically designed application cases are conducted to analyze the performance benefits of the vLEC waveriders. The results of these cases indicate that, due to their variable shock angle distributions, the vLEC waveriders exhibit higher lift-to-drag ratios and better longitudinal static stability than conventional waveriders. Additionally, the vLEC waveriders demonstrate superior volumetric capacities near the symmetry plane, albeit with a minor decrease in volumetric efficiency.展开更多
Large-scale Language Models(LLMs)have achieved significant breakthroughs in Natural Language Processing(NLP),driven by the pre-training and fine-tuning paradigm.While this approach allows models to specialize in speci...Large-scale Language Models(LLMs)have achieved significant breakthroughs in Natural Language Processing(NLP),driven by the pre-training and fine-tuning paradigm.While this approach allows models to specialize in specific tasks with reduced training costs,the substantial memory requirements during fine-tuning present a barrier to broader deployment.Parameter-Efficient Fine-Tuning(PEFT)techniques,such as Low-Rank Adaptation(LoRA),and parameter quantization methods have emerged as solutions to address these challenges by optimizing memory usage and computational efficiency.Among these,QLoRA,which combines PEFT and quantization,has demonstrated notable success in reducing memory footprints during fine-tuning,prompting the development of various QLoRA variants.Despite these advancements,the quantitative impact of key variables on the fine-tuning performance of quantized LLMs remains underexplored.This study presents a comprehensive analysis of these key variables,focusing on their influence across different layer types and depths within LLM architectures.Our investigation uncovers several critical findings:(1)Larger layers,such as MLP layers,can maintain performance despite reductions in adapter rank,while smaller layers,like self-attention layers,aremore sensitive to such changes;(2)The effectiveness of balancing factors depends more on specific values rather than layer type or depth;(3)In quantization-aware fine-tuning,larger layers can effectively utilize smaller adapters,whereas smaller layers struggle to do so.These insights suggest that layer type is a more significant determinant of fine-tuning success than layer depth when optimizing quantized LLMs.Moreover,for the same discount of trainable parameters,reducing the trainable parameters in a larger layer is more effective in preserving fine-tuning accuracy than in a smaller one.This study provides valuable guidance for more efficient fine-tuning strategies and opens avenues for further research into optimizing LLM fine-tuning in resource-constrained environments.展开更多
We consider a single server constant retrial queue,in which a state-dependent service policy is used to control the service rate.Customer arrival follows Poisson process,while service time and retrial time are exponen...We consider a single server constant retrial queue,in which a state-dependent service policy is used to control the service rate.Customer arrival follows Poisson process,while service time and retrial time are exponential distributions.Whenever the server is available,it admits the retrial customers into service based on a first-come first-served rule.The service rate adjusts in real-time based on the retrial queue length.An iterative algorithm is proposed to numerically solve the personal optimal problem in the fully observable scenario.Furthermore,we investigate the impact of parameters on the social optimal threshold.The effectiveness of the results is illustrated by two examples.展开更多
With the development of the Internet,image encryption technology has become critical for network security.Traditional methods often suffer from issues such as insufficient chaos,low randomness in key generation,and po...With the development of the Internet,image encryption technology has become critical for network security.Traditional methods often suffer from issues such as insufficient chaos,low randomness in key generation,and poor encryption efficiency.To enhance performance,this paper proposes a new encryption algorithm designed to optimize parallel processing and adapt to images of varying sizes and colors.The method begins by using SHA-384 to extract the hash value of the plaintext image,which is then processed to determine the chaotic system’s initial value and block size.The image is padded and divided into blocks for further processing.A novel two-dimensional infinite collapses hyperchaotic map(2DICHM)is employed to generate the intra-block scrambling sequence,while an improved variable Joseph traversal sequence is used for inter-block scrambling.After removing the padding,3D forward and backward shift diffusions,controlled by the 2D-ICHM sequences,are applied to the scrambled image,producing the ciphertext.Simulation results demonstrate that the proposed algorithm outperforms others in terms of entropy,anti-noise resilience,correlation coefficient,robustness,and encryption efficiency.展开更多
基金The Social Development Projects of Jiangsu Science and Technology Department(No.BE2018704)the Technological Innovation Projects of Ministry of Public Security of China(No.20170001)。
文摘To meet the requirements of quick positioning of mobile terminals from base stations(BSs)or third-party devices,as well as to improve the convergence speed and reduce the steady state maladjustment of the least mean square(LMS)method,a new logarithmic-sigmoid variable step-size LMS(LG-SVSLMS)was proposed and applied to estimate the direction of arrival(DOA)of orthogonal frequency division multiple access(OFDMA)signals.Based on the proposed LG-SVSLMS,a non-blind DOA estimation system for OFDMA signals was constructed.The proposed LG-SVSLMS adopts a new multi-parameter step-size update function which combines the sigmoid function and the logarithmic function.It controls the adjustment magnitude of step-size during the initial and steady state phases of the LMS method to achieve both a high convergence speed and low steady state maladjustment.Finally,simulation was conducted to verify the performance of the LG-SVSLMS.The simulation results show that the non-blind DOA estimation system based on the LG-SVSLMS can accurately estimate the DOA of the target signal in the scenario where interference signals from multi-source and multi-path fading signals arrive at the third-party devices asynchronously with the target signal,and the estimation deviation is within±3°.The non-blind DOA estimation for OFDMA signals with the proposed LG-SVSLMS is of great significance for the instant positioning technology of mobile terminals based on the adaptive antenna array.
基金supported by the National Natural Science Foundation of China(No.52272382)the Fundamental Research Funds for the Central Universities,China。
文摘Path planning is crucial for autonomous flight of fixed-wing Unmanned Aerial Vehicles(UAVs).However,due to the high-speed flight and complex control of fixed-wing UAVs,ensuring the feasibility and safety of planned paths in complex environments is challenging.This paper proposes a feasible path planning algorithm named Closed-loop Radial Ray A^(*)(CL-RaA^(*)).The core components of the CL-RaA^(*)include an adaptive variable-step-size path search and a just-in-time expansion primitive.The former enables fast path search in complex environments,while the latter ensures the feasibility of the generated paths.By integrating these two components and conducting safety checks on the trajectories to be expanded,the CL-RaA^(*)can rapidly generate safe and feasible paths that satisfy the differential constraints that comprehensively consider the dynamics and control characteristics of six-degree-of-freedom fixed-wing UAVs.The final performance tests and simulation validations demonstrate that the CL-RaA^(*)can generate safe and feasible paths in various environments.Compared to feasible path planning algorithms that use the rapidlyexploring random trees,the CL-RaA^(*)not only ensures deterministic planning results in the same scenarios but also generates smoother feasible paths for fixed-wing UAVs more efficiently.In environments with dense grid obstacles,the feasible paths generated by the CL-RaA^(*)are more conducive to UAV tracking compared to those planned using Dubins curves.
基金This work was supported in part by the National Fundamental Research Program(Grant No.G1998030406)the National Natural Science Foundation of China(Grant No.69972020)by the State Key Lab on Microwave and Digital Communications,Department of Electronics Engineering,Tsinghua University.
文摘To solve the contradiction between convergence rate and steady-state error in least mean square (LMS) algorithm, basing on independence assumption, this paper proposes and proves the optimal step-size theorem from the view of minimizing mean squared error (MSE). The theorem reveals the one-to-one mapping between the optimal step-size and MSE. Following the theorem, optimal variable step-size LMS (OVS-LMS) model, describing the theoretical bound of the convergence rate of LMS algorithm, is constructed. Then we discuss the selection of initial optimal step-size and updating of optimal step-size at the time of unknown system changing. At last an optimal step-size LMS algorithm is proposed and tested in various environments. Simulation results show the proposed algorithm is very close to the theoretical bound.
基金supported by an NSERC Canada Postgraduate Scholarshipsupported by a grant from NSERC Canada
文摘Implicit-explicit （IMEX） linear multistep methods are popular techniques for solving partial differential equations （PDEs） with terms of different types. While fixed timestep versions of such schemes have been developed and studied, implicit-explicit schemes also naturally arise in general situations where the temporal smoothness of the solution changes. In this paper we consider easily implementable variable step-size implicit-explicit （VSIMEX） linear multistep methods for time-dependent PDEs. Families of order-p, pstep VSIMEX schemes are constructed and analyzed, where p ranges from 1 to 4. The corresponding schemes are simple to implement and have the property that they reduce to the classical IMEX schemes whenever constant time step-sizes are imposed. The methods are validated on the Burgers＇ equation. These results demonstrate that by varying the time step-size, VSIMEX methods can outperform their fixed time step counterparts while still maintaining good numerical behavior.
基金supported by the Science Fund for Distinguished Young Scholars of Gansu Province(Grant No.23JRRA1020)the Fundamental Research Funds for the Central Universities(Grant No.lzujbky-2023-06).
文摘In this work,we analyze the three-step backward differentiation formula(BDF3)method for solving the Allen-Cahn equation on variable grids.For BDF2 method,the discrete orthogonal convolution(DOC)kernels are positive,the stability and convergence analysis are well established in[Liao and Zhang,Math.Comp.,90(2021),1207–1226]and[Chen,Yu,and Zhang,arXiv:2108.02910,2021].However,the numerical analysis for BDF3 method with variable steps seems to be highly nontrivial due to the additional degrees of freedom and the non-positivity of DOC kernels.By developing a novel spectral norm inequality,the unconditional stability and convergence are rigorously proved under the updated step ratio restriction rk:=τk/τk−1≤1.405 for BDF3 method.Finally,numerical experiments are performed to illustrate the theoretical results.To the best of our knowledge,this is the first theoretical analysis of variable steps BDF3 method for the Allen-Cahn equation.
文摘With independence assumption, this paper proposes and proves the superior step-size theorem on least mean square (LMS) algorithm, from the view of minimizing mean squared error (MSE). Following the theorem we construct a parallel variable step-size LMS filters algorithm. The theoretical model of the proposed algorithm is analyzed in detail. Simulations show the proposed theoretical model is quite close to the optimal variable step-size LMS (OVS-LMS) model. The experimental learning curves of the proposed algorithm also show the fastest convergence and fine tracking performance. The proposed algorithm is therefore a good realization of the OVS-LMS model.
文摘In this paper,we establish some strong laws of large numbers,which are for nonindependent random variables under the framework of sublinear expectations.One of our main results is for blockwise m-dependent random variables,and another is for sub-orthogonal random variables.Both extend the strong law of large numbers for independent random variables under sublinear expectations to the non-independent case.
基金Supported by NSFC(No.12101482)the Natural Science Foundation of Shaanxi Province,China(No.2018JQ1052)。
文摘In this paper,we consider the fourth-order parabolic equation with p(x)Laplacian and variable exponent source ut+∆^(2)u−div(|■u|^(p(x)−2■u))=|u|^(q(x))−1u.By applying potential well method,we obtain global existence,asymptotic behavior and blow-up of solutions with initial energy J(u_(0))≤d.Moreover,we estimate the upper bound of the blow-up time for J(u_(0))≤0.
基金funded by the National Natural Science Foundation of China(Nos.52209130 and 52379100)Shandong Provincial Natural Science Foundation(No.ZR2024ME112).
文摘Thermal-mechanical damage and deformation at the interface between shotcrete linings and the surrounding rock of tunnels under high-temperature and variable-temperature conditions are critical to the safe construction and operation of tunnel engineering.This study investigated the thermo-mechanical damage behavior of the composite interface between alkali-resistant glass fiber-reinforced concrete(ARGFRC)and granite,focusing on a plateau railway tunnel.Laboratory triaxial tests,laser scanning,XRD analysis,numerical simulations,and theoretical analyses were employed to investigate how different initial curing temperatures and joint roughness coefficient(JRC)influence interfacial damage behavior.The results indicate that an increase in interface roughness exacerbates the structural damage at the interface.At a JRC of 19.9 and a temperature of 70℃,crack initiation in granite was notably restrained when the confining pressure rose from 7 MPa to 10 MPa.Roughness-induced stress distribution at the interface was notably altered,although this effect became less pronounced under high confining pressure conditions.Additionally,during high-temperature curing,thermal stress concentration at the tips of micro-convex protrusions on the granite surface induced microcracks in the adjacent ARGFRC matrix,followed by deformation.These findings provide practical guidelines for designing concrete support systems to ensure tunnel structural safety in high-altitude regions with harsh thermal environments.
基金supported by the National Key Research and Development Program Project(2023YFC3107804)Planning Fund Project of Humanities and Social Sciences Research of the Ministry of Education(24YJA880097)the Graduate Education Reform Project in North China University of Technology(217051360025XN095-17)。
文摘Marine forecasting is critical for navigation safety and disaster prevention.However,traditional ocean numerical forecasting models are often limited by substantial errors and inadequate capture of temporal-spatial features.To address the limitations,the paper proposes a TimeXer-based numerical forecast correction model optimized by an exogenous-variable attention mechanism.The model treats target forecast values as internal variables,and incorporates historical temporal-spatial data and seven-day numerical forecast results from traditional models as external variables based on the embedding strategy of TimeXer.Using a self-attention structure,the model captures correlations between exogenous variables and target sequences,explores intrinsic multi-dimensional relationships,and subsequently corrects endogenous variables with the mined exogenous features.The model’s performance is evaluated using metrics including MSE(Mean Squared Error),MAE(Mean Absolute Error),RMSE(Root Mean Square Error),MAPE(Mean Absolute Percentage Error),MSPE(Mean Square Percentage Error),and computational time,with TimeXer and PatchTST models serving as benchmarks.Experiment results show that the proposed model achieves lower errors and higher correction accuracy for both one-day and seven-day forecasts.
基金supported by the Key Program of National Natural Science Foundation of China(Grant No.41930650)Young Scientists Fund of the National Natural Science Foundation of China(Grant No.42301310).
文摘Sustained and spatially explicit monitoring of the United Nations 2030 Agenda for Sustainable Development is critical for effectively tracking progress toward the global Sustainable Development Goals(SDGs).Although land cover information has long been recognized as an essential component for monitoring SDGs,a standardized scientific framework for identifying and prioritizing land cover related essential variables does not exist.Therefore,we propose a novel expert-and data-driven framework for identifying,refining,and selecting a priority list of Essential Land cover-related Variables for SDGs(ELcV4SDGs).This framework integrates methods including expert knowledge-based analysis,clustering of variables with similar attributes,and quantified index calculation to establish the priority list.Applying the framework to 15 specific SDG indicators,we found that the ELcV4SDGs priority list comprises three main categories,type and structure,pattern and intensity,and process and evolution of land cover,which are further divided into 19 subcategories and ultimately encompass 50 general variables.The ELcV4SDGs will support detailed spatial monitoring and enhance their scientific applications for SDG monitoring and assessment,thereby guiding future SDG priority actions and informing decision-making to advance the 2030 SDGs agenda at local,national,and global levels.
基金supported by Supported by the Scientific Research Foundation for High-Level Talents of Zhoukou Normal University(ZKNUC2024018).
文摘Energy shortage has become one of themost concerning issues in the world today,and improving energy utilization efficiency is a key area of research for experts and scholars worldwide.Small-diameter heat exchangers offer advantages such as reduced material usage,lower refrigerant charge,and compact structure.However,they also face challenges,including increased refrigerant pressure drop and smaller heat transfer area inside the tubes.This paper combines the advantages and disadvantages of both small and large-diameter tubes and proposes a combined-diameter heat exchanger,consisting of large and small diameters,for use in the indoor units of split-type air conditioners.There are relatively few studies in this area.In this paper,A theoretical and numerical computation method is employed to establish a theoretical-numerical calculation model,and its reliability is verified through experiments.Using this model,the optimal combined diameters and flow path design for a combined-diameter heat exchanger using R32 as the working fluid are derived.The results show that the heat transfer performance of all combined diameter configurations improves by 2.79%to 8.26%compared to the baseline design,with the coefficient of performance(COP)increasing from 4.15 to 4.27~4.5.These designs can save copper material,but at the cost of an increase in pressure drop by 66.86%to 131.84%.The scheme IIIH,using R32,is the optimal combined-diameter and flow path configuration that balances both heat transfer performance and economic cost.
基金This work was supported by the National Key Research and Development Program of China(Grant No.2018YFF0213602).
文摘Acoustic echo cancellation is often applied in communication and video call system to reduce unnecessary echoes generated between speakers and microphones.In these systems,the speech input signal of the adaptive filter is often colored and unstable,which decays the convergence rate of the adaptive filter if the NLMS algorithm is used.In this paper,an improved nonparametric variable step-size subband(NPVSS-NSAF)algorithm is proposed to address the problem.The variable step-size is derived by minimizing the sum of the square Euclidean norm of the difference between the optimal weight vectors to be updated and the past estimated weight vectors.Then the parameters are eliminated by using the power of subband signal noise equal to the power of subband posteriori error.The performance of the proposed algorithm is simulated in the aspects of misalignment and return loss enhancement.Experiment results show a fast convergence rate and low misalignment of the proposed algorithm in system identification.
文摘This paper proposes a robust adaptive filter based on the exponent sin cost to improve the capability against Gaussian or multiple types of non-Gaussian noises of the adaptive filtering algorithm when dealing with time-varying/time-invariant linear systems function exponent sin(ExpSin).Then a variable step-size(VSS)-ExpSin algorithm is extended further.Besides,the stepsize,the convergence,and the steady-state performance of the proposed algorithm are validated experimentally.The Monte Carlo simulation results of linear system identification illustrate the principle and efficiency of this proposed adaptive filtering algorithm.Results suggest that the proposed adaptive filtering algorithm has superior performance when estimating the unknown linear systems under multiple-types measurement noises.
基金supported by the National Natural Science Foundation of China(No.51905123)Major Scientific and Technological Innovation Program of Shandong Province,China(Nos.2020CXGC010303,2022ZLGX04)Key R&D Programme of Shandong Province,China(No.2022JMRH0308).
文摘An internal state variable(ISV)model was established according to the experimental results of hot plane strain compression(PSC)to predict the microstructure evolution during hot spinning of ZK61 alloy.The effects of the internal variables were considered in this ISV model,and the parameters were optimized by genetic algorithm.After validation,the ISV model was used to simulate the evolution of grain size(GS)and dynamic recrystallization(DRX)fraction during hot spinning via Abaqus and its subroutine Vumat.By comparing the simulated results with the experimental results,the application of the ISV model was proven to be reliable.Meanwhile,the strength of the thin-walled spun ZK61 tube increased from 303 to 334 MPa due to grain refinement by DRX and texture strengthening.Besides,some ultrafine grains(0.5μm)that played an important role in mechanical properties were formed due to the proliferation,movement,and entanglement of dislocations during the spinning process.
文摘In order to solve the problem of the variable coefficient ordinary differen-tial equation on the bounded domain,the Lagrange interpolation method is used to approximate the exact solution of the equation,and the error between the numerical solution and the exact solution is obtained,and then compared with the error formed by the difference method,it is concluded that the Lagrange interpolation method is more effective in solving the variable coefficient ordinary differential equation.
基金supported by grants from the National Natural Science Foundation of China(No.U20B2006)the Guangdong Basic and Applied Basic Research Foundation(No.2022A1515110145)Young Elite Scientists Sponsorship Program by China Association for Science and Technology(No.2022QNRC001).
文摘The optimization of the waverider is constrained by the reversely designed leading edge and the constant shock angle distribution. This paper proposes a design method called the variable Leading-Edge Cone (vLEC) method to address these limitations. In the vLEC method, the waverider is directly designed from the preassigned leading edge and the variable shock angle distribution based on the Leading-Edge Cone (LEC) concept. Since the vLEC method is an approximate method, two test waveriders are designed and evaluated using numerical simulations to validate the shock design accuracy and the effectiveness of the vLEC method. The results show that the shocks of the test waveriders coincide well with the preassigned positions. Furthermore, four specifically designed application cases are conducted to analyze the performance benefits of the vLEC waveriders. The results of these cases indicate that, due to their variable shock angle distributions, the vLEC waveriders exhibit higher lift-to-drag ratios and better longitudinal static stability than conventional waveriders. Additionally, the vLEC waveriders demonstrate superior volumetric capacities near the symmetry plane, albeit with a minor decrease in volumetric efficiency.
基金supported by the National Key R&D Program of China(No.2021YFB0301200)National Natural Science Foundation of China(No.62025208).
文摘Large-scale Language Models(LLMs)have achieved significant breakthroughs in Natural Language Processing(NLP),driven by the pre-training and fine-tuning paradigm.While this approach allows models to specialize in specific tasks with reduced training costs,the substantial memory requirements during fine-tuning present a barrier to broader deployment.Parameter-Efficient Fine-Tuning(PEFT)techniques,such as Low-Rank Adaptation(LoRA),and parameter quantization methods have emerged as solutions to address these challenges by optimizing memory usage and computational efficiency.Among these,QLoRA,which combines PEFT and quantization,has demonstrated notable success in reducing memory footprints during fine-tuning,prompting the development of various QLoRA variants.Despite these advancements,the quantitative impact of key variables on the fine-tuning performance of quantized LLMs remains underexplored.This study presents a comprehensive analysis of these key variables,focusing on their influence across different layer types and depths within LLM architectures.Our investigation uncovers several critical findings:(1)Larger layers,such as MLP layers,can maintain performance despite reductions in adapter rank,while smaller layers,like self-attention layers,aremore sensitive to such changes;(2)The effectiveness of balancing factors depends more on specific values rather than layer type or depth;(3)In quantization-aware fine-tuning,larger layers can effectively utilize smaller adapters,whereas smaller layers struggle to do so.These insights suggest that layer type is a more significant determinant of fine-tuning success than layer depth when optimizing quantized LLMs.Moreover,for the same discount of trainable parameters,reducing the trainable parameters in a larger layer is more effective in preserving fine-tuning accuracy than in a smaller one.This study provides valuable guidance for more efficient fine-tuning strategies and opens avenues for further research into optimizing LLM fine-tuning in resource-constrained environments.
基金supported by the National Natural Science Foundation of China(Grant No.11971486)。
文摘We consider a single server constant retrial queue,in which a state-dependent service policy is used to control the service rate.Customer arrival follows Poisson process,while service time and retrial time are exponential distributions.Whenever the server is available,it admits the retrial customers into service based on a first-come first-served rule.The service rate adjusts in real-time based on the retrial queue length.An iterative algorithm is proposed to numerically solve the personal optimal problem in the fully observable scenario.Furthermore,we investigate the impact of parameters on the social optimal threshold.The effectiveness of the results is illustrated by two examples.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.62105004 and 52174141)the College Student Innovation and Entrepreneurship Fund Project(Grant No.202210361053)+4 种基金Anhui Mining Machinery and Electrical Equipment Coordination Innovation Center,Anhui University of Science&Technology(Grant No.KSJD202304)the Anhui Province Digital Agricultural Engineering Technology Research Center Open Project(Grant No.AHSZNYGC-ZXKF021)the Talent Recruitment Special Fund of Anhui University of Science and Technology(Grant No.2024yjrc175)the Graduate Innovation Fund Project of Anhui University of Science and Technology(Grant Nos.2024cx2067,2024cx2107,and 2024cx2064)Seed Support Project for Postgraduate Innovation,Entrepreneurship and Practice at Anhui University of Science and Technology(Grant No.2024cxcysj084).
文摘With the development of the Internet,image encryption technology has become critical for network security.Traditional methods often suffer from issues such as insufficient chaos,low randomness in key generation,and poor encryption efficiency.To enhance performance,this paper proposes a new encryption algorithm designed to optimize parallel processing and adapt to images of varying sizes and colors.The method begins by using SHA-384 to extract the hash value of the plaintext image,which is then processed to determine the chaotic system’s initial value and block size.The image is padded and divided into blocks for further processing.A novel two-dimensional infinite collapses hyperchaotic map(2DICHM)is employed to generate the intra-block scrambling sequence,while an improved variable Joseph traversal sequence is used for inter-block scrambling.After removing the padding,3D forward and backward shift diffusions,controlled by the 2D-ICHM sequences,are applied to the scrambled image,producing the ciphertext.Simulation results demonstrate that the proposed algorithm outperforms others in terms of entropy,anti-noise resilience,correlation coefficient,robustness,and encryption efficiency.
