The dynamic optimal interpolation(DOI)method is a technique based on quasi-geostrophic dynamics for merging multi-satellite altimeter along-track observations to generate gridded absolute dynamic topography(ADT).Compa...The dynamic optimal interpolation(DOI)method is a technique based on quasi-geostrophic dynamics for merging multi-satellite altimeter along-track observations to generate gridded absolute dynamic topography(ADT).Compared with the linear optimal interpolation(LOI)method,the DOI method can improve the accuracy of gridded ADT locally but with low computational efficiency.Consequently,considering both computational efficiency and accuracy,the DOI method is more suitable to be used only for regional applications.In this study,we propose to evaluate the suitable region for applying the DOI method based on the correlation between the absolute value of the Jacobian operator of the geostrophic stream function and the improvement achieved by the DOI method.After verifying the LOI and DOI methods,the suitable region was investigated in three typical areas:the Gulf Stream(25°N-50°N,55°W-80°W),the Japanese Kuroshio(25°N-45°N,135°E-155°E),and the South China Sea(5°N-25°N,100°E-125°E).We propose to use the DOI method only in regions outside the equatorial region and where the absolute value of the Jacobian operator of the geostrophic stream function is higher than1×10^(-11).展开更多
This paper investigates the optimal Birkhoff interpolation and Birkhoff numbers of some function spaces in space L∞[-1,1]and weighted spaces Lp,ω[-1,1],1≤p<∞,with w being a continuous integrable weight function...This paper investigates the optimal Birkhoff interpolation and Birkhoff numbers of some function spaces in space L∞[-1,1]and weighted spaces Lp,ω[-1,1],1≤p<∞,with w being a continuous integrable weight function in(-1,1).We proved that the Lagrange interpolation algorithms based on the zeros of some polynomials are optimal.We also show that the Lagrange interpolation algorithms based on the zeros of some polynomials are optimal when the function values of the two endpoints are included in the interpolation systems.展开更多
The objective of this research is to analyze optimal interpolation and Kriging mapping of soil characters in Glacial Moraine Landscapes. The research site is located in sloping landscapes, Kuehren, North Germany. The ...The objective of this research is to analyze optimal interpolation and Kriging mapping of soil characters in Glacial Moraine Landscapes. The research site is located in sloping landscapes, Kuehren, North Germany. The survey method was detailed using maps with scales of 1:5,000. Soil sampling was performed by soil pits and borings and completely analyzed in laboratory. Collected data were evaluated by Geostatistics program for spatial soil variability analyses. All maps (produced by Kriging interpolation) picture redistribution of soil nutrients and soil fractions and all map isolines run in similar directions according to landscape nets. The position in the landscape is responsible for increased soil variability. Soil variability becomes higher with decreasing elevation; this means it increases from hilltops to lower slopes. All observed soil characters show relationships to the soil variability. This variability system is caused by convex depressions and hedgerows (Knicks) function as barriers for the redistribution of transported material and offsite sedimentation. Therefore fluxes can be assessed by soil gain and loss balances.展开更多
The objective of reliability-based design optimization(RBDO)is to minimize the optimization objective while satisfying the corresponding reliability requirements.However,the nested loop characteristic reduces the effi...The objective of reliability-based design optimization(RBDO)is to minimize the optimization objective while satisfying the corresponding reliability requirements.However,the nested loop characteristic reduces the efficiency of RBDO algorithm,which hinders their application to high-dimensional engineering problems.To address these issues,this paper proposes an efficient decoupled RBDO method combining high dimensional model representation(HDMR)and the weight-point estimation method(WPEM).First,we decouple the RBDO model using HDMR and WPEM.Second,Lagrange interpolation is used to approximate a univariate function.Finally,based on the results of the first two steps,the original nested loop reliability optimization model is completely transformed into a deterministic design optimization model that can be solved by a series of mature constrained optimization methods without any additional calculations.Two numerical examples of a planar 10-bar structure and an aviation hydraulic piping system with 28 design variables are analyzed to illustrate the performance and practicability of the proposed method.展开更多
The ensemble optimal interpolation (EnOI) is applied to the regional ocean modeling system (ROMS) with the ability to assimilate the along-track sea level anomaly (TSLA). This system is tested with an eddy-resol...The ensemble optimal interpolation (EnOI) is applied to the regional ocean modeling system (ROMS) with the ability to assimilate the along-track sea level anomaly (TSLA). This system is tested with an eddy-resolving system of the South China Sea (SCS). Background errors are derived from a running seasonal ensemble to account for the seasonal variability within the SCS. A fifth-order localization function with a 250 km localization radius is chosen to reduce the negative effects of sampling errors. The data assimilation system is tested from January 2004 to December 2006. The results show that the root mean square deviation (RMSD) of the sea level anomaly decreased from 10.57 to 6.70 cm, which represents a 36.6% reduction of error. The data assimilation reduces error for temperature within the upper 800 m and for salinity within the upper 200 m, although error degrades slightly at deeper depths. Surface currents are in better agreement with trajectories of surface drifters after data assimilation. The variance of sea level improves significantly in terms of both the amplitude and position of the strong and weak variance regions after assimilating TSLA. Results with AGE error (AGE) perform better than no AGE error (NoAGE) when considering the improvements of the temperature and the salinity. Furthermore, reasons for the extremely strong variability in the northern SCS in high resolution models are investigated. The results demonstrate that the strong variability of sea level in the high resolution model is caused by an extremely strong Kuroshio intrusion. Therefore, it is demonstrated that it is necessary to assimilate the TSLA in order to better simulate the SCS with high resolution models.展开更多
The current lack of high-precision information on subsurface seawater is a constraint in fishery research.Based on Argo temperature and salinity profiles,this study applied the gradient-dependent optimal interpolation...The current lack of high-precision information on subsurface seawater is a constraint in fishery research.Based on Argo temperature and salinity profiles,this study applied the gradient-dependent optimal interpolation to reconstruct daily subsurface oceanic environmental information according to fishery dates and locations.The relationship between subsurface information and matching yellowfin tuna(YFT)in the western and central Pacific Ocean(WCPO)was examined using catch data from January 1,2008 to August 31,2017.The seawater temperature and salinity results showed differences of less than±0.5°C and±0.01 compared with the truth observations respectively.Statistical analysis revealed that the most suitable temperature for YFT fishery was 28–29°C at the near-surface.The most suitable salinity range for YFT fishery was 34.5–36.0 at depths shallower than 300 m.The suitable upper and lower bounds on the depths of the thermocline were 90–100 m and 300–350 m,respectively.The thermocline characteristics were prominent,with a mean temperature gradient exceeding 0.08°C/m.These results indicate that the profiles constructed by gradient-dependent optimal interpolation were more accurate than those of the nearest profiles adopted.展开更多
The application of ensemble optimal interpolation in wave data assimilation in the South China Sea is presented. A sampling strategy for a stationary ensemble is first discussed. The stationary ensemble is constructed...The application of ensemble optimal interpolation in wave data assimilation in the South China Sea is presented. A sampling strategy for a stationary ensemble is first discussed. The stationary ensemble is constructed by sampling from 24-h-interval significant wave height differences of model outputs over a long period,and is validated with altimeter significant wave height data,indicating that the ensemble errors have nearly the same probability distribution function. The background error covariance fields expressed by the ensemble sampled are anisotropic. Updating the static samples by season,the seasonal characteristics of the correlation coefficient distribution are reflected. Hindcast experiments including assimilation and control runs are conducted for the summer of 2010 in the South China Sea. The effect of ensemble optimal interpolation assimilation on wave hindcasts is validated using different satellite altimeter data(Jason-1 and 2 and ENVISAT) and buoy observations. It is found that the ensemble-optimal-interpolation-based wave assimilation scheme for the South China Sea achieves improvements similar to those of the previous optimal-interpolation-based scheme,indicating that the practical application of this computationally cheap ensemble method is feasible.展开更多
In this paper,the kernel of the cubic spline interpolation is given.An optimal error bound for the cu- bic spline interpolation of lower smooth functions is obtained.
Abstract In this paper, by using the explicit expression of the kernel of the cubic spline interpolation, the optimal error bounds for the cubic spline interpolation of lower soomth functions are obtained.
In this paper, a new derivative free trust region method is developed based on the conic interpolation model for the unconstrained optimization. The conic interpolation model is built by means of the quadratic model f...In this paper, a new derivative free trust region method is developed based on the conic interpolation model for the unconstrained optimization. The conic interpolation model is built by means of the quadratic model function, the collinear scaling formula, quadratic approximation and interpolation. All the parameters in this model are determined by objective function interpolation condition. A new derivative free method is developed based upon this model and the global convergence of this new method is proved without any information on gradient.展开更多
A numerical control (NC) tool path of digital CAD model is widely generated as a set of short line segments in machining. However, there are three shortcomings in the linear tool path, such as discontinuities of tange...A numerical control (NC) tool path of digital CAD model is widely generated as a set of short line segments in machining. However, there are three shortcomings in the linear tool path, such as discontinuities of tangency and curvature, huge number of line segments, and short lengths of line segments. These disadvantages hinder the development of high speed machining. To smooth the linear tool path and improve machining efficiency of short line segments, this paper presents an optimal feed interpolator based on G^2 continuous Bézier curves for the linear tool path. First, the areas suitable for fitting are screened out based on the geometric characteristics of continuous short segments (CSSs). CSSs in every area are compressed and fitted into a G^2 Continuous Bézier curve by using the least square method. Then a series of cubic Bézier curves are generated. However, the junction between adjacent Bézier curves is only G^0 continuous. By adjusting the control points and inserting Bézier transition curves between adjacent Bézier curves, the G^2 continuous tool path is constructed. The fitting error is estimated by the second-order Taylor formula. Without iteration, the fitting algorithm can be implemented in real-time environment. Second, the optimal feed interpolator considering the comprehensive constraints (such as the chord error constraint, the maximum normal acceleration, servo capacity of each axis, etc.) is proposed. Simulation and experiment are conducted. The results shows that the proposed method can generate smooth path, decrease the amount of segments and reduce machining time for machining of linear tool path. The proposed research provides an effective method for high-speed machining of complex 2-D/3-D profiles described by short line segments.展开更多
This work presents a novel approach combining radial basis function(RBF)interpolation with Galerkin projection to efficiently solve general optimal control problems.The goal is to develop a highly flexible solution to...This work presents a novel approach combining radial basis function(RBF)interpolation with Galerkin projection to efficiently solve general optimal control problems.The goal is to develop a highly flexible solution to optimal control problems,especially nonsmooth problems involving discontinuities,while accounting for trajectory accuracy and computational efficiency simultaneously.The proposed solution,called the RBF-Galerkin method,offers a highly flexible framework for direct transcription by using any interpolant functions from the broad class of global RBFs and any arbitrary discretization points that do not necessarily need to be on a mesh of points.The RBF-Galerkin costate mapping theorem is developed that describes an exact equivalency between the Karush-Kuhn-Tucker(KKT)conditions of the nonlinear programming problem resulted from the RBF-Galerkin method and the discretized form of the first-order necessary conditions of the optimal control problem,if a set of discrete conditions holds.The efficacy of the proposed method along with the accuracy of the RBF-Galerkin costate mapping theorem is confirmed against an analytical solution for a bang-bang optimal control problem.In addition,the proposed approach is compared against both local and global polynomial methods for a robot motion planning problem to verify its accuracy and computational efficiency.展开更多
With the continuous advancement in topology optimization and additive manufacturing(AM)technology,the capability to fabricate functionally graded materials and intricate cellular structures with spatially varying micr...With the continuous advancement in topology optimization and additive manufacturing(AM)technology,the capability to fabricate functionally graded materials and intricate cellular structures with spatially varying microstructures has grown significantly.However,a critical challenge is encountered in the design of these structures–the absence of robust interface connections between adjacent microstructures,potentially resulting in diminished efficiency or macroscopic failure.A Hybrid Level Set Method(HLSM)is proposed,specifically designed to enhance connectivity among non-uniform microstructures,contributing to the design of functionally graded cellular structures.The HLSM introduces a pioneering algorithm for effectively blending heterogeneous microstructure interfaces.Initially,an interpolation algorithm is presented to construct transition microstructures seamlessly connected on both sides.Subsequently,the algorithm enables the morphing of non-uniform unit cells to seamlessly adapt to interconnected adjacent microstructures.The method,seamlessly integrated into a multi-scale topology optimization framework using the level set method,exhibits its efficacy through numerical examples,showcasing its prowess in optimizing 2D and 3D functionally graded materials(FGM)and multi-scale topology optimization.In essence,the pressing issue of interface connections in complex structure design is not only addressed but also a robust methodology is introduced,substantiated by numerical evidence,advancing optimization capabilities in the realm of functionally graded materials and cellular structures.展开更多
Spatial optimization as part of spatial modeling has been facilitated significantly by integration with GIS techniques. However, for certain research topics, applying standard GIS techniques may create problems which ...Spatial optimization as part of spatial modeling has been facilitated significantly by integration with GIS techniques. However, for certain research topics, applying standard GIS techniques may create problems which require attention. This paper serves as a cautionary note to demonstrate two problems associated with applying GIS in spatial optimization, using a capacitated p-median facility location optimization problem as an example. The first problem involves errors in interpolating spatial variations of travel costs from using kriging, a common set of techniques for raster files. The second problem is inaccuracy in routing performed on a graph directly created from polyline shapefiles, a common vector file type. While revealing these problems, the paper also suggests remedies. Specifically, interpolation errors can be eliminated by using agent-based spatial modeling while the inaccuracy in routing can be improved through altering the graph topology by splitting the long edges of the shapefile. These issues suggest the need for caution in applying GIS in spatial optimization study.展开更多
Curve and surface interpolation is the core of geometric modeling. The paper gives a new method to interpolate B spline curves and surfaces based on nonlinear optimization. The beauties of the method are: it is not ne...Curve and surface interpolation is the core of geometric modeling. The paper gives a new method to interpolate B spline curves and surfaces based on nonlinear optimization. The beauties of the method are: it is not necessary to calculate parameter values of data points, and the curves and surfaces generated have good behavior of fairness. The theory and procedures of the method are introduced in detail, the differences between the conventional method and the new one are discussed, and some figures generated by this new technique are presented.展开更多
Curvature lines are special and important curves on surfaces.It is of great significance to construct developable surface interpolated on curvature lines in engineering applications.In this paper,the shape optimizatio...Curvature lines are special and important curves on surfaces.It is of great significance to construct developable surface interpolated on curvature lines in engineering applications.In this paper,the shape optimization of generalized cubic ball developable surface interpolated on the curvature line is studied by using the improved reptile search algorithm.Firstly,based on the curvature line of generalized cubic ball curve with shape adjustable,this paper gives the construction method of SGC-Ball developable surface interpolated on the curve.Secondly,the feedback mechanism,adaptive parameters and mutation strategy are introduced into the reptile search algorithm,and the Feedback mechanism-driven improved reptile search algorithm effectively improves the solving precision.On IEEE congress on evolutionary computation 2014,2017,2019 and four engineering design problems,the feedback mechanism-driven improved reptile search algorithm is compared with other representative methods,and the result indicates that the solution performance of the feedback mechanism-driven improved reptile search algorithm is competitive.At last,taking the minimum energy as the evaluation index,the shape optimization model of SGC-Ball interpolation developable surface is established.The developable surface with the minimum energy is achieved with the help of the feedback mechanism-driven improved reptile search algorithm,and the comparison experiment verifies the superiority of the feedback mechanism-driven improved reptile search algorithm for the shape optimization problem.展开更多
We’ll study the FEM for a model for compressible miscible displacement in porous media which includes molecular diffusion and mechanical dispersion in one-dimensional space.A class of vertices-edges-elements interpol...We’ll study the FEM for a model for compressible miscible displacement in porous media which includes molecular diffusion and mechanical dispersion in one-dimensional space.A class of vertices-edges-elements interpolation operator ink is introduced.With the help of ink(not elliptic projection),the optimal error estimate in L∞(J;L2(Ω)) norm of FEM is proved.展开更多
In abandoned mine sites, i.e., mine sites where mining operations have ended, wide spread contaminations are often evident, but the potential sources and pathways of contamination especially through the subsurface, ar...In abandoned mine sites, i.e., mine sites where mining operations have ended, wide spread contaminations are often evident, but the potential sources and pathways of contamination especially through the subsurface, are difficult to identify due to inadequate and sparse geochemical measurements available. Therefore, it is essential to design and implement a planned monitoring net-work to obtain essential information required for establishing the potential contamination source locations, i.e., waste dumps, tailing dams, pits and possible pathways through the subsurface, and to design a remediation strategy for rehabilitation. This study presents an illustrative application of modeling the flow and transport processes and monitoring network design in a study area hydrogeologically resembling an abandoned mine site in Queensland, Australia. In this preliminary study, the contaminant transport process modeled does not incorporate the reactive geochemistry of the contaminants. The transport process is modeled considering a generic conservative contaminant for the illustrative purpose of showing the potential application of an optimal monitoring design methodology. This study aims to design optimal monitoring network to: 1) minimize the contaminant solute mass estimation error;2) locate the plume boundary;3) select the monitoring locations with (potentially) high concentrations. A linked simulation optimization based methodology is utilized for optimal monitoring network design. The methodology is applied utilizing a recently developed software package CARE-GWMND, developed at James Cook University for optimal monitoring network design. Given the complexity of the groundwater systems and the sparsity of pollutant concentration observation data from the field, this software is capable of simulating the groundwater flow and solute transport with spatial interpolation of data from a sparse set of available data, and it utilizes the optimization algorithm to determine optimum locations for implementing monitoring wells.展开更多
In this paper, we present an algorithm for reconstruction of B-spline surface such that it interpolates the four given bound- ary curves and simultaneously approximates some given inner points. The main idea of our me...In this paper, we present an algorithm for reconstruction of B-spline surface such that it interpolates the four given bound- ary curves and simultaneously approximates some given inner points. The main idea of our method is: first, we construct an initial surface which interpolates the four given boundary curves; then, while keeping the boundary control points of the initial surface un- changed, we reposition the inner control points of the surface with energy optimization method. Examples show that our algorithm is practicable and effective.展开更多
基金supported by National Natural Science Foundation of China under Grants 42192531 and 42192534the Special Fund of Hubei Luojia Laboratory(China)under Grant 220100001the Natural Science Foundation of Hubei Province for Distinguished Young Scholars(China)under Grant 2022CFA090。
文摘The dynamic optimal interpolation(DOI)method is a technique based on quasi-geostrophic dynamics for merging multi-satellite altimeter along-track observations to generate gridded absolute dynamic topography(ADT).Compared with the linear optimal interpolation(LOI)method,the DOI method can improve the accuracy of gridded ADT locally but with low computational efficiency.Consequently,considering both computational efficiency and accuracy,the DOI method is more suitable to be used only for regional applications.In this study,we propose to evaluate the suitable region for applying the DOI method based on the correlation between the absolute value of the Jacobian operator of the geostrophic stream function and the improvement achieved by the DOI method.After verifying the LOI and DOI methods,the suitable region was investigated in three typical areas:the Gulf Stream(25°N-50°N,55°W-80°W),the Japanese Kuroshio(25°N-45°N,135°E-155°E),and the South China Sea(5°N-25°N,100°E-125°E).We propose to use the DOI method only in regions outside the equatorial region and where the absolute value of the Jacobian operator of the geostrophic stream function is higher than1×10^(-11).
基金supported by National Natural Science Foundation of China(11871006,11671271)。
文摘This paper investigates the optimal Birkhoff interpolation and Birkhoff numbers of some function spaces in space L∞[-1,1]and weighted spaces Lp,ω[-1,1],1≤p<∞,with w being a continuous integrable weight function in(-1,1).We proved that the Lagrange interpolation algorithms based on the zeros of some polynomials are optimal.We also show that the Lagrange interpolation algorithms based on the zeros of some polynomials are optimal when the function values of the two endpoints are included in the interpolation systems.
文摘The objective of this research is to analyze optimal interpolation and Kriging mapping of soil characters in Glacial Moraine Landscapes. The research site is located in sloping landscapes, Kuehren, North Germany. The survey method was detailed using maps with scales of 1:5,000. Soil sampling was performed by soil pits and borings and completely analyzed in laboratory. Collected data were evaluated by Geostatistics program for spatial soil variability analyses. All maps (produced by Kriging interpolation) picture redistribution of soil nutrients and soil fractions and all map isolines run in similar directions according to landscape nets. The position in the landscape is responsible for increased soil variability. Soil variability becomes higher with decreasing elevation; this means it increases from hilltops to lower slopes. All observed soil characters show relationships to the soil variability. This variability system is caused by convex depressions and hedgerows (Knicks) function as barriers for the redistribution of transported material and offsite sedimentation. Therefore fluxes can be assessed by soil gain and loss balances.
基金supported by the Innovation Fund Project of the Gansu Education Department(Grant No.2021B-099).
文摘The objective of reliability-based design optimization(RBDO)is to minimize the optimization objective while satisfying the corresponding reliability requirements.However,the nested loop characteristic reduces the efficiency of RBDO algorithm,which hinders their application to high-dimensional engineering problems.To address these issues,this paper proposes an efficient decoupled RBDO method combining high dimensional model representation(HDMR)and the weight-point estimation method(WPEM).First,we decouple the RBDO model using HDMR and WPEM.Second,Lagrange interpolation is used to approximate a univariate function.Finally,based on the results of the first two steps,the original nested loop reliability optimization model is completely transformed into a deterministic design optimization model that can be solved by a series of mature constrained optimization methods without any additional calculations.Two numerical examples of a planar 10-bar structure and an aviation hydraulic piping system with 28 design variables are analyzed to illustrate the performance and practicability of the proposed method.
基金The Major State Basic Research Development Program of China under contract Nos 201-1CB403606 and 2011CB403500the National Natural Science Foundation of China under contract Nos 41222038,41076011and 41206023the National Marine Environmental Forecasting Center Operational Development Foundation of the State Oceanic Administration of China under contract No.2013002
文摘The ensemble optimal interpolation (EnOI) is applied to the regional ocean modeling system (ROMS) with the ability to assimilate the along-track sea level anomaly (TSLA). This system is tested with an eddy-resolving system of the South China Sea (SCS). Background errors are derived from a running seasonal ensemble to account for the seasonal variability within the SCS. A fifth-order localization function with a 250 km localization radius is chosen to reduce the negative effects of sampling errors. The data assimilation system is tested from January 2004 to December 2006. The results show that the root mean square deviation (RMSD) of the sea level anomaly decreased from 10.57 to 6.70 cm, which represents a 36.6% reduction of error. The data assimilation reduces error for temperature within the upper 800 m and for salinity within the upper 200 m, although error degrades slightly at deeper depths. Surface currents are in better agreement with trajectories of surface drifters after data assimilation. The variance of sea level improves significantly in terms of both the amplitude and position of the strong and weak variance regions after assimilating TSLA. Results with AGE error (AGE) perform better than no AGE error (NoAGE) when considering the improvements of the temperature and the salinity. Furthermore, reasons for the extremely strong variability in the northern SCS in high resolution models are investigated. The results demonstrate that the strong variability of sea level in the high resolution model is caused by an extremely strong Kuroshio intrusion. Therefore, it is demonstrated that it is necessary to assimilate the TSLA in order to better simulate the SCS with high resolution models.
基金The National Natural Science Foundation of China under contract No.4210060098the Foundation of Key Laboratory of Sustainable Exploitation of Oceanic Fisheries Resources under contract No.A1-2006-21-200201.
文摘The current lack of high-precision information on subsurface seawater is a constraint in fishery research.Based on Argo temperature and salinity profiles,this study applied the gradient-dependent optimal interpolation to reconstruct daily subsurface oceanic environmental information according to fishery dates and locations.The relationship between subsurface information and matching yellowfin tuna(YFT)in the western and central Pacific Ocean(WCPO)was examined using catch data from January 1,2008 to August 31,2017.The seawater temperature and salinity results showed differences of less than±0.5°C and±0.01 compared with the truth observations respectively.Statistical analysis revealed that the most suitable temperature for YFT fishery was 28–29°C at the near-surface.The most suitable salinity range for YFT fishery was 34.5–36.0 at depths shallower than 300 m.The suitable upper and lower bounds on the depths of the thermocline were 90–100 m and 300–350 m,respectively.The thermocline characteristics were prominent,with a mean temperature gradient exceeding 0.08°C/m.These results indicate that the profiles constructed by gradient-dependent optimal interpolation were more accurate than those of the nearest profiles adopted.
基金Supported by the National Special Research Fund for Non-Profit Marine Sector(Nos.201005033,201105002)the National Natural Science Foundation of China(No.U1133001)+1 种基金the National High Technology Research and Development Program of China(863 Program)(No.2012AA091801)the NSFC-Shandong Joint Fund for Marine Science Research Centers(No.U1406401)
文摘The application of ensemble optimal interpolation in wave data assimilation in the South China Sea is presented. A sampling strategy for a stationary ensemble is first discussed. The stationary ensemble is constructed by sampling from 24-h-interval significant wave height differences of model outputs over a long period,and is validated with altimeter significant wave height data,indicating that the ensemble errors have nearly the same probability distribution function. The background error covariance fields expressed by the ensemble sampled are anisotropic. Updating the static samples by season,the seasonal characteristics of the correlation coefficient distribution are reflected. Hindcast experiments including assimilation and control runs are conducted for the summer of 2010 in the South China Sea. The effect of ensemble optimal interpolation assimilation on wave hindcasts is validated using different satellite altimeter data(Jason-1 and 2 and ENVISAT) and buoy observations. It is found that the ensemble-optimal-interpolation-based wave assimilation scheme for the South China Sea achieves improvements similar to those of the previous optimal-interpolation-based scheme,indicating that the practical application of this computationally cheap ensemble method is feasible.
文摘In this paper,the kernel of the cubic spline interpolation is given.An optimal error bound for the cu- bic spline interpolation of lower smooth functions is obtained.
文摘Abstract In this paper, by using the explicit expression of the kernel of the cubic spline interpolation, the optimal error bounds for the cubic spline interpolation of lower soomth functions are obtained.
基金This work was supported by the National Natural Science Foundation of China(10071037)
文摘In this paper, a new derivative free trust region method is developed based on the conic interpolation model for the unconstrained optimization. The conic interpolation model is built by means of the quadratic model function, the collinear scaling formula, quadratic approximation and interpolation. All the parameters in this model are determined by objective function interpolation condition. A new derivative free method is developed based upon this model and the global convergence of this new method is proved without any information on gradient.
基金Supported by National Natural Science Foundation of China(Grant No.50875171)National Hi-tech Research and Development Program of China(863 Program,Grant No.2009AA04Z150)
文摘A numerical control (NC) tool path of digital CAD model is widely generated as a set of short line segments in machining. However, there are three shortcomings in the linear tool path, such as discontinuities of tangency and curvature, huge number of line segments, and short lengths of line segments. These disadvantages hinder the development of high speed machining. To smooth the linear tool path and improve machining efficiency of short line segments, this paper presents an optimal feed interpolator based on G^2 continuous Bézier curves for the linear tool path. First, the areas suitable for fitting are screened out based on the geometric characteristics of continuous short segments (CSSs). CSSs in every area are compressed and fitted into a G^2 Continuous Bézier curve by using the least square method. Then a series of cubic Bézier curves are generated. However, the junction between adjacent Bézier curves is only G^0 continuous. By adjusting the control points and inserting Bézier transition curves between adjacent Bézier curves, the G^2 continuous tool path is constructed. The fitting error is estimated by the second-order Taylor formula. Without iteration, the fitting algorithm can be implemented in real-time environment. Second, the optimal feed interpolator considering the comprehensive constraints (such as the chord error constraint, the maximum normal acceleration, servo capacity of each axis, etc.) is proposed. Simulation and experiment are conducted. The results shows that the proposed method can generate smooth path, decrease the amount of segments and reduce machining time for machining of linear tool path. The proposed research provides an effective method for high-speed machining of complex 2-D/3-D profiles described by short line segments.
文摘This work presents a novel approach combining radial basis function(RBF)interpolation with Galerkin projection to efficiently solve general optimal control problems.The goal is to develop a highly flexible solution to optimal control problems,especially nonsmooth problems involving discontinuities,while accounting for trajectory accuracy and computational efficiency simultaneously.The proposed solution,called the RBF-Galerkin method,offers a highly flexible framework for direct transcription by using any interpolant functions from the broad class of global RBFs and any arbitrary discretization points that do not necessarily need to be on a mesh of points.The RBF-Galerkin costate mapping theorem is developed that describes an exact equivalency between the Karush-Kuhn-Tucker(KKT)conditions of the nonlinear programming problem resulted from the RBF-Galerkin method and the discretized form of the first-order necessary conditions of the optimal control problem,if a set of discrete conditions holds.The efficacy of the proposed method along with the accuracy of the RBF-Galerkin costate mapping theorem is confirmed against an analytical solution for a bang-bang optimal control problem.In addition,the proposed approach is compared against both local and global polynomial methods for a robot motion planning problem to verify its accuracy and computational efficiency.
基金the National Key Research and Development Program of China(Grant Number 2021YFB1714600)the National Natural Science Foundation of China(Grant Number 52075195)the Fundamental Research Funds for the Central Universities,China through Program No.2172019kfyXJJS078.
文摘With the continuous advancement in topology optimization and additive manufacturing(AM)technology,the capability to fabricate functionally graded materials and intricate cellular structures with spatially varying microstructures has grown significantly.However,a critical challenge is encountered in the design of these structures–the absence of robust interface connections between adjacent microstructures,potentially resulting in diminished efficiency or macroscopic failure.A Hybrid Level Set Method(HLSM)is proposed,specifically designed to enhance connectivity among non-uniform microstructures,contributing to the design of functionally graded cellular structures.The HLSM introduces a pioneering algorithm for effectively blending heterogeneous microstructure interfaces.Initially,an interpolation algorithm is presented to construct transition microstructures seamlessly connected on both sides.Subsequently,the algorithm enables the morphing of non-uniform unit cells to seamlessly adapt to interconnected adjacent microstructures.The method,seamlessly integrated into a multi-scale topology optimization framework using the level set method,exhibits its efficacy through numerical examples,showcasing its prowess in optimizing 2D and 3D functionally graded materials(FGM)and multi-scale topology optimization.In essence,the pressing issue of interface connections in complex structure design is not only addressed but also a robust methodology is introduced,substantiated by numerical evidence,advancing optimization capabilities in the realm of functionally graded materials and cellular structures.
文摘Spatial optimization as part of spatial modeling has been facilitated significantly by integration with GIS techniques. However, for certain research topics, applying standard GIS techniques may create problems which require attention. This paper serves as a cautionary note to demonstrate two problems associated with applying GIS in spatial optimization, using a capacitated p-median facility location optimization problem as an example. The first problem involves errors in interpolating spatial variations of travel costs from using kriging, a common set of techniques for raster files. The second problem is inaccuracy in routing performed on a graph directly created from polyline shapefiles, a common vector file type. While revealing these problems, the paper also suggests remedies. Specifically, interpolation errors can be eliminated by using agent-based spatial modeling while the inaccuracy in routing can be improved through altering the graph topology by splitting the long edges of the shapefile. These issues suggest the need for caution in applying GIS in spatial optimization study.
文摘Curve and surface interpolation is the core of geometric modeling. The paper gives a new method to interpolate B spline curves and surfaces based on nonlinear optimization. The beauties of the method are: it is not necessary to calculate parameter values of data points, and the curves and surfaces generated have good behavior of fairness. The theory and procedures of the method are introduced in detail, the differences between the conventional method and the new one are discussed, and some figures generated by this new technique are presented.
基金supported by the National Natural Science Foundation of China(Grant No.52375264).
文摘Curvature lines are special and important curves on surfaces.It is of great significance to construct developable surface interpolated on curvature lines in engineering applications.In this paper,the shape optimization of generalized cubic ball developable surface interpolated on the curvature line is studied by using the improved reptile search algorithm.Firstly,based on the curvature line of generalized cubic ball curve with shape adjustable,this paper gives the construction method of SGC-Ball developable surface interpolated on the curve.Secondly,the feedback mechanism,adaptive parameters and mutation strategy are introduced into the reptile search algorithm,and the Feedback mechanism-driven improved reptile search algorithm effectively improves the solving precision.On IEEE congress on evolutionary computation 2014,2017,2019 and four engineering design problems,the feedback mechanism-driven improved reptile search algorithm is compared with other representative methods,and the result indicates that the solution performance of the feedback mechanism-driven improved reptile search algorithm is competitive.At last,taking the minimum energy as the evaluation index,the shape optimization model of SGC-Ball interpolation developable surface is established.The developable surface with the minimum energy is achieved with the help of the feedback mechanism-driven improved reptile search algorithm,and the comparison experiment verifies the superiority of the feedback mechanism-driven improved reptile search algorithm for the shape optimization problem.
基金This research is supported by the Foundation for Talents for Next Century of Shandong University
文摘We’ll study the FEM for a model for compressible miscible displacement in porous media which includes molecular diffusion and mechanical dispersion in one-dimensional space.A class of vertices-edges-elements interpolation operator ink is introduced.With the help of ink(not elliptic projection),the optimal error estimate in L∞(J;L2(Ω)) norm of FEM is proved.
文摘In abandoned mine sites, i.e., mine sites where mining operations have ended, wide spread contaminations are often evident, but the potential sources and pathways of contamination especially through the subsurface, are difficult to identify due to inadequate and sparse geochemical measurements available. Therefore, it is essential to design and implement a planned monitoring net-work to obtain essential information required for establishing the potential contamination source locations, i.e., waste dumps, tailing dams, pits and possible pathways through the subsurface, and to design a remediation strategy for rehabilitation. This study presents an illustrative application of modeling the flow and transport processes and monitoring network design in a study area hydrogeologically resembling an abandoned mine site in Queensland, Australia. In this preliminary study, the contaminant transport process modeled does not incorporate the reactive geochemistry of the contaminants. The transport process is modeled considering a generic conservative contaminant for the illustrative purpose of showing the potential application of an optimal monitoring design methodology. This study aims to design optimal monitoring network to: 1) minimize the contaminant solute mass estimation error;2) locate the plume boundary;3) select the monitoring locations with (potentially) high concentrations. A linked simulation optimization based methodology is utilized for optimal monitoring network design. The methodology is applied utilizing a recently developed software package CARE-GWMND, developed at James Cook University for optimal monitoring network design. Given the complexity of the groundwater systems and the sparsity of pollutant concentration observation data from the field, this software is capable of simulating the groundwater flow and solute transport with spatial interpolation of data from a sparse set of available data, and it utilizes the optimization algorithm to determine optimum locations for implementing monitoring wells.
基金Supported by the Natural Science Foundation of Hebei Province
文摘In this paper, we present an algorithm for reconstruction of B-spline surface such that it interpolates the four given bound- ary curves and simultaneously approximates some given inner points. The main idea of our method is: first, we construct an initial surface which interpolates the four given boundary curves; then, while keeping the boundary control points of the initial surface un- changed, we reposition the inner control points of the surface with energy optimization method. Examples show that our algorithm is practicable and effective.