This paper shows the importance of the optimal smoothing scheme in Microphone Array Post-Filtering(MAPF) under a combined Deterministic-Stochastic Hybrid Model(DSHM).We reveal that some of the well-known MAPF algorith...This paper shows the importance of the optimal smoothing scheme in Microphone Array Post-Filtering(MAPF) under a combined Deterministic-Stochastic Hybrid Model(DSHM).We reveal that some of the well-known MAPF algorithms may cause serious speech distortion without using the optimal smoothing scheme,which is resulted from oversmoothing the raw periodogram over time.Using a minimum conditional mean square error criterion,we derive the optimal smoothing factor under the DSHM,where the Deterministic-to-Stochastic-Ratio(DSR) and the stationarity determine the value of the optimal smoothing factor.The optimal smoothing scheme is applied to the Tran-sient-Beam-to-Reference-Ratio(TBRR)-based MAPF algorithm and experimental results show its better performance in terms of both the Log-Spectral Distance(LSD) and the Perceptual Evaluation of Speech Quality(PESQ).展开更多
In this paper we consider the transmission of stored video from a server to a client for medical applications such as, Telemonitoring, to optimize medical quality of service (m-QoS) and to examine how the client buffe...In this paper we consider the transmission of stored video from a server to a client for medical applications such as, Telemonitoring, to optimize medical quality of service (m-QoS) and to examine how the client buffer space can be used efficiently and effectively towards reducing the rate variability of the compressed variable bit rate (VBR) video. Three basic results are presented. First, we show how to obtain the greatest possible reduction in rate variability when sending stored video to client with a given buffer size. Second, how to reduce high peak data rate of compressed VBR video when a patient is moving/walking very fast in hospital. Third, we evaluate the impact of optimal smoothing algorithm on the network parameters such as, peak-to-mean ratio, standard deviation, delay, jitter, average delay and average jitter to optimize the m-QoS. To resolve these all problems we used optimal smoothing algorithm and show its performance over a set of long MPEG-4 encoded video traces. Simulation results show that m-QoS is optimized by minimizing network metrics.展开更多
In this paper, an approximate smoothing approach to the non-differentiable exact penalty function is proposed for the constrained optimization problem. A simple smoothed penalty algorithm is given, and its convergence...In this paper, an approximate smoothing approach to the non-differentiable exact penalty function is proposed for the constrained optimization problem. A simple smoothed penalty algorithm is given, and its convergence is discussed. A practical algorithm to compute approximate optimal solution is given as well as computational experiments to demonstrate its efficiency.展开更多
The traditional topology optimization method of continuum structure generally uses quadrilateral elements as the basic mesh.This approach often leads to jagged boundary issues,which are traditionally addressed through...The traditional topology optimization method of continuum structure generally uses quadrilateral elements as the basic mesh.This approach often leads to jagged boundary issues,which are traditionally addressed through post-processing,potentially altering the mechanical properties of the optimized structure.A topology optimization method of Movable Morphable Smooth Boundary(MMSB)is proposed based on the idea of mesh adaptation to solve the problem of jagged boundaries and the influence of post-processing.Based on the ICM method,the rational fraction function is introduced as the filtering function,and a topology optimization model with the minimum weight as the objective and the displacement as the constraint is established.A triangular mesh is utilized as the base mesh in this method.The mesh is re-divided in the optimization process based on the contour line,and a smooth boundary parallel to the contour line is obtained.Numerical examples demonstrate that the MMSB method effectively resolves the jagged boundary issues,leading to enhanced structural performance.展开更多
<div style="text-align:justify;"> In order to speed up the global optimization-based mesh smoothing, an enhanced steepest descent method is presented in the paper. Numerical experiment results show tha...<div style="text-align:justify;"> In order to speed up the global optimization-based mesh smoothing, an enhanced steepest descent method is presented in the paper. Numerical experiment results show that the method performs better than the steepest descent method in the global smoothing. We also presented a physically-based interpretation to explain why the method works better than the steepest descent method. </div>展开更多
Laser vision correction is a rapidly growing field for correcting nearsightedness, farsightedness as well as astigmatism with dominating laser-assisted in situ keratomileusis (LASIK) procedures. While the technique wo...Laser vision correction is a rapidly growing field for correcting nearsightedness, farsightedness as well as astigmatism with dominating laser-assisted in situ keratomileusis (LASIK) procedures. While the technique works well for correcting spherocylindrical aberrations, it does not fully correct high order aberrations (HOAs), in particular spherical aberration (SA), due to unexpected induction of HOAs post-surgery. Corneal epithelial remodeling was proposed as one source to account for such HOA induction process. This work proposes a dual-scale linear filtering kernel to model such a process. Several retrospective clinical data sets were used as training data sets to construct the model, with a downhill simplex algorithm to optimize the two free parameters of the kernel. The performance of the optimized kernel was testedon new clinical data sets that were not previously used for the optimization.展开更多
We propose a new unified path to approximately smoothing the nonsmooth exact penalty function in this paper. Based on the new smooth penalty function, we give a penalty algorithm to solve the constrained optimization ...We propose a new unified path to approximately smoothing the nonsmooth exact penalty function in this paper. Based on the new smooth penalty function, we give a penalty algorithm to solve the constrained optimization problem, and discuss the convergence of the algorithm under mild conditions.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.
In this paper, a fast approach to generate time optimal and smooth trajectory has been developed and tested. Minimum time is critical for the productivity in industrial applications. Meanwhile, smooth trajectories bas...In this paper, a fast approach to generate time optimal and smooth trajectory has been developed and tested. Minimum time is critical for the productivity in industrial applications. Meanwhile, smooth trajectories based on cubic splines are desirable for their ability to limit vibrations and ensure the continuity of position, velocity and acceleration during the robot movement. The main feature of the approach is a satisfactory solution that can be obtained by a local modification process among each intermal between two consecutive via-points. An analytical formulation simplifies the approach to smooth trajectory and few,iterations are enough to determine the correct values. The approach can be applied in many robot manipulators which require high performance on time and smooth. The simulation and application of the approach on a palletizer robot are performed, and the experimental results provide evidence that the approach can realize the robot manipulators more efficiency and high smooth performance.展开更多
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.
A concept of the independent-continuous topological variable is proposed to establish its corresponding smooth model of structural topological optimization. The method can overcome difficulties that are encountered in...A concept of the independent-continuous topological variable is proposed to establish its corresponding smooth model of structural topological optimization. The method can overcome difficulties that are encountered in conventional models and algorithms for the optimization of the structural topology. Its application to truss topological optimization with stress and displacement constraints is satisfactory, with convergence faster than that of sectional optimizations.展开更多
In parallel hybrid electrical vehicle(PHEV)equipped with automatic mechanical transmission(AMT),the driving smoothness and the clutch abrasion are the primary considerations for powertrain control during gearshift and...In parallel hybrid electrical vehicle(PHEV)equipped with automatic mechanical transmission(AMT),the driving smoothness and the clutch abrasion are the primary considerations for powertrain control during gearshift and clutch operation.To improve these performance indexes of PHEV,a coordinated control system is proposed through the analyzing of HEV powertrain dynamic characteristics.Using the method of minimum principle,the input torque of transmission is optimized to improve the driving smoothness of vehicle.Using the methods of fuzzy logic and fuzzy-PID,the engaging speed of clutch and the throttle opening of engine are manipulated to ensure the smoothness of clutch engagement and reduce the abrasion of clutch friction plates.The motor provides the difference between the required input torque of transmission and the torque transmitted through clutch plates.Results of simulation and experiments show that the proposed control strategy performs better than the contrastive control system,the smoothness of driving and the abrasion of clutch can be improved simultaneously.展开更多
This paper addresses the high dimension sample problem in discriminate analysis under nonparametric and supervised assumptions. Since there is a kind of equivalence between the probabilistic dependence measure and the...This paper addresses the high dimension sample problem in discriminate analysis under nonparametric and supervised assumptions. Since there is a kind of equivalence between the probabilistic dependence measure and the Bayes classification error probability, we propose to use an iterative algorithm to optimize the dimension reduction for classification with a probabilistic approach to achieve the Bayes classifier. The estimated probabilities of different errors encountered along the different phases of the system are realized by the Kernel estimate which is adjusted in a means of the smoothing parameter. Experiment results suggest that the proposed approach performs well.展开更多
By means of Lagrange duality of Hill＇s maximum plastic work principle theory of the convex program, a dual problem under Mises＇ yield condition has been derived and whereby a non-differentiable convex optimization m...By means of Lagrange duality of Hill＇s maximum plastic work principle theory of the convex program, a dual problem under Mises＇ yield condition has been derived and whereby a non-differentiable convex optimization model for the limit analysis is developed. With this model, it is not necessary to linearize the yield condition and its discrete form becomes a minimization problem of the sum of Euclidean norms subject to linear constraints. Aimed at resolving the non-differentiability of Euclidean norms, a smoothing algorithm for the limit analysis of perfect-plastic continuum media is proposed. Its efficiency is demonstrated by computing the limit load factor and the collapse state for some plane stress and plain strain problems.展开更多
In this paper, we consider the three dimensional compressible viscous magnetohydrodynamic equations（MHD） with the external potential force. We first derive the corresponding non-constant stationary solutions. Next, ...In this paper, we consider the three dimensional compressible viscous magnetohydrodynamic equations（MHD） with the external potential force. We first derive the corresponding non-constant stationary solutions. Next, we show global wellposedness of the initial value problem for the three dimensional compressible viscous magnetohydrodynamic equations, provided that the initial data is close to the stationary solution. Finally, based on the elaborate energy estimates for the nonlinear system and L^p-L^q decay estimates of the linearized equation, we show the optimal convergence rates of the solution in L^q-norm with 2≤q≤6 and its first derivative in L^2-norm when the initial perturbation is bounded in L^p-norm with 1≤p〈6/5.展开更多
This paper discusses the two-block large-scale nonconvex optimization problem with general linear constraints.Based on the ideas of splitting and sequential quadratic optimization(SQO),a new feasible descent method fo...This paper discusses the two-block large-scale nonconvex optimization problem with general linear constraints.Based on the ideas of splitting and sequential quadratic optimization(SQO),a new feasible descent method for the discussed problem is proposed.First,we consider the problem of quadratic optimal(QO)approximation associated with the current feasible iteration point,and we split the QO into two small-scale QOs which can be solved in parallel.Second,a feasible descent direction for the problem is obtained and a new SQO-type method is proposed,namely,splitting feasible SQO(SF-SQO)method.Moreover,under suitable conditions,we analyse the global convergence,strong convergence and rate of superlinear convergence of the SF-SQO method.Finally,preliminary numerical experiments regarding the economic dispatch of a power system are carried out,and these show that the SF-SQO method is promising.展开更多
The concept of optimal Delaunay triangulation (ODT) and the corresponding error-based quality metric are first introduced. Then one kind of mesh smoothing algorithm for tetrahedral mesh based on the concept of ODT is ...The concept of optimal Delaunay triangulation (ODT) and the corresponding error-based quality metric are first introduced. Then one kind of mesh smoothing algorithm for tetrahedral mesh based on the concept of ODT is examined. With regard to its problem of possible producing illegal elements, this paper proposes a modified smoothing scheme with a constrained optimization model for tetrahedral mesh quality improvement. The constrained optimization model is converted to an unconstrained one and then solved by integrating chaos search and BFGS (Broyden-Fletcher-Goldfarb-Shanno) algorithm efficiently. Quality improvement for tetrahedral mesh is finally achieved by alternately applying the presented smoothing scheme and re-triangulation. Some testing examples are given to demonstrate the effectiveness of the proposed approach.展开更多
A smooth bidirectional evolutionary structural optimization(SBESO),as a bidirectional version of SESO is proposed to solve the topological optimization of vibrating continuum structures for natural frequencies and dyn...A smooth bidirectional evolutionary structural optimization(SBESO),as a bidirectional version of SESO is proposed to solve the topological optimization of vibrating continuum structures for natural frequencies and dynamic compliance under the transient load.A weighted function is introduced to regulate the mass and stiffness matrix of an element,which has the inefficient element gradually removed from the design domain as if it were undergoing damage.Aiming at maximizing the natural frequency of a structure,the frequency optimization formulation is proposed using the SBESO technique.The effects of various weight functions including constant,linear and sine functions on structural optimization are compared.With the equivalent static load(ESL)method,the dynamic stiffness optimization of a structure is formulated by the SBESO technique.Numerical examples show that compared with the classic BESO method,the SBESO method can efficiently suppress the excessive element deletion by adjusting the element deletion rate and weight function.It is also found that the proposed SBESO technique can obtain an efficient configuration and smooth boundary and demonstrate the advantages over the classic BESO technique.展开更多
The aim of this work is to employ a modified cell-based smoothed finite element method(S-FEM)for topology optimization with the domain discretized with arbitrary polygons.In the present work,the linear polynomial basi...The aim of this work is to employ a modified cell-based smoothed finite element method(S-FEM)for topology optimization with the domain discretized with arbitrary polygons.In the present work,the linear polynomial basis function is used as the weight function instead of the constant weight function used in the standard S-FEM.This improves the accuracy and yields an optimal convergence rate.The gradients are smoothed over each smoothing domain,then used to compute the stiffness matrix.Within the proposed scheme,an optimum topology procedure is conducted over the smoothing domains.Structural materials are distributed over each smoothing domain and the filtering scheme relies on the smoothing domain.Numerical tests are carried out to pursue the performance of the proposed optimization by comparing convergence,efficiency and accuracy.展开更多
基金Supported by the National Natural Science Foundation of China (No. 61072123)
文摘This paper shows the importance of the optimal smoothing scheme in Microphone Array Post-Filtering(MAPF) under a combined Deterministic-Stochastic Hybrid Model(DSHM).We reveal that some of the well-known MAPF algorithms may cause serious speech distortion without using the optimal smoothing scheme,which is resulted from oversmoothing the raw periodogram over time.Using a minimum conditional mean square error criterion,we derive the optimal smoothing factor under the DSHM,where the Deterministic-to-Stochastic-Ratio(DSR) and the stationarity determine the value of the optimal smoothing factor.The optimal smoothing scheme is applied to the Tran-sient-Beam-to-Reference-Ratio(TBRR)-based MAPF algorithm and experimental results show its better performance in terms of both the Log-Spectral Distance(LSD) and the Perceptual Evaluation of Speech Quality(PESQ).
文摘In this paper we consider the transmission of stored video from a server to a client for medical applications such as, Telemonitoring, to optimize medical quality of service (m-QoS) and to examine how the client buffer space can be used efficiently and effectively towards reducing the rate variability of the compressed variable bit rate (VBR) video. Three basic results are presented. First, we show how to obtain the greatest possible reduction in rate variability when sending stored video to client with a given buffer size. Second, how to reduce high peak data rate of compressed VBR video when a patient is moving/walking very fast in hospital. Third, we evaluate the impact of optimal smoothing algorithm on the network parameters such as, peak-to-mean ratio, standard deviation, delay, jitter, average delay and average jitter to optimize the m-QoS. To resolve these all problems we used optimal smoothing algorithm and show its performance over a set of long MPEG-4 encoded video traces. Simulation results show that m-QoS is optimized by minimizing network metrics.
文摘In this paper, an approximate smoothing approach to the non-differentiable exact penalty function is proposed for the constrained optimization problem. A simple smoothed penalty algorithm is given, and its convergence is discussed. A practical algorithm to compute approximate optimal solution is given as well as computational experiments to demonstrate its efficiency.
基金supported by the National Natural Science Foundation of China(Grant 12472113).
文摘The traditional topology optimization method of continuum structure generally uses quadrilateral elements as the basic mesh.This approach often leads to jagged boundary issues,which are traditionally addressed through post-processing,potentially altering the mechanical properties of the optimized structure.A topology optimization method of Movable Morphable Smooth Boundary(MMSB)is proposed based on the idea of mesh adaptation to solve the problem of jagged boundaries and the influence of post-processing.Based on the ICM method,the rational fraction function is introduced as the filtering function,and a topology optimization model with the minimum weight as the objective and the displacement as the constraint is established.A triangular mesh is utilized as the base mesh in this method.The mesh is re-divided in the optimization process based on the contour line,and a smooth boundary parallel to the contour line is obtained.Numerical examples demonstrate that the MMSB method effectively resolves the jagged boundary issues,leading to enhanced structural performance.
文摘<div style="text-align:justify;"> In order to speed up the global optimization-based mesh smoothing, an enhanced steepest descent method is presented in the paper. Numerical experiment results show that the method performs better than the steepest descent method in the global smoothing. We also presented a physically-based interpretation to explain why the method works better than the steepest descent method. </div>
文摘Laser vision correction is a rapidly growing field for correcting nearsightedness, farsightedness as well as astigmatism with dominating laser-assisted in situ keratomileusis (LASIK) procedures. While the technique works well for correcting spherocylindrical aberrations, it does not fully correct high order aberrations (HOAs), in particular spherical aberration (SA), due to unexpected induction of HOAs post-surgery. Corneal epithelial remodeling was proposed as one source to account for such HOA induction process. This work proposes a dual-scale linear filtering kernel to model such a process. Several retrospective clinical data sets were used as training data sets to construct the model, with a downhill simplex algorithm to optimize the two free parameters of the kernel. The performance of the optimized kernel was testedon new clinical data sets that were not previously used for the optimization.
文摘We propose a new unified path to approximately smoothing the nonsmooth exact penalty function in this paper. Based on the new smooth penalty function, we give a penalty algorithm to solve the constrained optimization problem, and discuss the convergence of the algorithm under mild conditions.
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In this paper, a fast approach to generate time optimal and smooth trajectory has been developed and tested. Minimum time is critical for the productivity in industrial applications. Meanwhile, smooth trajectories based on cubic splines are desirable for their ability to limit vibrations and ensure the continuity of position, velocity and acceleration during the robot movement. The main feature of the approach is a satisfactory solution that can be obtained by a local modification process among each intermal between two consecutive via-points. An analytical formulation simplifies the approach to smooth trajectory and few,iterations are enough to determine the correct values. The approach can be applied in many robot manipulators which require high performance on time and smooth. The simulation and application of the approach on a palletizer robot are performed, and the experimental results provide evidence that the approach can realize the robot manipulators more efficiency and high smooth performance.
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The project supported by State Key Laboratory of Structural Analyses of Industrial Equipment
文摘A concept of the independent-continuous topological variable is proposed to establish its corresponding smooth model of structural topological optimization. The method can overcome difficulties that are encountered in conventional models and algorithms for the optimization of the structural topology. Its application to truss topological optimization with stress and displacement constraints is satisfactory, with convergence faster than that of sectional optimizations.
基金supported by National Hi-tech Research and Development Program of China(863 Program,No.2001AA501200,2003AA501200).
文摘In parallel hybrid electrical vehicle(PHEV)equipped with automatic mechanical transmission(AMT),the driving smoothness and the clutch abrasion are the primary considerations for powertrain control during gearshift and clutch operation.To improve these performance indexes of PHEV,a coordinated control system is proposed through the analyzing of HEV powertrain dynamic characteristics.Using the method of minimum principle,the input torque of transmission is optimized to improve the driving smoothness of vehicle.Using the methods of fuzzy logic and fuzzy-PID,the engaging speed of clutch and the throttle opening of engine are manipulated to ensure the smoothness of clutch engagement and reduce the abrasion of clutch friction plates.The motor provides the difference between the required input torque of transmission and the torque transmitted through clutch plates.Results of simulation and experiments show that the proposed control strategy performs better than the contrastive control system,the smoothness of driving and the abrasion of clutch can be improved simultaneously.
文摘This paper addresses the high dimension sample problem in discriminate analysis under nonparametric and supervised assumptions. Since there is a kind of equivalence between the probabilistic dependence measure and the Bayes classification error probability, we propose to use an iterative algorithm to optimize the dimension reduction for classification with a probabilistic approach to achieve the Bayes classifier. The estimated probabilities of different errors encountered along the different phases of the system are realized by the Kernel estimate which is adjusted in a means of the smoothing parameter. Experiment results suggest that the proposed approach performs well.
基金Project supported by the National Natural Science Foundation of China (Nos.10572031, 10332010)
文摘By means of Lagrange duality of Hill＇s maximum plastic work principle theory of the convex program, a dual problem under Mises＇ yield condition has been derived and whereby a non-differentiable convex optimization model for the limit analysis is developed. With this model, it is not necessary to linearize the yield condition and its discrete form becomes a minimization problem of the sum of Euclidean norms subject to linear constraints. Aimed at resolving the non-differentiability of Euclidean norms, a smoothing algorithm for the limit analysis of perfect-plastic continuum media is proposed. Its efficiency is demonstrated by computing the limit load factor and the collapse state for some plane stress and plain strain problems.
基金Supported by the National Natural Science Foundation of China(11671134)
文摘In this paper, we consider the three dimensional compressible viscous magnetohydrodynamic equations（MHD） with the external potential force. We first derive the corresponding non-constant stationary solutions. Next, we show global wellposedness of the initial value problem for the three dimensional compressible viscous magnetohydrodynamic equations, provided that the initial data is close to the stationary solution. Finally, based on the elaborate energy estimates for the nonlinear system and L^p-L^q decay estimates of the linearized equation, we show the optimal convergence rates of the solution in L^q-norm with 2≤q≤6 and its first derivative in L^2-norm when the initial perturbation is bounded in L^p-norm with 1≤p〈6/5.
基金supported by the National Natural Science Foundation of China(12171106)the Natural Science Foundation of Guangxi Province(2020GXNSFDA238017 and 2018GXNSFFA281007)the Shanghai Sailing Program(21YF1430300)。
文摘This paper discusses the two-block large-scale nonconvex optimization problem with general linear constraints.Based on the ideas of splitting and sequential quadratic optimization(SQO),a new feasible descent method for the discussed problem is proposed.First,we consider the problem of quadratic optimal(QO)approximation associated with the current feasible iteration point,and we split the QO into two small-scale QOs which can be solved in parallel.Second,a feasible descent direction for the problem is obtained and a new SQO-type method is proposed,namely,splitting feasible SQO(SF-SQO)method.Moreover,under suitable conditions,we analyse the global convergence,strong convergence and rate of superlinear convergence of the SF-SQO method.Finally,preliminary numerical experiments regarding the economic dispatch of a power system are carried out,and these show that the SF-SQO method is promising.
文摘The concept of optimal Delaunay triangulation (ODT) and the corresponding error-based quality metric are first introduced. Then one kind of mesh smoothing algorithm for tetrahedral mesh based on the concept of ODT is examined. With regard to its problem of possible producing illegal elements, this paper proposes a modified smoothing scheme with a constrained optimization model for tetrahedral mesh quality improvement. The constrained optimization model is converted to an unconstrained one and then solved by integrating chaos search and BFGS (Broyden-Fletcher-Goldfarb-Shanno) algorithm efficiently. Quality improvement for tetrahedral mesh is finally achieved by alternately applying the presented smoothing scheme and re-triangulation. Some testing examples are given to demonstrate the effectiveness of the proposed approach.
基金supported by the National Natural Science Foundation of China (Grant No.51505096)the Natural Science Foundation of Heilongjiang Province (Grant No.LH2020E064).
文摘A smooth bidirectional evolutionary structural optimization(SBESO),as a bidirectional version of SESO is proposed to solve the topological optimization of vibrating continuum structures for natural frequencies and dynamic compliance under the transient load.A weighted function is introduced to regulate the mass and stiffness matrix of an element,which has the inefficient element gradually removed from the design domain as if it were undergoing damage.Aiming at maximizing the natural frequency of a structure,the frequency optimization formulation is proposed using the SBESO technique.The effects of various weight functions including constant,linear and sine functions on structural optimization are compared.With the equivalent static load(ESL)method,the dynamic stiffness optimization of a structure is formulated by the SBESO technique.Numerical examples show that compared with the classic BESO method,the SBESO method can efficiently suppress the excessive element deletion by adjusting the element deletion rate and weight function.It is also found that the proposed SBESO technique can obtain an efficient configuration and smooth boundary and demonstrate the advantages over the classic BESO technique.
基金support by Basic Science Research Program through the National Research Foundation(NRF)funded by Korea Ministry of Education(No.2016R1A6A1A0312812).
文摘The aim of this work is to employ a modified cell-based smoothed finite element method(S-FEM)for topology optimization with the domain discretized with arbitrary polygons.In the present work,the linear polynomial basis function is used as the weight function instead of the constant weight function used in the standard S-FEM.This improves the accuracy and yields an optimal convergence rate.The gradients are smoothed over each smoothing domain,then used to compute the stiffness matrix.Within the proposed scheme,an optimum topology procedure is conducted over the smoothing domains.Structural materials are distributed over each smoothing domain and the filtering scheme relies on the smoothing domain.Numerical tests are carried out to pursue the performance of the proposed optimization by comparing convergence,efficiency and accuracy.
