In the context of global mean square error concerning the number of random variables in the representation,the Karhunen–Loève(KL)expansion is the optimal series expansion method for random field discretization.T...In the context of global mean square error concerning the number of random variables in the representation,the Karhunen–Loève(KL)expansion is the optimal series expansion method for random field discretization.The computational efficiency and accuracy of the KL expansion are contingent upon the accurate resolution of the Fredholm integral eigenvalue problem(IEVP).The paper proposes an interpolation method based on different interpolation basis functions such as moving least squares(MLS),least squares(LS),and finite element method(FEM)to solve the IEVP.Compared with the Galerkin method based on finite element or Legendre polynomials,the main advantage of the interpolation method is that,in the calculation of eigenvalues and eigenfunctions in one-dimensional random fields,the integral matrix containing covariance function only requires a single integral,which is less than a two-folded integral by the Galerkin method.The effectiveness and computational efficiency of the proposed interpolation method are verified through various one-dimensional examples.Furthermore,based on theKL expansion and polynomial chaos expansion,the stochastic analysis of two-dimensional regular and irregular domains is conducted,and the basis function of the extended finite element method(XFEM)is introduced as the interpolation basis function in two-dimensional irregular domains to solve the IEVP.展开更多
Sensors for fire alarms require a high level of predictive variables to ensure accurate detection, injury prevention, and loss prevention. Bayesian networks can aid in enhancing early fire detection capabilities and r...Sensors for fire alarms require a high level of predictive variables to ensure accurate detection, injury prevention, and loss prevention. Bayesian networks can aid in enhancing early fire detection capabilities and reducing the frequency of erroneous fire alerts, thereby enhancing the effectiveness of numerous safety monitoring systems. This research explores the development of optimized probabilistic graphic models for the discretization thresholds of alarm system predictor variables. The study presents a statistical model framework that increases the efficacy of fire detection by predicting the discretization thresholds of alarm system predictor variable fluctuations used to detect the onset of fire. The work applies the Bayesian networks and probabilistic visual models to reveal the specific characteristics required to cope with fire detection strategies and patterns. The adopted methodology utilizes a combination of prior knowledge and statistical data to draw conclusions from observations. Utilizing domain knowledge to compute conditional dependencies between network variables enabled predictions to be made through the application of specialized analytical and simulation techniques.展开更多
A discrete Boltzmann model(DBM) with symmetric velocity discretization is constructed for compressible systems with an adjustable specific heat ratio in the external force field. The proposed two-dimensional(2D) nine-...A discrete Boltzmann model(DBM) with symmetric velocity discretization is constructed for compressible systems with an adjustable specific heat ratio in the external force field. The proposed two-dimensional(2D) nine-velocity scheme has better spatial symmetry and numerical accuracy than the discretized velocity model in literature [Acta Aerodyn. Sin.40 98108(2022)] and owns higher computational efficiency than the one in literature [Phys. Rev. E 99 012142(2019)].In addition, the matrix inversion method is adopted to calculate the discrete equilibrium distribution function and force term, both of which satisfy nine independent kinetic moment relations. Moreover, the DBM could be used to study a few thermodynamic nonequilibrium effects beyond the Euler equations that are recovered from the kinetic model in the hydrodynamic limit via the Chapman–Enskog expansion. Finally, the present method is verified through typical numerical simulations, including the free-falling process, Sod’s shock tube, sound wave, compressible Rayleigh–Taylor instability,and translational motion of a 2D fluid system.展开更多
This paper presents a procedure for assessing the reinforcement force of geosynthetics required for maintaining dynamic stability of a steep soil slope. Such a procedure is achieved with the use of the discretization ...This paper presents a procedure for assessing the reinforcement force of geosynthetics required for maintaining dynamic stability of a steep soil slope. Such a procedure is achieved with the use of the discretization technique and kinematic analysis of plasticity theory, i.e. discretization-based kinematic analysis. The discretization technique allows discretization of the analyzed slope into various components and generation of a kinematically admissible failure mechanism based on an associated flow rule.Accordingly, variations in soil properties including soil cohesion, internal friction angle and unit weight are accounted for with ease, while the conventional kinematic analysis fails to consider the changes in soil properties. The spatialetemporal effects of dynamic accelerations represented by primary and shear seismic waves are considered using the pseudo-dynamic approach. In the presence of geosynthetic reinforcement, tensile failure is discussed providing that the geosynthetics are installed with sufficient length. Equating the total rates of work done by external forces to the internal rates of work yields the upper bound solution of required reinforcement force, below which slopes fail. The reinforcement force is sought by optimizing the objective function with regard to independent variables, and presented in a normalized form. Pseudo-static analysis is a special case and hence readily transformed from pseudodynamic analysis. Comparisons of the pseudo-static/dynamic solutions calculated in this study are highlighted. Although the pseudo-static approach yields a conservative solution, its ability to give a reasonable result is substantiated for steep slopes. In order to provide a more meaningful solution to a stability analysis, the pseudo-dynamic approach is recommended due to considerations of spatial etemporal effect of earthquake input.展开更多
The selection of a suitable discretization method(DM) to discretize spatially continuous variables(SCVs)is critical in ML-based natural hazard susceptibility assessment. However, few studies start to consider the infl...The selection of a suitable discretization method(DM) to discretize spatially continuous variables(SCVs)is critical in ML-based natural hazard susceptibility assessment. However, few studies start to consider the influence due to the selected DMs and how to efficiently select a suitable DM for each SCV. These issues were well addressed in this study. The information loss rate(ILR), an index based on the information entropy, seems can be used to select optimal DM for each SCV. However, the ILR fails to show the actual influence of discretization because such index only considers the total amount of information of the discretized variables departing from the original SCV. Facing this issue, we propose an index, information change rate(ICR), that focuses on the changed amount of information due to the discretization based on each cell, enabling the identification of the optimal DM. We develop a case study with Random Forest(training/testing ratio of 7 : 3) to assess flood susceptibility in Wanan County, China.The area under the curve-based and susceptibility maps-based approaches were presented to compare the ILR and ICR. The results show the ICR-based optimal DMs are more rational than the ILR-based ones in both cases. Moreover, we observed the ILR values are unnaturally small(<1%), whereas the ICR values are obviously more in line with general recognition(usually 10%–30%). The above results all demonstrate the superiority of the ICR. We consider this study fills up the existing research gaps, improving the MLbased natural hazard susceptibility assessments.展开更多
AIM: To evaluate the use of short-duration transient visual evoked potentials(VEP) and color reflectivity discretization analysis(CORDA) in glaucomatous eyes,eyes suspected of having glaucoma,and healthy eyes.METHODS:...AIM: To evaluate the use of short-duration transient visual evoked potentials(VEP) and color reflectivity discretization analysis(CORDA) in glaucomatous eyes,eyes suspected of having glaucoma,and healthy eyes.METHODS: The study included 136 eyes from 136 subjects: 49 eyes with glaucoma,45 glaucoma suspect eyes,and 42 healthy eyes.Subjects underwent Humphrey visual field(VF) testing,VEP testing,as well as peripapillary retinal nerve fiber layer optical coherence tomography imaging studies with post-acquisition CORDA applied.Statistical analysis was performed using means and ranges,ANOVA,post-hoc comparisons using Turkey's adjustment,Fisher's Exact test,area under the curve,and Spearman correlation coefficients.RESULTS: Parameters from VEP and CORDA correlated significantly with VF mean deviation(MD)(P<0.05).In distinguishing glaucomatous eyes from controls,VEP demonstrated area under the curve(AUC) values of 0.64-0.75 for amplitude and 0.67-0.81 for latency.The CORDA HR1 parameter was highly discriminative for glaucomatous eyes vs controls(AUC=0.94).CONCLUSION: Significant correlations are found between MD and parameters of short-duration transient VEP and CORDA,diagnostic modalities which warrant further consideration in identifying glaucoma characteristics.展开更多
In this paper we discuss the smoothness of inertial manifolds under time discretization. By the fibre contract principle, see Section 4, we obtain a sufficient condition for Ck(k≥1) inertial manifolds. In view of the...In this paper we discuss the smoothness of inertial manifolds under time discretization. By the fibre contract principle, see Section 4, we obtain a sufficient condition for Ck(k≥1) inertial manifolds. In view of the numerical computation for dissipative nonlinear evolution equations, it is more important to consider the discretized case than continuous case[3].展开更多
The authors announce a newly proved theorem of theirs. This theorem is of principal significance to numerical computation of operator equations of the first kind.
In this paper, we consider the upwind difference scheme for singular perturbation problem (1.1). On a special discretization mesh, it is proved that the solution of the upwind difference scheme is first order converge...In this paper, we consider the upwind difference scheme for singular perturbation problem (1.1). On a special discretization mesh, it is proved that the solution of the upwind difference scheme is first order convergent, uniformly in the small parameter ε, to the solution of problem (1.1). Numerical results are finally provided.展开更多
In order to reduce the partial derivative errors in Preisach hysteresis model caused by inaccurate experimental data,the concept and correlative method of discretization of Preisach hysteresis model are proposed,the e...In order to reduce the partial derivative errors in Preisach hysteresis model caused by inaccurate experimental data,the concept and correlative method of discretization of Preisach hysteresis model are proposed,the essential of which is to centralize the distribution density of Preisach hysteresis model in local region as an integral,which is defined as the weight of a certain point in that region.For the input composed of an ascending segment and a descending segment,a method to determine the initial weights together with an additional method to determine present weights is given according to the number of input ascending segments.If the number of input ascending segments increases,the weights of the corresponding points in updating rectangle are updated by adding the initial weights of corresponding points.A prominent advantage of discrete Preisach hysteresis model is its memory efficiency.Another advantage of discrete Preisach hysteresis model is that there is no function in the model,and thus,it can be expediently operated using a computer.By generalizing the above updating rectangle method to the continuous Preisach hysteresis model,identification method of distribution density can be given as well.展开更多
The insulated gate bipolar transistor(IGBT)module is one of the most age-affected components in the switch power supply, and its reliability prediction is conducive to timely troubleshooting and reduction in safety ri...The insulated gate bipolar transistor(IGBT)module is one of the most age-affected components in the switch power supply, and its reliability prediction is conducive to timely troubleshooting and reduction in safety risks and unnecessary costs. The pulsed current pattern of the accelerator power supply is different from other converter applications;therefore, this study proposed a lifetime estimation method for IGBT modules in pulsed power supplies for accelerator magnets. The proposed methodology was based on junction temperature calculations using square-wave loss discretization and thermal modeling.Comparison results showed that the junction temperature error between the simulation and IR measurements was less than 3%. An AC power cycling test under real pulsed power supply applications was performed via offline wearout monitoring of the tested power IGBT module. After combining the IGBT4 PC curve and fitting the test results,a simple corrected lifetime model was developed to quantitatively evaluate the lifetime of the IGBT module,which can be employed for the accelerator pulsed power supply in engineering. This method can be applied to other IGBT modules and pulsed power supplies.展开更多
In this paper,we present a nonrecursive residual Monte Carlo method for estimating discretization errors associated with the S_(N) transport solution to radiation transport problems.Although this technique is general,...In this paper,we present a nonrecursive residual Monte Carlo method for estimating discretization errors associated with the S_(N) transport solution to radiation transport problems.Although this technique is general,we applied it to the mono-energetic 1-D S_(N) equation with linear-discontinuous finite element method spatial discretization as a demonstration of the theory for the purpose of this study.Two angular flux representations:conforming and simplified representations were considered in this analysis,and the results were compared.It is shown that the simplified representation dramatically reduces the memory footprint and computational complexity of residual source generation and sampling while accurately capturing the error associated with certain types of responses.展开更多
In this paper, a new approach using linear combination property of intervals and discretization is proposed to solve a class of nonlinear optimal control problems, containing a nonlinear system and linear functional, ...In this paper, a new approach using linear combination property of intervals and discretization is proposed to solve a class of nonlinear optimal control problems, containing a nonlinear system and linear functional, in three phases. In the first phase, using linear combination property of intervals, changes nonlinear system to an equivalent linear system, in the second phase, using discretization method, the attained problem is converted to a linear programming problem, and in the third phase, the latter problem will be solved by linear programming methods. In addition, efficiency of our approach is confirmed by some numerical examples.展开更多
In this paper we prove a theorem about existence of best appraximantion in a class of spaces involving Besov spaces,via a discretization technique.It is a consequence of this theorem that rational functions and expone...In this paper we prove a theorem about existence of best appraximantion in a class of spaces involving Besov spaces,via a discretization technique.It is a consequence of this theorem that rational functions and exponencial sums are proximinal subsets of B (φ). It is also proved the proximinality of R[a,b] in B(φ) for arbitrary p,q and α.展开更多
In this article, we report the derivation of high accuracy finite difference method based on arithmetic average discretization for the solution of Un=F(x,u,u′)+∫K(x,s)ds , 0 x s < 1 subject to natural boundary co...In this article, we report the derivation of high accuracy finite difference method based on arithmetic average discretization for the solution of Un=F(x,u,u′)+∫K(x,s)ds , 0 x s < 1 subject to natural boundary conditions on a non-uniform mesh. The proposed variable mesh approximation is directly applicable to the integro-differential equation with singular coefficients. We need not require any special discretization to obtain the solution near the singular point. The convergence analysis of a difference scheme for the diffusion convection equation is briefly discussed. The presented variable mesh strategy is applicable when the internal grid points of the solution space are both even and odd in number as compared to the method discussed by authors in their previous work in which the internal grid points are strictly odd in number. The advantage of using this new variable mesh strategy is highlighted computationally.展开更多
We construct optimal k-step, 5- to 10-stage, explicit, strong-stability-preserving Hermite-Birkhoff (SSP HB) methods of order 12 with nonnegative coefficients by combining linear k-step methods of order 9 with 5- to 1...We construct optimal k-step, 5- to 10-stage, explicit, strong-stability-preserving Hermite-Birkhoff (SSP HB) methods of order 12 with nonnegative coefficients by combining linear k-step methods of order 9 with 5- to 10-stage Runge-Kutta (RK) methods of order 4. Since these methods maintain the monotonicity property, they are well suited for solving hyperbolic PDEs by the method of lines after a spatial discretization. It is seen that the 8-step 7-stage HB methods have largest effective SSP coefficient among the HB methods of order 12 on hand. On Burgers’ equations, some of the new HB methods have larger maximum effective CFL numbers than Huang’s 7-step hybrid method of order 7, thus allowing larger step size.展开更多
This paper is concerned with the discretization of the fractional-order differentiator and integrator, which is the foundation of the digital realization of fractional order controller. Firstly, the parameterized Al-A...This paper is concerned with the discretization of the fractional-order differentiator and integrator, which is the foundation of the digital realization of fractional order controller. Firstly, the parameterized Al-Alaoui transform is presented as a general generating function with one variable parameter, which can be adjusted to obtain the commonly used generating functions (e.g. Euler operator, Tustin operator and Al-Alaoui operator). However, the following simulation results show that the optimal variable parameters are different for different fractional orders. Then the weighted square integral index about the magtitude and phase is defined as the objective functions to achieve the optimal variable parameter for different fractional orders. Finally, the simulation results demonstrate that there are great differences on the optimal variable parameter for differential and integral operators with different fractional orders, which should be attracting more attentions in the design of digital fractional order controller.展开更多
We’ll consider the model of two-phase compressible miscible displacement in porous media which includes molecular diffusion and dispersion in one dimensional space. Time-discretization procedure is established and an...We’ll consider the model of two-phase compressible miscible displacement in porous media which includes molecular diffusion and dispersion in one dimensional space. Time-discretization procedure is established and analysed. The optimal error estimate in L2 norm is proved by introducing a new interpolation operator R.展开更多
Numerical diffusion and oscillatory behavior characteristics are averted applying numerical solutions of advection-diffusion equation are themselves immensely sophisticated. In this paper, two numerical methods have b...Numerical diffusion and oscillatory behavior characteristics are averted applying numerical solutions of advection-diffusion equation are themselves immensely sophisticated. In this paper, two numerical methods have been used to solve the advection diffusion equation. We use an explicit finite difference scheme for the advection diffusion equation and semi-discretization on the spatial variable for advection-diffusion equation yields a system of ordinary differential equations solved by Euler’s method. Numerical assessment has been executed with specified initial and boundary conditions, for which the exact solution is known. We compare the solutions of the advection diffusion equation as well as error analysis for both schemes.展开更多
This paper considers pricing European options under the well-known of SVJ model of Bates and related computational methods. According to the no-arbitrage principle, we first derive a partial differential equation that...This paper considers pricing European options under the well-known of SVJ model of Bates and related computational methods. According to the no-arbitrage principle, we first derive a partial differential equation that the value of any European contingent claim should satisfy, where the asset price obeys the SVJ model. This equation is numerically solved by using the implicit- explicit backward difference method and time semi-discretization. In order to explain the validity of our method, the stability of time semi-discretization scheme is also proved. Finally, we use a simulation example to illustrate the efficiency of the method.展开更多
基金The authors gratefully acknowledge the support provided by the Postgraduate Research&Practice Program of Jiangsu Province(Grant No.KYCX18_0526)the Fundamental Research Funds for the Central Universities(Grant No.2018B682X14)Guangdong Basic and Applied Basic Research Foundation(No.2021A1515110807).
文摘In the context of global mean square error concerning the number of random variables in the representation,the Karhunen–Loève(KL)expansion is the optimal series expansion method for random field discretization.The computational efficiency and accuracy of the KL expansion are contingent upon the accurate resolution of the Fredholm integral eigenvalue problem(IEVP).The paper proposes an interpolation method based on different interpolation basis functions such as moving least squares(MLS),least squares(LS),and finite element method(FEM)to solve the IEVP.Compared with the Galerkin method based on finite element or Legendre polynomials,the main advantage of the interpolation method is that,in the calculation of eigenvalues and eigenfunctions in one-dimensional random fields,the integral matrix containing covariance function only requires a single integral,which is less than a two-folded integral by the Galerkin method.The effectiveness and computational efficiency of the proposed interpolation method are verified through various one-dimensional examples.Furthermore,based on theKL expansion and polynomial chaos expansion,the stochastic analysis of two-dimensional regular and irregular domains is conducted,and the basis function of the extended finite element method(XFEM)is introduced as the interpolation basis function in two-dimensional irregular domains to solve the IEVP.
文摘Sensors for fire alarms require a high level of predictive variables to ensure accurate detection, injury prevention, and loss prevention. Bayesian networks can aid in enhancing early fire detection capabilities and reducing the frequency of erroneous fire alerts, thereby enhancing the effectiveness of numerous safety monitoring systems. This research explores the development of optimized probabilistic graphic models for the discretization thresholds of alarm system predictor variables. The study presents a statistical model framework that increases the efficacy of fire detection by predicting the discretization thresholds of alarm system predictor variable fluctuations used to detect the onset of fire. The work applies the Bayesian networks and probabilistic visual models to reveal the specific characteristics required to cope with fire detection strategies and patterns. The adopted methodology utilizes a combination of prior knowledge and statistical data to draw conclusions from observations. Utilizing domain knowledge to compute conditional dependencies between network variables enabled predictions to be made through the application of specialized analytical and simulation techniques.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 51806116, U2242214, and 11875329)Guangdong Basic and Applied Basic Research Foundation (Grant No. 2022A1515012116)the Natural Science Foundation of Fujian Province, China (Grant Nos. 2021J01652 and 2021J01655)。
文摘A discrete Boltzmann model(DBM) with symmetric velocity discretization is constructed for compressible systems with an adjustable specific heat ratio in the external force field. The proposed two-dimensional(2D) nine-velocity scheme has better spatial symmetry and numerical accuracy than the discretized velocity model in literature [Acta Aerodyn. Sin.40 98108(2022)] and owns higher computational efficiency than the one in literature [Phys. Rev. E 99 012142(2019)].In addition, the matrix inversion method is adopted to calculate the discrete equilibrium distribution function and force term, both of which satisfy nine independent kinetic moment relations. Moreover, the DBM could be used to study a few thermodynamic nonequilibrium effects beyond the Euler equations that are recovered from the kinetic model in the hydrodynamic limit via the Chapman–Enskog expansion. Finally, the present method is verified through typical numerical simulations, including the free-falling process, Sod’s shock tube, sound wave, compressible Rayleigh–Taylor instability,and translational motion of a 2D fluid system.
基金financial support for the first author’s PhD program by the President’s Graduate Fellowship in Singapore
文摘This paper presents a procedure for assessing the reinforcement force of geosynthetics required for maintaining dynamic stability of a steep soil slope. Such a procedure is achieved with the use of the discretization technique and kinematic analysis of plasticity theory, i.e. discretization-based kinematic analysis. The discretization technique allows discretization of the analyzed slope into various components and generation of a kinematically admissible failure mechanism based on an associated flow rule.Accordingly, variations in soil properties including soil cohesion, internal friction angle and unit weight are accounted for with ease, while the conventional kinematic analysis fails to consider the changes in soil properties. The spatialetemporal effects of dynamic accelerations represented by primary and shear seismic waves are considered using the pseudo-dynamic approach. In the presence of geosynthetic reinforcement, tensile failure is discussed providing that the geosynthetics are installed with sufficient length. Equating the total rates of work done by external forces to the internal rates of work yields the upper bound solution of required reinforcement force, below which slopes fail. The reinforcement force is sought by optimizing the objective function with regard to independent variables, and presented in a normalized form. Pseudo-static analysis is a special case and hence readily transformed from pseudodynamic analysis. Comparisons of the pseudo-static/dynamic solutions calculated in this study are highlighted. Although the pseudo-static approach yields a conservative solution, its ability to give a reasonable result is substantiated for steep slopes. In order to provide a more meaningful solution to a stability analysis, the pseudo-dynamic approach is recommended due to considerations of spatial etemporal effect of earthquake input.
文摘The selection of a suitable discretization method(DM) to discretize spatially continuous variables(SCVs)is critical in ML-based natural hazard susceptibility assessment. However, few studies start to consider the influence due to the selected DMs and how to efficiently select a suitable DM for each SCV. These issues were well addressed in this study. The information loss rate(ILR), an index based on the information entropy, seems can be used to select optimal DM for each SCV. However, the ILR fails to show the actual influence of discretization because such index only considers the total amount of information of the discretized variables departing from the original SCV. Facing this issue, we propose an index, information change rate(ICR), that focuses on the changed amount of information due to the discretization based on each cell, enabling the identification of the optimal DM. We develop a case study with Random Forest(training/testing ratio of 7 : 3) to assess flood susceptibility in Wanan County, China.The area under the curve-based and susceptibility maps-based approaches were presented to compare the ILR and ICR. The results show the ICR-based optimal DMs are more rational than the ILR-based ones in both cases. Moreover, we observed the ILR values are unnaturally small(<1%), whereas the ICR values are obviously more in line with general recognition(usually 10%–30%). The above results all demonstrate the superiority of the ICR. We consider this study fills up the existing research gaps, improving the MLbased natural hazard susceptibility assessments.
文摘AIM: To evaluate the use of short-duration transient visual evoked potentials(VEP) and color reflectivity discretization analysis(CORDA) in glaucomatous eyes,eyes suspected of having glaucoma,and healthy eyes.METHODS: The study included 136 eyes from 136 subjects: 49 eyes with glaucoma,45 glaucoma suspect eyes,and 42 healthy eyes.Subjects underwent Humphrey visual field(VF) testing,VEP testing,as well as peripapillary retinal nerve fiber layer optical coherence tomography imaging studies with post-acquisition CORDA applied.Statistical analysis was performed using means and ranges,ANOVA,post-hoc comparisons using Turkey's adjustment,Fisher's Exact test,area under the curve,and Spearman correlation coefficients.RESULTS: Parameters from VEP and CORDA correlated significantly with VF mean deviation(MD)(P<0.05).In distinguishing glaucomatous eyes from controls,VEP demonstrated area under the curve(AUC) values of 0.64-0.75 for amplitude and 0.67-0.81 for latency.The CORDA HR1 parameter was highly discriminative for glaucomatous eyes vs controls(AUC=0.94).CONCLUSION: Significant correlations are found between MD and parameters of short-duration transient VEP and CORDA,diagnostic modalities which warrant further consideration in identifying glaucoma characteristics.
文摘In this paper we discuss the smoothness of inertial manifolds under time discretization. By the fibre contract principle, see Section 4, we obtain a sufficient condition for Ck(k≥1) inertial manifolds. In view of the numerical computation for dissipative nonlinear evolution equations, it is more important to consider the discretized case than continuous case[3].
文摘The authors announce a newly proved theorem of theirs. This theorem is of principal significance to numerical computation of operator equations of the first kind.
文摘In this paper, we consider the upwind difference scheme for singular perturbation problem (1.1). On a special discretization mesh, it is proved that the solution of the upwind difference scheme is first order convergent, uniformly in the small parameter ε, to the solution of problem (1.1). Numerical results are finally provided.
基金Project(2013CB733000)supported by the National Basic Research Program of China
文摘In order to reduce the partial derivative errors in Preisach hysteresis model caused by inaccurate experimental data,the concept and correlative method of discretization of Preisach hysteresis model are proposed,the essential of which is to centralize the distribution density of Preisach hysteresis model in local region as an integral,which is defined as the weight of a certain point in that region.For the input composed of an ascending segment and a descending segment,a method to determine the initial weights together with an additional method to determine present weights is given according to the number of input ascending segments.If the number of input ascending segments increases,the weights of the corresponding points in updating rectangle are updated by adding the initial weights of corresponding points.A prominent advantage of discrete Preisach hysteresis model is its memory efficiency.Another advantage of discrete Preisach hysteresis model is that there is no function in the model,and thus,it can be expediently operated using a computer.By generalizing the above updating rectangle method to the continuous Preisach hysteresis model,identification method of distribution density can be given as well.
基金supported by the National Key Research and Development Program of China (No. 2019YFA0405402)。
文摘The insulated gate bipolar transistor(IGBT)module is one of the most age-affected components in the switch power supply, and its reliability prediction is conducive to timely troubleshooting and reduction in safety risks and unnecessary costs. The pulsed current pattern of the accelerator power supply is different from other converter applications;therefore, this study proposed a lifetime estimation method for IGBT modules in pulsed power supplies for accelerator magnets. The proposed methodology was based on junction temperature calculations using square-wave loss discretization and thermal modeling.Comparison results showed that the junction temperature error between the simulation and IR measurements was less than 3%. An AC power cycling test under real pulsed power supply applications was performed via offline wearout monitoring of the tested power IGBT module. After combining the IGBT4 PC curve and fitting the test results,a simple corrected lifetime model was developed to quantitatively evaluate the lifetime of the IGBT module,which can be employed for the accelerator pulsed power supply in engineering. This method can be applied to other IGBT modules and pulsed power supplies.
文摘In this paper,we present a nonrecursive residual Monte Carlo method for estimating discretization errors associated with the S_(N) transport solution to radiation transport problems.Although this technique is general,we applied it to the mono-energetic 1-D S_(N) equation with linear-discontinuous finite element method spatial discretization as a demonstration of the theory for the purpose of this study.Two angular flux representations:conforming and simplified representations were considered in this analysis,and the results were compared.It is shown that the simplified representation dramatically reduces the memory footprint and computational complexity of residual source generation and sampling while accurately capturing the error associated with certain types of responses.
文摘In this paper, a new approach using linear combination property of intervals and discretization is proposed to solve a class of nonlinear optimal control problems, containing a nonlinear system and linear functional, in three phases. In the first phase, using linear combination property of intervals, changes nonlinear system to an equivalent linear system, in the second phase, using discretization method, the attained problem is converted to a linear programming problem, and in the third phase, the latter problem will be solved by linear programming methods. In addition, efficiency of our approach is confirmed by some numerical examples.
文摘In this paper we prove a theorem about existence of best appraximantion in a class of spaces involving Besov spaces,via a discretization technique.It is a consequence of this theorem that rational functions and exponencial sums are proximinal subsets of B (φ). It is also proved the proximinality of R[a,b] in B(φ) for arbitrary p,q and α.
文摘In this article, we report the derivation of high accuracy finite difference method based on arithmetic average discretization for the solution of Un=F(x,u,u′)+∫K(x,s)ds , 0 x s < 1 subject to natural boundary conditions on a non-uniform mesh. The proposed variable mesh approximation is directly applicable to the integro-differential equation with singular coefficients. We need not require any special discretization to obtain the solution near the singular point. The convergence analysis of a difference scheme for the diffusion convection equation is briefly discussed. The presented variable mesh strategy is applicable when the internal grid points of the solution space are both even and odd in number as compared to the method discussed by authors in their previous work in which the internal grid points are strictly odd in number. The advantage of using this new variable mesh strategy is highlighted computationally.
文摘We construct optimal k-step, 5- to 10-stage, explicit, strong-stability-preserving Hermite-Birkhoff (SSP HB) methods of order 12 with nonnegative coefficients by combining linear k-step methods of order 9 with 5- to 10-stage Runge-Kutta (RK) methods of order 4. Since these methods maintain the monotonicity property, they are well suited for solving hyperbolic PDEs by the method of lines after a spatial discretization. It is seen that the 8-step 7-stage HB methods have largest effective SSP coefficient among the HB methods of order 12 on hand. On Burgers’ equations, some of the new HB methods have larger maximum effective CFL numbers than Huang’s 7-step hybrid method of order 7, thus allowing larger step size.
文摘This paper is concerned with the discretization of the fractional-order differentiator and integrator, which is the foundation of the digital realization of fractional order controller. Firstly, the parameterized Al-Alaoui transform is presented as a general generating function with one variable parameter, which can be adjusted to obtain the commonly used generating functions (e.g. Euler operator, Tustin operator and Al-Alaoui operator). However, the following simulation results show that the optimal variable parameters are different for different fractional orders. Then the weighted square integral index about the magtitude and phase is defined as the objective functions to achieve the optimal variable parameter for different fractional orders. Finally, the simulation results demonstrate that there are great differences on the optimal variable parameter for differential and integral operators with different fractional orders, which should be attracting more attentions in the design of digital fractional order controller.
基金This work was supported by National Science Foundation and China State Major Key Project for Basic Research
文摘We’ll consider the model of two-phase compressible miscible displacement in porous media which includes molecular diffusion and dispersion in one dimensional space. Time-discretization procedure is established and analysed. The optimal error estimate in L2 norm is proved by introducing a new interpolation operator R.
文摘Numerical diffusion and oscillatory behavior characteristics are averted applying numerical solutions of advection-diffusion equation are themselves immensely sophisticated. In this paper, two numerical methods have been used to solve the advection diffusion equation. We use an explicit finite difference scheme for the advection diffusion equation and semi-discretization on the spatial variable for advection-diffusion equation yields a system of ordinary differential equations solved by Euler’s method. Numerical assessment has been executed with specified initial and boundary conditions, for which the exact solution is known. We compare the solutions of the advection diffusion equation as well as error analysis for both schemes.
文摘This paper considers pricing European options under the well-known of SVJ model of Bates and related computational methods. According to the no-arbitrage principle, we first derive a partial differential equation that the value of any European contingent claim should satisfy, where the asset price obeys the SVJ model. This equation is numerically solved by using the implicit- explicit backward difference method and time semi-discretization. In order to explain the validity of our method, the stability of time semi-discretization scheme is also proved. Finally, we use a simulation example to illustrate the efficiency of the method.
