We consider the persistence of affine periodic solutions for perturbed affine periodic systems.Such(Q,T)-affine periodic solutions have the form x(t+T)=Qx(t)for all t∈R,where T>0 is fixed and Q is a nonsingular ma...We consider the persistence of affine periodic solutions for perturbed affine periodic systems.Such(Q,T)-affine periodic solutions have the form x(t+T)=Qx(t)for all t∈R,where T>0 is fixed and Q is a nonsingular matrix.These are a kind of spatiotemporal symmetric solutions,e.g.spiral waves.We give the averaging method for the existence of affine periodic solutions in two situations:one in which the initial values of the affine periodic solutions of the unperturbed system form a manifold,and another that does not rely on the structure of the initial values of the unperturbed system's affine periodic solutions.The transversal condition is determined using the Brouwer degree.We also present a higher order averaging method for general degenerate systems by means of the Brouwer degree and a Lyapunov-Schmidt reduction.展开更多
The energy preserving average vector field （AVF） method is applied to the coupled Schr6dinger-KdV equations. Two energy preserving schemes are constructed by using Fourier pseudospectral method in space direction di...The energy preserving average vector field （AVF） method is applied to the coupled Schr6dinger-KdV equations. Two energy preserving schemes are constructed by using Fourier pseudospectral method in space direction discretization. In order to accelerate our simulation, the split-step technique is used. The numerical experiments show that the non-splitting scheme and splitting scheme are both effective, and have excellent long time numerical behavior. The comparisons show that the splitting scheme is faster than the non-splitting scheme, but it is not as good as the non-splitting scheme in preserving the invariants.展开更多
The paper studies the parametric stochastic roll motion in the random waves.The differential equation of the ship parametric roll under random wave is established with considering the nonlinear damping and ship speed....The paper studies the parametric stochastic roll motion in the random waves.The differential equation of the ship parametric roll under random wave is established with considering the nonlinear damping and ship speed.Random sea surface is treated as a narrow-band stochastic process,and the stochastic parametric excitation is studied based on the effective wave theory.The nonlinear restored arm function obtained from the numerical simulation is expressed as the approximate analytic function.By using the stochastic averaging method,the differential equation of motion is transformed into Ito’s stochastic differential equation.The steady-state probability density function of roll motion is obtained,and the results are validated with the numerical simulation and model test.展开更多
This paper puts forward a complex inner product averaging method for calculating normal form of ODE. Compared with conventional averaging method, the theoretic analytical process has such simple forms as to realize co...This paper puts forward a complex inner product averaging method for calculating normal form of ODE. Compared with conventional averaging method, the theoretic analytical process has such simple forms as to realize computer program easily. Results can be applied in both autonomous and non-autonomous systems. At last, an example is resolved to verify the method.展开更多
In recent times, lithium-ion batteries have been widely used owing to their high energy density, extended cycle lifespan, and minimal self-discharge rate. The design of high-speed rechargeable lithium-ion batteries fa...In recent times, lithium-ion batteries have been widely used owing to their high energy density, extended cycle lifespan, and minimal self-discharge rate. The design of high-speed rechargeable lithium-ion batteries faces a significant challenge owing to the need to increase average electric power during charging. This challenge results from the direct influence of the power level on the rate of chemical reactions occurring in the battery electrodes. In this study, the Taguchi optimization method was used to enhance the average electric power during the charging process of lithium-ion batteries. The Taguchi technique is a statistical strategy that facilitates the systematic and efficient evaluation of numerous experimental variables. The proposed method involved varying seven input factors, including positive electrode thickness, positive electrode material, positive electrode active material volume fraction, negative electrode active material volume fraction, separator thickness, positive current collector thickness, and negative current collector thickness. Three levels were assigned to each control factor to identify the optimal conditions and maximize the average electric power during charging. Moreover, a variance assessment analysis was conducted to validate the results obtained from the Taguchi analysis. The results revealed that the Taguchi method was an eff ective approach for optimizing the average electric power during the charging of lithium-ion batteries. This indicates that the positive electrode material, followed by the separator thickness and the negative electrode active material volume fraction, was key factors significantly infl uencing the average electric power during the charging of lithium-ion batteries response. The identification of optimal conditions resulted in the improved performance of lithium-ion batteries, extending their potential in various applications. Particularly, lithium-ion batteries with average electric power of 16 W and 17 W during charging were designed and simulated in the range of 0-12000 s using COMSOL Multiphysics software. This study efficiently employs the Taguchi optimization technique to develop lithium-ion batteries capable of storing a predetermined average electric power during the charging phase. Therefore, this method enables the battery to achieve complete charging within a specific timeframe tailored to a specificapplication. The implementation of this method can save costs, time, and materials compared with other alternative methods, such as the trial-and-error approach.展开更多
Considering the rainfall’s importance in hydrological modeling, the objective of this study was the performance comparison, in convergence terms, of techniques often used to estimate the average rainfall over an area...Considering the rainfall’s importance in hydrological modeling, the objective of this study was the performance comparison, in convergence terms, of techniques often used to estimate the average rainfall over an area: Thiessen Polygon (TP) Method;Reciprocal Distance Squared (RDS) Method;Kriging Method (KM) and Multiquadric Equations (ME) Method. The comparison was done indirectly, using GORE and BALANCE index to assess the convergence results from each method by increasing the rain gauges density in a region, through six scenarios. The Coremas/Mae D’água Watershed employed as study area, with an area of 8385 km2, is situated on Brazilian semi-arid. The results showed the TP, as RDS and ME techniques to be employed successfully to obtain the average rainfall over an area, highlighting the MEM. On the other hand, KM, using two variograms models, had an unstable behavior, pointing the prior study of data and variogram’s choice as a need to practical applying.展开更多
A multi-objective linear programming problem is made from fuzzy linear programming problem. It is due the fact that it is used fuzzy programming method during the solution. The Multi objective linear programming probl...A multi-objective linear programming problem is made from fuzzy linear programming problem. It is due the fact that it is used fuzzy programming method during the solution. The Multi objective linear programming problem can be converted into the single objective function by various methods as Chandra Sen’s method, weighted sum method, ranking function method, statistical averaging method. In this paper, Chandra Sen’s method and statistical averaging method both are used here for making single objective function from multi-objective function. Two multi-objective programming problems are solved to verify the result. One is numerical example and the other is real life example. Then the problems are solved by ordinary simplex method and fuzzy programming method. It can be seen that fuzzy programming method gives better optimal values than the ordinary simplex method.展开更多
The energy approach is used to theoretically verify that the average acceleration method （AAM）, which is unconditionally stable for linear dynamic systems, is also unconditionally stable for structures with typical ...The energy approach is used to theoretically verify that the average acceleration method （AAM）, which is unconditionally stable for linear dynamic systems, is also unconditionally stable for structures with typical nonlinear damping, including the special case of velocity power type damping with a bilinear restoring force model. Based on the energy approach, the stability of the AAM is proven for SDOF structures using the mathematical features of the velocity power function and for MDOF structures by applying the virtual displacement theorem. Finally, numerical examples are given to demonstrate the accuracy of the theoretical analysis.展开更多
Numerical properties of the time integration method proposed by the first author of this paper in 2007 are the same as those of the constant average acceleration method （AAM） for linear elastic systems, except that ...Numerical properties of the time integration method proposed by the first author of this paper in 2007 are the same as those of the constant average acceleration method （AAM） for linear elastic systems, except that the capability to capture dynamic loading was not explored. It was found that there were different quadrature equations to predict the next step displacement increment. A modified quadrature equation of this method was derived so that the equation to determine the next step displacement was numerically equivalent to the equation used in the constant AAM. It was verified that the original form of this method, in general, had a better capability to capture dynamic loadings than the constant AAM. This excellent property, in addition to computational efficiency, will help to make this method competitive with general secondorder accurate integration methods.展开更多
Neutrons have been extensively used in many fields,such as nuclear physics,biology,geology,medical science,and national defense,owing to their unique penetration characteristics.Gamma rays are usually accompanied by t...Neutrons have been extensively used in many fields,such as nuclear physics,biology,geology,medical science,and national defense,owing to their unique penetration characteristics.Gamma rays are usually accompanied by the detection of neutrons.The capability to discriminate neutrons from gamma rays is important for evaluating plastic scintillator neutron detectors because similar pulse shapes are generated from both forms of radiation in the detection system.The pulse signals measured by plastic scintillators contain noise,which decreases the accuracy of n-y discrimination.To improve the performance of n-y discrimination,the noise of the pulse signals should be filtered before the n-y discrimination process.In this study,the influences of the Fourier transform,wavelet transform,moving-average filter,and Kalman algorithm on the charge comparison method,fractal spectrum method,and back-propagation neural network methods were studied.It was found that the Fourier transform filtering algorithm exhibits better adaptability to the charge comparison method than others,with an increasing accuracy of 6.87%compared to that without the filtering process.Meanwhile,the Kalman filter offers an improvement of 3.04%over the fractal spectrum method,and the adaptability of the moving-average filter in backpropagation neural network discrimination is better than that in other methods,with an increase in 8.48%.The Kalman filtering algorithm has a significant impact on the peak value of the pulse,reaching 4.49%,and it has an insignificant impact on the energy resolution of the spectrum measurement after discrimination.展开更多
A stochastic averaging method for predicting the response of quasi partially integrable and non-resonant Hamiltoniansystems to fractional Gaussian noise （fGla） with the Hurst index 1/2〈H〈l is proposed. The average...A stochastic averaging method for predicting the response of quasi partially integrable and non-resonant Hamiltoniansystems to fractional Gaussian noise （fGla） with the Hurst index 1/2〈H〈l is proposed. The averaged stochastic differential equa-tions （SDEs） for the first integrals of the associated Hamiltonian system are derived. The dimension of averaged SDEs is less thanthat of the original system. The stationary probability density and statistics of the original system are obtained approximately fromsolving the averaged SDEs numerically. Two systems are worked out to illustrate the proposed stochastic averaging method. It isshown that the results obtained by using the proposed stochastic averaging method and those from digital simulation of originalsystem agree well, and the computational time for the former results is less than that for the latter ones.展开更多
A stochastic averaging method of quasi integrable and resonant Hamiltonian systems under excitation of fractional Gaussian noise （fGn） with the Hurst index 1/2 〈 H 〈 1 is proposed. First, the definition and the ba...A stochastic averaging method of quasi integrable and resonant Hamiltonian systems under excitation of fractional Gaussian noise （fGn） with the Hurst index 1/2 〈 H 〈 1 is proposed. First, the definition and the basic property of fGn and related fractional Brownian motion （iBm） are briefly introduced. Then, the averaged fractional stochastic differential equations （SDEs） for the first integrals and combinations of angle variables of the associated Hamiltonian systems are derived. The stationary probability density and statistics of the original systems are then obtained approximately by simulating the averaged SDEs numerically. An example is worked out to illustrate the proposed stochastic averaging method. It is shown that the results obtained by using the proposed stochastic averaging method and those from digital simulation of original system agree well.展开更多
In the process of large-scale,grid-connected wind power operations,it is important to establish an accurate probability distribution model for wind farm fluctuations.In this study,a wind power fluctuation modeling met...In the process of large-scale,grid-connected wind power operations,it is important to establish an accurate probability distribution model for wind farm fluctuations.In this study,a wind power fluctuation modeling method is proposed based on the method of moving average and adaptive nonparametric kernel density estimation(NPKDE)method.Firstly,the method of moving average is used to reduce the fluctuation of the sampling wind power component,and the probability characteristics of the modeling are then determined based on the NPKDE.Secondly,the model is improved adaptively,and is then solved by using constraint-order optimization.The simulation results show that this method has a better accuracy and applicability compared with the modeling method based on traditional parameter estimation,and solves the local adaptation problem of traditional NPKDE.展开更多
By analyzing the existing average skidding distance formulac and the shape of the landing area, theauthors put forward that the average skidding distance is the shortest when the ratio of length and width is 1, and th...By analyzing the existing average skidding distance formulac and the shape of the landing area, theauthors put forward that the average skidding distance is the shortest when the ratio of length and width is 1, and the landing collectioll area is in proportion to of average geometrical skidding distance. The new models of calculating average distance are presented.展开更多
A simple,efficient and accurate high resolution method to tracking moving-interfaces-the characteristic integral-averaging finite volume method on unstructured meshes is proposed. And some numerical tests and evaluati...A simple,efficient and accurate high resolution method to tracking moving-interfaces-the characteristic integral-averaging finite volume method on unstructured meshes is proposed. And some numerical tests and evaluation of six main efficient methods for interface reconstruction are made. Through strict numerical simulation,their characters,advantages and shortcomings are compared,analyzed and commended in particular.展开更多
The averaging analysis was carried out to study the motion of a quasi axisymmetrical gyrostat under a small magnitude self excited control torque. The common approach to investigating the problem of rigid body rot...The averaging analysis was carried out to study the motion of a quasi axisymmetrical gyrostat under a small magnitude self excited control torque. The common approach to investigating the problem of rigid body rotation under the action of a small torque known in the body frame was described. Using this approach, the problem (Grammel's problem for the case of small torque) that is maintaining the angular velocity of a quasi axisymmetrical gyrostat using a control torque quadratic in the angular velocity was solved.展开更多
A new method to measure the average plasma velocity in a Hall-effect thruster is presented. The method is brought forward in virtue of the characteristics of low frequency oscillation induced by the propellant ionizat...A new method to measure the average plasma velocity in a Hall-effect thruster is presented. The method is brought forward in virtue of the characteristics of low frequency oscillation induced by the propellant ionization in the channel and the oriented movement feature of the plasma density out of the channel. The method, equivalent to the correlation method generally used in the signal processing field, provides a solution to the problem of specific impulse measurement on a timescale of hundreds of microseconds and makes the time evolution of average plasma velocity clear. The comparison between the measured value and the calibrated value shows that the relative error is about 3%.展开更多
Increasing incidents of indoor air quality(IAQ) related complaints lead us to the fact that IAQ has become a significant occupational health and environmental issue. However, how to effectively evaluate IAQ under diff...Increasing incidents of indoor air quality(IAQ) related complaints lead us to the fact that IAQ has become a significant occupational health and environmental issue. However, how to effectively evaluate IAQ under different scale of multiple indicators is still a challenge. The traditional single-indicator method is subjected to uncertainties in assessing IAQ due to different subjectivity on good or bad quality and scalar differences of data set. In this study, a multilevel integrated weighted average IAQ method including initial walking through assessment(IWA) and two-layers weighted average method are developed and applied to evaluate IAQ of the laboratory building at the University of Regina in Canada. Some important chemical parameters related to IAQ in terms of volatile organic compounds(VOCs), methanol(HCHO), carbon dioxide(CO2), and carbon monoxide(CO) are evaluated based on 5 months continuous monitoring data. The new integrated assessment result can not only indicates the risk of an individual parameter, but also able to quantify the overall IAQ risk on the sampling site. Finally, some recommendations based on the result are proposed to address sustainable IAQ practices in the sampling area.展开更多
Effect of residual Doppler averaging on the probe absorption in an alkali vapor medium in the presence of a coherent pump beam is studied analytically for the Ξ type system. A coherent probe field is assumed to conne...Effect of residual Doppler averaging on the probe absorption in an alkali vapor medium in the presence of a coherent pump beam is studied analytically for the Ξ type system. A coherent probe field is assumed to connect the ground level with the intermediate level whereas a coherent control beam is supposed to act between the intermediate energy level and the uppermost level. Optical Bloch equations（OBE） for a three-level Ξ type system and a four-level Ξ type system are derived by using density matrix formalism. These equations are solved by an analytic method to determine the probe response, which not only depends on the wavelength difference between the control（pump） field and the probe field but shows substantially different features depending on whether the wavelength of the control field is greater than that of the probe field or the reverse. The effect of temperature on probe response is also shown. Enhancement in probe absorption and additional features are noticed under a strong probe limit at room temperature. The four-level Ξ type system has two ground levels and this leads to substantial modification in the simulated probe absorption as compared to the three-level system.展开更多
In this paper, the evaluation of discretely sampled Asian options was considered by numerically solving the associated partial differential equations with the Legendre spectral method. Double average options were disc...In this paper, the evaluation of discretely sampled Asian options was considered by numerically solving the associated partial differential equations with the Legendre spectral method. Double average options were discussed as examples. The problem is a parabolic one on a finite domain whose equation degenerates into ordinary differential equations on the boundaries. A fully discrete scheme was established by using the Legendre spectral method in space and the Crank-Nicolson finite difference scheme in time. The stability and convergence of the scheme were analyzed. Numerical results show that the method can keep the spectral accuracy in space for such degenerate problems.展开更多
基金supported by the National Natural Science Foundation of China(1237119112071175)+4 种基金supported by the NSFC(1207117511901080)supported by the NSFC(12071175)the Fundamental Research Funds For the Central Universities(2412023YQ003)the Natural Science Foundation of Jilin Province(20200201253JC)。
文摘We consider the persistence of affine periodic solutions for perturbed affine periodic systems.Such(Q,T)-affine periodic solutions have the form x(t+T)=Qx(t)for all t∈R,where T>0 is fixed and Q is a nonsingular matrix.These are a kind of spatiotemporal symmetric solutions,e.g.spiral waves.We give the averaging method for the existence of affine periodic solutions in two situations:one in which the initial values of the affine periodic solutions of the unperturbed system form a manifold,and another that does not rely on the structure of the initial values of the unperturbed system's affine periodic solutions.The transversal condition is determined using the Brouwer degree.We also present a higher order averaging method for general degenerate systems by means of the Brouwer degree and a Lyapunov-Schmidt reduction.
基金supported by the National Natural Science Foundation of China(Grant No.91130013)the Open Foundation of State Key Laboratory of HighPerformance Computing of China
文摘The energy preserving average vector field （AVF） method is applied to the coupled Schr6dinger-KdV equations. Two energy preserving schemes are constructed by using Fourier pseudospectral method in space direction discretization. In order to accelerate our simulation, the split-step technique is used. The numerical experiments show that the non-splitting scheme and splitting scheme are both effective, and have excellent long time numerical behavior. The comparisons show that the splitting scheme is faster than the non-splitting scheme, but it is not as good as the non-splitting scheme in preserving the invariants.
基金the State Administration of Science,Technology and Industry for National Defense of China(Grant No.B2420132001).
文摘The paper studies the parametric stochastic roll motion in the random waves.The differential equation of the ship parametric roll under random wave is established with considering the nonlinear damping and ship speed.Random sea surface is treated as a narrow-band stochastic process,and the stochastic parametric excitation is studied based on the effective wave theory.The nonlinear restored arm function obtained from the numerical simulation is expressed as the approximate analytic function.By using the stochastic averaging method,the differential equation of motion is transformed into Ito’s stochastic differential equation.The steady-state probability density function of roll motion is obtained,and the results are validated with the numerical simulation and model test.
文摘This paper puts forward a complex inner product averaging method for calculating normal form of ODE. Compared with conventional averaging method, the theoretic analytical process has such simple forms as to realize computer program easily. Results can be applied in both autonomous and non-autonomous systems. At last, an example is resolved to verify the method.
文摘In recent times, lithium-ion batteries have been widely used owing to their high energy density, extended cycle lifespan, and minimal self-discharge rate. The design of high-speed rechargeable lithium-ion batteries faces a significant challenge owing to the need to increase average electric power during charging. This challenge results from the direct influence of the power level on the rate of chemical reactions occurring in the battery electrodes. In this study, the Taguchi optimization method was used to enhance the average electric power during the charging process of lithium-ion batteries. The Taguchi technique is a statistical strategy that facilitates the systematic and efficient evaluation of numerous experimental variables. The proposed method involved varying seven input factors, including positive electrode thickness, positive electrode material, positive electrode active material volume fraction, negative electrode active material volume fraction, separator thickness, positive current collector thickness, and negative current collector thickness. Three levels were assigned to each control factor to identify the optimal conditions and maximize the average electric power during charging. Moreover, a variance assessment analysis was conducted to validate the results obtained from the Taguchi analysis. The results revealed that the Taguchi method was an eff ective approach for optimizing the average electric power during the charging of lithium-ion batteries. This indicates that the positive electrode material, followed by the separator thickness and the negative electrode active material volume fraction, was key factors significantly infl uencing the average electric power during the charging of lithium-ion batteries response. The identification of optimal conditions resulted in the improved performance of lithium-ion batteries, extending their potential in various applications. Particularly, lithium-ion batteries with average electric power of 16 W and 17 W during charging were designed and simulated in the range of 0-12000 s using COMSOL Multiphysics software. This study efficiently employs the Taguchi optimization technique to develop lithium-ion batteries capable of storing a predetermined average electric power during the charging phase. Therefore, this method enables the battery to achieve complete charging within a specific timeframe tailored to a specificapplication. The implementation of this method can save costs, time, and materials compared with other alternative methods, such as the trial-and-error approach.
文摘Considering the rainfall’s importance in hydrological modeling, the objective of this study was the performance comparison, in convergence terms, of techniques often used to estimate the average rainfall over an area: Thiessen Polygon (TP) Method;Reciprocal Distance Squared (RDS) Method;Kriging Method (KM) and Multiquadric Equations (ME) Method. The comparison was done indirectly, using GORE and BALANCE index to assess the convergence results from each method by increasing the rain gauges density in a region, through six scenarios. The Coremas/Mae D’água Watershed employed as study area, with an area of 8385 km2, is situated on Brazilian semi-arid. The results showed the TP, as RDS and ME techniques to be employed successfully to obtain the average rainfall over an area, highlighting the MEM. On the other hand, KM, using two variograms models, had an unstable behavior, pointing the prior study of data and variogram’s choice as a need to practical applying.
文摘A multi-objective linear programming problem is made from fuzzy linear programming problem. It is due the fact that it is used fuzzy programming method during the solution. The Multi objective linear programming problem can be converted into the single objective function by various methods as Chandra Sen’s method, weighted sum method, ranking function method, statistical averaging method. In this paper, Chandra Sen’s method and statistical averaging method both are used here for making single objective function from multi-objective function. Two multi-objective programming problems are solved to verify the result. One is numerical example and the other is real life example. Then the problems are solved by ordinary simplex method and fuzzy programming method. It can be seen that fuzzy programming method gives better optimal values than the ordinary simplex method.
基金National Natural Science Foundation of ChinaUnder Grant No. 50578047, 50338020 China Ministry ofEducation (Program for New Century Excellent Talents inUniversity) China Ministry of Science and Technology UnderGrant No.2003AA602150
文摘The energy approach is used to theoretically verify that the average acceleration method （AAM）, which is unconditionally stable for linear dynamic systems, is also unconditionally stable for structures with typical nonlinear damping, including the special case of velocity power type damping with a bilinear restoring force model. Based on the energy approach, the stability of the AAM is proven for SDOF structures using the mathematical features of the velocity power function and for MDOF structures by applying the virtual displacement theorem. Finally, numerical examples are given to demonstrate the accuracy of the theoretical analysis.
基金Science Council (NSC),Chinese Taipei Under Grant No.NSC-96-2221-E-027-030
文摘Numerical properties of the time integration method proposed by the first author of this paper in 2007 are the same as those of the constant average acceleration method （AAM） for linear elastic systems, except that the capability to capture dynamic loading was not explored. It was found that there were different quadrature equations to predict the next step displacement increment. A modified quadrature equation of this method was derived so that the equation to determine the next step displacement was numerically equivalent to the equation used in the constant AAM. It was verified that the original form of this method, in general, had a better capability to capture dynamic loadings than the constant AAM. This excellent property, in addition to computational efficiency, will help to make this method competitive with general secondorder accurate integration methods.
基金supported by the Key Natural Science Projects of the Sichuan Education Department(No.18ZA0067)the Key Science and Technology Projects of Leshan(No.19SZD117)。
文摘Neutrons have been extensively used in many fields,such as nuclear physics,biology,geology,medical science,and national defense,owing to their unique penetration characteristics.Gamma rays are usually accompanied by the detection of neutrons.The capability to discriminate neutrons from gamma rays is important for evaluating plastic scintillator neutron detectors because similar pulse shapes are generated from both forms of radiation in the detection system.The pulse signals measured by plastic scintillators contain noise,which decreases the accuracy of n-y discrimination.To improve the performance of n-y discrimination,the noise of the pulse signals should be filtered before the n-y discrimination process.In this study,the influences of the Fourier transform,wavelet transform,moving-average filter,and Kalman algorithm on the charge comparison method,fractal spectrum method,and back-propagation neural network methods were studied.It was found that the Fourier transform filtering algorithm exhibits better adaptability to the charge comparison method than others,with an increasing accuracy of 6.87%compared to that without the filtering process.Meanwhile,the Kalman filter offers an improvement of 3.04%over the fractal spectrum method,and the adaptability of the moving-average filter in backpropagation neural network discrimination is better than that in other methods,with an increase in 8.48%.The Kalman filtering algorithm has a significant impact on the peak value of the pulse,reaching 4.49%,and it has an insignificant impact on the energy resolution of the spectrum measurement after discrimination.
基金supported by the National Natural Science Foundation of China(Nos.11172259,11272279,11321202,and 11432012)
文摘A stochastic averaging method for predicting the response of quasi partially integrable and non-resonant Hamiltoniansystems to fractional Gaussian noise （fGla） with the Hurst index 1/2〈H〈l is proposed. The averaged stochastic differential equa-tions （SDEs） for the first integrals of the associated Hamiltonian system are derived. The dimension of averaged SDEs is less thanthat of the original system. The stationary probability density and statistics of the original system are obtained approximately fromsolving the averaged SDEs numerically. Two systems are worked out to illustrate the proposed stochastic averaging method. It isshown that the results obtained by using the proposed stochastic averaging method and those from digital simulation of originalsystem agree well, and the computational time for the former results is less than that for the latter ones.
基金supported by the National Natural Science Foundation of China under grants nos.:11272279,11321202 and 11432012
文摘A stochastic averaging method of quasi integrable and resonant Hamiltonian systems under excitation of fractional Gaussian noise （fGn） with the Hurst index 1/2 〈 H 〈 1 is proposed. First, the definition and the basic property of fGn and related fractional Brownian motion （iBm） are briefly introduced. Then, the averaged fractional stochastic differential equations （SDEs） for the first integrals and combinations of angle variables of the associated Hamiltonian systems are derived. The stationary probability density and statistics of the original systems are then obtained approximately by simulating the averaged SDEs numerically. An example is worked out to illustrate the proposed stochastic averaging method. It is shown that the results obtained by using the proposed stochastic averaging method and those from digital simulation of original system agree well.
基金supported by Science and Technology project of the State Grid Corporation of China“Research on Active Development Planning Technology and Comprehensive Benefit Analysis Method for Regional Smart Grid Comprehensive Demonstration Zone”National Natural Science Foundation of China(51607104)
文摘In the process of large-scale,grid-connected wind power operations,it is important to establish an accurate probability distribution model for wind farm fluctuations.In this study,a wind power fluctuation modeling method is proposed based on the method of moving average and adaptive nonparametric kernel density estimation(NPKDE)method.Firstly,the method of moving average is used to reduce the fluctuation of the sampling wind power component,and the probability characteristics of the modeling are then determined based on the NPKDE.Secondly,the model is improved adaptively,and is then solved by using constraint-order optimization.The simulation results show that this method has a better accuracy and applicability compared with the modeling method based on traditional parameter estimation,and solves the local adaptation problem of traditional NPKDE.
文摘By analyzing the existing average skidding distance formulac and the shape of the landing area, theauthors put forward that the average skidding distance is the shortest when the ratio of length and width is 1, and the landing collectioll area is in proportion to of average geometrical skidding distance. The new models of calculating average distance are presented.
文摘A simple,efficient and accurate high resolution method to tracking moving-interfaces-the characteristic integral-averaging finite volume method on unstructured meshes is proposed. And some numerical tests and evaluation of six main efficient methods for interface reconstruction are made. Through strict numerical simulation,their characters,advantages and shortcomings are compared,analyzed and commended in particular.
文摘The averaging analysis was carried out to study the motion of a quasi axisymmetrical gyrostat under a small magnitude self excited control torque. The common approach to investigating the problem of rigid body rotation under the action of a small torque known in the body frame was described. Using this approach, the problem (Grammel's problem for the case of small torque) that is maintaining the angular velocity of a quasi axisymmetrical gyrostat using a control torque quadratic in the angular velocity was solved.
基金supported by National Natural Science Foundation of China(No.50676026)
文摘A new method to measure the average plasma velocity in a Hall-effect thruster is presented. The method is brought forward in virtue of the characteristics of low frequency oscillation induced by the propellant ionization in the channel and the oriented movement feature of the plasma density out of the channel. The method, equivalent to the correlation method generally used in the signal processing field, provides a solution to the problem of specific impulse measurement on a timescale of hundreds of microseconds and makes the time evolution of average plasma velocity clear. The comparison between the measured value and the calibrated value shows that the relative error is about 3%.
文摘Increasing incidents of indoor air quality(IAQ) related complaints lead us to the fact that IAQ has become a significant occupational health and environmental issue. However, how to effectively evaluate IAQ under different scale of multiple indicators is still a challenge. The traditional single-indicator method is subjected to uncertainties in assessing IAQ due to different subjectivity on good or bad quality and scalar differences of data set. In this study, a multilevel integrated weighted average IAQ method including initial walking through assessment(IWA) and two-layers weighted average method are developed and applied to evaluate IAQ of the laboratory building at the University of Regina in Canada. Some important chemical parameters related to IAQ in terms of volatile organic compounds(VOCs), methanol(HCHO), carbon dioxide(CO2), and carbon monoxide(CO) are evaluated based on 5 months continuous monitoring data. The new integrated assessment result can not only indicates the risk of an individual parameter, but also able to quantify the overall IAQ risk on the sampling site. Finally, some recommendations based on the result are proposed to address sustainable IAQ practices in the sampling area.
文摘Effect of residual Doppler averaging on the probe absorption in an alkali vapor medium in the presence of a coherent pump beam is studied analytically for the Ξ type system. A coherent probe field is assumed to connect the ground level with the intermediate level whereas a coherent control beam is supposed to act between the intermediate energy level and the uppermost level. Optical Bloch equations（OBE） for a three-level Ξ type system and a four-level Ξ type system are derived by using density matrix formalism. These equations are solved by an analytic method to determine the probe response, which not only depends on the wavelength difference between the control（pump） field and the probe field but shows substantially different features depending on whether the wavelength of the control field is greater than that of the probe field or the reverse. The effect of temperature on probe response is also shown. Enhancement in probe absorption and additional features are noticed under a strong probe limit at room temperature. The four-level Ξ type system has two ground levels and this leads to substantial modification in the simulated probe absorption as compared to the three-level system.
文摘In this paper, the evaluation of discretely sampled Asian options was considered by numerically solving the associated partial differential equations with the Legendre spectral method. Double average options were discussed as examples. The problem is a parabolic one on a finite domain whose equation degenerates into ordinary differential equations on the boundaries. A fully discrete scheme was established by using the Legendre spectral method in space and the Crank-Nicolson finite difference scheme in time. The stability and convergence of the scheme were analyzed. Numerical results show that the method can keep the spectral accuracy in space for such degenerate problems.
