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Solving Multi-Objective Linear Programming Problem by Statistical Averaging Method with the Help of Fuzzy Programming Method
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作者 Samsun Nahar Marin Akter Md. Abdul Alim 《American Journal of Operations Research》 2023年第2期19-32,共14页
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
关键词 Fuzzy Programming method Fuzzy Linear Programming Problem Multi-Objective Linear Programming Problem Statistical averaging method New Statistical averaging method
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Studies on Stochastic Parametric Roll of Ship with Stochastic Averaging Method 被引量:4
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作者 WANG Li-yuan TANG You-gang +2 位作者 LI Yan ZHANG Jing-chen LIU Li-qin 《China Ocean Engineering》 SCIE EI CSCD 2020年第2期289-298,共10页
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
关键词 parametric roll random wave stochastic averaging method probability density function
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COMPLEX INNER PRODUCT AVERAGING METHOD FOR CALCULATING NORMAL FORM OF ODE 被引量:1
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作者 CHEN Yu-shu(陈予恕) +1 位作者 SUN Hong-jun(孙洪军) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第12期1368-1374,共7页
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
关键词 nonlinear dynamic system normal form complex inner product averaging method
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Quantum generative adversarial networks based on a readout error mitigation method with fault tolerant mechanism
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作者 赵润盛 马鸿洋 +2 位作者 程涛 王爽 范兴奎 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第4期285-295,共11页
Readout errors caused by measurement noise are a significant source of errors in quantum circuits,which severely affect the output results and are an urgent problem to be solved in noisy-intermediate scale quantum(NIS... Readout errors caused by measurement noise are a significant source of errors in quantum circuits,which severely affect the output results and are an urgent problem to be solved in noisy-intermediate scale quantum(NISQ)computing.In this paper,we use the bit-flip averaging(BFA)method to mitigate frequent readout errors in quantum generative adversarial networks(QGAN)for image generation,which simplifies the response matrix structure by averaging the qubits for each random bit-flip in advance,successfully solving problems with high cost of measurement for traditional error mitigation methods.Our experiments were simulated in Qiskit using the handwritten digit image recognition dataset under the BFA-based method,the Kullback-Leibler(KL)divergence of the generated images converges to 0.04,0.05,and 0.1 for readout error probabilities of p=0.01,p=0.05,and p=0.1,respectively.Additionally,by evaluating the fidelity of the quantum states representing the images,we observe average fidelity values of 0.97,0.96,and 0.95 for the three readout error probabilities,respectively.These results demonstrate the robustness of the model in mitigating readout errors and provide a highly fault tolerant mechanism for image generation models. 展开更多
关键词 readout errors quantum generative adversarial networks bit-flip averaging method fault tolerant mechanisms
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Response regimes of nonlinear energy harvesters with a resistorinductor resonant circuit by complexification-averaging method 被引量:8
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作者 HUANG DongMei CHEN JiaYi +2 位作者 ZHOU ShengXi FANG XueLai LI Wei 《Science China(Technological Sciences)》 SCIE EI CAS CSCD 2021年第6期1212-1227,共16页
In this paper, the steady-state response regimes of nonlinear energy harvesters with a resistor-inductor resonant circuit are theoretically investigated. The complexification averaging(CA) method is used to theoretica... In this paper, the steady-state response regimes of nonlinear energy harvesters with a resistor-inductor resonant circuit are theoretically investigated. The complexification averaging(CA) method is used to theoretically analyze the energy harvesting performance and reduce the motion equations into a set of first-order differential equations. The amplitudes and phases of both the response displacement and the output voltage are derived, and the corresponding stability conditions are determined. The response regimes are studied with the variation of nonlinear stiffness coefficients and coupling parameters, which are verified by the time domain analysis. The frequency island phenomenon is found and analyzed. Additionally, the backbone curve for deducing the extreme vibration frequency and amplitude is derived. Simultaneously, the analytical expressions of the switching points(critical amplitude and frequency) to identify the hardening and softening properties are established. Accordingly, a criterion is given to determine the occurrence of the jump phenomenon, and its effectiveness is verified. Overall, this paper presents an in-depth theoretical analysis of nonlinear energy harvesters with a resistor-inductor resonant circuit. It presents the theoretical framework and guidance for more extensive evaluations and understanding the theoretical analysis of nonlinear energy harvesters with external circuits. 展开更多
关键词 energy harvesting complexification averaging method nonlinear vibration
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Affine-periodic solutions by averaging methods 被引量:1
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作者 Jiamin Xing Xue Yang Yong Li 《Science China Mathematics》 SCIE CSCD 2018年第3期439-452,共14页
This paper concerns the existence of affine-periodic solutions for perturbed affine-periodic systems.This kind of affine-periodic solutions has the form of x(t+T)≡Qx(t) with some nonsingular matrix Q,which may be qua... This paper concerns the existence of affine-periodic solutions for perturbed affine-periodic systems.This kind of affine-periodic solutions has the form of x(t+T)≡Qx(t) with some nonsingular matrix Q,which may be quasi-periodic when Q is an orthogonal matrix. It can be even unbounded but x(t)/|x(t)| is quasi-periodic,like a helical line. for example x(t)=e^(at)(cos ωt, sin ωt), when Q is not an orthogonal matrix. The averaging method of higher order for finding affine-periodic solutions is given by topological degree. 展开更多
关键词 affine-periodic solutions averaging method topological degree
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Characteristics of Multi-Objective Linear Programming Problem and Multi-Objective Linear Fractional Programming Problem Taking Maximum Value of Multi-Objective Functions
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作者 Samsun Nahar Md. Asadujjaman +2 位作者 Khadiza Begum Mahede-Ul-Hassan Md. Abdul Alim 《Applied Mathematics》 2024年第1期22-32,共11页
In this paper, a new statistical averaging technique is proposed for finding an optimal solution to a multi-objective linear fractional programming problem (MOLFPP) and multi-objective linear programming problem (MOLP... In this paper, a new statistical averaging technique is proposed for finding an optimal solution to a multi-objective linear fractional programming problem (MOLFPP) and multi-objective linear programming problem (MOLPP) by using new arithmetic averaging method and new geometric averaging method. It is significantly noticeable same characteristics among all the technique while taking maximum or minimum among all optimized values for multi-objective functions using simplex algorithm. The characteristics provided from the problems are verified by the numerical examples. 展开更多
关键词 MOLPP MOLFPP New Arithmetic averaging method New Geometric averaging method
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Performance enhancement of a viscoelastic bistable energy harvester using time-delayed feedback control
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作者 黄美玲 杨勇歌 刘洋 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第6期142-154,共13页
This paper focuses on the stochastic analysis of a viscoelastic bistable energy harvesting system under colored noise and harmonic excitation, and adopts the time-delayed feedback control to improve its harvesting eff... This paper focuses on the stochastic analysis of a viscoelastic bistable energy harvesting system under colored noise and harmonic excitation, and adopts the time-delayed feedback control to improve its harvesting efficiency. Firstly, to obtain the dimensionless governing equation of the system, the original bistable system is approximated as a system without viscoelastic term by using the stochastic averaging method of energy envelope, and then is further decoupled to derive an equivalent system. The credibility of the proposed method is validated by contrasting the consistency between the numerical and the analytical results of the equivalent system under different noise conditions. The influence of system parameters on average output power is analyzed, and the control effect of the time-delayed feedback control on system performance is compared. The output performance of the system is improved with the occurrence of stochastic resonance(SR). Therefore, the signal-to-noise ratio expression for measuring SR is derived, and the dependence of its SR behavior on different parameters is explored. 展开更多
关键词 energy harvesting BISTABILITY stochastic averaging method stochastic resonance time-delayed feedback control
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Stochastic Bifurcation of an SIS Epidemic Model with Treatment and Immigration
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作者 Weipeng Zhang Dan Gu 《Journal of Applied Mathematics and Physics》 2024年第6期2254-2280,共27页
In this paper, we investigate an SIS model with treatment and immigration. Firstly, the two-dimensional model is simplified by using the stochastic averaging method. Then, we derive the local stability of the stochast... In this paper, we investigate an SIS model with treatment and immigration. Firstly, the two-dimensional model is simplified by using the stochastic averaging method. Then, we derive the local stability of the stochastic system by computing the Lyapunov exponent of the linearized system. Further, the global stability of the stochastic model is analyzed based on the singular boundary theory. Moreover, we prove that the model undergoes a Hopf bifurcation and a pitchfork bifurcation. Finally, several numerical examples are provided to illustrate the theoretical results. . 展开更多
关键词 Epidemic Model Stochastic averaging method Singular Boundary Theory Stochastic Bifurcation
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Solving Fuzzy Multi-Objective Linear Programming Problem by Applying Statistical Method
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作者 Samsun Nahar Marin Akter Md. Abdul Alim 《American Journal of Operations Research》 2022年第6期293-309,共17页
In this paper, the statistical averaging method and the new statistical averaging methods have been used to solve the fuzzy multi-objective linear programming problems. These methods have been applied to form a single... In this paper, the statistical averaging method and the new statistical averaging methods have been used to solve the fuzzy multi-objective linear programming problems. These methods have been applied to form a single objective function from the fuzzy multi-objective linear programming problems. At first, a numerical example of solving fuzzy multi-objective linear programming problem has been provided to validate the maximum risk reduction by the proposed method. The proposed method has been applied to assess the risk of damage due to natural calamities like flood, cyclone, sidor, and storms at the coastal areas in Bangladesh. The proposed method of solving the fuzzy multi-objective linear programming problems by the statistical method has been compared with the Chandra Sen’s method. The numerical results show that the proposed method maximizes the risk reduction capacity better than Chandra Sen’s method. 展开更多
关键词 Fuzzy Multi-Objective Linear Programming Problem Fuzzy Linear Programming Problem Chandra Sen’s method Statistical averaging method New Statistical averaging method
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A Semi-Analytical Method for the PDFs of A Ship Rolling in Random Oblique Waves 被引量:2
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作者 LIU Li-qin LIU Ya-liu +2 位作者 XU Wan-hai LI Yan TANG You-gang 《China Ocean Engineering》 SCIE EI CSCD 2018年第1期74-84,共11页
The PDFs(probability density functions) and probability of a ship rolling under the random parametric and forced excitations were studied by a semi-analytical method. The rolling motion equation of the ship in random ... The PDFs(probability density functions) and probability of a ship rolling under the random parametric and forced excitations were studied by a semi-analytical method. The rolling motion equation of the ship in random oblique waves was established. The righting arm obtained by the numerical simulation was approximately fitted by an analytical function. The irregular waves were decomposed into two Gauss stationary random processes, and the CARMA(2, 1) model was used to fit the spectral density function of parametric and forced excitations. The stochastic energy envelope averaging method was used to solve the PDFs and the probability. The validity of the semi-analytical method was verified by the Monte Carlo method. The C11 ship was taken as an example, and the influences of the system parameters on the PDFs and probability were analyzed. The results show that the probability of ship rolling is affected by the characteristic wave height, wave length, and the heading angle. In order to provide proper advice for the ship’s manoeuvring, the parametric excitations should be considered appropriately when the ship navigates in the oblique seas. 展开更多
关键词 ship random rolling parametric and forced excitations stochastic energy envelope averaging method probability density function parameter influence analysis
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Averaging Analysis of Self-Excited Motion of a Quasi-Axisymmetrical Gyrostat
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作者 薛纭 陈立群 《Journal of Shanghai University(English Edition)》 CAS 2002年第2期125-129,共5页
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
关键词 GYROSTAT self excited motion averaging method phase trajectories.
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Stability of average acceleration method for structures with nonlinear damping 被引量:4
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作者 李妍 吴斌 欧进萍 《Earthquake Engineering and Engineering Vibration》 SCIE EI CSCD 2006年第1期87-92,共6页
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
关键词 unconditional stability average acceleration method nonlinear systems nonlinear damping
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Modal Identification of Offshore Platforms Using Statistical Method Based on ERA 被引量:6
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作者 王树青 李华军 T.Takayama 《China Ocean Engineering》 SCIE EI 2005年第2期175-184,共10页
Identification of modal parameters of a linear structure with output-only measurements has received much attention over the past decades. In the paper, the Natural Excitation Technique (NExT) is used for acquisition o... Identification of modal parameters of a linear structure with output-only measurements has received much attention over the past decades. In the paper, the Natural Excitation Technique (NExT) is used for acquisition of the impulse signals from the structural responses. Then Eigensystem Realization Algorithm (ERA) is utilized for modal identification. For disregarding the fictitious ‘computational modes', a procedure, Statistically Averaging Modal Frequency Method (SAMFM), is developed to distinguish the true modes from noise modes, and to improve the precision of the identified modal frequencies of the structure. An offshore platform is modeled with the finite element method. The theoretical modal parameters are obtained for a comparison with the identified values. The dynamic responses of the platform under random wave loading are computed for providing the output signals used for identification with ERA. Results of simulation demonstrate that the proposed method can determine the system modal frequency with high precision. 展开更多
关键词 modal identification eigensystem realization algorithm statistically averaging modal frequency method offshore platform
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Probability distribution of wind power volatility based on the moving average method and improved nonparametric kernel density estimation 被引量:4
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作者 Peizhe Xin Ying Liu +2 位作者 Nan Yang Xuankun Song Yu Huang 《Global Energy Interconnection》 2020年第3期247-258,共12页
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
关键词 Moving average method Signal decomposition Wind power fluctuation characteristics Kernel density estimation Constrained order optimization
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Average vector field methods for the coupled Schrdinger KdV equations 被引量:3
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作者 张弘 宋松和 +1 位作者 陈绪栋 周炜恩 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第7期242-250,共9页
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
关键词 coupled Schrodinger-KdV equations average vector field method splitting method Fourier pseu-dospectral method
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Comparison of capability of time integration methods in capturing dynamic loading 被引量:2
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作者 Shuenn-Yih Chang Chi-Wei Hsu 《Earthquake Engineering and Engineering Vibration》 SCIE EI CSCD 2010年第3期409-423,共15页
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
关键词 equations of motion quadrature equation constant average acceleration method integration methods
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Indoor air quality risk assessment on the Canadian campus by a multilevel integrated weighted average method
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作者 夏瑞 张远 +4 位作者 ZHANG Meng-heng LIU Ke-xin WU Jie-yun ZHENG Zhi-rong GONG Yao 《Journal of Chongqing University》 CAS 2015年第3期87-100,共14页
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
关键词 indoor air quality risk assessment weighted average method CAMPUS CANADA
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Novel energy dissipative method on the adaptive spatial discretization for the Allen–Cahn equation
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作者 Jing-Wei Sun Xu Qian +1 位作者 Hong Zhang Song-He Song 《Chinese Physics B》 SCIE EI CAS CSCD 2021年第7期107-115,共9页
We propose a novel energy dissipative method for the Allen–Cahn equation on nonuniform grids.For spatial discretization,the classical central difference method is utilized,while the average vector field method is app... We propose a novel energy dissipative method for the Allen–Cahn equation on nonuniform grids.For spatial discretization,the classical central difference method is utilized,while the average vector field method is applied for time discretization.Compared with the average vector field method on the uniform mesh,the proposed method can involve fewer grid points and achieve better numerical performance over long time simulation.This is due to the moving mesh method,which can concentrate the grid points more densely where the solution changes drastically.Numerical experiments are provided to illustrate the advantages of the proposed concrete adaptive energy dissipative scheme under large time and space steps over a long time. 展开更多
关键词 moving mesh energy dissipative average vector field method Allen–Cahn equation
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Fuzzy Synthetic Evaluation Model for Smart Washing Machine
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作者 Samsun Nahar Marin Akter +2 位作者 Khadiza Begum Mahede Ul Hassan Md. Abdul Alim 《American Journal of Operations Research》 2023年第4期93-109,共17页
Generally fuzzy control system (FCS) is worked in washing machine. For the fuzzy set theory, membership functions are the building blocks. In a fuzzy set, fuzziness is determined by its membership functions. The shape... Generally fuzzy control system (FCS) is worked in washing machine. For the fuzzy set theory, membership functions are the building blocks. In a fuzzy set, fuzziness is determined by its membership functions. The shapes of membership functions are important, because it has an effect on fuzzy inference system. The shapes of membership functions can be triangular, trapezoidal and gaussian. The most widely used triangular membership function is used in this paper, because it can capture the short time period. In washing machine, open loop control system is found. This paper applies a fuzzy synthetic evaluation method (FSEM) for washing cloth in washing machine as FSEM can handle the multiple criteria with the help of evaluation matrix generated from membership function and weight matrix generated by Analytical Hierarchy Process (AHP). The purpose of this research is to minimize the wash time. By applying FSEM, we get a wash time which is less than that wash time got from applying the Mamdani approach in FCS. An example is given for illustration. For more reduction of wash time, statistical averaging method is also used. To reduce the wash time, statistical averaging method can be used in Mamdani approach also. 展开更多
关键词 Fuzzy Control System Fuzzy Synthetic Evaluation method Analytic Hierarchy Process method Mamdani Approach Statistical averaging method
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