Quantum generative adversarial networks based on a readout error mitigation method with fault tolerant mechanism

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.

Solving Multi-Objective Linear Programming Problem by Statistical Averaging Method with the Help of Fuzzy Programming Method

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.

Performance enhancement of a viscoelastic bistable energy harvester using time-delayed feedback control

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.

Characteristics of Multi-Objective Linear Programming Problem and Multi-Objective Linear Fractional Programming Problem Taking Maximum Value of Multi-Objective Functions

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.

Stochastic Bifurcation of an SIS Epidemic Model with Treatment and Immigration

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. .

Studies on Stochastic Parametric Roll of Ship with Stochastic Averaging Method

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.

Stability of average acceleration method for structures with nonlinear damping

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.

Modal Identification of Offshore Platforms Using Statistical Method Based on ERA

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.

A Semi-Analytical Method for the PDFs of A Ship Rolling in Random Oblique Waves

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.

Average vector field methods for the coupled Schrdinger KdV equations

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.

Comparison of capability of time integration methods in capturing dynamic loading

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.

Probability distribution of wind power volatility based on the moving average method and improved nonparametric kernel density estimation

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.

Indoor air quality risk assessment on the Canadian campus by a multilevel integrated weighted average method

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.

COMPLEX INNER PRODUCT AVERAGING METHOD FOR CALCULATING NORMAL FORM OF ODE

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.

Novel energy dissipative method on the adaptive spatial discretization for the Allen–Cahn equation

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.

Solving Fuzzy Multi-Objective Linear Programming Problem by Applying Statistical Method

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.

Research on hunting stability and bifurcation characteristics of nonlinear stochastic wheelset system

A stochastic wheelset model with a nonlinear wheel-rail contact relationship is established to investigate the stochastic stability and stochastic bifurcation of the wheelset system with the consideration of the stochastic parametric excitations of equivalent conicity and suspension stiffness.The wheelset is systematized into a onedimensional(1D)diffusion process by using the stochastic average method,the behavior of the singular boundary is analyzed to determine the hunting stability condition of the wheelset system,and the critical speed of stochastic bifurcation is obtained.The stationary probability density and joint probability density are derived theoretically.Based on the topological structure change of the probability density function,the stochastic Hopf bifurcation form and bifurcation condition of the wheelset system are determined.The effects of stochastic factors on the hunting stability and bifurcation characteristics are analyzed,and the simulation results verify the correctness of the theoretical analysis.The results reveal that the boundary behavior of the diffusion process determines the hunting stability of the stochastic wheelset system,and the left boundary characteristic value cL=1 is the critical state of hunting stability.Besides,stochastic D-bifurcation and P-bifurcation will appear in the wheelset system,and the critical speeds of the two kinds of stochastic bifurcation decrease with the increase in the stochastic parametric excitation intensity.

Resonance and Bifurcation of Fractional Nonlinear Systems with Power Damping Term for Robot Grinding

A fractional nonlinear system with power damping term is introduced to study the forced vibration system in order to solve the resonance and bifurcation problems between grinding wheel and steel bar during robot grinding.The robot,grinding wheel and steel bar are reduced to a spring-damping second-order system model.The implicit function equations of vibration amplitude of the dynamic system with coulomb friction damping,linear damping,square damping and cubic damping are obtained by average method.The stability of the system is analyzed and explained,and the stability condition of the system is proposed.Then,the amplitude-frequency characteristic curves of the system under different fractional differential orders,nonlinear stiffness parameters,fractional differential term coefficients and external excitation amplitude are analyzed.It is shown that the fractional differential term in the dynamic system is the damping characteristic.Then the influence of four kinds of damping on the vibration amplitude of the system under the same parameter is investigated and it is proved that the cubic damping suppresses the vibration of the system to the maximum extent.Finally,based on the idea that the equilibrium point of the system is the constant part of the Fourier series expansion term,the bifurcation behavior caused by the change of damping parameters in linear damping,square damping and cubic damping systems with different values of fractional differential order is investigated.

Improvement of circuit oscillation generated by underwater high voltage pulse discharges based on pulse power thyristor

High voltage fracturing technology was widely used in the field of reservoir reconstruction due to its advantages of being clean, pollution-free, and high-efficiency. However, high-frequency circuit oscillation occurs during the underwater high voltage pulse discharge process, which brings security risks to the stability of the pulse fracturing system. In order to solve this problem, an underwater pulse power discharge system was established, the circuit oscillation generation conditions were analyzed and the circuit oscillation suppression method was proposed. Firstly, the system structure was introduced and the charging model of the energy storage capacitor was established by the state space average method. Next, the electrode high-voltage breakdown model was established through COMSOL software, the electrode breakdown process was analyzed according to the electron density distribution image, and the plasma channel impedance was estimated based on the conductivity simulation results. Then the underwater pulse power discharge process and the circuit oscillation generation condition were analyzed, and the circuit oscillation suppression strategy of using the thyristor to replace the gas spark switch was proposed. Finally, laboratory experiments were carried out to verify the precision of the theoretical model and the suppression effect of circuit oscillation. The experimental results show that the voltage variation of the energy storage capacitor, the impedance change of the pulse power discharge process, and the equivalent circuit in each discharge stage were consistent with the theoretical model. The proposed oscillation suppression strategy cannot only prevent the damage caused by circuit oscillation but also reduce the damping oscillation time by77.1%, which can greatly improve the stability of the system. This research has potential application value in the field of underwater pulse power discharge for reservoir reconstruction.

Analysis of Dynamic Characteristics of Forced and Free Vibrations of Mill Roll System Based on Fractional Order Theory

In this paper,the main researches are focused on the horizontal nonlinear vibration characteristics of roll systems for rolling mill,mainly including the study of forced vibration and free vibration of the roller.Firstly,the nonlinear damping parameters and nonlinear stiffness parameters within interface of the rolling mill are both considered,and a fractional-order differential term is also introduced to model the horizontal nonlinear vibration.Secondly,the averaging method is introduced to solve the forced vibration system of the mill roll system,and the amplitude-frequency characteristic curves of the system are obtained for different orders,external excitation amplitudes,stiffness and fractional order coefficients.Thirdly,the amplitude-frequency and phasefrequency characteristics of the free vibration of the mill roll system are investigated at different fractional orders.Then,the accuracy of the averaging method for solving the dynamic characteristics of the system is verified by numerical analysis,and the effect of the fractional differential term coefficients and order on the dynamic characteristics of the roll system are investigated.Finally,the time-frequency characteristics and phase-frequency characteristics of free vibration systems at different fractional orders are studied.The validity of the theoretical study is also verified through experiments.