Method of variation of parameters for solving a constrained Birkhoffian system

For an in-depth study on the integration problem of the constrained mechanical systems the method of integration for the Birkhoffian system with constraints is discussed and the method of variation of parameters for solving the dynamical equations of the constrained Birkhoffian system is provided.First the differential equations of motion for the constrained Birkhoffian system as well as for the corresponding free Birkhoffian system are established.Secondly a system of auxiliary equations is constructed and the general solution of the equations is found.Finally by varying the parameters and utilizing the properties of the generalized canonical transformation of the Birkhoffian system the solution of the problem can be obtained.The proposed method reveals the inherent relationship between the solution of a free Birkhoffian system and that of a constrained Birkhoffian system. The research results are of universal significance which can be further used in a variety of constrained mechanical systems such as non-conservative systems and nonholonomic systems etc.

The method of variation on parameters for integration of a generalized Birkhoffian system

This paper focuses on studying the integration method of a generalized Birkhoffian system.The method of variation on parameters for the dynamical equations of a generalized Birkhoffian system is presented.The procedure for solving the problem can be divided into two steps：the first step,a system of auxiliary equations is constructed and its general solution is given;the second step,the parameters are varied,and the solution of the problem is obtained by using the properties of generalized canonical transformation.The method of variation on parameters for the generalized Birkhoffian system is of universal significance,and we take a nonholonomic system and a nonconservative system as examples to illustrate the application of the results of this paper.

Parameter Variations of Identified Model for Static Deformation Analysis of Arch Dam

The structural health monitoring of a dam is important for maintaining the safe operation and longevity of the dam system. The structural health of a large dam can be monitored from the measured static deformation. This paper presents an investigation of the parameter variations of the identified model of the measured long-term static deformation for the structural health monitoring of Fui-Tsui Dam, which is located in a very active seismic zone of Taiwan. The measured static deformation is characterized as a function of the measured physical parameters, including the effects of hydrostatic pressure and temperature variation. The identified parameters, associated with the effects of hydrostatic pressure and temperature variation, change with environmental factors, such as flooding, earthquake and foundation change.

INFLUENCE OF NOISE AND DELAY ON REACTION-DIFFUSION RECURRENT NEURAL NETWORKS

In this paper, the influence of the noise and delay upon the stability property of reaction-diffusion recurrent neural networks （RNNs） with the time-varying delay is discussed. The new and easily verifiable conditions to guarantee the mean value exponential stability of an equilibrium solution are derived. The rate of exponential convergence can be estimated by means of a simple computation based on these criteria.

Effect of Oxidation-Induced Material Parameter Variation on the High Temperature Oxidation Behavior of Nickel

In high temperature oxidation environment, the oxidation reaction will induce variations in material parameters, such as Young's modulus, thermal expansion coefficient (CTE), coefficient of oxygen diffusion (COD), etc. The oxidation -induced material parameter variations should be considered in high temperature mechanical analysis. In this paper, high temperature oxidation behavior of an oxide film/metal substrate system was investigated through a modified phase field approach. The oxidative stress and oxidation weight gain induced by high temperature oxidation were studied. Effects of Young's modulus, COD and CTE on oxidative stress in the oxide film were studied particularly. The simulation results showed that a better agreement with the experimental results could be obtained when considering the oxidation -induced material parameter variations in the high temperature mechanical analysis of oxide film/metal substrate system. The simulation results demonstrated that oxidative stress and oxidation weight gain were more sensitive to the variation of Young's modulus than to the variations of COD and CTE.

Scintrex CG5 used for superconducting gravimeter calibration

The scale factor accuracy of superconducting gravimeters （SG） can be largely improved by a high repetition rate of calibration experiments. At stations where the availability of absolute gravimeters is limited, carefully calibrated spring gravimeters can be used for providing the reference signal assuming the irregular drift is properly adjusted. The temporal stability of the SG scale factor is assessable by comparing the temporal variations of M2 tidal parameters observed at neighboring SG sites or from synthetic tide models. Combining these methods reduces the SG scale factor error to a few 0.1%0. The paper addresses the particular procedure required for evaluating the calibration experiments based on spring gravimeters and presents results obtained at Conrad observatory （Austria）. Comparing the M2 amplitude factor modulation helped to reveal a SG scale factor offset of about 0.2%0 due to re-installation.

Variation of Parameters Formula and Gronwall Inequality for Differential Equations with a General Piecewise Constant Argument

A variation of parameters formula and Gronwall type integral inequality are proved for a differential equation involving general piecewise alternately advanced and retarded argument.

Artificial Sun synchronous frozen orbit control scheme design based on J_2 perturbation

Sun synchronous orbit and frozen orbit formed due to J 2 perturbation have very strict constraints on orbital parameters,which have restricted the application a lot.In this paper,several control strategies were illustrated to realize Sun synchronous frozen orbit with arbitrary orbital elements using continuous low-thrust.Firstly,according to mean element method,the averaged rate of change of the orbital elements,originating from disturbing constant accelerations over one orbital period,was derived from Gauss＇ variation of parameters equations.Then,we proposed that binormal acceleration could be used to realize Sun synchronous orbit,and radial or transverse acceleration could be adopted to eliminate the rotation of the argument of the perigee.Finally,amending methods on the control strategies mentioned above were presented to eliminate the residual secular growth.Simulation results showed that the control strategies illustrated in this paper could realize Sun synchronous frozen orbit with arbitrary orbital elements,and can save much more energy than the schemes presented in previous studies,and have no side effect on other orbital parameters＇ secular motion.

Numerical model of soft ground improvement by vertical drain combined with vacuum preloading

The rapid development of high-speed transportation infrastructure such as highway and high-speed railway has resulted in the advancement of soft soil improvement techniques. Vacuum preloading combined with vertical drains has been proved to be an effective method in the treatment of soft foundation. A three-dimensional numerical analysis of the coupled methods was presented, in which the smear zone and the well resistance were taken into account. The variations of the basic soil parameters including the permeability coefficient and the coefficient of volume compressibility were considered in the numerical model. The result of the numerical model was then compared to the measured value. The results indicate that the decrease of coefficient of volume compressibility accelerates the consolidation of the soil while the influence of hydraulic conductivity is insignificant. A cube drain presents the closest result to the real situation compared to the other equivalent methods of prefabricated vertical drain (PVD). The case study indicates that the numerical model with variation of soil parameters is closer to the measured value than the numerical model without variation of soil parameters.

An efficient prediction framework for multi-parametric yield analysis under parameter variations

Due to continuous process scaling, process, voltage, and temperature （PVT） parameter variations have become one of the most problematic issues in circuit design. The resulting correlations among performance metrics lead to a significant parametric yield loss. Previous algorithms on parametric yield prediction are limited to predicting a single-parametric yield or performing balanced optimization for several single-parametric yields. Consequently, these methods fail to predict the multiparametric yield that optimizes multiple performance metrics simultaneously, which may result in significant accuracy loss. In this paper we suggest an efficient multi-parametric yield prediction framework, in which multiple performance metrics are considered as simultaneous constraint conditions for parametric yield prediction, to maintain the correlations among metrics. First, the framework models the performance metrics in terms of PVT parameter variations by using the adaptive elastic net （AEN） method. Then the parametric yield for a single performance metric can be predicted through the computation of the cumulative distribution function （CDF） based on the multiplication theorem and the Markov chain Monte Carlo （MCMC） method. Finally, a copula-based parametric yield prediction procedure has been developed to solve the multi-parametric yield prediction problem, and to generate an accurate yield estimate. Experimental results demonstrate that the proposed multi-parametric yield prediction framework is able to provide the designer with either an accurate value for parametric yield under specific performance limits, or a multi-parametric yield surface under all ranges of performance limits.

An efficient bi-objective optimization framework for statistical chip-level yield analysis under parameter variations

With shrinking technology,the increase in variability of process,voltage,and temperature(PVT) parameters significantly impacts the yield analysis and optimization for chip designs.Previous yield estimation algorithms have been limited to predicting either timing or power yield.However,neglecting the correlation between power and delay will result in significant yield loss.Most of these approaches also suffer from high computational complexity and long runtime.We suggest a novel bi-objective optimization framework based on Chebyshev affine arithmetic(CAA) and the adaptive weighted sum(AWS) method.Both power and timing yield are set as objective functions in this framework.The two objectives are optimized simultaneously to maintain the correlation between them.The proposed method first predicts the guaranteed probability bounds for leakage and delay distributions under the assumption of arbitrary correlations.Then a power-delay bi-objective optimization model is formulated by computation of cumulative distribution function(CDF) bounds.Finally,the AWS method is applied for power-delay optimization to generate a well-distributed set of Pareto-optimal solutions.Experimental results on ISCAS benchmark circuits show that the proposed bi-objective framework is capable of providing sufficient trade-off information between power and timing yield.

State-of-Charge Estimation of Lithium-Ion Battery for Electric Vehicles Using Deep Neural Network

It is critical to have precise data about Lithium-ion batteries,such as the State-of-Charge(SoC),to maintain a safe and consistent functioning of battery packs in energy storage systems of electric vehicles.Numerous strategies for estimating battery SoC,such as by including the coulomb counting and Kalman filter,have been established.As a result of the differences in parameter values between each cell,when these methods are applied to highcapacity battery packs,it has difficulties sustaining the prediction accuracy of overall cells.As a result of aging,the variation in the parameters of each cell is higher as more time is spent in operation.It is suggested in this study to establish an SoC estimate model for a Lithium-ion battery by employing an enhanced Deep Neural Network(DNN)approach.This is because the proposed DNN has a substantial hidden layer,which can accurately predict the SoC of an unknown driving cycle during training,making it ideal for SoC estimation.To evaluate the nonlinearities between voltage and current at various SoCs and temperatures,the proposed DNN is applied.Using current and voltage data measured at various temperatures throughout discharge/charge cycles is necessary for training and testing purposes.When the method has been thoroughly trained with the data collected,it is used for additional cells cycle tests to predict their SoC.The simulation has been conducted for two different Li-ion battery datasets.According to the experimental data,the suggested DNN-based SoC estimate approach produces a low mean absolute error and root-mean-square-error values,say less than 5%errors.

BIFURCATIONS AND CHAOS CONTROL IN TCP-RED SYSTEM

Objective Analyzing the nonlinear dynamics of the TCP-RED congestion control system is of great importance. This study will help investigate the loss of stability in Internet and design a proper method for controlling bifurcation and chaos in such system. Methods Based on bifurcation diagram, the effect of parameter on system performance is discussed. By using the state feedback and parameter variation strategy, a simple real time control method is proposed to modify the existing RED scheme. Results With our control method, the parametric sensitivity of RED mechanism is attenuated. Moreover, a sufficient condition on the robust stability of the system is also derived to adjust the parameters in TCP-RED system. Conclusion The proposed method has the advantages of simple implementation and unnecessary knowledge of the exact system.

Ma’s Variation of Parameters Method for Fisher’s Equations

In this paper,we apply Ma’s variation of parameters method(VPM)for solving Fisher’s equations.The suggested algorithm proved to be very efficient and finds the solution without any discretization,linearization,perturbation or restrictive assumptions.Numerical results reveal the complete reliability of the proposed VPM.

Variation of Parameters Method for Solving System of NonlinearVolterra Integro-Differential Equations

It is well known that nonlinear integro-differential equations play vital role in modeling of many physical processes,such as nano-hydrodynamics,drop wise condensation,oceanography,earthquake and wind ripple in desert.Inspired and motivated by these facts,we use the variation of parameters method for solving system of nonlinear Volterra integro-differential equations.The proposed technique is applied without any discretization,perturbation,transformation,restrictive assumptions and is free from Adomian’s polynomials.Several examples are given to verify the reliability and efficiency of the proposed technique.

Study on Variation of Parameters Formula and Stability for Impulsive Time－Delay Nonlinear Large Scale Systems

This work concerns the representation and stability properties of impulsive solutions for a class of time-delay and measure nonlinear large scale systems. On the basis of fundamental solution of the correspollding ordinary time-delay nonlinear large scale systems is established.By lumped Picard and Gauss-Seidel iteration methods which avoided the difficulties of constructing lyapunov functin, the explicit algebraic criteria of exponential stability for the impulsive and time-delay system are obtained.

The future is frozen:cryogenic CMOS for high-performance computing

Low temperature complementary metal oxide semiconductor(CMOS)or cryogenic CMOS is a promising avenue for the continuation of Moore’s law while serving the needs of high performance computing.With temperature as a control“knob”to steepen the subthreshold slope behavior of CMOS devices,the supply voltage of operation can be reduced with no impact on operating speed.With the optimal threshold voltage engineering,the device ON current can be further enhanced,translating to higher performance.In this article,the experimentally calibrated data was adopted to tune the threshold voltage and investigated the power performance area of cryogenic CMOS at device,circuit and system level.We also presented results from measurement and analysis of functional memory chips fabricated in 28 nm bulk CMOS and 22 nm fully depleted silicon on insulator(FDSOI)operating at cryogenic temperature.Finally,the challenges and opportunities in the further development and deployment of such systems were discussed.

Analysis of process variations impact on the single-event transient quenching in 65 nm CMOS combinational circuits

Single-event transient pulse quenching （Quenching effect） is employed to effectively mitigate WSET （SET pulse width）. It en- hanced along with the increased charge sharing which is norm for future advanced technologies. As technology scales, param- eter variation is another serious issue that significantly affects circuit＇s performance and single-event response. Monte Carlo simulations combined with TCAD （Technology Computer-Aided Design） simulations are conducted on a six-stage inverter chain to identify and quantify the impact of charge sharing and parameter variation on pulse quenching. Studies show that charge sharing induce a wider WSET spread range. The difference of WSET range between no quenching and quenching is smaller in NMOS （N-Channel Metal-Oxide-Semiconductor Field-Effect Transistor） simulation than that in PMOS＇ （P-Channel Met- N-Oxide-Semiconductor Field-Effect Transistor）, so that from parameter variation view, quenching is beneficial in PMOS SET mitigation. The individual parameter analysis indicates that gate oxide thickness （TOXE） and channel length variation （XL） mostly affect SET response of combinational circuits. They bring 14.58% and 19.73% average WSET difference probabilities for no-quenching cases, and 105.56% and 123.32% for quenching cases.

Artificial frozen orbit control scheme based on J_2 perturbation

Since the inclination of frozen orbit with non-rotation of the perigee that occurs due to J2 perturbation must be equal to the critical inclination, this regulation has restricted the application of frozen orbit a lot. In this paper, we propose two control strategies to eliminate the secular growth of the argument of the perigee for orbits that are not at the critical inclination. One control strategy is using transverse continuous low-thrust, and the other is using both the transverse and the radial continuous low-thrusts. Fuel optimization in the second control strategy is addressed to make sure that the fuel consumption is the minimum. Both strategies have no effect on other orbital parameters’ secular motion. It is proved that the strategy with transverse control could save more energy than the one with radial control. Simulations show that the second control strategy could save 54.6% and 86% of energy, respectively, compared with the two methods presented in the references.

On generalized impulsive piecewise constant delay differential equations

A variation of parameters formula with Green function type and Gronwall type integral inequality are proved for impulsive differential equations involving piecewise constant delay of generalized type. Some results for piecewise constant linear and nonlinear delay differential equations with impulsive effects are obtained.They include existence and uniqueness theorems, a variation of parameters formula, integral inequalities, the oscillation property and some applications.