Accelerated Primal-Dual Projection Neurodynamic Approach With Time Scaling for Linear and Set Constrained Convex Optimization Problems

The Nesterov accelerated dynamical approach serves as an essential tool for addressing convex optimization problems with accelerated convergence rates.Most previous studies in this field have primarily concentrated on unconstrained smooth con-vex optimization problems.In this paper,on the basis of primal-dual dynamical approach,Nesterov accelerated dynamical approach,projection operator and directional gradient,we present two accelerated primal-dual projection neurodynamic approaches with time scaling to address convex optimization problems with smooth and nonsmooth objective functions subject to linear and set constraints,which consist of a second-order ODE(ordinary differential equation)or differential conclusion system for the primal variables and a first-order ODE for the dual vari-ables.By satisfying specific conditions for time scaling,we demonstrate that the proposed approaches have a faster conver-gence rate.This only requires assuming convexity of the objective function.We validate the effectiveness of our proposed two accel-erated primal-dual projection neurodynamic approaches through numerical experiments.

Bi-Fo time scaling method in the numerical simulation of transient conjugate heat transfer

Reliable transient thermal analysis plays a very important role in the engine safety analysis.Transient conjugate heat transfer simulation is an important way of temperature analysis.But there exists a great disparity in the time scales between solid conduction and fluid convection.The calculation cost of transient conjugate heat transfer analysis is very huge because of the tiny time step of computational fluid dynamics.The Bi-Fo time scaling method is proposed to improve the computational efficiency of transient conjugate heat transfer.On the one hand,this method carries out a similar transformation on solid heat conduction,scaling the calculation time with the product of density and specific heat capacity to maintain the consistency of Fourier number.On the other hand,it takes very short time for the fluid domain to recover stability after a boundary disturbance.Based on the above characteristic,the flow time is directly compressed to the same as that of the solid domain.It is verified by Mark II vane that increasing the solid thermal diffusivity can reduce the time scale of heat conduction.In the situation of rapidly stable flow field,scaling flow time does not affect the solid thermal boundary under corresponding dimensionless time.Within the application scope,the Bi-Fo time scaling method can greatly reduce the time cost of transient conjugate heat transfer simulation while maintaining the accuracy of transient temperature analysis.

A real-time performance improvement method for composite time scale

The composite time scale(CTS)provides a stable,accurate,and reliable time scale for modern society.The improvement of CTS’s real-time performance will improve its stability,which strengths related applications’performance.Aiming at this goal,a method achieved by determining the optimal calculation interval and accelerating adjustment stage is proposed in this paper.The determinants of the CTS’s calculation interval(characteristics of the clock ensemble,the measurement noise,the time and frequency synchronization system’s noise and the auxiliary output generator noise floor)are studied and the optimal calculation interval is obtained.We also investigate the effect of ensemble algorithm’s initial parameters on the CTS’s adjustment stage.A strategy to get the reasonable initial parameters of ensemble algorithm is designed.The results show that the adjustment stage can be finished rapidly or even can be shorten to zero with reasonable initial parameters.On this basis,we experimentally generate a distributed CTS with a calculation interval of 500 s and its stability outperforms those of the member clocks when the averaging time is longer than1700 s.The experimental result proves that the CTS’s real-time performance is significantly improved.

A step to the decentralized real-time timekeeping network

The composite time scale(CTS) provides an accurate and stable time-frequency reference for modern science and technology. Conventional CTS always features a centralized network topology, which means that the CTS is accompanied by a local master clock. This largely restricts the stability and reliability of the CTS. We simulate the restriction and analyze the influence of the master clock on the CTS. It proves that the CTS's long-term stability is also positively related to that of the master clock, until the region dominated by the frequency drift of the H-maser(averaging time longer than ~10~5s).Aiming at this restriction, a real-time clock network is utilized. Based on the network, a real-time CTS referenced by a stable remote master clock is achieved. The experiment comparing two real-time CTSs referenced by a local and a remote master clock respectively reveals that under open-loop steering, the stability of the CTS is improved by referencing to a remote and more stable master clock instead of a local and less stable master clock. In this way, with the help of the proposed scheme, the CTS can be referenced to the most stable master clock within the network in real time, no matter whether it is local or remote, making democratic polycentric timekeeping possible.

Optimal Multi-Timescale Scheduling of Integrated Energy Systems with Hybrid Energy Storage System Based on Lyapunov Optimization

The economic operation of integrated energy system(IES)faces new challenges such as multi-timescale characteristics of heterogeneous energy sources,and cooperative operation of hybrid energy storage system(HESS).To this end,this paper investigates the multi-timescale rolling opti-mization problem for IES integrated with HESS.Firstly,the architecture of IES with HESS is established,a comparative analysis is conducted to evaluate the advantages of the HESS over a single energy storage system(SESS)in stabilizing power fluctuations.Secondly,the dayahead and real-time scheduling cost functions of IES are established,the day-ahead scheduling mainly depends on operation costs of the components in IES,the real-time optimal scheduling adopts the Lya-punov optimization method to schedule the battery and hydrogen energy storage in each time slot,so as to minimize the real-time average scheduling operation cost,and the problem of day-ahead and real-time scheduling error,which caused by the uncertainty of the energy storage is solved by online optimization.Finally,the proposed model is verified to reduce the scheduling operation cost and the dispatching error by performing an arithmetic example analysis of the IES in Shanghai,which provides a reference for the safe and stable operation of the IES.

Multi-Time Scale Operation and Simulation Strategy of the Park Based on Model Predictive Control

Due to the impact of source-load prediction power errors and uncertainties,the actual operation of the park will have a wide range of fluctuations compared with the expected state,resulting in its inability to achieve the expected economy.This paper constructs an operating simulation model of the park power grid operation considering demand response and proposes a multi-time scale operating simulation method that combines day-ahead optimization and model predictive control(MPC).In the day-ahead stage,an operating simulation plan that comprehensively considers the user’s side comfort and operating costs is proposed with a long-term time scale of 15 min.In order to cope with power fluctuations of photovoltaic,wind turbine and conventional load,MPC is used to track and roll correct the day-ahead operating simulation plan in the intra-day stage to meet the actual operating operation status of the park.Finally,the validity and economy of the operating simulation strategy are verified through the analysis of arithmetic examples.

Estimation of Dynamic VaR in Chinese Stock Markets Based on Time Scale and Extreme Value Theory

The accuracy and time scale invariance of value-at-risk （VaR） measurement methods for different stock indices and at different confidence levels are tested. Extreme value theory （EVT） is applied to model the extreme tail of standardized residual series of daily/weekly indices losses, and parametric and nonparametric methods are used to estimate parameters of the general Pareto distribution （GPD）, and dynamic VaR for indices of three stock markets in China. The accuracy and time scale invariance of risk measurement methods through back-testing approach are also examined. Results show that not all the indices accept time scale invariance; there are some differences in accuracy between different indices at various confidence levels. The most powerful dynamic VaR estimation methods are EVT-GJR-Hill at 97.5% level for weekly loss to Shanghai stock market, and EVT-GARCH-MLE （Hill） at 99.0% level for weekly loss to Taiwan and Hong Kong stock markets, respectively.

Climate Change and Its Effects on Runoff of Kaidu River, Xinjiang, China:A Multiple Time-scale Analysis

This paper applied an integrated method combining grey relation analysis, wavelet analysis and statistical analysis to study climate change and its effects on runoff of the Kaidu River at multi-time scales. Major findings are as follows: 1) Climatic factors were ranked in the order of importance to annual runoff as average annual temperature, average temperature in autumn, average temperature in winter, annual precipitation, precipitation in flood season, average temperature in summer, and average temperature in spring. The average annual temperature and annual precipi- tation were selected as the two representative factors that impact the annual runoff. 2) From the 32-year time scale, the annual runoff and the average annual temperature presented a significantly rising trend, whereas the annual precipita- tion showed little increase over the period of 1957-2002. By changing the time scale from 32-year to 4-year, we ob- served nonlinear trends with increasingly obvious oscillations for annual runoff, average annual temperature, and annual precipitation. 3) The changes of the runoff and the regional climate are closely related, indicating that the runoff change is the result of the regional climate changes. With time scales ranging from 32-year, 16-year, 8-year and to 4-year, there are highly significant linear correlations between the annual runoff and the average annual temperature and the annual precipitation.

To Improve the Accuracy of Laser Pulse Range Finding by Time Scale-Up

A method of improving the accuracy of laser pulse range finding from ±10 m to ±1 m inexpensively by means of time scale up is described. Time scale up can stretch the entire flight time by a factor of 1 000 and then the stretched result is counted to calculate the distance. The use of this technique decreases the resolution of counting from nanosecond to microsecond, therefore a separate counting oscillator followed by an interpolation operation is unnecessary. This technique can improve the accuracy of laser pulse range finding inexpensively and effectively.

Multiple Time Scale Analysis of River Runoff Using Wavelet Transform for Dagujia River Basin, Yantai, China

Based on monthly river runoff and meteorological data, a method of Morlet wavelet transform was used to analyze the multiple time scale characteristics of river runoff in the Dagujia River Basin, Yantai City, Shandong Province. The results showed that the total annual river runoffin the Dagujia River Basin decreased significantly from 1966 to 2004, and the rate of decrease was 48× 10^6ma/10yr, which was higher than the mean value of most rivers in China. Multiple time scale characteristics existed, which accounted for different aspects of the changes in annual river runoff, and the major periods of the runofftime series were identified as about 28 years, 14 years and 4 years with decreasing levels of fluctuation. The river runoff evolution process was controlled by changes in precipitation to a certain extent, but it was also greatly influenced by human activities. Also, for different time periods and scales, the impacts of climate changes and human activities on annual river runoff evolution occurred at the same time. Changes in the annual river runoffwere mainly associated with climate change before the 1980s and with human activities after 1981.

Noether symmetry and conserved quantity for dynamical system with non-standard Lagrangians on time scales

This paper focuses on studying the Noether symmetry and the conserved quantity with non-standard Lagrangians, namely exponential Lagrangians and power-law Lagrangians on time scales. Firstly, for each case, the Hamilton prin- ciple based on the action with non-standard Lagrangians on time scales is established, with which the corresponding Euler-Lagrange equation is given. Secondly, according to the invariance of the Hamilton action under the infinitesimal transformation, the Noether theorem for the dynamical system with non-standard Lagrangians on time scales is established. The proof of the theorem consists of two steps. First, it is proved under the infinitesimal transformations of a special one-parameter group without transforming time. Second, utilizing the technique of time-re-parameterization, the Noether theorem in a general form is obtained. The Noether-type conserved quantities with non-standard Lagrangians in both clas- sical and discrete cases are given. Finally, an example in Friedmann-Robertson-Walker spacetime and an example about second order Duffing equation are given to illustrate the application of the results.

Astronomical time scale of the Turonian constrained by multiple paleoclimate proxies

One of the clocks that record the Earth history is(quasi-) periodic astronomical cycles.These cycles influence the climate that can be ultimately stored in sedimentary rocks.By cracking these(quasi-) periodic sedimentation signals,high resolution astronomical time scale(ATS) can be obtained.Paleoclimate proxies are widely used to extract astronomical cycles.However different proxies may respond differently to astronomical signals and nonastronomical noises including tectonics,diagenesis,and measurement error among others.Astronomical time scale constructed based on a single proxy where its signal-to-noise ratio is low may have uncertainty that is difficult to evaluate but can be revealed by utilizing other proxies.Here,we test eight astronomical age models using two astrochro no logical methods from four paleoclimate proxies(i.e.,color reflection L~* and b~*,natural gamma radiation,and bulk density) from the Turonian to the Coniacian of the Cretaceous Period at the Demerara Rise in the equatorial Atlantic.The two astrochronological methods are time calibration using long eccentricity bandpass filtering(E1 bandpass) and tracking the long eccentricity from evolutive harmonic analysis(tracking EHA).The statistical mean and standard deviation of four age models from the four proxies are calculated to construct one integrated age model with age uncertainty in each method.Results demonstrate that extracting astronomical signals from multiple paleoclimate proxies is a valid method to estimate age model uncertainties.Anchored at the Cenomanian/Turonian boundary with an age of 93.9 ± 0.15 Ma from biostratigraphy,the ages for CC11/CC12(calcareous nannofossil zones),Turonian/Coniacian(CC12/CC13),CC13/CC14,and Coniacian/Santonian boundaries are 91.25±0.20 Ma,89.87±0.20 Ma,86.36±0.33 Ma,and 86.03±0.32 Ma in E1 bandpass method,compared with 91.17±0.36 Ma,89.74±0.38 Ma,86.13±1.31 Ma,and 85.80±1.33 Ma respectively in tracking EHA method.These results are consistent with previous studies within error and provide a reliable estimation of uncertainties of the ages.

Modeling of Fluid Turbulence Modification Using Two-time-scale Dissipation Models and Accounting for the Particle Wake Effect

Presently developed two-phase turbulence models under-predict the gas turbulent fluctuation, because their turbulence modification models cannot fully reflect the effect of particles. In this paper, a two-time-scale dissipation model of turbulence modification, developed for the two-phase velocity correlation and for the dissipation rate of gas turbulent kinetic energy, is proposed and used to simulate sudden-expansion and swirling gas-particle flows. The proposed two-time scale model gives better results than the single-time scale model. Besides, a gas turbulence augmentation model accounting for the f＇mite-size particle wake effect in the gas Reynolds stress equation is proposed. The proposed turbulence modification models are used to simulate two-phase pipe flows. It can properly predict both turbulence reduction and turbulence enhancement for a certain size of particles observed in experiments.

OSCILLATION FOR NONAUTONOMOUS NEUTRAL DYNAMIC DELAY EQUATIONS ON TIME SCALES

The article is concerned with oscillation of nonautonomous neutral dynamic delay equations on time scales. Sufficient conditions are established for the existence of bounded positive solutions and for oscillation of all solutions of this equation. Some results extend known results for difference equations when the time scale is the set Z^＋ of positive integers and for differential equations when the time scale is the set IR of real numbers.

Mei’s symmetry theorem for time scales nonshifted mechanical systems

We focus on Mei symmetry for time scales nonshifted mechanical systems within Lagrangian framework and its resulting new conserved quantities.Firstly,the dynamic equations of time scales nonshifted holonomic systems and time scales nonshifted nonholonomic systems are derived from the generalized Hamilton’s principle.Secondly,the definitions of Mei symmetry on time scales are given and its criterions are deduced.Finally,Mei’s symmetry theorems for time scales nonshifted holonomic conservative systems,time scales nonshifted holonomic nonconservative systems and time scales nonshifted nonholonomic systems are established and proved,and new conserved quantities of above systems are obtained.Results are illustrated with two examples.

Oscillation of Second-order Nonlinear Dynamic Equation on Time Scales

： The oscillation for a class of second order nonlinear variable delay dynamic equation on time scales with nonlinear neutral term and damping term was discussed in this article. By using the generalized Riccati technique, integral averaging technique and the time scales theory, some new sufficient conditions for oscillation of the equation are proposed. These results generalize and extend many knownresults for second order dynamic equations. Some examples are given to illustrate the main results of this article.

Generalized Chaplygin equations for nonholonomic systems on time scales

The generalized Chaplygin equations for nonholonomic systems on time scales are proposed and studied. The Hamil- ton principle for nonholonomic systems on time scales is established, and the corresponding generalized Chaplygin equa- tions are deduced. The reduced Chaplygin equations are also presented. Two special cases of the generalized Chaplygin equations on time scales, where the time scales are equal to the set of real numbers and the integer set, are discussed. Finally, several examples are given to illustrate the application of the results.

Oscillation of Third-order Delay Dynamic Equations on Time Scales

This paper is concerned with the oscillatory behavior of a class of third-order noonlinear variable delay neutral functional dynamic equations on time scale. By using the generalized Riccati transformation and inequality technique, we establish some new oscilla- tion criteria for the equations. Our results extend and improve some known results, but also unify the oscillation of third-order nonlinear variable delay functional differential equations and functional difference equations with a nonlinear neutral term. Some examples are given to illustrate the importance of our results.

Southern Ocean SST Variability and Its Relationship with ENSO on Inter-Decadal Time Scales

Empirical orthogonal function （EOF） analysis reveals a co-variability of Sea surface temperatures （SSTs） in the Southern Hemisphere （0°-60°S）. In the South Indian and Atlantic Oceans, there is a subtropical dipole pattern slanted in the southwest-northeast direction. In the South Pacific Ocean, a meridional tripole structure emerges, whose middle pole co-varies with the dipoles in the South Indian and Atlantic Oceans and is used in this study to track subtropical Pacific variability. The South Indian and Atlantic Ocean dipoles and the subtropical Pacific variability are phase-locked in austral summer. On the inter-decadal time scales, the dipoles in the South Indian and Atlantic Oceans weaken in amplitude after 1979/1980. No such weakening is found in the subtropical South Pacific Ocean. Interestingly, despite the reduced amplitude, the correlation of the Indian Ocean and Atlantic dipoles with E1 Nino and Southern Oscillation （ENSO） are enhanced after 1979/1980. The same increase in correlation is found for subtropical South Pacific variability after 1979/1980. These inter-decadal modulations imply that the Southern Hemisphere participates in part of the climate shift in the late 1970s. The correlation between Southern Hemisphere SST and ENSO reduces after 2000.

Methods of reduction for Lagrange systems on time scales with nabla derivatives

The Routh and Whittaker methods of reduction for Lagrange system on time scales with nabla derivatives are studied.The equations of motion for Lagrange system on time scales are established, and their cyclic integrals and generalized energy integrals are given. The Routh functions and Whittaker functions of Lagrange system are constructed, and the order of differential equations of motion for the system are reduced by using the cyclic integrals or the generalized energy integrals with nabla derivatives. The results show that the reduced Routh equations and Whittaker equations hold the form of Lagrnage equations with nabla derivatives. Finally, two examples are given to illustrate the application of the results.