Multiple Time Variables Research Articles

A novel Domain Adaptive Deep Recurrent Network for multivariate time series prediction

Multivariate time series prediction has attracted growing interest in many research fields. Recently, deep learning has been applied to multivariate time series prediction and has achieved encouraging results. However, in real-world scenarios, the insufficient data of multivariate time series at the beginning of the observation causes the deep learning model unable to exert its expected performance. Furthermore, there is the distribution discrepancy between different multivariate time series caused by many factors, making it unfeasible to reuse existing data or models directly. Therefore, a novel Domain Adaptive Deep Recurrent Network (DADRN) is proposed for multivariate time series prediction with insufficient data, which transferring the knowledge of the target-related time series (source domain) to the target time series (target domain) by minimizing distribution mismatch in the feature sharing space. The DADRN automatically learns the temporal dependence of predictive time series and the dynamic dependencies between multiple time variables through the deep recurrent neural network. Besides, a special transfer learning method, domain adaptation, is embedded in the constructed deep recurrent network to reduce the distribution discrepancy between different domains. The proposed domain independence strategy and domain weighted loss further enhance the DADRN’s transfer learning capability by improving the distribution estimation of the target domain and balancing the network’s learning on two domains. The reasonable combination of deep recurrent network and domain adaptation endows DADRN with favorable transfer learning capability, and its effectiveness is demonstrated by the experimental results on two real-world datasets.

A theoretical survey of two-dimensional coherent spectroscopy in strongly-correlated electronic systems

Two-dimensional coherent spectroscopy (2DCS) diagnoses a material’s nonlinear optical response with multiple time variables, thus offering information that is inaccessible with conventional linear optical spectroscopy. The 2DCS in the infrared, visible, and ultraviolet frequency range has yielded fruitful results in chemistry and biology. In the terahertz (THz) frequency window, 2DCS has shown its promise in the study of strongly-correlated electronic systems. As a guide to this rapidly developing field, we survey the current status of the theory of THz-2DCS in strongly-correlated electronic systems. We then introduce the basic concepts and theoretical methods of 2DCS, and analyze the main characteristics of the two-dimensional spectra. Finally, we summarize our latest theoretical research in this field.

A Novel Ensemble Approach for the Forecasting of Energy Demand Based on the Artificial Bee Colony Algorithm

Accurate forecasting of the energy demand is crucial for the rational formulation of energy policies for energy management. In this paper, a novel ensemble forecasting model based on the artificial bee colony (ABC) algorithm for the energy demand was proposed and adopted. The ensemble model forecasts were based on multiple time variables, such as the gross domestic product (GDP), industrial structure, energy structure, technological innovation, urbanization rate, population, consumer price index, and past energy demand. The model was trained and tested using the primary energy demand data collected in China. Seven base models, including the regression-based model and machine learning models, were utilized and compared to verify the superior performance of the ensemble forecasting model proposed herein. The results revealed that (1) the proposed ensemble model is significantly superior to the benchmark prediction models and the simple average ensemble prediction model just in terms of the forecasting accuracy and hypothesis test, (2) the proposed ensemble approach with the ABC algorithm can be employed as a promising framework for energy demand forecasting in terms of the forecasting accuracy and hypothesis test, and (3) the forecasting results obtained for the future energy demand by the ensemble model revealed that the future energy demand of China will maintain a steady growth trend.

Extended Lindstedt–Poincare method for non-stationary resonances of dynamical systems with cubic nonlinearities

This paper presents the extended Lindstedt–Poincare (EL–P) method, which applies multiple time variables to treat non-stationary oscillations arising in dynamical systems with cubic nonlinearities due to the slowly varied excitation parameters. The method is applied extensively in research of non-stationary vibrations of clamped-hinged beams. Recognizing the aperiodic nature of non-stationary oscillations, the new formulation is presented by adding an additional, slow time scale beside time scales of the nonlinear system, which generally correspond to the incommensurate nonlinear frequencies of the response. Using this concept, a generalized approach of the study to the passage through fundamental, superharmonic and subharmonic resonances is presented in the paper. Effects of slowly varying excitation frequency and slowly varying excitation amplitude on the non-stationary oscillations are studied with the computation of deviations from the stationary response. Although the method is formulated for N-dof dynamical systems having weak cubic nonlinearities, it is applied for non-stationary vibrations, where two-mode shape approximation of damped and undamped clamped-hinged beam, respectively, is used and the simultaneous appearance of internal resonance is taken into account. Stability analysis of stationary solutions is performed and comparisons of stationary resonance curves by results obtained with the incremental harmonic balance (IHB) method show good agreement. The passage through the fundamental resonance of damped and undamped clamped-hinged beam, respectively, is investigated in detail.

Incremental harmonic balance method with multiple time variables for dynamical systems with cubic non‐linearities

AbstractThe incremental harmonic balance method with multiple time variables is developed for analysis of almost periodic oscillations in multi‐degree‐of‐freedom dynamical systems with cubic non‐linearities, subjected to the external multi‐tone excitation. The method is formulated to treat non‐autonomous as well as autonomous dynamical systems. The almost periodic oscillations, which coexist with periodic oscillations in a rotating system model with cubic restoring force and an electromagnetic eddy‐current damper are analysed. The closed form solutions based on generalized Fourier series containing two incommensurate frequencies are obtained in the case of small non‐dimensional stiffness ratio. Almost periodic oscillations of a rotating system model in dependence on variable parameters are also analysed, where solutions are computed through an augmentation process including a greater number of harmonics and combination frequencies involved. Copyright © 2003 John Wiley & Sons, Ltd.

Analyzing circuits with widely separated time scales using numerical PDE methods

Widely separated time scales arise in many kinds of circuits, e,g., switched-capacitor filters, mixers, switching power converters, etc. Numerical solution of such circuits is often difficult, especially when strong nonlinearities are present. In this paper, the author presents a mathematical formulation and numerical methods for analyzing a broad class of such circuits or systems. The key idea is to use multiple time variables, which enable signals with widely separated rates of variation to be represented efficiently. This results in the transformation of differential equation descriptions of a system to partial differential ones, in effect decoupling different rates of variation from each other. Numerical methods can then be used to solve the partial differential equations (PDEs). In particular, time-domain methods can be used to handle the hitherto difficult case of strong nonlinearities together with widely separated rates of signal variation. The author examines methods for obtaining quasiperiodic and envelope solutions, and describes how the PDE formulation unifies existing techniques for separated-time-constant problems. Several applications are described. Significant computation and memory savings result from using the new numerical techniques, which also scale gracefully with problem size.

Modified Kortweg–de Vries hierarchies in multiple–time variables and the solutions of modified Boussinesq equations

We study solitary-wave and kink-wave solutions of a modified Boussinesq equation through a multiple-time reductive perturbation method. We use appropriated modified Korteweg-de Vries hierarchies to eliminate secular producing terms in each order of the perturbative scheme. We show that the multiple-time variables needed to obtain a regular perturbative series are completely determined by the associated linear theory in the case of a solitary-wave solution, but requires the knowledge of each order of the perturbative series in the case of a kink-wave solution. These appropriate multiple-time variables allow us to show that the solitary-wave as well as the kink-wave solutions of the modified Botussinesq equation are actually respectively a solitary-wave and a kink-wave satisfying all the equations of suitable modified Korteweg-de Vries hierarchies.