BDS Satellite Clock Prediction Considering Periodic Variations

The periodic noise exists in BeiDou navigation satellite system (BDS) clock offsets. As a commonly used satellite clock prediction model, the spectral analysis model (SAM) typically detects and identifies the periodic terms by the Fast Fourier transform (FFT) according to long-term clock offset series. The FFT makes an aggregate assessment in frequency domain but cannot characterize the periodic noise in a time domain. Due to space environment changes, temperature variations, and various disturbances, the periodic noise is time-varying, and the spectral peaks vary over time, which will affect the prediction accuracy of the SAM. In this paper, we investigate the periodic noise and its variations present in BDS clock offsets, and improve the clock prediction model by considering the periodic variations. The periodic noise and its variations over time are analyzed and quantified by short time Fourier transform (STFT). The results show that both the amplitude and frequency of the main periodic term in BDS clock offsets vary with time. To minimize the impact of periodic variations on clock prediction, a time frequency analysis model (TFAM) based on STFT is constructed, in which the periodic term can be quantified and compensated accurately. The experiment results show that both the fitting and prediction accuracy of TFAM are better than SAM. Compared with SAM, the average improvement of the prediction accuracy using TFAM of the 6 h, 12 h, 18 h and 24 h is in the range of 6.4% to 10% for the GNSS Research Center of Wuhan University (WHU) clock offsets, and 11.1% to 14.4% for the Geo Forschungs Zentrum (GFZ) clock offsets. For the satellites C06, C14, and C32 with marked periodic variations, the prediction accuracy is improved by 26.7%, 16.2%, and 16.3% for WHU clock offsets, and 29.8%, 16.0%, 21.0%, and 9.0% of C06, C14, C28, and C32 for GFZ clock offsets.

Response Characteristics of Systems With Parametric Excitation Through Damping and Stiffness

Floquet theory is combined with harmonic balance to study parametrically excited systems with combination of both time varying damping and stiffness. An approximated solution having an exponential part with unknown exponents and a periodic term consisting of a truncated Fourier series is considered. When applied to a system with parametric damping and stiffness the analysis shows that combination of parametric damping and stiffness alters stability characteristics, particularly in the primary and superharmonic instabilities comparing to the system with only parametric damping or stiffness. We also look at the initial conditions response and its frequency content. The second excitation harmonic in the system with parametric damping is seen to disrupt the coexistence phenomenon which is observed in the parametric damping case.

Spatiotemporal forecasting for groundwater level using a WT-LSTM model

<p>Accurate groundwater level forecasting models is essential to ensure the sustainable utilization and efficient protection of groundwater resources. In this paper, a novel method for groundwater level forecasting is proposed on the basis of coupling discrete wavelet transforms (WT) and long and short term memory neural network (LSTM) . In this model, the wavelet transform is used to decompose the cumulative displacement into the term of trend and term of periodicity . The trend term reflects the long-term tendency of groundwater level variation, which is simulated by a linear regression method. The periodic term driven by external factors such as rainfall, the river stage and the distance from river, is modelled using a LSTM method. The distance from river and the distance from observation wells are used for spatiotemporal model interpretation. Finally, the trend term and periodic term are superposed to achieve the cumulative spatiotemporal prediction of groundwater level. A typical study area located in Haihe basin is taken as an example to validate the performance of the proposed model. The proposed mode (WT-LSTM) is compared with the regular artificial neural network (ANN) model and autoregressive integrated moving average (ARIMA) model. The results show that the prediction accuracy of WT-LSTM model is higher than ANN model and ARIMA model, especially during the flood period. Furthermore, the spatiotemporal groundwater level forecasting is not only included the observation of groundwater and precipitation, but should also take the influence factors of surface water into consideration. The proposed model gives a new sight in the prediction of groundwater level.</p>

Analytical solutions of a particular Hill's differential system

Consider a second order differential linear periodic equation. This equation is recast as a first-order homogeneous Hill’s system. For this system we obtain analytical solutions in explicit form. The first solution is a periodic function. The second solution is a sum of two functions; the first is a continuous periodic function, but the second is an oscillating function with monotone linear increasing amplitude. We give a formula to directly compute the slope of this increase, without knowing the second numerical solution. The periodic term of second solution may be computed directly. The coefficients of fundamental matrix of the system are analytical functions.

Response Characteristics of Systems With Two-Harmonic Parametric Excitation

Floquet theory is combined with harmonic balance to study parametrically excited systems with two harmonics of excitation, where the second harmonic has twice the frequency of the first one. An approximated solution composed of an exponential part with unknown exponents and a periodic term consisting of a truncated Fourier series is considered. When applied to a two-harmonic Mathieu equation the analysis shows that the second harmonic alters stability characteristics, particularly in the primary and superharmonic instabilities. We also look at the initial conditions response and its frequency content. The second excitation harmonic in the system with parametric damping is seen to disrupt the coexistence phenomenon which is observed in the single-harmonic case.

Stability Prediction on Mathieu Equation of Delayed Periodic Term Based on Full-Discretization Method

Delay Periodic Mathieu Equation (DPME), a kind of Delay differential equation (DDE), is used modeling machining operation. Stability analysis of DDE denotes the stable and unstable area between spindle speed and cutting depth of machining situation. This paper presents full-discretization method (FDM) to analyze stability for delayed periodic Mathieu Equation. Stability lobes are constructed for DPME with different time-period/time-delay ratios

Earth’s rotation irregularities derived from UTIBLI by method of multi-composing of ordinates

Using the method of multi-composing of ordinates we have identified in Earth?s rotation a long-periodic term with a period similar to the relaxation time of Chandler nutation. There was not enough information to assess its origin. We demonstrate that the method can be used even in the case when the data time span is comparable to the period of harmonic component.