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Accurate flight trajectory prediction is a crucial and challenging task in air traffic control, especially for maneuver operations. Modern data-driven methods are typically formulated as a time series forecasting task and fail to retain high accuracy. Meantime, as the primary modeling method for time series forecasting, frequency-domain analysis is underutilized in the flight trajectory prediction task. In this work, an innovative wavelet transform-based framework is proposed to perform time-frequency analysis of flight patterns to support trajectory forecasting. An encoder-decoder neural architecture is developed to estimate wavelet components, focusing on the effective modeling of global flight trends and local motion details. A real-world dataset is constructed to validate the proposed approach, and the experimental results demonstrate that the proposed framework exhibits higher accuracy than other comparative baselines, obtaining improved prediction performance in terms of four measurements, especially in the climb and descent phase with maneuver control. Most importantly, the time-frequency analysis is confirmed to be effective to achieve the flight trajectory prediction task. Accurate flight trajectory prediction can be a challenging task in air traffic control, especially for maneuver operations. Here, authors develop a time-frequency analysis based on an encoder-decoder neural architecture to estimate wavelet components and model global flight trends and local motion details.

Summary For cable bridges, the cable tension force plays a crucial role in their construction, assessment and long‐term structural health monitoring. Cable tension forces vary in real time with the change of the moving vehicle loads and environmental effects, and this continual variation in tension force may cause fatigue damage of a cable. Traditional vibration‐based cable tension force estimation methods can only obtain the time‐averaged cable tension force and not the instantaneous force. This paper proposes a new approach to identify the time‐varying cable tension forces of bridges based on an adaptive sparse time‐frequency analysis method. This is a recently developed method to estimate the instantaneous frequency by looking for the sparsest time‐frequency representation of the signal within the largest possible time‐frequency dictionary (i.e. set of expansion functions). In the proposed approach, first, the time‐varying modal frequencies are identified from acceleration measurements on the cable, then, the time‐varying cable tension is obtained from the relation between this force and the identified frequencies. By considering the integer ratios of the different modal frequencies to the fundamental frequency of the cable, the proposed algorithm is further improved to increase its robustness to measurement noise. A cable experiment is implemented to illustrate the validity of the proposed method. For comparison, the Hilbert–Huang transform is also employed to identify the time‐varying frequencies, which are then used to calculate the time‐varying cable‐tension force. The results show that the adaptive sparse time‐frequency analysis method produces more accurate estimates of the time‐varying cable tension forces than the Hilbert–Huang transform method. Copyright © 2016 John Wiley & Sons, Ltd.

Signal processing techniques play an important role in seismic data analysis. Variational mode decomposition (VMD), as a powerful signal processing method, has been extensively applied in seismic signal processing. A large number of papers on the application of VMD in seismic data analysis have appeared in various journals, conference proceedings, and technical communications. The paper aims to investigate and summarize the recent advancements of VMD and its application in seismic data analysis and give a comprehensive reference for scholars that may be interested in this topic so that researchers can select a more in-depth research direction. Firstly, the VMD principle is briefly introduced, and the advantage and limitations of this approach are illustrated in detail. Secondly, recent applications of the VMD in seismic data analysis are summarized in terms of specific scenarios, such as seismic time–frequency analysis (TFA), seismic denoising, and other applications. Finally, the key problems of VMD in seismic data analysis are discussed, and the potential research directions are listed. It is expected that the review would be constructive to the basic understanding of the VMD concept for beginners and insightful exploration of VMD’s applications in seismic data analysis for advanced researchers.Article HighlightsSeismic data analysis plays an important role in extracting valuable information from seismic recordsThis paper surveys the VMD and its applications in the field of seismic data analysis in a comprehensive wayPromising research prospects of VMD in seismic data analysis are proposed

In most nations across the world, the fundamental goal of economic policy is to achieve sustainable economic growth. Economic development, on the other hand, may have an influence on climate change and global warming, which are major worldwide concerns and problems. Thus, this research offers a new perceptive on the influence of renewable and nonrenewable energy consumption on CO 2 emissions in Argentina utilizing data from the period between 1965 and 2019. The current research applied the wavelet tools to assess these interconnections. The outcomes of these analyses reveal that the association between the series evolves over both frequency and time. The current analysis uncovers notable wavelet coherence and significant lead and lag connections in the frequency domain, while in the time domain, contradictory correlations are indicated among the variables of interest. From an economic perspective, the outcomes of the wavelet analysis affirm that in the medium and long term, renewable energy consumption contributes to environmental sustainability. Furthermore, in the medium term, trade openness mitigates CO 2 , although in the long term, no significant connection was found. Moreover, both nonrenewable energy and economic growth contribute to environmental degradation in the short and long term. Finally, the frequency domain causality outcomes reveal that in the long term, economic growth, trade openness, and nonrenewable energy can predict CO 2 emissions. The present analysis offers an innovative insight into the interconnection and comovement between CO 2 and trade openness, renewable energy utilization, and GDP in the Argentinean economy. The findings from this research should be of interest to economists, researchers, and policymakers.

To investigate the influence of a rapid water drawdown (RWD) on the seismic response characteristics of reservoir rock slopes, numerical dynamic analyses and shaking table tests are conducted on a rock slope containing discontinuities under a RWD using time–frequency analysis from the perspective of spectral and energy propagation characteristics. The results show that a RWD has a magnification effect on the seismic response of a surface slope, which is mainly manifested as the RWD causing the seismic energy of the surface slope to increase significantly. The RWD has a magnification effect on the Fourier spectrum amplitude of the low-order natural frequency band. A time–frequency domain analysis shows that the RWD has an influence on the characteristics of the seismic Hilbert energy spectrum (HES) in the low-frequency band of the surface slope and magnifies the amplitude of the marginal spectrum (MS) in the high-frequency band. In addition, the applicability of the Fourier spectrum, HES and MS in analysing the relationship between the RWD and the slope dynamic response is discussed. An analysis of the seismic HES shows that the RWD has a major impact on the overall dynamic response of the surface slope, while the RWD has a significant impact on the local dynamic response of the surface slope based on the Fourier spectrum and the MS. The influence mechanism of the RWD on the HES and MS of the slope is also discussed. Moreover, the influence of a RWD on the development process of seismic damage to the slope is clarified using an energy-based method.

A novel data-driven modal analysis method, reduced-order variational mode decomposition (RVMD), is proposed, inspired by the Hilbert–Huang transform and variational mode decomposition (VMD), to resolve transient or statistically non-stationary flow dynamics. First, the form of RVMD modes (referred to as an ‘elementary low-order dynamic process’, ELD) is constructed by combining low-order representation and the idea of intrinsic mode function, which enables the computed modes to characterize the non-stationary properties of space–time fluid flows. Then, the RVMD algorithm is designed based on VMD to achieve a low-redundant adaptive extraction of ELDs in flow data, with the modes computed by solving an elaborate optimization problem. Further, a combination of RVMD and Hilbert spectral analysis leads to a modal-based time-frequency analysis framework in the Hilbert view, providing a potentially powerful tool to discover, quantify and analyse the transient and non-stationary dynamics in complex flow problems. To provide a comprehensive evaluation, the computational cost and parameter dependence of RVMD are discussed, as well as the relations between RVMD and some classic modal decomposition methods. Finally, the virtues and utility of RVMD and the modal-based time-frequency analysis framework are well demonstrated via two canonical problems: the transient cylinder wake and the planar supersonic screeching jet.

The geological structure and stratum lithology have important roles in the seismic stability of complex slopes; however, their roles complicate engineering construction. Four three-dimensional, layered granite slope models with infinite boundaries were modeled via the finite element method. The seismic response characteristics of slopes are systematically analyzed in the time–frequency domain. A frequency-domain analysis method of complex slopes, including modal and spectrum conjoint analysis, is proposed. Modal analysis can directly display the main vibration modes of slopes. The combination of modal and spectral analysis can clarify the inherent characteristics of slopes and reveal the interaction mechanism between the inherent frequency of slopes and their dynamic characteristics. The results illustrate that structural planes have significant effects on the propagation characteristics of waves within rock masses, and complex refraction/reflection phenomena occur near these discontinuities, thus leading to different dynamic response characteristics in the slope. Layered slopes have an apparent magnification effect of slope surface and altitude. The directions of seismic excitation and structural plane types affect the dynamic response of slopes. Horizontal waves mainly affect the middle and upper parts of high-steep slopes, while vertical waves have an obvious influence on the slope crest. Additionally, Fourier spectral analysis shows that structural planes have filtering effects on high-frequency waves. Combined with modal analysis, this finding further explains that the high-frequency section of waves mainly triggers local deformation of slopes, while the low-frequency component controls their overall deformation. The instability regions and evolution process of slopes were predicted based on time–frequency conjoint analysis.

Magnetoencephalography and electroencephalography (M/EEG) measure the weak electromagnetic signals originating from neural currents in the brain. Using these signals to characterize and locate brain activity is a challenging task, as evidenced by several decades of methodological contributions. MNE, whose name stems from its capability to compute cortically-constrained minimum-norm current estimates from M/EEG data, is a software package that provides comprehensive analysis tools and workflows including preprocessing, source estimation, time–frequency analysis, statistical analysis, and several methods to estimate functional connectivity between distributed brain regions. The present paper gives detailed information about the MNE package and describes typical use cases while also warning about potential caveats in analysis. The MNE package is a collaborative effort of multiple institutes striving to implement and share best methods and to facilitate distribution of analysis pipelines to advance reproducibility of research. Full documentation is available at http://martinos.org/mne. [Display omitted] •The MNE software provides a complete pipeline for MEG and EEG data analysis.•MNE covers preprocessing, forward modeling, inverse methods, and visualization.•MNE supports advanced analysis: time-frequency, statistics, and connectivity.•MNE-Python enables fast and memory-efficient processing of large data sets.•MNE-Python is an open-source software supporting a collaborative development effort.

The concept of return period in stationary univariate frequency analysis is prone to misconceptions and misuses that are well known but still widespread. In this study we highlight how nonstationary and multivariate extensions of such a concept are affected by additional misconceptions, thus easily resulting in further ill-posed procedures and misleading conclusions. We also show that the concepts of probability of exceedance and risk of failure over a given design life period provide more coherent, general and well devised tools for risk assessment and communication.

We examine the time-frequency spillovers, contagion, and pairwise interrelations between the BRIC index and its constituents, and between BRIC and G7 economies. The extent of interdependencies between market blocs and their constituents needs to be ascertained in the time-frequency domain for efficient asset allocation and portfolio management. Accordingly, the Baruník and Křehlík spillover index is employed with daily data between 11 th December 2015 and 28 th May 2021. We find the overall and net spillovers between BRIC and G7 to be significant in the short-term, with France, Germany, and the UK transmitting the greatest shocks to BRIC markets. We find no significant evidence of any sporadic volatilities for the studied markets in the COVID-19 period across all frequencies. However, we reveal contagious spillovers between the BRIC and G7 economies across all time scales in 2017 and 2019, which respectively reflect the persistent effect of Brexit and the US-China trade tension. Our findings divulge that in the short-term (mid-to-long-term), France and the UK (Canada and the US), are the sources of contagion between the BRIC and G7 markets. From the net-pairwise spillovers, we report high connectedness between the BRIC index and its members. BRIC countries are found to be transmitters of net-pairwise spillovers to the G7 markets excluding Japan. We recommend portfolio diversification using BRIC and G7 stocks in the intermediate-to-long-term horizon, where spillovers are less concentrated. Additionally, since individual markets are impacted by their unique shocks, investors should pay close attention to these shocks when distributing assets. In the interim, policy-makers and governments across the globe should ensure effective liberalisation of their economies to encourage international trade flows to boost portfolio diversification.