Advances in Data Science and Adaptive Analysis

This paper explores a new method to model and forecast the global earthquake energy release time series. The ISC-GEM catalogue of global events with magnitude $\mathrm{\text{Mw}}\ge 6.4$ is used in this study. The magnitudes of individual events are converted into seismic energy using an empirical relation. The annual earthquake energy time series is constructed by adding the energy releases of all the events in a particular year. Then, the energy time series is decomposed into finite number of intrinsic mode functions (IMFs) using empirical mode decomposition (EMD) technique. The periodicities of these IMF’s and their contribution to the total variance of the data are examined to identify the influence of natural phenomenon on earthquake energy release. The artificial neural network technique (ANN) is further used for modeling the energy-time series. The model is verified with an independent subset of data and validated using statistical parameters. The forecast of the annual earthquake energy release is provided for the year 2016.

Continuous biological signals, like blood pressure recordings, exhibit nonlinear and nonstationary properties which must be considered during their analysis. Heart rate variability analyses have identified several frequency components and their autonomic origin. There is need for more knowledge on the time-changing properties of these frequencies. The power spectrum, continuous wavelet transform and Hilbert–Huang transform are applied on a continuous blood pressure signal to investigate how the different methods compare to each other. The Hilbert–Huang transform shows high ability to analyze such data, and can, by identifying instantaneous frequency shifts, provide new insights into the nature of these kinds of data.

In this paper, we consider multiple signals sharing the same instantaneous frequencies. This kind of data is very common in scientific and engineering problems. To take advantage of this special structure, we modify our data-driven time-frequency analysis by updating the instantaneous frequencies simultaneously. Moreover, based on the simultaneous sparsity approximation and the Fast Fourier Transform, we develop several efficient algorithms to solve this problem. Since the information of multiple signals is used, this method is very robust to the perturbation of noise and it is applicable to the general nonperiodic signals even with missing samples or outliers. Several synthetic and real signals are used to demonstrate the robustness of this method. The performances of this method seems quite promising.