Advances in Adaptive Data Analysis

Information extraction from time series has traditionally been done with Fourier analysis, which use stationary sines and cosines as basis functions. However, data that come from most natural phenomena are mostly nonstationary. A totally adaptive alternative method has been developed called the Hilbert–Huang transform (HHT), which involves generating basis functions called the intrinsic mode functions (IMFs) via the empirical mode decomposition (EMD). The EMD is a numerical procedure that is prone to numerical errors that may persist in the decomposition as extra IMFs. In this study, results of numerical experiments are presented, which would establish a stringent threshold by which relevant IMFs are distinguished from IMFs that may have been generated by numerical errors. The threshold is dependent on the correlation coefficient between the IMFs and the original signal. Finally, the threshold is applied to IMFs of earthquake signals from five accelerometers located in a building.

The empirical mode decomposition (EMD) is the core of the Hilbert–Huang transform (HHT). In HHT, the EMD is responsible for decomposing a signal into intrinsic mode functions (IMFs) for calculating the instantaneous frequency and eventually the Hilbert spectrum. The EMD method as originally proposed, however, has an annoying mode mixing problem caused by the signal intermittency, making the physical interpretation of each IMF component unclear. To resolve this problem, the ensemble EMD (EEMD) was subsequently developed. Unlike the conventional EMD, the EEMD defines the true IMF components as the mean of an ensemble of trials, each consisting of the signal with added white noise of finite, not infinitesimal, amplitude. In this study, we further proposed an extension and alternative to EEMD designated as the noise-modulated EMD (NEMD). NEMD does not eliminate mode but intensify and amplify mixing by suppressing the small amplitude signal but the larger signals would be preserved without waveform deformation. Thus, NEMD may serve as a new adaptive threshold amplitude filtering. The principle, algorithm, simulations, and applications are presented in this paper. Some limitations and additional considerations of using the NEMD are also discussed.

This work defines the unique instantaneous frequency (IF) of an arbitrary time signal to be the circular instantaneous frequency (cIF) of the curvature radius of the signal's trajectory on the phase plane, where the signal's conjugate part is obtained from Hilbert transform (HT). Because a general signal of a dynamical system of multiple degrees of freedom contains multiple modal vibrations, its cIF varies dramatically and is not useful for system identification and other applications. If the signal is decomposed into modal vibration components without moving average, each component has no local extrema within each fundamental period and no local loops on the phase plane, each component's referred instantaneous frequency (rIF) with respect to the origin on the phase plane may be non-circular but is always non-negative, and the time-varying rIF and referred instantaneous amplitude (rIA) are convenient for combining the use of perturbation analysis for system identification. The empirical mode decomposition (EMD) of Hilbert–Huang transform (HHT) is valuable for decomposing a general nonlinear nonstationary signal into zero-mean intrinsic mode functions (IMFs), and HT enables accurate calculation of rIF and rIA of each IMF. Although the concept of circular frequency cannot be used for signal decomposition, it enables the development of time-domain-only techniques for online frequency tracking. A 5-point frequency tracking method is developed to eliminate the incapability of the original 4-point Teager–Kaiser algorithm (TKA) for frequency tracking of signals with moving averages. Moreover, a 3-point conjugate-pair decomposition (CPD) method is derived based on circle-fitting using a pair of conjugate harmonic functions. It is shown that both CPD and TKA are based on the concept of circle fitting, but TKA uses finite difference and CPD uses curve fitting in numerical implementation. However, the accuracy of TKA is easily destroyed by noise because of the use of finite difference. On the other hand, because CPD is based on curve fitting, noise filtering is an implicit capability and its accuracy increases with the number of processed data points. The rIF from HHT and the cIF from CPD and TKA are different by definition. Moreover, because the instantaneous frequency and amplitude are assumed to be constant in CPD and TKA, the cIF from CPD and TKA also deviates from the exact cIF.

In this paper a new method for voiced speech enhancement combining the Empirical Mode Decomposition (EMD) and the Adaptive Center Weighted Average (ACWA) filter is introduced. Noisy signal is decomposed adaptively into intrinsic oscillatory components called Intrinsic Mode Functions (IMFs). Since voiced speech structure is mostly distributed on both medium and low frequencies, the shorter scale IMFs of the noisy signal are beneath noise, however the longer scale ones are less noisy. Therefore, the main idea of the proposed approach is to only filter the shorter scale IMFs, and to keep the longer scale ones unchanged. In fact, the filtering of longer scale IMFs will introduce distortion rather than reducing noise. The denoising method is applied to several voiced speech signals with different noise levels and the results are compared with wavelet approach, ACWA filter and EMD–ACWA (filtering of all IMFs using ACWA filter). Relying on exhaustive simulations, we show the efficiency of the proposed method for reducing noise and its superiority over other denoising methods, i.e. to improve Signal-to-Noise Ratio (SNR), and to offer better listening quality based on a Perceptual Evaluation of Speech Quality (PESQ). The present study is limited to signals corrupted by additive white Gaussian noise.

In this article, a new strategy for modeling and forecasting the air traffic data series is presented. The empirical mode decomposition technique is used to decompose the monthly air traffic time series into finite number of intrinsic modes. This helps in identifying the last empirical mode as a trend and the summation of remaining modes as the fluctuation in the data. The fluctuation part is handled by artificial neural network (ANN) techniques, whereas the trend is amenable for modeling through simple regression concepts. It is found that the proposed model explains 46–89% of the variability of five air traffic time series considered here. The model is efficient in statistical forecasting of air traffic as verified on an independent subset of the data series.

Kernels have become an integral part of most data classification algorithms. However, the kernel parameters are generally not optimized during learning. In this work a novel adaptive technique called Sequential Function Approximation (SFA) has been developed for classification that determines the values of the control and kernel hyper-parameters during learning. This tool constructs sparse radial basis function networks in a greedy fashion. Experiments were carried out on synthetic and real-world data sets where SFA had comparable performance to other popular classification schemes with parameters optimized by an exhaustive grid search.

In this paper, the mechanical behaviors of bridges with unseating prevention devices in the superstructure were investigated. These devices can prevent bridge from unseating and divert most of the seismic forces from transferring to the bridge columns. The models of the rubber bearing, restrainer, and shear key were proposed and implemented into the SAP 2000 to obtain the seismic response of the bridge. The nonlinear time history analysis was used to determine the time history response of the superstructure of the bridge. In the meantime, the Hilbert–Huang Transform (HHT) was used to transfer the displacement–time responses of the superstructure of the bridge into the time–frequency domain, while the spectra are a function of both frequency and time. The spectra of the HHT can be used to determine the operation sequences of the unseating prevention devices.