Advances in Adaptive Data Analysis

The composite mean difference (CMD) projection method is similar to the empirical orthogonal function (EOF) expansion commonly used in climate data analysis except that its first mode is empirically defined to be phenomenon-specific instead of being the mode that explains the most variance in the data as in the latter. The EOF, being a mathematically defined statistical quantity, may contain contributions from several phenomena, making its physical interpretation difficult. Furthermore, because the modes in the EOF expansion are ordered according to the magnitudes of their variances, the first few modes are often made up of internal variability, with smaller forced responses relegated to the higher modes, which are seldom studied. In CMD, a known (forcing) index of a quasi-periodic phenomenon under consideration is used to define two groups (e.g., high and low index years) by CMD of the data segregated in time into these two groups, yielding a spatial pattern of the "response" to this forcing. An associated time series that represents the temporal behavior of this "response" is then obtained by projecting the original spatial-time data onto the spatial CMD pattern. Bootstrap Monte Carlo statistical tests have been devised to test if the association of the "response" with the "forcing" index is distinguishable from that obtained by random chance. In this paper, synthetic data that simulate the real temperature observations will be used to empirically examine how trustworthy the conclusion from such statistical tests is. The results confirm the conclusions from bootstrap tests previously proposed, even in the presence of deterministic variability in the "noise."

To mitigate end effects of empirical mode decomposition (EMD), a novel approach inspired by the nonlinear gray model (GM) termed as GM(1,1,α) is presented. Other than traditional linear or mirror extension on the boundary, the GM(1,1,α) model is applied to predict two extrema at both ends of the data. It is worth noting that our GM(1,1,α) model is particularly useful for predicting uncertainty data. According to numerical experiments on synthetic signal as well as real data series, the proposed method gives very comparable results with other three generally acknowledged methods, including the linear extension (LE), window function (WF), and mirror symmetry (MS) based methods. That is, the proposed method can reduce end effects and improve decomposition results of EMD significantly.

Ensemble empirical mode decomposition (EEMD) is a novel adaptive time-frequency analysis method, which is particularly suitable for extracting useful information from noisy nonlinear or nonstationary data. This paper presents the utilization of EEMD for hyperspectral images to extract signals from them, generated in noisy nonlinear and nonstationary processes. First, EEMD is applied to each hyperspectral image band and defines the true intrinsic mode function (IMF) components as the mean of an ensemble of trials, each consisting of the signal plus a white noise of finite amplitude. After EEMD is performed to each band, new bands are reconstructed as the sum of IMFs and the trend, and classification is executed over these new bands. Finally, the hyperspectral image with new bands was classified with support vector machine (SVM) to show the classification performance of the proposed approach. Experimental results show that the utilization of the EEMD significantly increases the classification accuracy compared to the dataset processed by empirical mode decomposition (EMD) and the original dataset.

In the process of photoacoustic imaging (PAI), the photoacoustic signals are polluted by a strong background white noise, which is caused by many factors such as the system thermal noise or short noise, the tissue reflecting or scattering interference, and the impedance match lack between the transducer and tissue. The inevitable noise can degrade the contrast sensitivity of photoacoustic images seriously. In this paper, based on the energy window, a CMSE-EMD denoising method is employed to photoacoustic image reconstruction. Results of the simulation demonstrate that it can eliminate the image artifacts more effectively and achieve great improvement in image quality.

This work proposes a feature extraction method from Hilbert–Huang-transform- or HHT-based data analysis of built-in test (BIT) signals, which are sampled on-site and without reference signals for fault diagnosis. The proposed method fully utilizes self-adaptation of the HHT method in characterizing the envelope amplitude and instantaneous frequency for the intrinsic mode function (IMF), so as to single out the features with most irregular characteristics. Simulations are carried out on steering gear feedback voltage signal of target drone aircraft, and the extracted features show great potential for the improvement in built-in fault diagnosis.

This paper presents a data-adaptive technique of cardiovascular disease diagnosis by analyzing electrocardiogram (ECG) signals. The separation of high-frequency (HF) and low-frequency (LF) components are performed by employing empirical mode decomposition (EMD) designed for analyzing nonstationary and non-linear signals. The EMD is used to decompose ECG signal into a finite set of band-limited AM–FM signals termed as intrinsic mode functions (IMFs). Then the LF and HF components of ECG signals are obtained by partial reconstruction based on the energy distribution of IMFs. The extracted HF and LF signals of the ECG are analyzed separately to make the remarks for better diagnosis of the cardiovascular diseases. The experimental results are also illustrated using some ECG signals of normal and abnormal subjects.

Through the empirical mode decomposition (EMD), we extrapolated the seasonal component of monthly temperature oscillation of N = 1167 distributed on whole USA covering a period of 111 years from 1898 to 2008. We found an occasional destabilization of the phase of the seasonal component; moreover, the time distribution of these anomaly events is strongly correlated in time with a dominant periodicity remarkably close to the 18.6-year period of the Earth's nutation that represents the stronger modulation to the Earth's precession. Probably, phase-shift effect of seasonal oscillation is due to an orbit-climate relationship related to nutational forcing.

This paper mainly focuses on discussing the following three suspensions about the intrinsic mode functions (IMFs): (1) Whether more sifting times lead better symmetry to the IMFs or not? (2) Whether the upper and lower envelopes of each IMF degenerate to a pair of symmetric straight lines as the sifting times tend to infinity or not? (3) Whether the average frequencies of the neighboring IMFs get closer enough as the sifting times tend to infinity or not? The first suspension has direct relation to the stoppage criteria, which is of critical importance in the successful implementation of empirical mode decomposition (EMD) method. The second suspension is actually a rigid theoretical result given by Wang et al. [2010], but it may be failed for the actual sifting. The third suspension is associated with the conjecture given by Wu and Huang [2010]. In addition, the frequency distribution problem is also on the way of the last suspension. By considering the variation of maximum amplitude for the mean curve, we find that, after a certain sifting times, the symmetry degree of the IMFs behaves in an intermittent manner. This asymptotic behavior indicates that the first suspension is false in all probability. Further investigation shows that the theoretical result given by Wang et al. [2010] is out of reach. It follows from the sifting tests that the frequency ratio for neighboring IMFs cannot decrease to 1 and the last suspension is cracked. Different from the common sense, there is a very interesting phenomenon that the extreme points of the first IMF may be more than that of the original data. The statistical results on a large quantity of field data show that the frequency distribution along the empirical modes roughly obeys an exponential law. In addition, a new mode-number formula is deduced, which is more reasonable than the one given by Wu and Huang [2009].

The notion of fuzzy entropy (FuzzyEn) is extended to the multiscale case by combining FuzzyEn and empirical mode decomposition (EMD). The proposed technique, fuzzy intrinsic entropy (FIMEn) performs better than its predecessor intrinsic monde entropy (IMEn) and it is less dependent on the algorithmic parameters. In a pattern recognition context, FIMEn provides more separable clusters than IMEn when used for feature extraction, thus allowing for less classification error. The above results suggest that the proposed multiscale entropy metric is a very promising technique for evaluating data regularity and can be used effectively for feature extraction in pattern recognition problems.

The bi-dimensional empirical mode decomposition (BEMD) is applied to analyze nonstationary Platinum (Pt) and Palladium (Pd) concentration data in the eastern Yunnan Province, the southwestern China. Two kinds of Pt and Pd anomalies are obtained. One is the regional Pt and Pd anomalies shown in the BIMF₃ component; the other is the local Pt and Pd anomalies shown in the BIMF₂ component. It has been illustrated by further study that the regional Pt and Pd anomalies associated with the Emeishan basalts formed in Permian are distributed along deep-seated faults such as the Xiaojiang fault and the Xundian–Xuanwei fault, and that the local Pt and Pd anomalies related to Pt and Pd mineralization are distributed along some secondary faults of the deep-seated faults. Thus, the local Pt and Pd anomalies controlled by some secondary faults of the deep-seated faults are prospective areas for finding Pt and Pd deposits. In conclusion, BEMD can be effectively applied in extracting different size of geochemical anomalies.

This study examines rationale of correction factor β in the formula of thickness resonant frequency, fundamental to the thickness estimation of impact-echo (IE) approach in nondestructive testing (NDT) for integrity appraisal and damage diagnosis of infrastructure systems. It shows the role of the factor in the formula from the perspective of testing equipment setup, wave propagation, and resonant frequency identification, much broader than what was first introduced empirically for shape correction of a structure under test. Emphasis is laid in wave-based interpretation of resonant frequency, typically obtained from traditional fast Fourier transform (FFT) data analysis of IE recordings. Since the FFT data analysis provides average, not true, characteristic of resonant frequency shown in the nonstationary IE recordings, it typically distorts the thickness estimation from the formula if the correction factor is not used. An adaptive time-frequency data analysis termed Hilbert–Huang transform (HHT) is then introduced to overcome the shortage of FFT analysis in identifying the resonant frequency from noise-added IE recordings. With FFT and HHT analyses of five data sets of sample IE recordings from sound and damaged concrete structures and comparison with referenced ones, this study reveals that the proposed IE approach with HHT data analysis not only eliminates the subjective use of correction factor in the formula, but it also improves greatly the accuracy in the thickness estimation.

We propose an atomic decomposition method (AD) based on adaptive chirplet dictionary for decomposing multicomponent nonstationary signals with polygonal instantaneous frequencies (IFs). These signals are waveforms of the very general form ∑ A_i(t)cos(φ_i(t)), where the phase φ_i(t) is time-varying and the amplitude A_i(t) is slowly varying. Different from the traditional four-parameters chirplet, the one applied in this paper only contains two parameters (chirp offset and chirp rate) and its IF can be regarded as a line on the time–frequency (TF) plane. The idea is to use matching pursuit (MP) algorithm to search for the chirplets, which provide the best trade-off between complexity and goodness of fitting and chain the chirplets together adaptively as to form the desired signals. Our particular application in conjunction with this problem is the decomposition of meshing frequency component and its modulating frequency components in gear fault diagnosis. This strategy is general and may be applied in many other problems. We complement our study with numerical experiments showing that our algorithm boasts of many advantages, such as favorable TF resolution, strong noise robust property (NRP), good decomposition precision, and acceptable algorithm efficiency and is highly competitive compared to the current TF analysis methods.

Ensemble empirical mode decomposition (EEMD) is a noise-assisted adaptive data analysis method to solve the problem of mode mixing caused by empirical mode decomposition (EMD). It is shown that the decomposition error tends to zero, as ensemble number increases to infinity in EEMD. In this paper, a novel EEMD-based ridge regression model (REEMD) is proposed, which solves the problem of mode mixing and achieves less decomposition error compared with the EEMD. When the ensemble number is small, the weights of outliers are constraint to zero to reduce the decomposition error in REEMD and the result of REEMD is asymptotic to that of EEMD, as the ensemble number increases. The proposed REEMD is suitable for tissue clutter rejection in color flow imaging system. Simulation shows that reasonable flow-frequency estimations can be achieved by REEMD and the estimation error limits to zero, as the flow frequency increases.

The time variability of solar activity indices such as sunspot areas (SAs) and green-line coronal emission, fluxes of solar energetic protons and galactic cosmic rays (CRs) in the period 1974–2001 has been investigated through the empirical mode decomposition (EMD). We found that the quasi-biennial periodicity is a prominent time scale of solar variability, having the energetic particle indices an amplitude comparable with the 11 years one. Moreover, we provide evidence for the quasi-biennial modulation of the solar neutrino flux, which results to be also significantly correlated with the fluxes of solar energetic protons and galactic CRs. The significance of all the correlation has been tested by applying both bootstrap and Monte Carlo methods.

We present a method for enhancing signals possessing nonlinear and nonstationary characteristics, which we call weighting functional-empirical mode decomposition (WF-EMD). The filtering method is based upon the empirical mode decomposition (EMD) and utilizes an energy-based weighting scheme to recombine the decomposed modes into a single cleansed version of the signal. The filter has been developed in such a way that no restrictive assumptions about the data are required. Furthermore, the temporal resolution of the data is left unaltered, as it would occur in many common data-smoothing methods. The design of this filter has been influenced by improving the calculation accuracy of dynamical measures, such as fractal dimensions and Lyapunov exponents, of neurodynamical recordings such as those obtained through electroencephalography (EEG) or magnetoencephalography (MEG).

The requirements for inspection and management of track irregularity have to be more rigorous due to safety and serviceability concerns as the increment of the train speed of high-speed train. The wavelength of track irregularity significantly affects running safety and riding comfort. To improve inspection, operation, efficiency, and address, the inability of the mid-chord offset method currently used on track inspection cars to identify some irregularity wavelengths, a measurement and assessment method is presented in this paper. Nonstationary and nonlinear vehicle dynamic response data caused by irregularities were measured by accelerometers mounted on the axle-box of a vehicle. The Hilbert–Huang transform (HHT) technique was applied to analyze the data. Components of specific irregularity wavelength could be effectively identified and accurately matched to the data measured by the track inspection car. Additionally, to obtain the complete waveform of the track irregularity, we propose a restoration method of track irregularity that combines the characteristics of the measurement magnification in the chord-based measuring system and the HHT signal-processing techniques.