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The purpose of this paper is to present the application of Hilbert–Huang transform (HHT) for fatigue damage feature characterisation in the time–frequency domain based on strain signals obtained from the automotive coil springs.

HHT was employed to detect the temporary changes in frequency characteristics of the vibration response of the signals. The extraction successfully reduced the length of the original signal to 40 per cent, whereas the fatigue damage was retained. The analysis process for this work is divided into three stages: signal characterisation with the application of fatigue data editing (FDE) for fatigue life assessment, empirical mode decomposition with Hilbert transform, an energy–time–frequency distribution analysis of each intrinsic mode function (IMF).

The edited signal had a time length of 72.5 s, which was 40 per cent lower than the original signal. Both signals were retained statistically with close mean, root-mean-square and kurtosis value. FDE improved the fatigue life, and the extraction did not affect the content and behaviour of the original signal because the editing technique only removed the minimal fatigue damage potential. HHT helped to remove unnecessary noise in the recorded signals. EMD produced sets of IMFs that indicated the differences between the original signal and mean of the signal to produce new components. The low-frequency energy was expected to cause large damage, whereas the high-frequency energy will cause small damage.

HHT and EMD can be used in the strain data signal analysis of the automotive component of a suspension system. This is to improve the fatigue life, where the extraction did not affect the content and behaviour of the original signal because the editing technique only removed the minimal fatigue damage potential.

The purpose of this paper is to simulate and analyze accurately the multi-scale characteristics, variation periods and trends of the annual streamflow series in the Haihe River Basin (HRB) using the Hilbert-Huang Transform (HHT).

The Empirical Mode Decomposition (EMD) approach is adopted to decompose the original signal into intrinsic mode functions (IMFs) in multi-scales. The Hilbert spectrum is applied to each IMF component and the localized time-frequency-energy distribution. The monotonic residues obtained by EMD can be treated as the trend of the original sequence.

The authors apply HHT to 14 hydrological stations in the HRB. The annual streamflow series are decomposed into four IMFs and a residual component, which exhibits the multi-scale characteristics. After the Hilbert transform, the instantaneous frequency, center frequency and mean period of the IMFs are obtained. Common multi-scale periods of the 14 series exist, e.g. 3.3a, 4∼7a, 8∼10a, 11-14a, 24∼25a and 43∼45a. The residues indicate that the annual streamflow series has exhibited a decreasing trend over the past 50 years.

The HHT method is still in its early stages of application in hydrology and needs to be further tested.

It is helpful for the study of the complex features of streamflow.

This paper will contribute to the sustainable utilization of water resources.

This study represents the first use of the HHT method to analyze the multi-scale characteristics of the streamflow series in the HRB. This paper provides an important theoretical support for water resources management.

This paper aims to present a new method for identification of some flight modes, including natural and non-standard modes, and extraction of their characteristics, directly from measurements of flight parameters in the time domain.

The Hilbert-Huang transform (HHT), as a novel prevailing tool in the signal analysis field, is used to attain the purpose. The study shows that the HHT has superior potential capabilities to improve the airplane flying quality analysis and to conquer some drawbacks of the classical method in flight dynamics.

The proposed method reveals the existence of some non-standard modes with small damping ratios at non-linear flight regions and obtains their characteristics.

The paper examines only airplane longitudinal dynamics. Further research is needed regarding lateral-directional dynamic modes and coupling effects of the longitudinal and lateral modes.

Application of the proposed method to the flight test data may result in real-time flying quality analysis, especially at the non-linear flight regions.

First, to utilize the empirical mode decomposition (EMD) capabilities in real time, a local-online algorithm is introduced which estimates the signal trend by the Savitzky-Golay sifting process and eliminates it from the signal in the EMD algorithm. Second, based on the local-online EMD algorithm, a systematic method is proposed to identify flight modes from flight parameters in the time domain.

This study aims to investigate the relationship between structural damage and sensitivity indices using the Hilbert‐Huang transform (HHT) method.

The relationship between structural damage and the sensitivity indices is obtained by using the HHT method. Three sensitivity indices are proposed: the ratio of rotation (RR), the ratio of shifting value (SV) and the ratio of bandwidth (RB). The nonlinear single degree of freedom and multiple degree of freedom models with various predominant frequencies are constructed using the SAP2000 program. Adjusted PGA El Centro and Chi‐Chi (TCU068) earthquake data are used as the excitations. Next, the sensitivity indices obtained using the HHT and the fast Fourier transform (FFT) methods are evaluated separately based on the acceleration responses of the roof structures to earthquakes.

Simulation results indicate that, when RR < 1, the structural response is in the elastic region, and neither the RB nor SV in the HHT and FFT spectra change. When the structural response is nonlinear, i.e. RR1, a positive trend of change occurs in RB and RR, while in the HHT spectra, SV increases with an increasing RR. Moreover, the FFT spectra reveal that SV changes only when the RR is sufficiently large. No steady relationship between the RB and the RR can be found.

The paper demonstrates the effectiveness of the HHT method.

This study aims to include the diagnosis of an old concrete deck steel truss rural road bridge in the damaged and retrofitted state through vibration response signals.

The analysis of the vibration response signals is performed in time and time-frequency domains using statistical features-root mean square, impulse factor, crest factor, kurtosis, peak2peak and Stockwell transform. The proposed methodology uses the Hilbert transform in combination with spectral kurtosis and bandpass filtering technique for obtaining robust outcomes of modal frequencies.

The absence or low amplitude of considered mode shape frequencies is observed both before and after retrofitting of bridge indicates the deficient nodes. The kurtosis feature among all statistical approaches is able to reflect significant variation in the amplitude of different nodes of the bridge. The Stockwell transform showed better resolution of present modal frequencies but due to the yield of additional frequency peaks in the vicinity of the first three analytical modal frequencies no decisive conclusions are achieved. The methodology shows promising outcomes in eliminating noise and visualizing distinct modal frequencies of a steel truss bridge.

The findings of the present study help in analyzing noisy vibration signals obtained from various structures (civil or mechanical) and determine vulnerable locations of the structure using mode shape frequencies.

The literature review gave an insight into few experimental investigations related to the combined application of Hilbert transform with spectral kurtosis and bandpass filtering technique in determining mode frequencies of a steel truss bridge.

Continuous on-line monitoring of structural integrity are in priority in many engineering fields such as aerospace, automotive, civilian structures, and industrial applications. Of all these possible applications, the aerospace industry has one of the highest payoffs. Possible damage can lead to catastrophic failures and costly inspections. On the other hand, processing a signal consists of important feature from sensors measurements to reach the considered target. Typically, the sensors translate a physical phenomenon from one or many sources in temporal variations or in spatial variations. The purpose of this paper is to investigate damages, in terms of suddenly screw removal or in a small cut, detection in vibrating (clamped-free) aluminum beam structures using the empirical mode decomposition (EMD) method along with the Hilbert-Huang transformation (HHT). The perspective is to identify very small defects in real aircraft structures.

The proposed method deals with a new time-frequency signal processing analysis tool, for damages detection in a vibrating plate. An experimental test ring is used in order to excite a clamped-free aluminum plate. Two types of excitations are used. The first one is a harmonic excitation and the second one is a random excitation provided by an impact hammer. A hole and its filled by a screw with mass of 0.2 g, and a small cut is created, simulating a cut creation, are produced afterword, and the HHT is used in order to arise the developed oscillations, and to reveal hidden reflections in the data and to provide a high-resolution energy-time frequency spectrum.

The major finding was the clear amplitude increment either for screw removal or for cut creation, using the EMD process with the HHT, giving the possibility to detect them.

The use of the HHT to detect, using an experimental procedure, two different defects: a suddenly screw removal and a cut creation, in a clamped-free beam, excited by non-stationary and non-linear signals.

The paper aims to present an innovative method for identification of flight modes in the spin maneuver, which is highly nonlinear and coupled dynamic.

To fix the mode mixing problem which is mostly happen in the EMD algorithm, the authors focused on the proposal of an optimized ensemble empirical mode decomposition (OEEMD) algorithm for processing of the flight complex signals that originate from FDR. There are two improvements with the OEEMD respect to the EEMD. First, this algorithm is able to make a precise reconstruction of the original signal. The second improvement is that the OEEMD performs the task of signal decomposition with fewer iterations and so with less complexity order rather than the competitor approaches.

By applying the OEEMD algorithm to the spin flight parameter signals, flight modes extracted, then with using systematic technique, flight modes characteristics are obtained. The results indicate that there are some non-standard modes in the nonlinear region due to couplings between the longitudinal and lateral motions.

Application of the proposed method to the spin flight test data may result accurate identification of nonlinear dynamics with high coupling in this regime.

First, to fix the mode mixing problem in EMD, an optimized ensemble empirical mode decomposition algorithm is introduced, which disturbed the original signal with a sort of white Gaussian noise, and by using white noise statistical characteristics the OEEMD fix the mode mixing problem with high precision and fewer calculations. Second, by applying the OEEMD to the flight output signals and with using the systematic method, flight mode characteristics which is very important in the simulation and controller designing are obtained.

This study aims to perform the experimental work on a laboratory-constructed steel truss bridge model on which hammer blows are applied for excitation. The vibration response signals of the bridge structure are collected using sensors placed at different nodes. The different damaged states such as no damage, single damage, double damage and triple damage are introduced by cutting members of the bridge. The masked noise with recorded vibration responses generates challenge to properly analyze the health of bridge structure.

The analytical modal properties are obtained from finite element model (FEM) developed using SAP2000 software. The response signals are analyzed in frequency domain by power spectrum and in time-frequency domain using spectrogram and Stockwell transform. Various low pass signal-filtering techniques such as variational filter, lowpass sparse banded (AB) filter and Savitzky–Golay (SG) differentiator filter are also applied to refine vibration signals. The proposed methodology further comprises application of Hilbert transform in combination with MUSIC and ESPRIT techniques.

The outcomes of SG filter provided the denoised signals using appropriate polynomial degree with proper selected window length. However, certain unwanted frequency peaks still appeared in the outcomes of SG filter. The SG-filtered signals are further analyzed using fused methodology of Hilbert transform-ESPRIT, which shows high accuracy in identifying modal frequencies at different states of the steel truss bridge.

The sequence of proposed methodology for denoising vibration response signals using SG filter with Hilbert transform-ESPRIT is a novel approach. The outcomes of proposed methodology are much refined and take less computational time.

The purpose of this paper is to propose a new fault feature extraction scheme for the rolling element bearing.

The generalized Stockwell transform (GST) and the singular value ratio spectrum (SVRS) methods are combined. A time-frequency distribution measurement criterion named the energy concentration measurement (ECM) is initially used to determine the parameter of the optimal GST method. Then, the optimal GST is applied to conduct a time-frequency transformation for a raw signal. Subsequently, the two-dimensional time-frequency matrix is obtained. Finally, the improved singular value decomposition (SVD) analysis is used to conduct a noise reduction of the time-frequency matrix. The SVRS is proposed to select the effective singular values. Furthermore, the time-domain feature of the impact signal is obtained by taking the inverse GST transform.

The simulated and experimental signals are used to verify the superiority of the proposed method over conventional methods. The obtained results show that the proposed method can effectively extract fault features of the rolling element bearing.

This paper mainly discusses the application of GST and SVRS methods to analyze the weak fault feature extraction problem. The next research direction is to explore the application of the Hilbert Huang transform (HHT) and variational modal decomposition (VMD) in the impact feature extraction of rolling bearing.

In the present study, a new SVRS method is proposed to select the number of effective singular values. This paper proposed an effective way to obtain the fault feature in monitoring of rotating machinery.

An electrical power system is expected to deliver undistorted sinusoidal, rated voltage and current continuously to the end-users. The problem of power quality (PQ) occurs when there is (are) deviation(s) in voltage and/or current which cause(s) failure or mal-operation of the customer's equipments. Various methods are suggested to detect and classify single PQ event in a power system, the performance of such methods to classify composite PQ events is limited. The purpose of this paper is the classification of composite PQ events in emerging power systems.

This paper proposes an effective method to classify composite PQ events using Hilbert Huang transform (HHT). The performance of probabilistic neural network (PNN) classifier and support vector machine (SVM) classifier to efficiently classify composite PQ events is compared.

The features extracted from HHT are simple yet effective. SVMs and PNN classifiers are used for PQ classification. It is found that PNN classifier outperforms SVM with the classification accuracy of 100 percent.

Different PQ signals used for analysis are generated by simulating a practical distribution system of an Indian academic institution.