Hilbert-Huang Transform Approach Research Articles

Detecting damage on engine mounts using hilbert-huang transform vibration analysis

Engine mounts, which are usually composed of elastomeric materials like rubber that can absorb excessive vibrations, are built to withstand vibration sources from engines. Engine mounts may eventually degrade from extended use. When rubber products age or sustain damage, they may grow harder and crack. Engine mounts need to be maintained regularly to ensure optimal performance. Visual examinations and the detection of excessive vibrations can be used to accomplish this. Vibration sensors are mounted on the engine mount in axial, vertical, and horizontal orientations using a vibration detection technique utilizing the Hilbert-Huang Transform (HHT) methodology. Matlab is used to examine the data that is gathered at three distinct rotational speeds: 750 rpm, 2000 rpm, and 3000 rpm. The HHT approach combines two key components: the Hilbert Transform, which analyzes the time-frequency signal of the first decomposition until only residuals remain, and Empirical Mode Decomposition (EMD), which breaks down the signal into Intrinsic Mode Functions (IMFs). According to test data, a damaged mount had an amplitude of 0.00005212 m/s² and a frequency of 8 Hz. On the other hand, in typical circumstances, the highest frequency was 7 Hz with the same amplitude. Five frequency increases were made in the damaged mount throughout this operation. In the damaged mount, the Hilbert Transform showed a frequency of 2124 Hz with an amplitude of 0.007594 m/s², indicating a significant resonance. This illustrates how the Hilbert-Huang Transform's capacity to handle non-stationary and nonlinear signal forms allows it to detect damage in components efficiently

Unbalance Bearing Fault Identification Using Highly Accurate Hilbert–Huang Transform Approach

Abstract The dynamic characteristics of rolling element bearings are strongly related to their geometric and operating parameters, most importantly the bearing unbalance. Modern condition monitoring necessitates the use of intrinsic mode functions (IMFs) to diagnose unbalance bearing failure. This paper presents a Hilbert–Huang transform (HHT) method to diagnose the unbalanced rolling bearing faults of rotating machinery. To initially reduce the noise levels with slight signal distortion, the noises of the sample in normal and unbalanced fault states are measured and denoised using the wavelet threshold approach. The complex vibration signatures are decomposed into finite IMFs with ensemble empirical mode decomposition technique. Fast Fourier techniques are employed to extract the vibration responses of bearings that are artificially damaged using electrochemical machining on a newly established test setup for rotor disc bearings. The similarities between the information-contained marginal Hilbert spectra can be used to diagnose rotating machinery bearing faults. The data marginal Hilbert spectra of Mahalanobis and cosine index are compared to determine the fault indicator index’s similarity score. The HHT model’s simplicity enhanced the precision of diagnosis correlated to the results of the experiments with weak fault characteristic signals. The effectiveness of the proposed approach is evaluated with several theoretical models from the literature. The HHT approach is experimentally proven with unbalance diagnosis and capable of classifying marginal Hilbert spectra distribution. Because of its superior time-frequency characteristics and pattern identification of marginal Hilbert spectra and fault indicator indices, the newly stated HHT can process nonlinear, non-stationary, and even transient signals. The findings demonstrate that the suggested method is superior in terms of unbalance fault identification accuracy for monitoring the dynamic stability of industrial rotating machinery.

A Classification Method for Power-Quality Disturbances Using Hilbert–Huang Transform and LSTM Recurrent Neural Networks

Power quality disturbances are one of the main problems in an electric power system, where deviations in the voltage and current signals can be evidenced. These sudden changes are potential causes of malfunctions and could affect equipment performance at different demand locations. For this reason, a classification strategy is essential to provide relevant information related to the occurrence of the disturbance. Nevertheless, traditional data extraction and detection methods have failed to carry out the classification process with the performance required, in terms of accuracy and efficiency, due to the presence of a non-stationary and non-linear dynamics, specific of these signals. This paper proposes a hybrid approach that involves the implementation of the Hilbert–Huang Transform (HHT) and long short-term memory (LSTM), recurrent neural networks (RNN) to detect and classify power quality disturbances. Nine types of synthetic signals were reproduced and pre-processed taking into account the mathematical models and their specifications established in the IEEE 1159 standard. In order to eliminate the presence of mode mixing, the ensemble empirical decomposition (EEMD) and masking signal methods were implemented. Additionally, based on the successful benefits of LSTM RNNs reported in the literature, associated to the high accuracy rates achieved at learning long short-term dependencies, this classification technique is implemented to analyze the sequences obtained from the HHT. Based on the experimental results, it is possible to show that the ensemble recognition approach using the EEMD yields a better classification accuracy rate (98.85%) compared with the masking signal and the traditional HHT approach.

False Data Injection Attack Detection based on Hilbert-Huang Transform in AC Smart Islands

In Smart Island (SI) systems, operators of power distribution system usually utilize actual-time measurement information as the Advanced Metering Infrastructure (AMI) to have an accurate, efficient, advanced control and monitor of whole their system. SI system can be vulnerable to complicated information integrity attacks such as False Data Injection Attack (FDIA) on some equipment including sensors and controllers, which can generate misleading operational decision in the system. Hence, lack of detailed research in the evaluation of power system that links the FDIAs with system stability is felt, and it will be important for both assessment of the effect of cyber-attack and taking preventive protection measures. In this regards, time-frequency-based differential approach is proposed for SI cyber-attack detection according to non-stationary signal assessment. In this paper, non-stationary signal processing approach of Hilbert-Huang Transform (HHT) is performed for the FDIA detection in several case studies. Since various critical case studies with a small FDIA in data where accurate and efficient detection can be a challenge, the simulation results confirm the efficiency of HHT approach and the proposed detection frame is compared with shallow model. In this research, the configuration of the SI test case is developed in the MATLAB software with several Distributed Generations (DGs). As a result, it is found that the HHT approach is completely efficient and reliable for FDIA detection target in AC-SI. The simulation results verify that the proposed model is able to achieve accuracy rate of 93.17% and can detect FDIAs less than 50 ms from cyber-attack starting in different kind of scenarios.

A novel HHT and KS statistic approach to detect RoQ attack in wireless sensor network

Reduction of quality (RoQ) attack is a special denial of service (DoS) attack. It is a serious threat to the security of wireless sensor network (WSN). The RoQ attack combines the attack effectiveness and the similarity to normal traffic, so it is difficult to detect by traditional methods. Hilbert-Huang transform (HHT) time frequency analysis method can be utilised to analyse the nonlinear small signal produced by RoQ attack. However, false IMF components are the challenge problems to detect the RoQ attack. Kolmogorov-Smirnov (KS) test approach is proposed to recognise the false intrinsic mode function (IMF) components. CC2530 system-on-chip is selected to build WSN experimental node. Ad hoc on-demand distance vector (AODV) routing protocol and random routing request (RREQ) flooding attack are simulated to implement RoQ attack in Zigbee wireless sensor network. Experimental results demonstrate that the novel approach is effective to detect RoQ attack in Zigbee WSN.

Evaluation of HHT approach for estimating agricultural drought trend and frequency based on modified soil water deficit index (MSWDI)

Accurate estimation of the agricultural drought trend and frequency is important to water resources planning and management. In this study, an effective analysis tool, the Hilbert–Huang Transform (HHT) method, was introduced to estimate the agricultural drought trend and frequency based on modified soil water deficit index (MSWDI). The results indicate that (1) based on HHT multiscale decomposition, the MSWDI of four stations has two intra-annual fluctuations, three intra-decadal fluctuations with periodicities between 1 and 6 years, and two inter-decadal fluctuations; (2) the main periodicities obtained from wavelet analysis can also be detected by HHT analysis. Furthermore, the HHT analysis decomposed more time scale patterns than wavelets; (3) the residue of HHT showed a decreasing trend during the 1960s–1980s but an increasing one since the 1980s for the drought index MSWDI series at most of the stations in the Songnen Plain (SNP). It is consistent with the result of Mann–Kendall and Spearman’s Rho; (4) the drought temporal distribution analysis showed that the relative high drought probability was identified during the initial stage of crop growth. It can be concluded that the HHT analysis is an effective approach to examine multiple time scales of frequencies and trend of agricultural drought from its multiscale decomposition and time–frequency characterization, which can not only be applied for other time series but also have the functions combining the wavelet analysis and non-parameter trend tests. The results of this study could also help and be used to improve the drought prediction and expand the application of HHT method in climatology.

A Novel Approach to Relative Radiometric Calibration on Spatial and Temporal Variations for FORMOSAT-5 RSI Imagery.

Radiometric calibration for imaging sensors is a crucial procedure to ensure imagery quality. One of the challenges in relative radiometric calibration is to correct detector-level artifacts due to the fluctuation in discrepant responses (spatial) and electronic instability (temporal). In this paper, the integration of the empirical mode decomposition (EMD) with Hilbert–Huang transform (HHT) in relative radiometric calibration was explored for a new sensor, FS-5 RSI (remote sensing instrument onboard the FORMOSAT-5 satellite). The key intrinsic mode functions (IMFs) analyzed by HHT were examined with the pre-flight datasets of the FS-5 RSI in temporal and spatial variations. The results show that the EMD–HHT method can stabilize and improve the radiometric quality of the FS-5 imagery as well as boost its application ability to a new level. It is noticed that the IMFs of the spatial variation would be disturbed by the instability of the temporal variation. The relative response discrepancies among detector chips can be well calibrated after considering the temporal effect. Taking a test imagery dataset of gain setting G2 as an example, the standard deviation (STD) of the discrepancy in the digital number after calibration was dramatically scaled down compared to the original ones (e.g., PAN: 66.31 to 1.85; B1: 54.19 to 1.90; B2: 36.50 to 1.49; B3: 32.43 to 1.56; B4: 37.67 to 1.20). The good performance of pre-flight imagery indicates that the EMD–HHT approach could be highly practical to the on-orbit relative radiometric calibration of the FS-5 RSI sensor and is applicable to other optical sensors. To our knowledge, the proposed EMD–HHT approach is used for the first time to explore relative radiometric calibration for optical sensors.

Time-Frequency analysis for nonlinear and non-stationary signals using HHT: A mode mixing separation technique

Time and frequency localizations are of crucial importance in the analysis of nonlinear and non-stationary processes, especially in systems with high level of complexity where detection of information/events, estimation of parameters and classification of signals in classes is necessary to take decisions. The Hilbert Huang Transform (HHT) offers an adaptive approach to analyze no-linear and non-stationary processes. This paper exposes the HHT approach and its new methodologies for improvement of the analysis, such as the masking process. Two examples are given to show the techniques, first a synthetic signal, representing a typical behavior of an electrical signal immersed in a power electronic environment and second a brain signal to extend the acknowledgment to a biological process. Finally a mode mixing separation technique is presented.

Hilbert-Huang transform in detecting and analyzing the uterine contraction activities.

The diagnosis of labor is currently one of the most difficult problems encountered by obstetrical healthcare providers. A major health problem is the increase in the rate of preterm delivery, which is responsible for 75% of all deaths in newborns. In addition, preterm delivery is associated with several cognitive and health problems in later life and enormous costs for the health system. A better understanding of myometrial activities could help to reduce preterm deliveries and the costs associated with prematurity in the following years. Therefore, the objective of this study was to determine whether using the Hilbert-Huang transform (HHT) to analyze the uterine contraction data would help us gain a better insight of the myometrial activities of the human uterus during pregnancy. Uterine magnetomyographic (MMG) signals were recorded from pregnant patients at gestational ages of 32-38 weeks. The study was approved by the Human Research Advisory Board of the University of Arkansas for Medical Sciences (UAMS) and performed after obtaining written consent from each patient. The recording of transabdominal MMG signals was conducted with the SQUID Array for Reproductive Assessment (SARA, VSM MedTech Inc; Coquitlam, BC, Canada) system, which has 151 primary magnetic sensors allocated approximately 3 cm apart over an area of 850 cm(2). The arrangement of sensors is concave in nature and, in a similar lateral distance, spans the maternal abdomen longitudinally from the symphysis pubis to the uterine fundus. The recording times ranged from 12 to 28 min, and the sampling rate was 250 Hz. The data were down-sampled to 25 Hz to reduce the computational complexity and post-processed with a bandpass filter (0.05-1 Hz) because the uterine contraction activity is a band-limited process (0.05-1 Hz). The recordings of one intrauterine pressure catheter (IUPC) dataset and two mother-perceived contraction datasets were compared with the HHT results, and HHT's potential was explored through the development of a module and a series of experiments. The local energy and the instantaneous frequency derived from the intrinsic mode functions (IMFs) through HHT provide a full energy-frequency-time distribution of the data. Our objective was to determine whether HHT for each channel can help identify and localize contractions in the uterus. Human studies have been reviewed by the appropriate ethics committee and have therefore been performed in accordance with the ethical standards described in an appropriate version of the 1975 Declaration of Helsinki, as revised in 2000. After comparing the IUPC and other mother-perceived contraction (STIM) datasets with HHT results, we were able to visually detect contraction locations in the HHT-processed uterine signals. For verification and validation purposes, when we further analyzed the delay time between two signals, the mechanical activity (i.e., IUPC) following the electrical activity (i.e., magnetic signal) was observed. In conclusion, our experimentations using the method introduced here revealed that there is a 75% correlation between the results obtained by HHT and IUPC data. This study compared uterine contractions and changes in the intrauterine pressure with results obtained by HHT. In addition, using IUPC data as a validation guide, we showed that the HHT approach can be used for noise removal. There is a need for time-saving and non-subjective automatic contraction detection in the field of prenatal examination.

Hilbert–Huang Transform Approach to Lorenz Signal Separation

This study uses the Hilbert–Huang transform (HHT), a signal analysis method for nonlinear and non-stationary processes, to separate signals of varying frequencies in a nonlinear system governed by the Lorenz equations. Similar to the Fourier series expansion, HHT decomposes a data time series into a sum of intrinsic mode functions (IMFs) using empirical mode decomposition (EMD). Unlike an infinite number of Fourier series terms, the EMD always yields a finite number of IMFs, whose sum is equal to the original time series exactly. Using the HHT approach, the properties of the Lorenz attractor are interpreted in a time–frequency frame. This frame shows that: (i) the attractor is symmetric for [Formula: see text] (i.e. invariant for [Formula: see text]), even though the signs on [Formula: see text] and [Formula: see text] are changed; (ii) the attractor is sensitive to initial conditions even by a small perturbation, measured by the divergence of the trajectories over time; (iii) the Lorenz system goes through “windows” of chaos and periodicity; and (iv) at times, a system can be both chaotic and periodic for a given [Formula: see text] value. IMFs are a finite collection of decomposed quasi-periodic signals, starting from the highest to lowest frequencies, providing detection of the lower frequency signals that may have otherwise been “hidden” by their higher frequency counterparts. EMD decomposes the original signal into a family of distinct IMF signals, the Hilbert spectra are a “family portrait” of time–frequency–amplitude interplay of all IMF members. Together with viewing the IMF energy, it is easy to discern where each IMF resides in the spectra in relation to one another. In this study, the majority of high amplitude signals appear at low frequencies, approximately 0.5–1.5. Although our numerical experiments are limited to only two specific cases, our HHT analyses of time–frequency, marginal spectra, and energy and quasi-periodicity of each IMF provide a novel approach to exploring the profound and phenomena-rich Lorenz system.

Improvement for the multi-scale periodic characteristics revealing of precipitation signals and its impact assessment on soil hydrological process by combining HHT and CWT approaches

Abstract. This study conducts a detailed analysis of multi-scale periodic features involved in the annual and seasonal precipitation signals at the typical coastal reclamation region in China by selecting the suitable continuous wavelet transform (CWT) and innovatively combining the improved Hilbert–Huang transform (HHT), and further deduces the precipitation trend and its impacts on the future soil hydrological process. The Morlet wavelet transform is proved suitable in revealing the precipitation signals broad-scale periodicities, however, the critical mode mixing problem in CWT causes the poor significance in the fine-scale periodicities, which cannot well match the climate background. By combining the HHT approach, the fine-scale mode mixing drawback in CWT is effectively eliminated, and the the studied precipitation signals multi-scale periodicities are accurately revealed. Consequently, an overall decreasing trend of annual and seasonal precipitation in future years is demonstrated. Furthermore, by novelly using the cross wavelet transform (XWT) and wavelet transform coherence (WTC) approaches, the prominent correlations between the precipitation dynamics and soil and groundwater salinities dynamics, it is demonstrated that the precipitation increase can effectively leach the surface soil salt downwards into the deeper soil layers and groundwater with 5–7-day lag in the new cultivated tidal land. The revealed future decreasing trend of precipitation, especially in spring and summer, may aggravate the soil salinization at the coastal reclamation region, thus some reasonable salt leaching and evaporation suppression measures need to be taken to prevent the possible soil secondary salinization process.

A case study of damage detection in four-bays steel structures using the HHT approach

This study aims to investigate the relationship between structural damage and sensitivity indices using the Hilbert-Huang transform (HHT) method. Two damage detection indices are proposed: the ratio of bandwidth (RB), and the ratio of effective stiffness (RES). The nonlinear four bays multiple degree of freedom models with various predominant frequencies are constructed using the SAP2000 program. Adjusted PGA earthquake data (Japan 311, Chi-Chi 921) are used as the excitations. Next, the damage detection indices obtained using the HHT and the fast Fourier transform (FFT) methods are evaluated based on the acceleration responses of the structures to earthquakes. Simulation results indicate that, the column of the 1st floor is the first yielding position and the RB value is changed when the RES<90% in all cases. Moreover, the RB value of the 1st floor changes more sensitive than those from the top floor. In addition, when the structural response is nonlinear (i.e., RES<100%), the RB and the RES curves indicate the incremental change in the HHT spectra. However, the same phenomenon can be found from FFT spectra only when the stiffness reduction is large enough. Therefore, the RB estimated from the smoothed HHT spectra is an effective and sensitive index for detecting structural damage.

Through-wall radar imaging using UWB noise waveforms

This paper examines the results of our research on the use of ultrawideband noise waveforms for imaging objects behind walls. The advantages of using thermally generated noise as a probing signal are introduced. The technique of heterodyne correlation used to inject coherence in the random noise probing signal and to collapse the wideband reflected signal into a single frequency are presented. Central to successful imaging through building walls is the characterization of the wideband propagation properties of wall materials and these are discussed. The basic concepts of synthetic aperture radar image formation using noise waveforms and the unique problems associated with the random nature of the transmit waveform are analyzed. We also address issues related to locating, detection, and tracking humans behind walls, using new tools for human activity characterization, namely the Hilbert-Huang Transform approach. The results indicate that noise radar technology combined with modern signal processing approaches is indeed a viable technique for covert high-resolution imaging of obscured stationary and moving targets.