Instantaneous Amplitude Research Articles

Multiple-Frequency Force Estimation of Controlled Vibrating Systems with Generalized Nonlinear Stiffness

An on-line estimation technique of multiple-frequency oscillatory forces combined with the Hilbert–Huang transform for an important class of actively controlled, forced vibrating mechanical systems with nonlinear stiffness forces is proposed. Polynomial parametric nonlinearities are incorporated in the significantly perturbed vibrating system dynamics. This class of nonlinear vibrating systems can exhibit harmful large-amplitude vibrations, which are inadmissible in many engineering applications. Disturbing oscillations can be also provoked due to interactions of the primary mechanical system to be actively protected against dangerous vibrations with other forced uncertain multidegree-of-freedom nonlinear vibrating systems. Taylor’s series expansion to dynamically model uncertain vibrating forces into a small time window for real-time estimation purposes is employed. Intrinsic mode functions of multiple-frequency vibrating forces can be then obtained by the Hilbert-Huang transform. Uncertain instantaneous frequencies and amplitudes of disturbing oscillations can be directly computed in temporal space. An active vibration control scheme for efficient and robust tracking of prescribed motion reference profiles based on multiple frequency force estimation is introduced as well. The presented closed-loop on-line estimation technique can be extended for other classes of nonlinear oscillatory systems. Analytical, experimental and numerical results to prove the estimation effectiveness are presented. Numerical results show reasonable estimation errors of less than 2%.

Direct Visualisation of Seismic Facies Boundaries and DHI Detection of Anomalous Gas

Complex seismic trace attribute analysis separates the amplitude and the phase information contained in the data and produces two basic attributes known as the instantaneous amplitude and instantaneous phase. Using these, two new attributes are being introduced, namely, the facies attribute called NRG derived as an extension of the instantaneous amplitude, and the second one based on instantaneous phase attribute is used to compute the reflector overlay times plotted on the display. The NRG attribute is intended as a first step in the seismic interpretation process because it delineates subsurface boundaries both laterally and vertically. It also detects DHI effects for bright spot and non-bright or dim spot anomalies as well as indications of gas/oil migration through the subsurface. In one of the real data applications the bright spot colour display is calibrated to agree with the producible gas. Besides, there are attribute signatures for both oil and gas when the geology does not support bright spots. The application of the second attribute on real seismic data demonstrates how flat spots and faults are immediately recognisable. The unambiguous determination of geologically meaningful lateral as well as vertical boundaries cannot be overstated for direct facies analysis to be useful.

Subsurface impact damage imaging for composite structures using 3D digital image correlation

An integrated system is proposed to visualize subsurface barely visible impact damage (BVID) in composite structures using three-dimensional (3D) digital image correlation (3D DIC). This system uses a pair of digital cameras to record video frames in the field-of-view (FOV) of the structure’s surface, capturing the wavefield generated via chirp excitation in the near-ultrasonic frequency range. Significant pitfalls of previous efforts of damage imaging using two-dimensional DIC have been largely mitigated. First, 3D DIC enables capturing out-of-plane displacements, which are much larger in amplitude versus in-plane displacements that a single camera would be limited to sensing, thus increasing the signal-to-noise ratio. This enhancement in turn increases the sensitivity of the stereo-camera system. Second, a total wave energy (TWE) damage imaging condition is proposed to visualize the local damage region. The monogenic signal obtained via Reisz transform (RT) is employed to compute the instantaneous amplitude, with which the local wave energy can be calculated spatially over time. Since a high displacement amplitude and thus high wave energy will occur in the damage region due to the local resonance, the proposed TWE imaging condition can relax the Nyquist sampling requirement, unlike guided-wave-based structural health monitoring techniques which require fully reconstructing the wavefield and wave modes through sampling that satisfies the Nyquist criterion. As such, a much lower camera frame rate is adequate for the proposed system. Consequently, the maximum spatial resolution of the camera for a given FOV can be achieved at the expense of a reduced frame rate. With the maximized pixel resolution and reduced frame rate for employing the TWE imaging condition, composite structures can be inspected or monitored with a larger FOV. As a result, there is no longer any need to apply signal enhancement techniques, such as sample interleaving, image stitching, or averaging, to increase the effective performance of the camera. Rather than needing thousands of repeated videos for minimizing the incoherent noise, only a single stereo-video with a few seconds of sampling duration is necessary for damage imaging. The use of a powerful piezo-shaker also increases the wave signal amplitude and further enhances sensitivity without permanent adhesion. To demonstrate this stereo-camera concept with the TWE imaging condition, the system was used to image damage in two carbon fiber reinforced polymer composite honeycomb panels, which had been subjected to low-velocity impacts (2 J). For each panel, two excitation configurations were used to verify the robustness of the system. Initial damage maps produced for a 100 × 100-mm FOV using a three-second stereo-video show accurate damage imaging ability that is independent of excitation location and comparable to benchmark damage images computed from laser Doppler vibrometer data and those gathered from ultrasonic and X-ray computerized tomography scans. This efficient and reliable integrated system demonstrated high potential for in-time damage inspection on composite aircraft and other critical structures.

Three-Phase Unbalance Analysis Method Based on Three-Phase Motor Current Instantaneous Information

Motor current signal analysis is a common method that can be applied to the monitoring and diagnosis of electromechanical equipment. Three-phase unbalance will increase the line power loss and affect the safe operation of power-using equipment. To quickly analyze motor current three-phase unbalance, we propose a method to analyze three-phase unbalance by calculating the coefficient of variation of the three-phase current’s instantaneous frequency and instantaneous amplitude. Simulations were conducted to analyze the effects of amplitude deviation and phase deviation on the coefficient of variation of instantaneous frequency and instantaneous amplitude. The three-phase unbalance with continuous amplitude change was simulated and its instantaneous performance was analyzed. Experiments were conducted to compare and analyze the instantaneous information characteristics of the motor with the continuous changing of three-phase unbalance under different speed conditions. Simulations and experiments show that the proposed method in this paper can analyze three-phase unbalance.

Non-contact detection of hidden damages in dispersive media using the instantaneous phase

The assessment of dispersive media may become a challenge due to the high attenuation ratios, anisotropy and geometrical particularities of the specimen under study. Besides, non-contact methods that preserve the integrity of samples are needed when some degree of purity is required, e.g., when water immersion is not allowed, and the direct contact is not feasible. In this work, we study composite plates, in which acoustic dispersion is present. We use a non-contact hybrid optoacoustic system to implement the experimental setup that makes it possible the detection of the non-exposed damages of the samples. Different relevant aspects, such as cost, maximum frequency achieved, bandwidth, sensitivity, signal-to-noise ratio and spatial resolution were considered before setting the experimental configuration. Though dispersion curves are reconstructed, we emphasize the use of the instantaneous information of signals to detect the faults. Moreover, the instantaneous phase front of the acoustic field becomes a relevant complementary tool for ultrasonic inspection and characterization of dispersive media. In particular, it highlights hidden characteristics which are not visible with other commonly-used representations, namely, the instantaneous amplitude, the time-frequency distributions or the dispersion curves widely employed in non-destructive testing. This work provides an alternative approach to study highly attenuating media where the signal-to-noise ratio is a challenge, and the available scanning path is limited, e.g., layered and poroelastic media such as biological tissues.

Theory for computing vehicle-rail contact responses from a multi-DOF test vehicle and detecting track modulus and rail damages

The vibration data recorded for the test vehicle cannot be directly used to detect the rail and bridge frequencies due to the overshadowing effect of vehicle's frequencies. To overcome this problem, the vehicle-rail contact response may be used instead. However, current techniques on this are available only for simple test vehicles with single or two degrees of freedom (DOFs). Normally, a train car contains a car body and two bogies (each of two wheelsets), and should be modeled by a multi-DOF system. The objective of this paper is first to solve the four wheelset-rail contact responses from the six measured vehicle responses. Then the contact responses are employed to retrieve the track modulus, while detecting the rail damages, for their salient feature of being free of the vehicle's frequencies. The railway track is modeled by a dual-beam system, with the upper (rail) and lower (bridge) beams connected by a spring-dashpot layer. The track modulus is retrieved through identification of the first “plus” frequency of the dual-beam, and the rail damage is detected from the instantaneous amplitude squared (IAS) generated from the driving component of the contact response. Through comparison with results by the finite element method (FEM), it is confirmed that: (1) the proposed procedure for computing the multi contact responses from the multi-DOF vehicle responses is reliable; (2) track irregularity presents a limited influence even for high disturbance; (3) to trade-off between efficiency and accuracy, a medium vehicle speed is suggested for the field measurement; (4) for the dual-beam with sufficient length, the use of simply supported condition is acceptable for rails; and (5) the effect of track damping is small and can be ignored.

Application of Air-Coupled Ground Penetrating Radar Based on F-K Filtering and BP Migration in High-Speed Railway Tunnel Detection.

As the number and length of high-speed railway tunnels increase in China, implicit defects such as insufficient lining thicknesses, voids, and poor compaction have become increasingly common, posing a serious threat to train operation safety. It is, therefore, imperative to conduct a comprehensive census of the defects within the tunnel linings. In response to this problem, this study proposes a high-speed railway tunnel detection method based on vehicle-mounted air-coupled GPR. Building on a forward simulation of air-coupled GPR, the study proposes the F-K filtering and BP migration algorithms based on the practical considerations of random noise and imaging interference from the inherent equipment. Through multi-dimensional quantitative comparisons, these algorithms are shown to improve the spectrum entropy values and instantaneous amplitude ratios by 4.6% and 11.6%; and 120% and 180%, respectively, over the mean and bandpass filtering algorithms, demonstrating their ability to suppress clutter and enhance the internal signal prominence of the lining. The experimental results are consistent with the forward simulation trends, and the verification using the ground-coupled GPR detection confirms that air-coupled GPR can meet the requirements of high-speed railway tunnel lining inspections. A comprehensive GPR detection model is proposed to lay the foundation for a subsequent defect census of high-speed railway tunnels.

Quantitative identification of pulse-like ground motions based on intrinsic time-scale decomposition technique

Pulse-like earthquake ground motions may cause great seismic demands in engineering structures, and identifying these ground motions is significant in earthquake engineering. The intrinsic time-scale decomposition (ITD) is a self-adaptive time-frequency decompaction method that decomposes signals into proper rotation components. The instantaneous frequency and amplitude of the components are well defined, and the temporal information of frequency and amplitude has the exact resolution with the time-scale of extreme of the original signal. ITD was introduced in this study to decompose the non-stationary earthquake ground motion signals. A procedure for filtering and extracting the low-frequency pulses was constructed, and a quantitative criterion for classifying the pulse-like ground motions was proposed. The proposed method was tested on many ground motions and compared with the existing classification methods. The proposed method was demonstrated as an effective way to identify the pulse-like ground motion records, which can be readily implemented in earthquake engineering practices.

Impact of Amplitude and Phase of fMRI time series for Functional Connectivity Analysis

PurposeSeveral studies in the field of fMRI have reported the synchrony between the brain regions using instantaneous phase (IP) representation (derived from analytic representation of BOLD time series). We hypothesized that instantaneous amplitude (IA) representation from different brain regions might give additional information to the functional brain networks. To validate this, we explored this representation of resting state BOLD fMRI signal for deriving resting state networks (RSNs) and compared it with the IP representation based RSNs. MethodResting state fMRI data of 100 healthy adults (age=20–35 years, 54 females) from the population of 500 Subjects of HCP dataset were studied. Data was acquired using a 3T scanner in four runs (15-min each) with the phase encoding directions: Left to Right (LR), Right to Left (RL). These four runs were acquired in two sessions, and subjects were asked to keep their eyes open with a fixation on a white cross. The IA and IP representations were derived from a narrow-band filtered BOLD time series using Hilbert transforms and a seed-based approach is used to compute the RSNs in the brain. ResultsThe experimental results demonstrate that within the frequency range 0.01–0.1 Hz, IA representation based RSNs have the highest similarity score between the two sessions for the motor network. Whereas for fronto-parietal network, IP based activation maps have the highest similarity score for all the frequency bands. For higher frequency band (0.198–0.25 Hz) consistency of the obtained RSNs across two sessions reduced for both IA and IP representations. Fusion of IA and IP representations based RSNs in comparison to those of IP based representation, leads to 3–10% improvement in the similarity scores between the default mode network obtained for the two sessions. In addition, the same comparison demonstrates 15–20% improvement for the motor network in the frequency bands: 0.01–0.04 Hz, 0.04–0.07 Hz, slow5 (0.01–0.027 Hz) and slow-4 (0.027–0.073 Hz). It is also observed that the similarity score between two sessions using instantaneous frequency (IF) (derivative of unwrapped IP) representation in exploring functional connectivity (FC) networks is comparable with those obtained using IP representation. ConclusionOur findings suggest that IA-representation based measures can estimate RSNs with the reproducibility between the sessions comparable to that of the IP representation-based methods. This study demonstrates that IA and IP representations contain the complementary information of BOLD signal, and their fusion improves the results of FC.

Inversion of reclaimed soil water content based on a combination of multi-attributes of ground penetrating radar signals

Rapid, accurate, and non-destructive acquisition of the distribution of reclaimed soil moisture information can provide data for the rapid monitoring of reclaimed soil in areas experiencing coal mining subsidence. However, the water content inversion methods based on ground penetrating radar (GPR) are mostly single-attribute analysis methods, which are easily affected by the soil structure. This paper proposes a multi-attribute joint analysis method, which can reduce the influence of complex soil structure on the prediction results. Surveys and soil sampling using GPR were performed on a subsided reclamation area in Huaibei City, Anhui Province, China. Correlation analysis of GPR attribute information and volumetric water content (VWC) showed that frequency peak (FP), average envelope amplitude (AEA), energy, instantaneous amplitude area, instantaneous frequency area, and average instantaneous frequency values were significantly related to the VWC of reclaimed soil. The applicability of different single-attribute analysis methods under the condition of reclaimed soil was compared. Results showed that the predictive effects of FP and AEA attributes were better than other attributes. Generally, the single-attribute analysis method was greatly affected by the structure of reclaimed soil, so the accuracy and reliability of this method need to be further optimized. The prediction results of the single- and multi-attribute joint analysis methods in the structure of reclaimed soil were compared and analyzed. This showed that the prediction accuracy and model reliability of the multi-attribute method are both higher than those of the single-attribute method. The multi-attribute method can overcome the problem of insufficient accuracy of water content detection of ground-seeking radar in soil with a complex structure. Finally, the multi-attribute method was used to obtain the water distribution information in the reclamation area. Results of this study provide new methods and ideas for the prediction of water content by GPR in soils with complex structure.

Research and implementation of modulation recognition based on cascaded feature fusion

AbstractAiming at the problems of weak robustness of single feature and limited recognition range in modulation recognition, this paper proposes a modulation recognition algorithm based on cascaded feature fusion and multi‐classifier combination, in which time‐frequency map and instantaneous amplitude spectral density features are extracted from low intermediate frequency (IF) signal, constellation map and high‐order cumulant features are extracted from zero IF signal, and a three‐level recognition algorithm is designed through the decision fusion of decision tree, convolutional neural network, and support vector machine. In order to verify the performance of the algorithm, a modulation recognition system is designed and built based on USRP2974. The low IF and zero IF modulation signals are received through two channels, and the RF signals are received and processed in real time with the help of the built‐in CPU of the receiver. The recognition of 13 kinds of analog modulation and digital modulation signals is realized. Under the condition of wireless reception, the recognition rate of this system is more than 93% at 5 to 10 dB.

Why EMD and similar decompositions are of little benefit for bearing diagnostics

Empirical mode decomposition (EMD) is a way of decomposing complex signals into a sum of “mono-components”, i.e. intrinsic mode functions (IMFs), each of which can be considered as a single carrier frequency, modulated in both amplitude and phase/frequency (an analytic signal), so that both amplitude and phase remain continuous and differentiable, the latter to instantaneous frequency. In many cases, the instantaneous frequency and amplitude could be valuable diagnostic features, for example with gear vibrations. Many authors have suggested applying this technique to the diagnostics of rolling element bearings (REBs), but this paper shows that REB signals intrinsically do not have such properties, except perhaps in short bursts, so that the excessive computation time trying to ensure continuous phase is wasted. Much more appropriate methods exist to extract the optimum envelope signal, which contains the desired diagnostic information, based on more relevant criteria. As its name suggests, the EMD process is empirical, with no analytical solution, so that different results can be obtained from different segments of the same signal, partly because of different noise content. Another way of obtaining IMFs is by using variational mode decomposition (VMD), which does have an analytical solution, making it less sensitive to noise, but still assumes that the signal can be validly decomposed into mono-components, which is not the case for bearing signals. The EMD process has two additional problems which make difficult its use for REB signals; (1) end effects, which usually mean that many, perhaps a majority, of IMFs are required purely to compensate for them, and which cannot be truncated for signals consisting of short bursts with sections of noise between them; and (2) mode mixing, meaning that repeatable results cannot be guaranteed, even for valid mono-components, let alone REB signals which are of a stochastic nature. The paper explains in detail why REB signals cannot be validly decomposed by EMD and similar methods, to give sub-components with properties directly related to bearing faults, even though many existing papers describe how the IMFs found by the EMD process might be selected or re-combined to have properties of interest in bearing diagnostics. In particular, the paper shows that the equivalent bandpass filters given by EMD have much poorer selectivity than most alternative filters. The paper uses many simulated and measured examples and demonstrations, to discuss these claims, including a number based on results from already published papers.

Damage Detection in Nonlinear Elastic Structures Using Individual Sensors

Natural frequencies have always been one of the most intuitive and widely used features for damage identification in civil structures. Even with the recent rapid technological and theoretical developments, frequency-based identification methods are of great interest for applications through low-cost sensing systems. Although most techniques for frequency identification assume a linear structural behavior, in real applications, variations in the amplitude of input excitation can lead to short-term frequency fluctuations due to the inherent nonlinearities of civil structures. This paper proposes a procedure for damage detection in nonlinear systems based on instantaneous resonant frequency and amplitude estimates. A statistical model was fitted to identified data, and a synthetic indicator was proposed to obtain robust damage detection, even when frequency shifts due to variations in the input excitation are comparable to those due to actual damage. The proposed method was applied to a dataset recorded from a reinforced concrete building with strongly nonlinear behavior.

Structural Nonlinear Model Updating Based on an Improved Generative Adversarial Network

This study proposes a novel nonlinear model updating approach based on an improved generative adversarial network (GAN). In the improved GAN, a convolutional neural network (CNN) surrogate model is added to the discriminator network to enhance the capability of the GAN to learn the complex mapping relationship between vibration responses and nonlinear model parameters. To avoid the gradient disappearance present in the traditional GAN, a combined objective function is added to the improved GAN model. In the network training process, the instantaneous amplitudes of the decomposed accelerations are extracted as input samples and the nonlinear model parameters are defined as the GAN output. When the improved GAN is trained, the trained network model is capable of estimating the nonlinear model parameters based on measured instantaneous acceleration amplitudes. To confirm the feasibility of the improved GAN for structural nonlinear model updating, a steel-concrete hybrid bridge tower subjected to seismic excitation is numerically simulated and the effects of different numbers of data points and noise levels are studied. Furthermore, the identification accuracy of the improved GAN is compared with the updated results. For experimental applications, the shake table test of a scaled steel-concrete hybrid bridge tower subjected to seismic excitations is employed to confirm the effectiveness of the proposed nonlinear model updating method. Both numerical and experimental results demonstrate that the improved GAN model is reliable and effective for the nonlinear model updating of structures subjected to seismic excitation.

Application of Feature Extraction Method Based on Empirical Fourier Decomposition in Rotor Rub-impact Fault

This paper provides a feature extraction technique primarily by using empirical Fourier decomposition (EFD) to reveal the time-frequency features of rotor rub-impact fault. The Hilbert transform estimates the instantaneous frequency (IF) and instantaneous amplitude (IA) of the signal generated by EFD. Finally, high-quality time-frequency representation (TFR) is reconstructed by the adaptive time-frequency spectrum (ATFS). An example of the rotor rub-impact fault is utilized to demonstrate efficiency of this technique, and the results are contrasted with those of empirical mode decomposition (EMD). EFD performs better in the modal mixing problem than EMD and has excellent decomposition efficiency. It realizes IF feature extraction and offers a more precise TFR.

Data-Driven Sparsity-Based Source Separation of the Aliasing Signal for Joint Communication and Radar Systems

Spectrum sharing between radar and communication systems has attracted substantial recent research attention. In order to avoid the mutual interference, source separation of the aliasing signal is a promising solution for joint communication and radar (JCR) sensing. However, most of the existing source separation methods are very sensitive to wide-band signals with rapidly varying instantaneous amplitude (IA) and not applicable to scenarios with complex overlapping subsignals. To overcome the above limitations, a data-driven sparsity-based source separation method is proposed. Without depending on signal parameters, a sparse signal observation model of the received signal is established. Then, source separation is transformed into estimation of the IA and instantaneous frequency (IF), and an iterative method is developed. Moreover, the Cramér-Rao lower bound (CRLB) of the source separation error (SSE) variance is derived based on the CRLB of IA and IF. Simulation results demonstrate that our proposed method is superior to the benchmark schemes and is robust to noise and initial IF errors.

Occurrence of Nighttime Irregularities and Their Scale Evolution in the Ionosphere Due To the Solar Eclipse Over East Asia on 21 June 2020

AbstractSolar eclipse is a daytime phenomenon that significantly disturbs the ionosphere, but whether the eclipse induces ionospheric irregularities in the nighttime remains unknown. In this study, we analyzed the dense total electron content (TEC) observations from the ground‐based Global Navigation Satellite System receivers over East and South Asia to examine the development of the irregularities in the nighttime on the day of the 21 June 2020 annular solar eclipse. The rate of TEC index (period <5 min) indicates the occurrence of the irregularities that evolve from the large or coarse structures with a period ranging from hours to dozens of minutes in the nighttime due to the eclipse. We take advantage of the data‐adaptive analysis method, Hilbert‐Huang transform, to derive the instantaneous amplitude and frequency of the TEC time series, which exposes the temporal and spatial evolutions of the irregularities from larger structures continuously.

Safety Monitor Symmetry Concerning Beam Bridge Damage Utilizing the Instantaneous Amplitude Square Method

It is critical for the safety monitoring of highway bridges that beam bridge damage can be identified from the dynamic response of passing vehicles. Numerical simulations of passing vehicles were conducted utilizing the vehicle–bridge coupling vibration theory and the indirect measurement method. Fast Fourier transform was performed on the time history response of vehicle acceleration, and the driving frequency component response and its instantaneous amplitude square value (IAS value) were obtained by band-pass filtering and Hilbert transform processing. The identified IAS value detected the damage location of the bridge. The identification method of IAS value is used to analyze the applicability of a simply supported beam bridge, a continuous beam bridge, and an irregular skew beam bridge. The effects of vehicle speed, vehicle damping, bridge damping, and a social vehicle on damage identification are discussed. The results show that the effect of damage location is better when the vehicle speed is less than 4 m/s. In the presence of social vehicles, the excitation on the bridge increases, and the damage location can still be accurately determined by the IAS method. Vehicle damping and bridge damping have little effect on the results of damage identification. In structural health monitoring for bridges, this paper can provide a theoretical reference for the application of IAS motion sensing to identify the damage location indirectly.

A Hybrid Approach for Low-Voltage AC Series Arc Fault Detection

In a low-voltage electric distribution network, arc fault presents a high energy density electricity-discharging phenomenon between conductors, which is often caused by aging of electric facilities, loose contacts and terminals, or insulation failure due to internal and external destructions. A large amount of heat may be created during this discharging, which will further cause the risk of fire hazards to mitigate in the residential environment. Currently, many utility grid operators and electricity users are still devoted to seeking effective detection technology for arc fault protection. This paper proposes a hybrid approach that combines discrete wavelet transform (DWT), empirical mode decomposition (EMD), and dynamic time warping (DTW) methods for low-voltage AC series arc fault detection. In DWT, it uses time–frequency domain characteristics of the arc current signal to extract the occurrence of arc fault. In EMD, it decomposes the complex arc fault current signal into a finite intrinsic mode (IMF) signal; then, instantaneous amplitude of IMF signal is obtained by Hilbert–Huang transform (HHT) as a feature for arc fault identification. Firstly, the results of arc fault detections depend on the results from DWT and EMD. When both two methods detect different results, DTW method will be activated, using the similarity measurements between normal and arc fault current waveforms as an assistant measure to determine the occurrence of arc fault. The performance of the proposed approach is tested and validated using various electric appliances, and the results show that the proposed approach can effectively detect low-voltage AC series arc fault.

"The Estimation of the Instantaneous Amplitudes and the Instantaneous Frequencies of the EEG when both are Stochastic Process"

In this report we model the EEG signal as a sum of sine waves. Each sine wave has a random frequency and a random amplitude. We use band pass filters to separate the different frequency segments of the EEG.