Instantaneous Energy Spectrum Research Articles

Discrete-coordinate crypto-Hermitian quantum system controlled by time-dependent Robin boundary conditions

A family of exactly solvable quantum square wells with discrete coordinates and with certain non-stationary Hermiticity-violating Robin boundary conditions is proposed and studied. Manifest non-Hermiticity of the model in conventional Hilbert space Hfriendly is required to coexist with the unitarity of system in another, ad hoc Hilbert space Hphysical . Thus, quantum mechanics in its non-Hermitian interaction picture (NIP) representation is to be used. We must construct the time-dependent states (say, ψ(t)) as well as the time-dependent observables (say, Λ(t)). Their evolution in time is generated by the operators denoted, here, by the respective symbols G(t) (a Schrödinger-equation generator) and Σ(t) (a Heisenberg-equation generator, a.k.a. quantum Coriolis force). The unitarity of evolution in Hphysical is then guaranteed by the reality of spectrum of the energy observable alias Hamiltonian H(t) = G(t) + Σ(t). The applicability of these ideas is illustrated via an N by N matrix model. At N = 2, closed formulae are presented not only for the measurable instantaneous energy spectrum but also for all of the eligible time-dependent physical inner-product metrics Θ(N=2)(t), for the related Dyson maps Ω(N=2)(t), for the Coriolis force Σ(N=2)(t) as well as, in the very ultimate step of the construction, for the truly nontrivial Schrödinger-equation generator G (N=2)(t).

Comparison and experiment validation of fatigue data editing methods for vehicle component

Fatigue data editing (FDE) is an effective scheme to shorten the time of durability bench testing of vehicle components. In this paper, four existing FDE method for vehicle components were evaluated and compared. Moreover, a novel FDE method based on variational mode decomposition (VMD) algorithm was proposed. In this method, the VMD algorithm was used to decompose the fatigue data into several intrinsic mode function (IMF) components. The instantaneous energy spectrum of the fatigue data was obtained using the Hilbert transform to analyze the IMF components. Then, the damaging segments were extracted to obtain the edited fatigue data. Fatigue data measured at powertrain mount was used for method comparative study. Results indicate that the time compression ratio of the VMD-based method is about 16.09%, which is larger than that of other editing methods. Furthermore, the experiment data shows that the editing effect of the proposed method were encouraging.

Accelerated Editing Method for Vehicle Durability Fatigue Load Spectrum Based on Wigner-Ville Transform.

A Wigner-Ville transform-based (WVT-based) load spectrum fast editing method for vehicle parts is proposed to improve the efficiency of durability tests. In this method, the instantaneous energy spectrum (IES) of the original time-domain signal is obtained via the Wigner-Ville transform, which is used as a criterion to identify time-domain points of ineffective damage contribution. A genetic algorithm (GA) based threshold optimization model is also proposed to automatically set the threshold of the IES under consideration of the relative damage requirements and statistical parameters of the signal. The effectiveness of the above proposed editing method is demonstrated by compiling an SUV's suspension coil spring signal obtained from physical sensor-based measurements. Meanwhile, the same spectrum is also processed using time-domain editing, Short-time Fourier-transform, and S-transform methods for comparison. The results show that the WVT-based edited spectrum has a time-duration retention ratio of about 76.30%, which is significantly superior to other methods, with the same pseudo-damage retention and statistical parameter error constraints. Moreover, in combination with the fatigue simulation analysis, it verifies that the load effect of the edited spectrum matches well with that of the original. Thus, the proposed method is considered more effective for compiling component load signals in vehicle acceleration durability tests.

Robust beam splitter with fast quantum state transfer through a topological interface

The Su–Schrieffer–Heeger (SSH) model, commonly used for robust state transfers through topologically protected edge pumping, has been generalized and exploited to engineer diverse functional quantum devices. Here, we propose to realize a fast topological beam splitter based on a generalized SSH model by accelerating the quantum state transfer (QST) process essentially limited by adiabatic requirements. The scheme involves delicate orchestration of the instantaneous energy spectrum through exponential modulation of nearest neighbor coupling strengths and onsite energies, yielding a significantly accelerated beam splitting process. Due to properties of topological pumping and accelerated QST, the beam splitter exhibits strong robustness against parameter disorders and losses of system. In addition, the model demonstrates good scalability and can be extended to two-dimensional crossed-chain structures to realize a topological router with variable numbers of output ports. Our work provides practical prospects for fast and robust topological QST in feasible quantum devices in large-scale quantum information processing.

Dynamic damage identification of tunnel portal and verification via shaking table test

Tunnel portals are seismically weak. Large-scale shaking-table tests of a tunnel portal were conducted. A method based on the Hilbert-Huang transform (HHT) for dynamic damage identification of tunnel portals was studied using the test results. The test preparation process and basic principles of the HHT are briefly described. The intrinsic-mode functions (IMFs) after empirical mode decomposition (EMD) were evaluated using multiple indicators, including the coefficient of determination (R2), root-mean-square error (Rmse), variance contribution rate (Mi), and energy moment (E). The time histories of the IMFs, marginal Hilbert spectrum, and Hilbert instantaneous energy spectrum were analysed. The results show that the damage development process of the lining and slope can be characterised by the marginal Hilbert spectrum and Hilbert Instantaneous energy spectrum. The slope had an obvious acceleration amplification effect with elevation and surface-trend amplification effect. Damage to the tunnel-portal slope is mainly caused by the development of tension cracks at the top of the slope, falling of scattered particles on the slope shoulder, development of cracks on the slope surface, and instability and collapse of the surrounding rock near the tunnel portal. Slope surface damage developed faster and to a greater extent than the interior of the slope. The lining of the portal section was dominated by longitudinal cracks, with some diagonal cracks. Damage to the invert at the tunnel portal occurs earlier than that of the crown, and the degree of injury is greater than that of the crown. The degree of damage and development speed of the tunnel portal were also greater than those of the tunnel body. The proposed method can serve as a guide for identifying the dynamic tunnel-portal damage.

Energy Evolution Mechanism of Air Shock Wave Propagation and Attenuation Based on VMD–HT Energy Spectrum

Energy spectrum is an important tool for reflecting time–frequency characteristics of signals. The energy spectra of air shock wave at different explosion distances ware analyzed to investigate the energy evolution mechanism in the propagation and attenuation process. Waveforms of air shock wave were obtained from explosion tests and numerical simulations. Energy propagation and attenuation mechanisms of air shock wave were discussed on the basis of the wave theory of fluid. Instantaneous and marginal energy spectra of air shock wave were calculated using variational modal decomposition (VMD) and Hilbert transform (HT). Energy evolution laws of air shock wave with time, frequency, and explosion distance were analyzed according to the statistical results of the energy spectra. Results showed that the instantaneous energy peak of air shock wave is directly proportional to the square of its pressure peak while inversely proportional to the third power of propagation distance. Nonlinear attenuation of air shock wave will cause frequency dispersion and decelerate the attenuation rate of the total energy of air shock wave. The energy evolution laws of air shock wave with time and frequency reflected by instantaneous and marginal energy spectra were consistent with the theoretical analysis results.

Hilbert spectrum analysis method of blast vibration signal based on HHT instantaneous phase optimization

Compared with wavelet analysis method of signal data, HHT (Hilbert-Huang Transform) method is widely used for the local signal data analysis in the time–frequency domain associated with adaptable capacity, which has been recognized as one of the most efficient method to address the non-stationary signals. In this study, Matlab software was used as the calculation code and field millisecond delay blasting data was collected as the research objects, the Hilbert time–frequency spectrum, marginal spectrum, instantaneous energy spectrum and Hilbert energy spectrum scatter were obtained for the signal IMF components under the standard instfreq.m function (as shown in Section 3.3) frequency modulation with the identified bandwidth of 1 Hz. The reasons of negative frequency for digital signals were discussed based on the theoretical analysis and the digitial signals were then summarized as two types of negative frequency according to the instantaneous phase characteristics. The field collected blasting vibration signals were used to illustrate the features of the negative frequency points such as large number, correlated relation between the signal amplitude extent and frequency band, and non-negligible of the total vibration energy. In addition, a theoretical equation was proposed for the instantaneous phase optimization function based on the HHT method, and a triple identification approach of millisecond time was proposed based on instantaneous phase optimization method. The process of Hilbert spectrum analysis based on HHT instantaneous phase optimization was implemented using Matlab, which was used to analyze Hilbert spectrum characteristics. Further, a theoretical comparison and analysis between the standard instfreq.m time–frequency modulation and the proposed phase optimized HHT spectrum were performed, and the results shows that the optimized HHT spectrum analysis improves the accuracy of time–frequency spectrum and Hilbert spectrum calculation, besides, the frequency domain recognition width is about 2∙r times of that from the standard solution. Finally, the phase optimization was used to analyze the amplitude spectrum, instantaneous velocity energy spectrum and 3D time–frequency seismic velocity energy spectrum features, application of HHT-based instantaneous phase optimization method is given for the accurate recognition application of multi-segment detonation millisecond time in underground blasting.

A Cell Condition-Sensitive Frequency Segmentation Method Based on the Sub-Band Instantaneous Energy Spectrum of Aluminum Electrolysis Cell Voltage

Cell voltage is a widely used signal that can be measured online from an industrial aluminum electrolysis cell. A variety of parameters for the analysis and control of industrial cells are calculated using the cell voltage. In this paper, the frequency segmentation of cell voltage is used as the basis for designing filters to obtain these parameters. Based on the qualitative analysis of the cell voltage, the sub-band instantaneous energy spectrum (SIEP) is first proposed, which is then used to quantitatively represent the characteristics of the designated frequency bands of the cell voltage under various cell conditions. Ultimately, a cell condition-sensitive frequency segmentation method is given. The proposed frequency segmentation method divides the effective frequency band into the [0, 0.001] Hz band of low-frequency signals and the [0.001, 0.050] Hz band of low-frequency noise, and subdivides the low-frequency noise into the [0.001, 0.010] Hz band of metal pad abnormal rolling and the [0.01, 0.05] Hz band of sub-low-frequency noise. Compared with the instantaneous energy spectrum based on empirical mode decomposition, the SIEP more finely represents the law of energy change with time in any designated frequency band within the effective frequency band of the cell voltage. The proposed frequency segmentation method is more sensitive to cell condition changes and can obtain more elaborate details of online cell condition information, thus providing a more reliable and accurate online basis for cell condition monitoring and control decisions.

Time-frequency energy analysis of deepwater explosion shock wave signals based on HHT

In order to study the time-frequency characteristics of shock wave signals under deep water explosion conditions, experiments are performed using water medium explosion containers to simulate different water depth conditions, and signal analysis is performed on the shock wave data obtained in the experiments. Traditional time-frequency analysis methods such as Fourier transform and wavelet transform have many limitations on deep-water explosion shock wave signal analysis, the HHT method is used to analyse the experimental data from the three-dimensional Hilbert spectrum, marginal spectrum and instantaneous energy spectrum. The results show that the time-frequency method can effectively extract the frequency components of the deep-water explosion load signal in different periods. It provides a reference for people to understand the time frequency characteristics of shock wave signals in deep water.

Lkurtogram Guided Adaptive Empirical Wavelet Transform and Purified Instantaneous Energy Operation for Fault Diagnosis of Wind Turbine Bearing

The periodic impacts are regarded as the typical characteristics of local defect of wind turbine bearing. For this reason, it is significant to extract the periodic impacts from the original measured vibration signal with background noise interferences during the defect identification process. For the purpose of effectively solving this issue, an innovative diagnostic frame based on Lkurtogram guided adaptive empirical wavelet transform (LGAEWT) and purified instantaneous energy operation (PIEO) is put forward. Within this diagnostic frame, the L-kurtosis indicator guided wavelet equivalent filter band mergence is carried out to confirm the optimal filter boundary, then the resonance frequency band containing rich characteristic information can be extracted, and the characteristic sensitive component is able to be separated from the original vibration signal. In addition, a novel signal processing strategy called PIEO is presented to inhibit the background interferences and enhance the periodic impact signatures in sensitive components, and the purified instantaneous energy spectrum is adopted to replace the traditional envelope spectrum for characteristic frequency spectral lines identification. The feasibility of the proposed diagnostic frame has been demonstrated by the experimental signals and the actual engineering case, and the results manifest that it is suitable for bearing fault enhance detection under low signal-to-noise ratio (SNR) environment. Furthermore, the comparison results with the widely used Kurtogram, Autogram, and DWT methods indicate that this innovative diagnostic strategy has more prominent advantages on background interference suppression and weak characteristic intensification.

Predicting the near-wall velocity of wall turbulence using a neural network for particle image velocimetry

Near-wall velocity prediction for wall-bounded turbulence is useful for constructing a wall model and estimating dissipation and wall shear stress. A convolutional neural network is developed to improve the near-wall velocity prediction and spatial resolution for wall-bounded turbulent velocity fields obtained using particle image velocimetry (PIV). To establish the relationship between the low-resolution and high-resolution fields, this machine learning model is trained on a synthetic PIV dataset generated based on velocity fields obtained from the direct numerical simulation of turbulent channel flows at Reτ = 1000. Using a test dataset with a higher Reynolds number of Reτ = 5200, the performance of this model is assessed in terms of instantaneous fields, error analysis, velocity statistics, and energy spectra. The influences of the interrogation window, image resolution, and particle concentration on the performance of this network are also considered. We further apply this network to practical PIV data from a turbulent boundary layer at Reτ = 2200 to assess the network performance under real experimental conditions. The results indicate that the proposed machine-learning-based model can predict missing near-wall velocity fields and enhance the spatial resolution of PIV fields, but the accuracy for Reynolds shear stress prediction needs to be further improved. The presented approach shows the potential ability to predict the near-wall instantaneous velocity of high-Reynolds-number turbulence from low-Reynolds-number flow fields.

A precise feature extraction method for shock wave signal with improved CEEMD-HHT

Efficient extraction of feature parameters is the key to evaluating weapon damage performance. At present, many classical feature extraction algorithms have the problem that the extraction cannot meet the actual needs. A precise feature extraction method based on improved complementary ensemble empirical mode decomposition (CEEMD) with Hilbert-Huang Transform (HHT) was proposed in this paper to solve problems such as large noise and difficulties in extracting features of shockwave overpressure signals in complex test environment. We introduced CEEMD to decompose original explosion shockwave signals and adopted wavelet packet threshold de-noising to extract useful information from noisy high-frequency intrinsic mode functions (IMFs). The correlation coefficient algorithm is introduced to remove unrelated IMFs. In addition, we performed reconstruction of original signals to extract true time-course feature and utilized Hilbert-Huang Transform (HHT) to achieve precise extraction of instantaneous feature and energy spectrum of the various IMFs. The improved CEEMD-HHT is a precise method for shock wave signal analysis. It not only effectively removes noise, but also retains effective high-frequency information without losing useful information. Additionally, it overcomes the problems of mode mixing in empirical mode decomposition (EMD), and has the advantages of feature extraction with high accuracy and self-adaptation. The effectiveness of the proposed method is demonstrated by 2 groups of experimental data, and it precisely extracts instantaneous feature and energy spectrum of shockwave overpressure signal, which provide new theoretical basis for the evaluation of weapon damage.

Time-frequency characteristics of the strain signal of the metal shell under internal explosion

In this paper, the empirical mode decomposition-Hilbert Huang transform (EMD-HHT) was used to characterize the strain signal within metal cylindrical shell structure under internal blast loading. The received vibration frequencies of signal were closely consistent with FT characterization results. Through the EMD-HHT, instantaneous energy spectrum, marginal energy spectrum and Hilbert energy spectrum were determined, and these reflected the change in trend of signal energy in time domain, frequency domain, and time-frequency domain, showing the instantaneity and locality of explosion signal. The frequency components of the signal at any time were also determined, which proved that signals generated by the metal shell were the result of the superposition of different frequency signals under internal blast loading. This paper explains more clearly the time and frequency characteristics of blast signal, providing the theoretical basis for the study of antiknock in structures.

Damage pattern recognition and damage evolution analysis of unidirectional CFRP tendons under tensile loading using acoustic emission technology

The purpose of this paperis to use acoustic emission (AE) technology to realize the damage pattern recognition and the damage evolution of unidirectional (UD) CFRP tendons in the tensile process. In order to realize this goal, the tensile test of UD CFRP tendons was carried out. The adaptive Hilbert–Huang transform was used to analyze the AE signal in time–frequency domain to obtain the Hilbert marginal energy spectrum (HMES) and instantaneous energy spectrum (IES) of the signal. Damage pattern recognition was realized through HMES and IES. In this paper, a mutation function and a cumulative function were proposed based on HMES to study the evolution of different damage mechanisms and the internal relationship between them. In order to verify the reliability of the proposed method, digital image correlation (DIC) technique was used to obtain the strain distribution of the UD CFRP tendon specimen to determine the occurrence of local damage. The results of this investigation can be used to guide the establishment of the health monitoring mechanism for prestressed CFRP structures based on AE technology.

Application of Hilbert-Huang Transform in Ultrasonic Echo Signal Processing of Composites

The ultrasonic nondestructive testing signals of carbon fiber reinforced composites have the characteristics of non-stationary and low signal-to-noise ratio, and Hilbert-Huang transform has unique advantages in feature extraction of such signals. This paper introduces the basic idea and method of Hilbert-Huang transform, which decomposes ultrasonic echo signals into several intrinsic mode functions, highlights the local characteristics of signals, and then obtains Hilbert spectrogram, marginal spectrum and instantaneous energy spectrum, so as to reveal the process of simultaneous changes of signal energy in time domain and frequency domain.

Non-adiabatic extension of the Zak phase and charge pumping in the Rice–Mele model

In this study, the Landau–Zener (LZ) transition method is applied to investigate a weak non-adiabatic effect on the Zak phase and the topological charge pumping in the Rice–Mele model. The non-adiabatic effect is formulated using the LZ transfer matrix. The effective lower band wave function picks up the Stokes phase as well as the usual dynamical phase through two avoided crossings appearing in the two band instantaneous energy spectrum. The interference effect from the upper band has a decisive influence on the decay behavior of the lower band population. A non-adiabatic extension of the Zak phase can then be formulated, corresponding to the center of mass of the lower band Wannier function. Furthermore, we estimate the validity of the LZ formalism and verify the breakdown of the quantization of the topological charge pumping by changing the sweeping speed.

Time‐frequency analysis and classification of power signals using adaptive cuckoo search algorithm

AbstractA new approach to Hilbert energy spectrum and pattern recognition of nonstationary power signals is presented in this paper. In the proposed work, visual localization, detection, and classification of nonstationary power signals are achieved using Hilbert transform (HT)–based adaptive local iterative filter (ALIF). The HT is applied on all the intrinsic mode functions that are obtained from both empirical mode decomposition (EMD) and ALIF to extract instantaneous amplitude and frequency components. The instantaneous Hilbert energy spectrum results in clear visual detection, localization, and classification of the different power signal disturbances. The visual energy spectrum by Hilbert‐Huang Transform (HHT) on ALIF showing a better result than HHT applied on EMD. The feature vectors are extracted from the Hilbert energy spectrum for automatic pattern recognition of various nonstationary signals using a traditional fuzzy C‐means algorithm (FCMA). Finally, the center of the cluster is further optimized using fuzzy C‐means–based adaptive cuckoo search algorithm. The average classification accuracy of the disturbances is 91.25% and 99.25% using fuzzy C‐means and adaptive cuckoo search–based FCMA, respectively.

Analysis of Acoustic Wave Frequency Spectrum Characters of Rock Mass under Blasting Damage Based on the HHT Method

The limitation associated with Fourier transform and wavelet analysis that they often fail to produce satisfactory resolution simultaneously in time and frequency when dealing with nonlinear and nonstationary signals is frequently encountered. Therefore, this paper aims at using the HHT (Hilbert–Huang transform) method, which is built on the basis of the EMD- (empirical mode decomposition-) based wavelet threshold denoising technique and the Hilbert transform, to analyze the blasting vibration signals in a south China lead-zinc mine. The analysis is conducted in terms of three-dimensional Hilbert spectrum, marginal spectrum, and instantaneous energy spectrum. The results indicate that the frequencies of the blasting vibration signals lie mainly within 0∼200 Hz, which consists of more than 90% of the total signal energy. At the onset of the blasting, the vibration frequency tends to be low, with the frequency that is less than 50 Hz being dominant. By using instantaneous energy spectrum, which can reveal the condition of energy release for detonator explosion, the initiation moments of detonators with 7 time-lag levels are accurately identified. This accurate identification demonstrates the superiority of the HHT method in coping with nonlinear and nonstationary signals. Additionally, the HHT method that is characterized by adaptivity, completeness, strong reconfigurability, and high accuracy provides an opportunity for reflecting signals’ change features with regard to time domain, frequency domain, and energy irrespective of the limitation of the Heisenberg uncertainty principle.

Investigation of Numerical Dissipation in Classical and Implicit Large Eddy Simulations

The quantitative measure of dissipative properties of different numerical schemes is crucial to computational methods in the field of aerospace applications. Therefore, the objective of the present study is to examine the resolving power of Monotonic Upwind Scheme for Conservation Laws (MUSCL) scheme with three different slope limiters: one second-order and two third-order used within the framework of Implicit Large Eddy Simulations (ILES). The performance of the dynamic Smagorinsky subgrid-scale model used in the classical Large Eddy Simulation (LES) approach is examined. The assessment of these schemes is of significant importance to understand the numerical dissipation that could affect the accuracy of the numerical solution. A modified equation analysis has been employed to the convective term of the fully-compressible Navier–Stokes equations to formulate an analytical expression of truncation error for the second-order upwind scheme. The contribution of second-order partial derivatives in the expression of truncation error showed that the effect of this numerical error could not be neglected compared to the total kinetic energy dissipation rate. Transitions from laminar to turbulent flow are visualized considering the inviscid Taylor–Green Vortex (TGV) test-case. The evolution in time of volumetrically-averaged kinetic energy and kinetic energy dissipation rate have been monitored for all numerical schemes and all grid levels. The dissipation mechanism has been compared to Direct Numerical Simulation (DNS) data found in the literature at different Reynolds numbers. We found that the resolving power and the symmetry breaking property are enhanced with finer grid resolutions. The production of vorticity has been observed in terms of enstrophy and effective viscosity. The instantaneous kinetic energy spectrum has been computed using a three-dimensional Fast Fourier Transform (FFT). All combinations of numerical methods produce a k − 4 spectrum at t * = 4 , and near the dissipation peak, all methods were capable of predicting the k − 5 / 3 slope accurately when refining the mesh.

Machinery running state identification based on discriminant semi-supervised local tangent space alignment for feature fusion and extraction

Extraction of sensitive features is a challenging but key task in data-driven machinery running state identification. Aimed at solving this problem, a method for machinery running state identification that applies discriminant semi-supervised local tangent space alignment (DSS-LTSA) for feature fusion and extraction is proposed. Firstly, in order to extract more distinct features, the vibration signals are decomposed by wavelet packet decomposition WPD, and a mixed-domain feature set consisted of statistical features, autoregressive (AR) model coefficients, instantaneous amplitude Shannon entropy and WPD energy spectrum is extracted to comprehensively characterize the properties of machinery running state(s). Then, the mixed-dimension feature set is inputted into DSS-LTSA for feature fusion and extraction to eliminate redundant information and interference noise. The proposed DSS-LTSA can extract intrinsic structure information of both labeled and unlabeled state samples, and as a result the over-fitting problem of supervised manifold learning and blindness problem of unsupervised manifold learning are overcome. Simultaneously, class discrimination information is integrated within the dimension reduction process in a semi-supervised manner to improve sensitivity of the extracted fusion features. Lastly, the extracted fusion features are inputted into a pattern recognition algorithm to achieve the running state identification. The effectiveness of the proposed method is verified by a running state identification case in a gearbox, and the results confirm the improved accuracy of the running state identification.