Time-domain Transformation Research Articles

Towards the Automation of Non-destructive Fault Recognition: Enhancement of Robustness and Accuracy Through AI Powered Acoustic and Thermal Signal Analysis in Time, Frequency- and Time-Frequency Domains

AbstractNon-destructive inspection and analysis techniques are crucial for quality assessment and defect analysis in various industries. They enable for screening and monitoring of parts and products without alteration or impact, facilitating the exploration of material interactions and defect formation. With increasing complexity in microelectronic technologies, high reliability, robustness and thus, successful failure analysis is essential. Machine learning (ML) approaches have been developed and evaluated for the analysis of acoustic echo signals and time-resolved thermal responses for assessing their ability for defect detection. In the present paper different ML architectures were evaluated, including 1D and 2D convolutional neural networks (CNNs) after transforming time domain data into the spectral- and wavelet domains. Results showed that 2D CNNs processing data in wavelet domain representation performed best, however at the expense of additional computational effort. Furthermore, ML-based analysis was explored for lock-in thermography to detect and locate defects in the axial dimension based on thermal emissions. While promising, further research is needed to fully realize its potential.

Hierarchical temporal sequence convergence in prescribed-time control for quadrotor UAVs under unknown dynamic disturbances

This paper studies the trajectory tracking control problem for quadrotor unmanned aerial vehicles (UAVs) under unknown disturbances and model uncertainties. A priori information about disturbances is required for most existing prescribed time-extended state observer (PTESO) methods. For unknown disturbances, a barrier function-based adaptive prescribed-time extended state observer (BFAPTESO) is designed by utilizing the time-domain transformation and adaptive mechanism in the prescribed time and using the barrier function method in the rest time. To improve tracking performance amidst model uncertainty, a finite-gain prescribed-time state observer (FGPTSO) is applied in the position loop. Then, the novel prescribed-time controllers are designed in conjunction with the above observers in the attitude and position loops. The proposed control scheme mitigates unknown dynamic disturbances and model uncertainties, guaranteeing that the tracking error achieves and sustains the preset accuracy within the prescribed time. Finally, numerical results indicate that the proposed control method is effective and robust.

Analytical study on dynamic performance of a hybrid system in real sea states

A mathematical model is developed to investigate the performance of a hybrid system comprising semi-submersible floating offshore wind turbines (FOWT) coupled to an array of point-absorbing wave energy converters (WECs) under irregular waves and dynamic winds. In this study, the hydrodynamic interaction of the hybrid system is conducted by applying the matching-method of eigenfunctions to solve the diffraction and radiation velocity potentials. Non-linearities of the hybrid system are taken into account in the Cummins framework, covering aerodynamic, catenary mooring, PTO system, fluid viscosity modeling, and frequency–time domain transformation of hydrodynamic coefficients. After running the convergence analysis and model validation, the present model is employed to perform a multiparameter effect analysis. Case studies are presented to clarify the effects of WEC parameters (including radius, draft, PTO damping, and layout) on the performance of a hybrid system. Nevertheless, a significant aspect of this work revolves around the development of a precise and efficient mathematical model, capable of accurately computing hydrodynamic coefficients for specific marine structures and evaluating the motion response of the interconnected floaters. Additionally, the study offers valuable insights into the preliminary design of hybrid systems and lays a mathematical foundation along with corresponding code for hybrid system projects.

Damage localization method using ultrasonic lamb waves and Wav2Vec2.0 neural network

In this paper, a Wav2Vec2.0 neural network based on an attention mechanism is proposed to locate defects in array ultrasonic testing signals. This method does not require knowledge of the a priori condition of the sample sound velocity or the feature extraction of ultrasonic scattering signals. First, an array piezoelectric ultrasonic testing system is used to detect a signal through hole defects at different positions in the plate structure. Then, three different neural networks—1D-CNN, Muti-Transformer, and Wav2Vec2.0—are used to locate the defects in the collected ultrasonic testing data. The performance of the network is verified with the data set collected through finite element simulation and the experimental system, and the identification accuracy and the calculation efficiency of different networks are compared and analyzed. To provide a solution for the poor balance of the experimental data set and the weak noise resistance of the simulation data set, a data set expansion method based on time domain transformation technology is proposed. The research results show that, the positioning accuracy of the Wav2Vec2.0 neural network proposed in this article is 98.46%, and the positioning accuracy is superior to Muti Transformer and ID-CNN.

Classification of mild Parkinson’s disease: data augmentation of time-series gait data obtained via inertial measurement units

Data-augmentation methods have emerged as a viable approach for improving the state-of-the-art performances for classifying mild Parkinson’s disease using deep learning with time-series data from an inertial measurement unit, considering the limited amount of training datasets available in the medical field. This study investigated effective data-augmentation methods to classify mild Parkinson’s disease and healthy participants with deep learning using a time-series gait dataset recorded via a shank-worn inertial measurement unit. Four magnitude-domain-transformation and three time-domain-transformation data-augmentation methods, and four methods involving mixtures of the aforementioned methods were applied to a representative convolutional neural network for the classification, and their performances were compared. In terms of data-augmentation, compared with baseline classification accuracy without data-augmentation, the magnitude-domain transformation performed better than the time-domain transformation and mixed-data augmentation. In the magnitude-domain transformation, the rotation method significantly contributed to the best performance improvement, yielding accuracy and F1-score improvements of 5.5 and 5.9%, respectively. The augmented data could be varied while maintaining the features of the time-series data obtained via the sensor for detecting mild Parkinson’s in gait; this data attribute may have caused the aforementioned trend. Notably, the selection of appropriate data extensions will help improve the classification performance for mild Parkinson’s disease.

Prescribed-time distributed optimization for time-varying objective functions: A perspective from time-domain transformation

This paper investigates the distributed prescribed- time optimization for time-varying objective functions. As opposed to the state-of-the-art in this field, our protocol is developed upon the methodology of time-domain transformation, based on which original prescribed-time problem is simplified as uniformly bounded counterpart in new spatiotemporal coordinate. Compared with the finite- and fixed-time works, the settling time of both consensus and optimization is independent of initial states as well as other parameters and therefore can be completely prespecified. Besides, the selection of parameters is free of any global information, which implies its feasibility in even fully distributed scenarios. Finally, a simulation is performed on cooperative hunting problem to validate the effectiveness of theoretical results.

Effective Identification and Localization of Single and Multiple Breathing Cracks in Beams under Gaussian Excitation Using Time-Domain Analysis

The output response of any intact oscillatory system subjected to a Gaussian excitation is also Gaussian in nature. On the contrary, when the system contains any type of underlying nonlinearity, the output signal is definitely non-Gaussian. In beam structures, the presence of fatigue-breathing cracks significantly influences the dynamic response characteristics under Gaussian excitation. The presence of such cracks alters the response to be nonlinear, and the non-Gaussianity of the system will arise. In order to examine the non-Gaussianity features and ability for the detection and localization of fatigue cracks, several breathing crack identification scenarios in beam-like structures are presented in this paper. The effects of single and multiple breathing cracks corresponding to different boundary conditions on the responses of beams are studied. The results are analyzed based on the higher-order time-domain transformations. Higher-order transformations, namely the skewness and kurtosis coefficients in addition to the Shannon entropy, are exploited to provide dynamic details about the response, which the conventional second-order statistics cannot show. The results exhibit that the proposed methods are robust and immune to noise and can detect and localize breathing cracks with different sensitivities.

Nonlinear Inversion Using Very Fast Simulated Annealing for Horizontal Electric Dipole Time-Domain Electromagnetic Data

A nonlinear stochastic inversion scheme, called very fast simulated annealing (VFSA), was applied to the time-domain electromagnetic data generated from a horizontal electric dipole. The forward formulation of the vertical magnetic field was expressed in the Laplace domain by applying the Hankel integral transform. Time-domain transformation was performed by applying the inverse Laplace transform using the Gaver–Stehfest algorithm. In this study, for noise-free synthetic data, the VFSA scheme yielded the smallest misfit and an inverted resistivity model that resembled the test model. The addition of 5% random noise to the synthetic data produced the same level of misfit and a model that still mimicked the test model. However, the addition of 10% noise to the synthetic data resulted in a misfit value that was three times that of the first two values and a resistivity model with a large discrepancy with the test model, particularly at large depths. These results indicate the efficacy of the VFSA inversion scheme for inferring the subsurface resistivity structure from the electromagnetic data. This inversion scheme was applied to field data measured in a volcanic environment. The general pattern of the resistivity structure inferred by the VFSA inversion is consistent with the structure obtained previously by using a deterministic inversion scheme.

A frequency adaptive control scheme for a three-phase shunt active power filter

The propagation of nonlinear loads and distributed power generation systems can cause power quality problems such as harmonic distortion, system imbalance, and resonance problems. Shunt active power filters are used to eliminate these power quality problems. A recently proposed control scheme for a shunt active power filter utilized a time-domain transformation to extract positive and negative sequence components of the system voltages and currents. These components are used in a modified version of instantaneous reactive power theory to calculate the reference currents for a three-phase inverter. Changes in the system operating conditions can cause the system frequency to vary, which can impact the performance of the time-domain transformation. Proposed in this paper is a frequency adaptive control scheme to compensate for frequency variations. Several simulation and experimental tests have been performed to validate the operation of the proposed frequency adaptive control scheme.

Echo signal simulation system

In order to meet the demand of realistic simulation for complex target echo signal in water, the indirect method of frequency domain is employed to simulate the target echo signal in this paper. The plate element method is first used to forecast complex target echo characteristics in typical water. After generating frequency response function data, the data is imported into the echo signal simulation system. The system adopts FPGA real-time signal processing system based on PXIe bus. It receives hydrophone output signal by A/D sampling, extracts the incident acoustic signal and makes frequency domain transformation. After multiplying the transformed signal and frequency response function, scattering echo spectrum is obtained. And then the time domain transformation is made to get the time series of the echo signal. The series is loaded into the transmitting transducer by the power amplifier and the echo signal is simulated. The system has the high fidelity of the model, stable and reliable hardware system, and software system for easy operation.

Robust Dynamic Hamiltonian Engineering of Many-Body Spin Systems

We introduce a new approach for the robust control of quantum dynamics of strongly interacting many-body systems. Our approach involves the design of periodic global control pulse sequences to engineer desired target Hamiltonians that are robust against disorder, unwanted interactions and pulse imperfections. It utilizes a matrix representation of the Hamiltonian engineering protocol based on time-domain transformations of the Pauli spin operator along the quantization axis. This representation allows us to derive a concise set of algebraic conditions on the sequence matrix to engineer robust target Hamiltonians, enabling the simple yet systematic design of pulse sequences. We show that this approach provides an efficient framework to (i) treat any secular many-body Hamiltonian and engineer it into a desired form, (ii) target dominant disorder and interaction characteristics of a given system, (iii) achieve robustness against imperfections, (iv) provide optimal sequence length within given constraints, and (v) substantially accelerate numerical searches of pulse sequences. Using this systematic approach, we develop novel sets of pulse sequences for the protection of quantum coherence, optimal quantum sensing and quantum simulation. Finally, we experimentally demonstrate the robust operation of these sequences in a system with the most general interaction form.

Rigid spacecraft robust adaptive attitude Stabilization Using state-dependent indirect Chebyshev pseudospectral method

In this paper, a robust control method is proposed for rigid spacecraft attitude stabilization under inertia matrix uncertainties and external disturbances. The attitude stabilization problem is firstly reformulated into an optimal control problem, then a state-dependent indirect Chebyshev pseudospectral (SDICP) method is designed to solve the resultant optimal control problem. It is proved that, by incorporating the uncertainties into the performance index and adaptively estimating the parameters, the stabilization problem can be converted into an infinite horizon optimal control problem. Based on successive state-dependent coefficient parameterization, time domain transformation and Chebyshev spectral discretization, the proposed SDICP method turns the resultant optimal control problem into a sequence of systems of linear equations, which can be efficiently solved by basic matrix operations. Simulation results also verify the effectiveness of the proposed robust adaptive attitude stabilization method.

Large Time Step Electromagnetic Transient Simulation of Large Scale Power System Based on Time Domain Transformation Method

Electromagnetic Transients (EMT) simulation is an effective approach to study the dynamic behavior of complex AC/DC power grids. However, with increasing applications of the electronic equipment and the expansion of power grid, conventional EMT simulation tools are facing significant challenges with regard to simulation speed and scale. In order to improve the performance of EMT simulation, some approaches have been proposed. A time domain transformation methodology [1] has recently been proposed. In this paper, based on the large time step EMT algorithm, an electromagnetic transient simulation program has been developed and is used to study large scale power system dynamic behaviors. The result shows that the new EMT algorithm can not only guarantee the simulation accuracy, but also effectively improve the speed of full electromagnetic transient simulation of large scale complex power grids.

Effect of cohesive powders on pressure fluctuation characteristics of a binary gas-solid fluidized bed

The effect of cohesive particles on the pressure fluctuations was experimentally investigated in a binary gas-solid fluidized bed. The pressure fluctuation signals were measured by differential pressure sensors under conditions of various weight percentages of cohesive particles. The cohesive particles increased the fixed bed pressure drop per unit height and decreased the minimum fluidization velocity. The Wen & Yu equation well predicts the minimum fluidization velocity of the binary system. The addition of cohesive particles slightly decreased the bubble size in bubbling flow regime when the cohesive particles and the coarse particles mixed well, while the bubble size greatly decreased when the cohesive particles agglomerated on the bed surface. The time series of pressure fluctuations was analyzed by using the methods of time domain, frequency domain and wavelet transformation. The normalized standard deviation of pressure fluctuations decreased with increasing weight percentages of cohesive particles. A wide bandwidth frequency of 0 to 1Hz got narrower with a single peak around 0.6Hz with an increase in proportion of the cohesive particles. The meso-energy and micro-energy of pressure fluctuations were decreasing with increasing cohesive particles proportions, which indicated that adding cohesive particles could reduce the energy dissipation of bubble and particle fluctuations.

Notice of Retraction: Free-Space Antenna Factor Computation Using Time-Domain Gating and Deconvolution Filter for Site Validation of Fully Anechoic Rooms

An alternative method to compute the free-space antenna factor using time-domain transformation and deconvolution filter for pulse compression is proposed. The deconvolution filter helps in compressing the time-domain pulse to distinguish the direct wave from the reflected wave and help evaluate the free-space antenna factor for site validation of fully anechoic rooms. The antenna pair of ETS-Lindgren Model 3110C and 3180C antennas, simulated with numerical electromagnetics code, is subjected to the proposed method with deconvolution filter and Wiener filter. Based on the simulation results, the proposed method is implemented over the measured results of the antenna pair and used for the site validation of a fully anechoic room. The free-space normalized site attenuation results of the fully anechoic room comply with the ±4 dB specification.

Compact and Passive Time-Domain Models Including Dispersive Materials Based on Order-Reduction in the Frequency Domain

In this paper, compact time-domain (TD) models featuring materials with frequency-dependent electromagnetic (EM) properties are derived. The considered frequency-dependent material models include multiterm Debye and Lorentz models for the electric permittivity and the magnetic permeability and a multiterm Drude model for the electric conductivity. The TD models are based on finite-element systems in the frequency domain (FD). To render the model compact and computationally efficient, the dimension of the FD system is compressed with the help of projection-based model-order reduction. In contrast to older approaches, the TD transformation is performed on the FD model itself rather than on the transfer function. The result is a state-space representation, which may either be solved by custom time integrators or imported into commercial circuit simulators. The advantages of the new approach include provable passivity of the FD model, provable causality of the TD model, and the ability to reconstruct the transient EM fields.

Computing Spatiotemporal Heat Maps of Lipid Electropore Formation: A Statistical Approach.

We extend the multiscale spatiotemporal heat map strategies originally developed for interpreting molecular dynamics simulations of well-structured proteins to liquids such as lipid bilayers and solvents. Our analysis informs the experimental and theoretical investigation of electroporation, that is, the externally imposed breaching of the cell membrane under the influence of an electric field of sufficient magnitude. To understand the nanoscale architecture of electroporation, we transform time domain data of the coarse-grained interaction networks of lipids and solvents into spatial heat maps of the most relevant constituent molecules. The application takes advantage of our earlier graph-based activity functions by accounting for the contact-forming and -breaking activity of the lipids in the bilayer. Our novel analysis of lipid interaction networks under periodic boundary conditions shows that the disruption of the bilayer, as measured by the breaking activity, is associated with the externally imposed pore formation. Moreover, the breaking activity can be used for statistically ranking the importance of individual lipids and solvent molecules through a bridging between fast and slow degrees of freedom. The heat map approach highlighted a small number of important lipids and solvent molecules, which allowed us to efficiently search the trajectories for any functionally relevant mechanisms. Our algorithms are freely disseminated with the open-source package TimeScapes.

EFFICIENT FLOATING POINT FAST FOURIER TRANSFORM BUTTERFLY ARCHITECTURE USING BINARY SIGNED DIGIT MULTIPLIER AND ADDERS

Fast Fourier transform (FFT) is one of the most important tools in digital signal processing as well as communication system because transforming time domain to S-plane is very convenient using FFT. As FFT uses various techniques to convert a signal from time domain to S-domain and inverse, out of which butterfly technique is the one on which paper is focused on. Butterfly technique uses additions and multiplications of operands to get the required output. Floating point (FP) is used as operands due to their flexibility. As the computations involving FP has less speed, we have used binary signed digit (BSD). BSD will take the less time for addition and subtraction. Three bit BSD adder and FP adder together will make a fused dot product add (FDPA) unit. In FDPA, unit addition and subtraction will be one group and multiplication will be one group and then their respective results will be fused. Modified booth encoding and decoding algorithm are used here to make the complex multiplication with ease.

Efficient fault diagnosis of ball bearing using ReliefF and Random Forest classifier

The present study focuses on identifying various faults present in ball bearing from the measured vibration signal. Features such as kurtosis, skewness, mean, and root mean square, and complexity measure such as Shannon Entropy are calculated from time domain and Discrete Wavelet Transform. To select the best wavelet function, Maximum Energy to Shannon Entropy ratio criterion is used. Information Gain and ReliefF ranking methods are used to assess the quality of features and features are ranked based on the weight gain obtained from the methods used. Support Vector Machine and Random Forest classifier are selected to identify bearing faults and comparison is made to diagnose faults on the ranked feature set. Experiments are conducted on Case Western Reserve University bearing data sets. Results show that ranking method is useful for identifying best feature set and to improve classification accuracy simultaneously. Cross-validation efficiency of 98.38% is obtained when ReliefF is used with Random Forest.

Spatial Heat Maps from Fast Information Matching of Fast and Slow Degrees of Freedom: Application to Molecular Dynamics Simulations.

We introduce a fast information matching (FIM) method for transforming time domain data into spatial images through handshaking between fast and slow degrees of freedom. The analytics takes advantage of the detailed time series available from biomolecular computer simulations, and it yields spatial heat maps that can be visualized on 3D molecular structures or in the form of interaction networks. The speed of our efficient mutual information solver is on the order of a basic Pearson cross-correlation calculation. We demonstrate that the FIM method is superior to linear cross-correlation for the detection of nonlinear dependence in challenging situations where measures for the global dynamics (the "activity") diverge. The analytics is applied to the detection of hinge-bending hot spots and to the prediction of pairwise contacts between residues that are relevant for the global activity exhibited by the molecular dynamics (MD) trajectories. Application examples from various MD laboratories include the millisecond bovine pancreatic trypsin inhibitor (BPTI) trajectory using canonical MD, a Gaussian accelerated MD folding trajectory of chignolin, and the heat-induced unfolding of engrailed homeodomain (EnHD). The FIM implementation will be freely disseminated with our open-source package, TimeScapes.