Traditional Frequency-domain Methods Research Articles

Fatigue assessment of directionally solidified superalloy thin plates under bimodal random processes

During actual service, aviation aircraft often experience multiple complex alternating loads coupled with each other. If the frequency range of the excitation load spectrum covers the first two resonance frequencies of the structure, it can significantly impact the vibration fatigue life of the structure. In this study, bimodal random vibration fatigue tests were conducted on thin plates composed of DZ125L directionally solidified superalloy. The impact of low-frequency and high-frequency vibration signal intensities on the vibration fatigue behavior of DZ125L alloy thin plates was investigated separately during bimodal random processes. The crack propagation mechanism of bimodal random vibration fatigue was proposed based on the fracture morphology observed in DZ125L alloy thin plates that failed due to vibration fatigue. The study findings indicate that the number and location of crack initiation zones can influence the mechanism of fatigue crack propagation. Additionally, a new model was developed in this study to enhance the sensitivity of the frequency domain method to the intensity of low-frequency and high-frequency vibration signals in bimodal random processes. Compared to traditional frequency domain methods used for broadband and bimodal processes, the new model can effectively describe the variation characteristics of bimodal fatigue life with different component process intensities. Furthermore, it has broader applicability for predicting the vibration fatigue life of bimodal random processes with varying vibration signal intensities.

Study of Shearlet Domain Scale-Angle Adaptive Surface Wave Separation

In the seismic data processing, high energy surface wave overlaps with effective wave, which affects the quality of seismic data imaging. The traditional frequency domain method can effectively remove surface wave, but it will damage the low frequency information of seismic data. In view of this, we proposed a scale-angle adaptive surface wave separation method based on Shearlet sparse transform. The surface wave model obtained by filtering method and the effective wave can decomposed in Shearlet domain, based on the characteristic differences between surface wave and effective wave in frequency, velocity and direction. At different scales and angles, an adaptive surface wave removal operator based on L2 norm of Shearlet coefficient is developed to remove surface wave information from seismic data. The actual seismic data application results show that compared with the traditional surface wave suppression method, the proposed method can thoroughly separate surface wave and effective wave, and obtain high quality denoising seismic data.

An Interpretable Method for Operational Modal Analysis in Time-Frequency Representation and Its Applications to Railway Sleepers

Operational modal analysis (OMA) enables the identification of modal characteristics under operational loads and conditions. Traditional frequency-domain methods cannot directly capture modal changes over time, while existing time-frequency representations are not sufficiently interpretable due to spurious modes and implicit parameter design. This paper develops a new OMA method in time-frequency representation based on frequency-domain decomposition (FDD). Short-time FDD and a convolution-based strategy are proposed to obtain singular values and local mode shape similarity, respectively, which are further fused into mode indicators by a fuzzy-based strategy mimicking the modal assurance criterion. The method provides not only a global view of the modal characteristics over time and frequency but also estimates of the modal parameters. It is applicable to strongly nonstationary responses under time-varying loads and conditions. All the parameters explicitly affect the time-frequency representation, and the interpretability is enhanced by including physical information from the user’s prior knowledge in selecting parameters and peak bands. The proposed method is validated based on a study of railway sleepers under train passage. The rigid-body motions and bending modes are identified at frequencies up to 6,500 Hz in laboratory tests and 4,500 Hz in field tests at speeds up to 200 km/h. The identified natural frequencies and mode shapes agree with experimental modal analysis (EMA). The proposed method outperforms EMA in terms of broad frequency range and low measurement cost and can be potentially applied to structural health monitoring under operational conditions.

Quantile-Frequency Analysis and Deep Learning for Signal Classification

This paper proposes a new method for signal classification based on a combination of deep-learning (DL) image classifiers and recently introduced nonlinear spectral analysis technique called quantile-frequency analysis (QFA). The QFA method converts a one-dimensional signal into a two-dimensional representation of quantile periodograms (QPER) which represent the signal’s oscillatory behavior in the frequency domain at different quantiles. With a moving window, the QFA method can also covert a signal into a sequence of such two-dimensional representations, called short-time quantile periodograms, that are localized in time to represent the signal’s time-dependent or nonstationary properties. The DL image classifiers take these representations as input for signal classification. The benefit of this QFA-DL classification method in comparison with the traditional frequency-domain method based on the power spectrum and spectrogram is demonstrated by a numerical experiment using real-world ultrasound signals from a nondestructive evaluation application.

A fast 3D gravity forward algorithm based on circular convolution

The dominant approach for calculating the gravity field from density sources is discretizing the density source into a collection of rectangular prisms with a regular grid distribution. In the case of an enormous number of model cells for large-scale data, however, the efficiency and storage requirements for calculation are usually confronted with challenges. In this paper, we propose an improved spatial domain convolutional forward algorithm for 3D fast and accurate gravity modeling. Compared with previous discrete-convolution-based algorithms, our approach inherits converting discrete convolution operations into frequency-domain dot products for an efficient forward process and features two improvements. (1) Generating the circular gravity kernel sensitivity matrix directly by padding the edges of the measurement grid and the model grid, which is based on the translational equivalence property of the potential field, leads the forwarding implementation process more concise. In previous methods, the construction of the circular kernel matrix is achieved by circular shifts of the original matrix only from the mathematical perspective, so we provide an alternative option, omitting matrices transformation. (2) The approach enables more flexible position relationships between the observed points and the model by introducing the distance vector between them, making the approach more practical and requiring less storage space. The accuracy and speed of our algorithm are comparable to the analytical solution and frequency domain methods, respectively. The presented algorithm efficacy and practicality are demonstrated by comparing it with the analytical formulation and the 3D traditional frequency domain method for synthetic models, as well as a real example for seawater correction. Our analysis indicates that the new algorithm is also applicable to fast-forward modeling for the magnetic field.

A Floquet theory‐based fast time‐domain stability analysis for N ‐parallel inverters system

Based on Floquet theory, a simple and fast time-domain stability analysis method for an N-parallel inverters system is proposed. Furthermore, a general time-domain model of the N-parallel inverters system in grid-connected mode and in island mode are derived, and the corresponding stability criteria are derived based on the Floquet theory. Subsequently, simulations and experiments of a two-parallel inverters system in island and grid-connected modes are conducted to verify the correctness and effectiveness of the proposed time-domain stability analysis method. To the end, the complexity comparison between the proposed time-domain method and the traditional frequency-domain method is presented to prove the advantages of the proposed method over the tedious manual derivation.

Wind-induced fatigue analysis of Yueyang Dongting Lake Suspension Bridge

Recent demand for a longer span has complicated the dynamic behaviours in the strong wind. The limited amplitude but frequent occurred buffeting response of bridge affect fatigue resistance of the bridge, which should be considered. The time-domain buffeting response and fatigue performance of Yue yang Dongting Lake Suspension Bridge are realized by mixed programming with MATLAB and ANSYS. The gusty wind was simulated by the WAWS method, while the self-excited force was modelled as the elemental aeroelastic stiffness and damp matrices by the element Matrix 27. The mode superposition method was then adapted to calculate the buffeting response of the bridge in ANSYS, and its accuracy is verified by the results of the RMS and PSD using the traditional frequency-domain method. It was found that the fatigue life reliability of the suspender neat tower of the leeward side is 97.54% during the structure's service in the design wind speed.

Simple Graphical Method for Detection of a Partial Blockage or Leak in a Single Pipeline

Abstract Transient-based methods in the frequency domain are used for fault detection in pipes. However, the required measurements are performed with a large number of valve frequencies. Sometimes the number of frequencies in traditional frequency-domain methods can be in the hundreds. More runs are required with higher harmonics when the required number of frequencies is more. The current study aims to overcome this difficulty of requirement of higher number of frequencies. The location and the size of a single leak or a single discrete blockage are proposed to be predicted using two appropriately chosen low frequencies. isopressure frequency responses (IPFRs) are generated by performing numerical experiments with these two low frequencies enabling determination of the fault. The methodology is demonstrated through various numerical examples. The results show that the procedure is quite accurate, with a high level of agreement between the actual and the predicted fault parameters. The error in the result is of the order of the chosen discretization. An uncertainty analysis is performed to illustrate that the prediction error caused by the error in the measurements of the pressure frequency responses (PFRs) depends on the location and the size of the fault itself. The error in prediction results is analyzed in uncertainty analysis with 0.10%, 0.15%, and 0.20% error in the peak head measurement. For the same error in the PFR measurement, the fault lying in a thin density of the contours would lead to a higher error in the final solution.

Topology optimization of bi-material structures with frequency-domain objectives using time-domain simulation and sensitivity analysis

In this paper, we propose to use time-domain transient analysis to compute the response of structures in a wide frequency band by means of Fourier transform. A time-domain adjoint variable method is then developed to carry out the sensitivity analysis of frequency-domain objective functions. By using the concept of frequency response function, it turns out that both the objective function and its sensitivity information at multiple frequencies can be obtained by one original simulation and at most one adjoint simulation, respectively. It is also demonstrated that some commonly used performance indices, e.g., dynamic compliance and input power, are indeed self-adjoint; thus, no extra adjoint simulations are needed, which makes the sensitivity analysis extremely efficient. An obvious distinction between the proposed method and the traditional frequency domain methods is that in our method, the frequency response curves in a wide band can be obtained in each iteration with no extra costs. It follows that it is easy to track the evolution of the frequency response curve in our method, which is essential in both computational and engineering sense. Several numerical examples are tested to show the effectiveness of the proposed method.

A hybrid time-frequency domain method to predict insertion loss of intake system.

A hybrid time-frequency domain method for predicting insertion loss (IL) of intake systems is investigated with detailed evaluation and optimization in terms of acoustic performance and intake efficiency for an automotive engine intake system. Instead of progressively coupling of both domain variables, as in the existing hybrid methods, the proposed method uses frequency-domain source impedance to characterize the acoustic source, and a time-domain method to analyze the acoustic transmission. A simplified equation is derived to predict IL using noise reduction (NR) and acoustic impedance Zl rather than four-pole transfer matrices as used in the traditional frequency-domain method and hybrid-domain method. The NR and Zl of intake systems calculated by the time-domain method are used to predict IL for the first time. This hybrid method has advantages of requiring no numerical engine model while considering the convective and dissipative effect of intake flow on a complex intake system. The predicted ILs of a quarter-wavelength tube and an optimized air cleaner were validated with the measured results. The proposed method and results are applicable and useful to the design of an intake system at an early stage of engine development.

A Simulation Tool for Accurate and Fast Assessment of Harmonic Propagation in Modern Residential Grids

A simulation tool for modeling harmonic propagation in low voltage distribution networks with manifold nonlinear equipment is developed. The tool is based on a hybrid domain approach representing each nonlinear household device with accurate and fast white box model and the supply network - with the harmonic admittance matrix in the frequency domain. Proposed tool features significant reduction of simulation time compared with the brute force time domain (BFTD) simulation, high level of accuracy as opposed to the traditional frequency domain methods, and improved convergence under weak grid conditions in respect to conventional iterative harmonic analysis. Eventually this preconditions the use of the proposed approach in computationally intensive simulations, e.g. in stochastic harmonic modeling with the Monte Carlo method. Additionally two application examples of the developed tool are provided demonstrating its effectiveness compared to the BFTD modeling.

Stability Analysis of Stochastic Linear Car-Following Models

Recent scholars have developed a number of stochastic car-following models that have successfully captured driver behavior uncertainties and reproduced stochastic traffic oscillation propagation. Whereas elegant frequency domain analytical methods are available for stability analysis of classic deterministic linear car-following models, there lacks an analytical method for quantifying the stability performance of their peer stochastic models and theoretically proving oscillation features observed in the real world. To fill this methodological gap, this study proposes a novel analytical method that measures traffic oscillation magnitudes and reveals oscillation characteristics of stochastic linear car-following models. We investigate a general class of stochastic linear car-following models that contain a linear car-following model and a stochastic noise term. Based on frequency domain analysis tools (e.g., Z-transform) and stochastic process theories, we propose analytical formulations for quantifying the expected speed variances of a stream of vehicles following one another according to one such stochastic car-following model, where the lead vehicle is subject to certain random perturbations. Our analysis on the homogeneous case (where all vehicles are identical) reveals two significant phenomena consistent with recent observations of traffic oscillation growth patterns from field experimental data: A linear stochastic car-following model with common parameter settings yields (i) concave growth of the speed oscillation magnitudes and (ii) reduction of oscillation frequency as oscillation propagates upstream. Numerical studies verify the universal soundness of the proposed analytical approach for both homogeneous and heterogeneous traffic scenarios, and both asymptotically stable and unstable underlying systems, as well as draw insights into traffic oscillation properties of a number of commonly used car-following models. Overall, the proposed method, as a stochastic peer, complements the traditional frequency-domain analysis method for deterministic car-following models and can be potentially used to investigate stability responses and mitigate traffic oscillation for various car-following behaviors with stochastic components.

A Time-Domain Approach to Channel Estimation and Equalization for the SC-FDM System

Similar to orthogonal frequency division multiplexing receiver, the frequency-domain (FD) channel estimation (CE) and equalization are indispensable parts in the coherent single carrier frequency division multiplexing (SC-FDM) receiver. When the channel varies slowly, the FD processing is cost effective. For the applications with high mobility, the traditional implementation of the SC-FDM receiver causes significant performance degradation. In this paper, we propose to estimate time-varying pieces of channel taps for pilot symbols based on basis expansion model (BEM), and subsequently to reconstruct time-domain (TD) channel response for data symbols by utilizing the Slepian sequences-based piece-wise interpolation. Furthermore, two simplified schemes, i.e., the Slepian sequences-based multiple-point interpolation and the segmented BEM, are developed to reduce the computational complexity of the TD-CE. The Cramer-Rao lower bound (CRLB) of channel impulse response (CIR) estimation is also analyzed. In the light of the sparsity of TD channel gain matrix, we design an iterative least-squares QR decomposition algorithm to equalize the SC-FDM symbols. In the simulated SC-FDM system, when considering the carrier frequency of 5.9 GHz and the velocity of about 510 km/h, we observe that the traditional FD methods cause the demodulation failure, while the proposed TD processing schemes achieve ideal error-probability performance and preserve a relatively low complexity.

A Simplified Time-Domain Fitting Method Based on Fractional Operational Matrix for Cole Parameter Estimation

The Cole model is widely used in bioimpedance spectroscopy (BIS) applications for evaluating the contents and status of biological tissues. Traditional frequency-domain fitting methods for Cole parameter estimation (CPE) often need wideband direct or indirect BIS measurements. The newly emerged time-domain fitting methods do not require BIS measurement, but they usually have unsatisfactory estimation accuracy and heavily rely on some specific excitations. This paper proposes a novel time-domain fitting method based on the fractional operational matrix (FOM) for CPE. First, the Cole model is represented as a FOM-based algebraic equation. Then, the model-based voltage response can be calculated as the product of the sampled current excitation and the FOM-based Cole equation. Finally, the Cole parameter can be estimated by minimizing the sum of squares error between the sampled voltage response and the model-based voltage response using an iterative nonlinear least-squares fitting algorithm. Experimental measurements are verified on three 2R1C circuits and in vivo leg muscle of a healthy volunteer. The results show that the Cole parameter can be accurately estimated by the proposed FOM-based fitting method directly using the sampled current and voltage signals. This paper establishes an effective time-domain fitting method for CPE, which could greatly simplify the hardware and software designs without the need for the BIS measurement.

Transient Response Estimation of an Offshore Wind Turbine Support System

To obtain reliable estimations of the dynamic responses of high-rising marine structures such as offshore wind turbines with obvious nonzero initial conditions, traditional frequency-domain methods cannot be employed because they provide only steady-state results. A novel frequency-domain transient response estimation method for offshore wind turbines is presented in this paper. This method builds upon a recent, significant theoretical development, which found that expressions of external loads in the frequency domain can be obtained by discretizing their eigenvalues and corresponding complex coefficients rather than directly by discrete Fourier transform (DFT) analysis, which makes it possible to deal with nonzero conditions in the frequency domain. One engineering advantage of this approach is its computational efficiency, as the motion equations of the system can be solved in the frequency domain. In order to demonstrate this approach, a case of a monopile-supported wind turbine with nonzero initial conditions was investigated. The numerical results indicate that the approach matches well with the time-domain method, except for a small, earlier portion of the estimated responses. A second case study of a sophisticated, jacket support wind turbine, involving practical issues such as complex external loads and computation efficiency, is also discussed, and comparisons of the results with the time-domain method and traditional frequency-domain method using the commercial software ANSYS are included here.

Hybrid Carrier Underwater Acoustic Communication Based on Joint Time-Frequency Domain Equalization

Weighted fractional Fourier transform-based hybrid carrier communication can be regarded as a combination of single-carrier communication and multicarrier communication, providing strong flexibility due to the changeable transform order. The hybrid carrier underwater acoustic communication based on the joint time-frequency domain equalization is proposed in this paper. With the time-domain equalization based on time reversal, multipath spreads of underwater acoustic channels can be greatly suppressed. Thus, the length of the required cycle prefix is shortened, improving the bandwidth efficiency. The residual inter-symbol interference can be removed using frequency-domain equalization based on the minimum mean square error or zero force. The experimental results show that the optimal transform orders to achieve the best communication performance are different in different environments. Compared with the traditional frequency-domain equalization method, the proposed method performs better with respect to bit error rate and bandwidth efficiency.

Enhanced disturbance rejection control based test rocket control system design and validation

Test rocket has been an attractive platform for scientific and educational experiments during the last several years. Aiming at providing a potential engineering application of disturbance rejection control to aircraft control system design following traditional frequency-domain methods, this paper presents an enhanced disturbance rejection control of two degrees of freedom based on H∞ synthesis and equivalent-input-disturbance (EID) for 3-axis attitude controller design of a small solid test rocket. The establishment of an EID system regards the mismatched disturbance as a ‘total disturbance’ in the input channel for compensation. The H∞ synthesis based on classical frequency-domain analysis is applied to the design of a disturbance filter and of a composite feedback controller. In terms of the controller design, the system including the filter is considered as a whole to guarantee the stability of the overall system without separate design. Furthermore, the proposed method is successfully applied to the 3-axis attitude controller design of the test rocket by modeling the nonlinear dynamics as linear EID formulations of attitudes. The simulation and validation including Monte-Carlo bias simulation and comparison with active disturbance rejection control (ADRC) based design, Hardware-in-the-Loop (HIL) simulation and flight test are conducted specifically. The results verify the effectiveness of the proposed method with excellent performance and practical prospects.

Improved disturbance rejection control based onH∞synthesis and equivalent-input-disturbance for aircraft longitudinal autopilot design

Disturbance rejection control has been developed over decades attracting wide interest and research attention. Aiming at providing a potential engineering application of disturbance rejection control to aircraft control system design following traditional frequency-domain methods, this paper presents an improved disturbance rejection control of two degrees of freedom based on [Formula: see text] synthesis and equivalent-input-disturbance for an aircraft longitudinal autopilot design. The mismatched disturbance is transformed as a “total disturbance” in the input channel for compensation through the establishment of an equivalent-input-disturbance system. The [Formula: see text] synthesis based on classical frequency-domain analysis is applied to a disturbance filter and a composite feedback controller design. In terms of the controller design, the system including the filter is considered as a whole in [Formula: see text] optimization process without separate design to guarantee the stability of the overall system. Furthermore, the proposed method is successfully implemented on the autopilot design by modeling nonlinear aircraft longitudinal dynamics as a linear equivalent-input-disturbance formulation of angle of attack. The simulation of tracking performance in comparison with existing renowned methods is conducted in the presence of aerodynamic uncertainties, gust disturbance, actuator characteristics and sensor noise. The results verify the effectiveness of the proposed method with excellent performance and practical prospects.

Simultaneously identifying displacement and strain flexibility using long-gauge fiber optic sensors

Abstract The method of simultaneously identifying displacement and strain flexibility matrices of the structure is proposed by performing the multiple reference impact test and using long-gauge (LG) fiber optic sensors. This method has the following promising features: (1) The impact test is performed in which not only structure responses but also the input force are measured, which ensures the consistency between the identified Frequency Response Function (FRF) and the analytical one, thus it has the advantage of identifying structural flexibility. In contrast, the ambient vibration test cannot output FRF magnitudes. (2) The long-gauge fiber optic sensors are used to measure structure strain responses, which has the merit of reflecting both the macro and micro characteristics of a structure. Both strain and displacement flexibility are identified simultaneously by establishing the relation between LG strain and displacement through an improved conjugate beam method. (3) The subspace identification method in the time domain is developed for structural flexibility identification. It has the merit to deal with the test data with multi-reference multi-peak impacting forces which can better excite the dynamic characteristics of the structure, while traditional frequency domain methods generally are difficult to do that due to the leakage problem. Numerical and experimental examples have been studied to verify the validity and demonstrate the promising features of the proposed method.

Impact of respiration on cardiovascular coupling using Granger causality analysis in healthy subjects

Abstract This quantitative study delineates the influence of respiratory rate on cardiovascular signal in healthy subjects using granger causality approach. Electrocardiogram (RR), arterial blood pressure (SBP) and respiration (RESP) were simultaneously recorded for 5 min from 20 subjects during normal (13–20 cycles/min) and deep breathing (5 cycles/min) with equal inspiration and expiration time. During deep breathing mean RR remains same but the variance increases. Also deep breathing lowers blood pressure, increases baroreflex sensitivity and improves oxygen saturation. The traditional frequency domain methods based power spectrum analysis and coherence analysis lacks to measure coupling changes among physiological subsystems. Therefore, frequency domain Granger causality method based on directed coherence is proposed to detect the changes in coupling strength among cardiovascular signals under different respiration rates. Directed coherence spectrum can separate RESP, SBP and RR components from each recorded signals. The RESP component of both RR (RRRESP) and SBP (SBPRESP) increases (coherence > 0.5) significantly during deep breathing indicate that respiration affects both cardiac and vascular system but at normal breathing only cardiac system (RRRESP) get affected by respiration. Also a significant increase in coherence is observed on baroreflex direction (RRSBP) indicating that deep breathing controls blood pressure. Hence, the observed directed coherence spectrum helps to detect coupling changes among cardiac, vascular and respiratory signal during autonomic regulation.