Exponential Window Research Articles

Structural modal parameter identification with the Power-Exponential window function

In view of the demand for accurate modal identification, and based on the characteristics of free vibration response, this paper introduces a new window function for Fourier Transform called the Power–Exponential window. The Power–Exponential window addresses the characteristics of free vibration response. It significantly enhances the accuracy of modal identification by improving the spectral properties of structural response. The proposed window function consists of exponential and power terms. This study focuses on the additional damping and frequency-domain differentiation introduced by the Power–Exponential window function. The exponential term weakens the boundary effect related to the time-domain truncation and suppresses the spectral leakage. Moreover, it can be interpreted in clear physical terms as providing additional damping to the signal. The power term in the window function corresponds to frequency domain differentiation, and it alleviates the spectral broadening that arises due to the additional damping. Furthermore, the analytical expression for the response spectrum confirms that the Power–Exponential window not only aligns the peak response frequency with the damped natural frequency but also establishes an explicit linear relationship between the actual structural damping ratio and the identification result from the half power bandwidth method. Both contribute to an improved accuracy and usability of certain frequency-domain modal identification methods. The influence of the Power–Exponential window parameters on modal parameter identification is analyzed, and the optimal selection principle and suggested parameter values are proposed. Finally, numerical simulations and an experimental frame model test are conducted to verify the accuracy and validity of modal parameter identification based on the Power–Exponential window.

Improving the efficiency of channel evaluation during high-speed data transmission in underwater acoustic communication with OFDM

Problem statement. The organization of noise-resistant wireless underwater acoustic communication is not a simple and solved task. One of the main problems is the multipath propagation of a sound acoustic wave as a result of re–reflections from the seabed surface and a change in the frequency of signal vibrations when the receiver and transmitter move relative to each other. Thus, finding a channel evaluation solution that can improve the quality of communication is an urgent task for developers of underwater acoustic communication systems. Purpose. To consider the possibility of developing effective methods for processing underwater acoustic communication signals with high noise immunity by evaluating the communication channel. Results. The possibility of using an adaptive filter with a sliding window to evaluate the channel during high-speed data transmission in underwater acoustic communication is shown. The simulation results showed that the proposed adaptive filter with a sliding window surpasses the normalized adaptive filters in terms of the BER bit error and wins over additive filters with an exponential window in reducing the number of mathematical operations. When modeling wireless acoustic communication systems with OFDM, error-free data transmission with a spectral efficiency of 0.33 bits/s/Hz was achieved. Practical significance. The obtained results can be used to improve the wireless transmission of data in underwater acoustic communication due to the proposed algorithm of the adaptive filter.

Enhancing damping estimation accuracy of exponential windowed responses of a GFRP plate through Finite Element Model Updating approach

Fibre reinforced polymer (FRP) panels are widely employed in ship and marine structures due to their better specific stiffness and strength when compared to metals. Therefore, an accurate estimation of the dynamic behaviour of such panels is necessary from its operational and serviceability point of view. In this study, the influence of exponential window functions and the associated decay rates on the damped dynamic responses of a Glass Fibre Reinforced Plastic (GFRP) plate has been investigated experimentally, using impact hammer testing. In a standard experimental modal testing of a structure, exponential window functions are commonly employed to prevent spectral leakage of the signal and achieve a good signal-to-noise ratio. However, this exercise modifies the Frequency Response Functions (FRFs) and introduces numerical damping into the measurements. A novel technique involving a Finite Element Model Updating using Inverse Eigen-Sensitivity algorithm is employed to estimate the unbiased FRFs and identify the induced numerical damping. The model updating is carried out in two stages: updating stiffness parameters first, followed by updating damping parameters in the second stage. The updating algorithm and the two-stage strategy adopted therein is found to be effective in identifying the induced numerical damping along with the unbiased FRF expressions.

A reduced-order computational homogenization framework for locally resonant metamaterial structures

A computational homogenization framework is presented to study the dynamics of locally resonant acoustic metamaterial structures. Modelling the resonant units at the microscale as representative volume elements and building on well-established scale transition relations, the framework brings as a main novelty a reduced-order macroscopic homogenized continuum whose governing equations involve no additional variables to describe the microscale dynamics unlike micromorphic homogenized continua obtained by alternative computational homogenization approaches. This model-order reduction is obtained by formulating the governing equations of the micro- and macroscale problems in the frequency domain, introducing a finite-element discretization of the two problems and performing an exact dynamic condensation of all the degrees of freedom at the microscale. An appropriate inverse Fourier transform approach is implemented on the frequency-domain equations to capture transient dynamics as well; notably, the implementation involves the Exponential Window Method, here applied for the first time to calculate the time-domain response of undamped locally resonant acoustic metamaterial structures. The framework may handle arbitrary geometries of micro- and macro-structures, any transient excitations and any boundary conditions on the macroscopic domain.

Doppler Parameters Estimation Using Digital PLL Based on SWIFT & αSWIFT Structures

A digital phase-locked loop (DPLL) based on sliding window infinite Fourier transform (SWIFT) and αSWIFT is proposed to extract the vibration and velocity parameters from the phase-modulated carrier signal. The phase of a carrier signal gets modulated when it is reflected from a vibration object due to the Doppler effect. Therefore, the phase-modulated carrier signal contains the Doppler signal that has the vibration information. The SWIFT or αSWIFT structure is designed from sliding discrete-time Fourier transform (DTFT) where the exponential window provides higher weightage to recent samples. It acts as a phase detector in the proposed DPLL, and its bandwidth can be varied based on the values of the time-constant. A controller unit, along with a bi-quad oscillator, is introduced in the proposed DPLL structure to remove any leakages in the system and to synchronize the system units in the parameter estimation. The proposed scheme is implemented in MATLAB/SIMULINK environment and validation for real-time applications is done using dSPACE 1202 MicrolabBox.

Active vibration control of inlet piping system with a time-variant secondary path using the mirror modified filtered-x least mean square algorithm

Active vibration control under a time-variant secondary path is a research priority in the field of vibration suppression. To track the varied secondary path, the mirror modified filtered-x least mean square (MMFxLMS) algorithm is proposed. However, due to the expensive computing cost and difficulty to adjust the modeling performance of the primary and secondary paths independently, the application of the MMFxLMS algorithm is limited. The algorithm is studied in this paper. First, the complexity is reduced by simplifying the normalization using an exponential window. The convergence of the overall modeling algorithm using different stepsizes and the influence of the background noise on the overall modeling results are analyzed, respectively. Simulation studies show that the algorithm using different stepsizes reaches a better performance than the classical MMFxLMS algorithm. To illustrate the proposed method is a promising algorithm, experiments on controlling the vibration of the piping system, which is basic cooling equipment on a ship propulsion system, are carried out. As these investigations illustrate, the proposed measures efficiently improve the performances of the MMFxLMS algorithm in convergence speed, control effect, and the property of dealing with time-varying parameters.

Static and dynamic analysis of couple-stress elastic structures by using peridynamic differential operator

In this paper, a peridynamic differential operator (PDDO) method is developed to analyze the static and dynamic responses of size-dependent elastic structures in the frame of a consistent couple stress theory (CCST). The displacement governing equations together with the boundary conditions of the couple-stress static problems are transformed from the local differential form to the nonlocal integral form through a fourth-order PDDO and then solved by a meshfree scheme. For dynamic cases, the time-domain problems are first transformed into frequency domain by Fourier transform, then solved by the PDDO meshless method in the frequency domain. The time-domain results are finally obtained by using an exponential window method (EWM). The size effects on the static and dynamic responses of some typical elastic problems are investigated by the developed PDDO method. A very high level of computational accuracy is achieved by comparing with the analytical solutions and the existing numerical results.

Frequency‐domain fundamental solutions and boundary element method for consistent couple stress elastodynamic problems

AbstractIn this article, the elastodynamic problems are investigated within the framework of a consistent couple‐stress theory (CCST). The basic equations for the CCST elastodynamic problems are derived at first. These dynamic formulas are then analyzed in the frequency domain by the Fourier transform. The frequency‐domain fundamental solutions to the transformed elastodynamic problems are subsequently derived for the two‐dimensional (2D) plane‐strain state. Based on the fundamental solutions and the elastodynamic reciprocal theorem, the frequency‐domain boundary integral equations (BIEs) are established. Then, the BIEs are numerically solved by a collocation method in conjunction with analytical and numerical treatments of the arising singular integrals. To obtain the time‐domain dynamic responses, an exponential window method (EWM) is adopted to transform the frequency‐domain results to the time‐domain solutions. By using the developed boundary element method (BEM), several typical couple‐stress elastodynamic problems are numerically investigated and the size‐effects are studied by using different values of the length‐scale parameter in the CCST. Good agreements between the results obtained by the developed BEM for a tiny length‐scale parameter and the corresponding classical BEM results or analytical solutions are achieved, which validates the high accuracy of the present BEM.

Equivalent linear method with complex frequency for response analyses of the ground subject to fling-step displacements

The equivalent linear (EL) method is one of the most commonly used methods for seismic ground response analyses in engineering practice. However, it cannot be used to directly calculate the displacement response of the ground subject to fling-step displacements because these are characterized by non-zero final values and ordinary Fourier transform with real frequency breaks down. This article shows that this difficulty can be overcome by introducing a complex frequency in the equivalent linear method. The technique of using complex frequency was used in existing studies for analyses of undamped structures and is known as the exponential window method (EWM). In essence, the same approach is effective for the analysis of fling-step displacement. Herein, why this works for fling-step displacements is described and an application to a vertical array record which captured near-fault fling-step displacements is shown. The reasonable agreement between the observed and synthetic time histories, both for acceleration and displacement, illustrates the applicability of the method to the response analyses of the ground subject to fling-step displacements.

Optimization Approach in Window Function Design for Real-Time Filter Applications

Eliminating the Gibbs oscillations that occur during the Finite Impulse Response (FIR) digital filter design with the Fourier Series method will ensure correct filtering. For this reason, the development of the window improves the performance of the filter and, therefore, the system. In this study, the cosh window function is designed using Particle Swarm Optimization, which is a preferred optimization method in many areas. Thus, alternatives to the standard results obtained from the existing traditional calculations will be produced, and different windows that perform the same function will be obtained. In addition, exponential and cosh window functions were designed in LabVIEW environment, which is a graphical programming language-based program, and the designed windows were analyzed at different parameter values. LabVIEW provides a fast and easy programming environment, and it provides the opportunity to realize real-time applications with its external hardware. Utilizing this feature, the amplitude spectrum of cosh window designed in LabVIEW is displayed in real time for different window parameter values. As a result, FIR digital filters were designed using cosh window based on optimization and the cosh window designed in LabVIEW, and the distorted EEG signal was filtered using these filters and displayed in real time.

Transient Dynamic Response Analysis of Two-Dimensional Saturated Soil with Singular Boundary Method

In this paper, the singular boundary method (SBM) in conjunction with the exponential window method (EWM) is firstly extended to simulate the transient dynamic response of two-dimensional saturated soil. The frequency-domain (Fourier space) governing equations of Biot theory is solved by the SBM with a linear combination of the fundamental solutions. In order to avoid the perplexing fictitious boundary in the method of fundamental solution (MFS), the SBM places the source point on the physical boundary and eliminates the source singularity of the fundamental solution via the origin intensity factors (OIFs). The EWM is carried out for the inverse Fourier transform, which transforms the frequency-domain solutions into the time-domain solutions. The accuracy and feasibility of the SBM-EWM are verified by three numerical examples. The numerical comparison between the MFS and SBM indicates that the SBM takes a quarter of the time taken by the MFS.

A boundary meshless method for dynamic coupled thermoelasticity problems

This work develops the boundary knot method (BKM) for two-dimensional (2D) coupled thermoelasticity problems in the frequency domain. By taking the non-singular general solution satisfying the governing equations as the basis function, the BKM does not require domain discretization. Nevertheless, the non-singular solution for the considered problems is absent. The Helmholtz decomposition and eigen-analysis are introduced to firstly derive the non-singular general solution, and thus the BKM can be formulated in terms of the discretized boundary points. In the final, the exponential window method (EWM) in conjunction with the BKM is employed to perform the transient analysis. The accuracy and feasibility of the proposed method are presented via numerical examples.

The Effect of Speed-Varying Micro-Cutting Tool Dynamics on Stability During High-Speed Micromilling of Ti6Al4V

Abstract Chatter-free machining is necessary in micromilling to avoid the catastrophic failure of micro-end mill. The accuracy of the prediction of chatter-free machining conditions in high-speed micromilling has been improved in this work by including speed-varying micro-end mill dynamics. An optimum design of exponential window has been devised to remove the unwanted spindle dynamics from the displacement signal to construct the speed-dependent frequency response function (FRF) of micro-end mill. The stiffness of the micro-end mill has been found to be increasing with increase in spindle speed and the natural frequency of the micro-end mill has been found to be changing with change in spindle speeds. The cutting velocity-chip load-dependent cutting coefficients have been included to predict the stability using Nyquist criterion. The predicted stability lobe with speed-varying micro-end mill dynamics has increased chatter-free depth of cut significantly compared to the chatter-free depth of cut predicted with static micro-end mill dynamics. The increase in depth of cut with speed-varying dynamics has been found to be 28% at 20,000 rpm, 150% at 52,000 rpm, and 250% at 70,000 rpm. A critical value of acceleration of the workpiece has been identified for chatter onset detection and it has been validated with machined surface image analysis. The magnitude of acceleration in both feed and normal to feed direction has been characterized to analyze the effect of spindle speed and depth of cut on the vibration of workpiece.

On a wave-based reduced order model for transient effects computation including mid frequencies

The wave-based computational method named Variational Theory of Complex Rays (VTCR) is revisited in order to improve its robustness and its efficiency to solve transient dynamic problems including medium frequencies. The first problem addressed in the paper concerns the ill-conditioning of wave-based computational approaches. We introduce the concept of “effective portrait” which provides a new framework to the VTCR with a strong reduction of the conditioning number. The second issue deals with the computation over a large frequency bandwidth for which the Proper Generalised Decomposition (PGD) has been retained. A thorough analysis of the efficiency and the limitations of the PGD-VTCR is given. The last issue concerns the synergy between the PGD-VTCR and the exponential window method for solving transient problems.

An explicit stabilization scheme for Q-compensated reverse time migration

Attenuation compensation in prestack depth migration typically requires nonphysical frequency-dependent energy amplification, which may lead to numerical instability. An explicit stabilization approach is developed for seismic [Formula: see text] compensation after deriving the [Formula: see text]-space Green’s function of the compensated constant-[Formula: see text] wave equation, which has decoupled fractional Laplacians. At high wavenumbers, as time increases, the time propagator of [Formula: see text]-space Green’s function increases exponentially. Therefore, an exponential window function is introduced to stabilize the exponentially divergent time propagator. Unlike the conventional low-pass filtering approach in the frequency or wavenumber domain, the proposed method assumes that the exponent of the chosen window is a power function of the wavenumber magnitude, which only involves explicit stabilization terms in the time-space domain. An explicit stabilization form helps to perform seismic data [Formula: see text] compensation more conveniently. We outline the basic structure of the proposed approach with explicit stabilization and highlight some numerical details using compute unified device architexture-based implementations. The strong scaling analysis justifies the good performance of the developed code package in terms of computational efficiency and scalability. In addition, we further analyze the optimal scheme parameter selection and the influence of parameters on filtering performance. The proposed [Formula: see text]-compensated reverse time migration is applied on the Marmousi model and synthetic and real crosswell examples to verify its feasibility and numerical stability.

Dynamic Hedge Fund Portfolio Construction: Exponentially Weighted Returns Approach

This article proposes an exponentially weighted returns approach for constructing portfolios of hedge funds. This approach, which gives more weight to more recent observations, allows for volatility and higher moment dynamics in portfolio construction. Using monthly hedge fund index returns from the Hedge Fund Research Database for January 1990 to December 2020, we find that the proposed approach significantly improves portfolio performance in terms of enhanced returns, reduced risk, and improved risk-adjusted returns compared to the benchmark equally weighted approach. However, the exponentially weighted method generally requires more frequent portfolio rebalancing to capture the return distribution dynamics, and the turnover varies across different portfolio optimization models. Therefore, investors should select an appropriate optimization strategy when implementing this approach for hedge fund portfolio construction. Moreover, we show that the results are robust to the choice of decay factor for the exponential weighting, target returns, and estimation window size, and across low-volatility, high-volatility, and most recent evaluation periods.

Adaptive Blind Channel Estimation for MIMO-OFDM Systems Based on PARAFAC

In order to track the changing channel in multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems, it is prior to estimate channel impulse response adaptively. In this paper, we proposed an adaptive blind channel estimation method based on parallel factor analysis (PARAFAC). We used an exponential window to weight the past observations; thus, the cost function can be constructed via a weighted least squares criterion. The minimization of the cost function is equivalent to the decomposition of third-order tensor which consists of the weighted OFDM data symbols. To reduce the computational load, we adopt a recursive singular value decomposition method for tensor decomposition; then, the channel parameters can be estimated adaptively. Simulation results validate the effectiveness of the proposed algorithm under diverse signalling conditions.

New Equations for Determination of Shaping Window in Stochastic Method of Simulating Ground Motion

ABSTRACT in this study, new prediction equations are proposed to determine the variables of gamma envelope-shape Function. Envelope-shape functions are employed for the simulation of ground motion using a stochastic method in order to form the white noise. A variety of Envelope-shape functions have been already proposed, among which gamma equations are more used in computational programs for the simulation of ground motion, e.g. SMSIM or EXSIM. In addition to the detection of influential variables of gamma envelope-shape function, their relationship with important seismic criteria such as moment magnitude, closest distance to rupture plane, site conditions and mechanism of faulting are determined and suitable models are presented in this study. Limited research has been already undertaken to specify the variables of envelope-shape equations and their relationships with the main seismic criteria. Hence the results of this study can almost demonstrate this relationship with seismic criteria. The new equations are developed using Iran strong ground motion database, which includes 2228 records of 749 earthquakes that covering up to 2018. The proposed equations can be used to determine exponential window function for earthquakes with moment magnitude from 4.5 to 7.6 and rupture distance up to 200 km. The proposed model is compared with some existing models and the results suggest that the equations can lead to better and more reasonable results in the ground motion simulation process, particularly for the estimation of response spectrum of velocity and displacement.

Joint Adaptive Blind Channel Estimation and Data Detection for MIMO-OFDM Systems

In order to track a changing channel in multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems, it is a priority to estimate channel impulse response adaptively. In this paper, we propose an adaptive blind channel estimation method based on parallel factor analysis (PARAFAC). We used an exponential window to weigh the past observations; thus, the cost function can be constructed via a weighted least squares criterion. The minimization of the cost function is equivalent to the decomposition of a third-order tensor, which consists of the weighted OFDM data symbols. By preserving the Khatri-Rao product, we used a recursive least squares solution to update the estimated subspace at each time instant, then the channel parameters can be estimated adaptively, and the algorithm achieves superior convergence performance. Simulation results validate the effectiveness of the proposed algorithm.

A Revised Dynamic Hurst Parameter Estimation Method Based on Generalized Exponential Window Function

Dynamic Hurst parameter estimation is very important in the data filtering and system modelling. It is difficult to accurately estimate the dynamic Hurst parameter of long memory processes. In this research, a generalized exponential window function based dynamic Hurst parameter estimation method is provided, and the effective performance of the method is analyzed using fractional Gaussian noise. In the end of this paper, the application of revised estimation method in sleeping electroencephalogram signal is given. The simulation and sleeping electroencephalogram signal analysis results show that the revised estimation method can effectively analyze the random signals with local correlation characteristics. This method can be widely used in biomedical signal analysis, network traffic analysis, vibration signal analysis, statistical data analysis, etc.