Frequency-domain Estimation Research Articles

Damage Assessment of Historic Buildings Hit by Earthquake

The Church of Gesù and the tower of the Cathedral were stricken and damaged by Emilia-Romagna earthquake sequence of May 2012. This paper presents the procedure for the structural identification of the most widespread types of religious monuments. The dynamic behavior was analyzed using the ambient vibrations test to measure the dynamical properties (mode of vibration, frequencies, displacements and damping ratios) of the constructions using a modal identification of output-only systems. The operational modal analysis OMA has been carried out to identify the modal characteristics through poly-reference Least Square Complex Frequency-domain (pLSFC) estimator. The global structural health monitoring was carried out to define the real dynamic behavior of the damaged constructions that are subjected to different mechanism. These researches are useful for the structural rehabilitation and to define the possible changes in the structural behavior.

Spectral estimation in frequency-domain by subspace techniques

In this paper, frequency-domain subspace-based algorithms are proposed to estimate discrete-time cross-power spectral density (cross-PSD) and auto-power spectral density (auto-PSD) matrices from samples of the Welch cross-PSD and auto-PSD estimators on uniform grids of frequencies. The proposed algorithms are shown to be strongly consistent. A link between the well-known time-domain covariance-based estimation methods and the frequency-domain realization-based methods of this paper is also established. The consistency of the proposed algorithms is not expected a priori since the periodograms are not consistent spectrum estimators even if the true power spectrum is rational. The algorithms are tested on numerical examples and a real-life application example concerned with the modeling of acoustic spectra for fault detection in induction motors.

Maximum likelihood estimator of operational modal analysis for linear time-varying structures in time–frequency domain

This paper investigates the problem of modal parameter estimation of time-varying structures under unknown excitation. A time–frequency-domain maximum likelihood estimator of modal parameters for linear time-varying structures is presented by adapting the frequency-domain maximum likelihood estimator to the time–frequency domain. The proposed estimator is parametric, that is, the linear time-varying structures are represented by a time-dependent common-denominator model. To adapt the existing frequency-domain estimator for time-invariant structures to the time–frequency methods for time-varying cases, an orthogonal polynomial and z-domain mapping hybrid basis function is presented, which has the advantageous numerical condition and with which it is convenient to calculate the modal parameters. A series of numerical examples have evaluated and illustrated the performance of the proposed maximum likelihood estimator, and a group of laboratory experiments has further validated the proposed estimator.

Subspace-based spectrum estimation in frequency-domain by regularized nuclear norm minimization

Subspace-based methods have been effectively used to estimate multi-input/multi-output, discrete-time, linear-time-invariant systems from noisy spectrum samples. In these methods, a critical step is splitting of two invariant subspaces associated with causal and non-causal eigenvalues of some structured matrices built from spectrum measurements via singular-value decomposition in order to determine model order. Mirror image symmetry with respect to the unit circle between the eigenvalue sets of the two invariant spaces, required by the subspace algorithms, is lost due to low signal-to-noise ratio, unmodeled dynamics, and insufficient amount of data. Consequently, the choice of model order is not straightforward. In this paper, we propose a new model order selection scheme that is insensitive to noise and undermodeling and based on the regularized nuclear norm optimization in combination with a recently developed subspace-based spectrum estimation algorithm which uses non-uniformly spaced, in frequencies, spectrum measurements. A detailed simulation study shows the effectiveness of the proposed scheme to large amplitude noise over short data records. Examples illustrating application of the proposed scheme to real-life problems are also presented. The proposed scheme can be readily integrated into frequency-domain instrumental variable subspace algorithms to estimate auto-power spectral density or cross-power spectral density function matrices from non-uniformly spaced, in frequencies, spectrum measurements.

Generating initial estimates for Wiener-Hammerstein systems using phase coupled multisines

Block oriented nonlinear models capture the dynamics of a nonlinear system with linear dynamic sub-systems (L), the nonlinear behavior is modelled using static nonlinear sub-blocks (N). In this paper we study the generation of initial estimates for the linear dynamic blocks of a Wiener-Hammerstein system that has a cascaded LNL structure. While it is very easy to identify the product of the transfer functions of the first and last dynamic block using linear system identification methods, it turns out to be very difficult to split the global dynamics over these individual blocks. In this paper a method is proposed that allows the poles of the best linear approximation to be assigned to the first or second linear block. Once this split is made, it is shown in the literature that the remaining initialization problem can be solved much easier than the original one. The first step of the method is the design of a special random phase multisine excitation, using pair-wise coupled random phases. Next, a modfied best linear approximation will be estimated on a shifted frequency grid. It will be shown that this procedure shifts the poles and zeros of the first linear sub-block with a known frequency offset, while those of the second sub-block are not changed. The shifted poles and zeros result in a transfer function with complex coefficients that can be identified using a modified frequency domain estimation method. This results in a simple initialization method, based on a linear system identification step.

Parameter Identification of Flexible Aircraft Using Frequency Domain Output Error Approach

Abstract Aerodynamic parameter estimation from flight data become a complex process when the aircraft has significant effects of flexibility on the flight dynamics, especially as the frequencies of the elastic modes become lower and approach those of the rigid body modes. In this paper, output error method (OEM) in frequency domain is applied to flight simulated data of a flexible aircraft to estimate the rigid body and aeroelastic derivatives. For the frequency domain estimation, flight data is generated using logarithmic frequency sweep input, and sensitivity of the estimated short period frequency and damping ratio to FFT window length is also investigated. Model validation is carried out by comparing time histories of the simulated and model predicted responses to multistep 3211 and sweep inputs.

Irrelevant speech effect under stationary and adaptive masking conditions

The irrelevant speech effect was investigated in this study where the serial-recall task was performed under six different conditions: Silence, speech-only, noise-only, speech masked by a stationary noise at two different signal-to-noise ratios (SNRs), and speech masked by an adaptive noise. Measured in five test blocks distributed throughout the four test days, the error rate of the serial-recall task under the silence condition sharply decreased in the first few test blocks, halved after completing about seven blocks. When the adaptive masking scheme was used, the error rate of the serial-recall test was reduced compared to the speech-only condition (by 9%) and to the lower-SNR stationary noise (by 4.4%). However, the serial-recall performance was not significantly different between the stationary and the adaptive maskers when the average sound level was carefully matched. Speech Transmission Index (STI) and the correlation coefficient of power spectra were used as the estimators of the temporal and spectral distinctiveness between sound tokens, respectively. The comparison to the test results implied that the frequency-domain estimator may be a better predictor of the relative ISE especially for a non-stationary masker, although it was also suggested that such estimators may have to be combined possibly with an appropriate weighting.

176Tb/s Nyquist PDM 16QAM signal transmission over 714km SSMF with the modified SCFDE technique

Nyquist pulse shaping is a promising technique for high-speed optical fiber transmission. We experimentally demonstrate the generation and transmission of a 1.76Tb/s, polarization-division-multiplexing (PDM) 16 quadrature amplitude modulation (QAM) Nyquist pulse shaping super-channel over 714km standard single-mode fiber (SSMF) with Erbium-doped fiber amplifier (EDFA) only amplification. The superchannel consists of 40 subcarriers tightly spaced at 6.25GHz with a spectral efficiency of 7.06b/s/Hz. The experiment is successfully enabled with the modified single carrier frequency domain estimation and equalization (SCFDE) scheme by performing training sequence based channel estimation in frequency domain and subsequent channel equalization in time domain. After 714km transmission, the bit-error-rate (BER) of all subcarriers are lower than the forward error correction limit of 3.8 × 10(-3).

A novel range alignment method for ISAR based on linear T/R array model

In inverse synthetic aperture radar (ISAR) imaging, translation compensation should be done before range-Doppler imaging process, and range alignment is the first step for translation compensation. In order to remove the limitation of integer range bin and align the echoes precisely for ISAR range alignment, combining with the advantage of array signal processing at fractional unit delay compensation, we propose a novel range alignment method based on linear transmitting/receiving (T/R) array. Firstly the ISAR imaging system is modeled as a linear T/R array. Then based on the snapshot imaging model of linear T/R array, range alignment is accomplished by wave path difference compensation which is transformed into the phase difference compensation in frequency domain between adjacent array elements. The phase difference compensation consists of integer range bin alignment and decimal time delay compensation which is implemented by the phase rotation's estimation and compensation in frequency domain. Finally, the results of simulation data and real radar data are provided to demonstrate the effectiveness of the proposed method.

IEEE 802.16.1a 기반 단말간 직접통신을 위한 시간 및 주파수 동기화 알고리즘

In this paper, we propose a new estimation method of time offset, frequency offset, and signal to interference plus noise ratio (SINR) using the synchronization channel preamble to provide IEEE 802.16.1a based talk-around direct communications (TDC). The proposed scheme estimates the time offset and frequency offset both in the time domain and in the frequency domain considering the preamble structure. In addition, it improves the estimation accuracy by combining the estimated values in two domains taking into account TDC synchronization scenarios. Through numerical simulations in the TDC channel environments, the performance of the proposed algorithm is compared with those of existing techniques such as the time domain estimation and the frequency domain estimation.

Fast maximum-likelihood identification of modal parameters with uncertainty intervals: A modal model-based formulation

A modal estimation method is presented, which estimates the parameters of the modal model directly instead of identifying a rational fraction polynomial model. The method also gives the uncertainty on the estimated parameters (i.e. poles, mode shapes, participation factors, lower and upper residual terms) without using linearization formulas which are needed when identifying a rational fraction polynomial model first. The proposed estimator belongs to the class of maximum likelihood estimators (MLE). The key challenges behind introducing this approach are to keep the benefits of the well-known poly-reference Least-squares Complex Frequency-domain (pLSCF) estimator—commercially known as PolyMAX—while giving other additional features like improved estimates in cases of high noise level and weakly exited modes together with a proper handling of the uncertainty on the measured data. The proposed method can be considered as an add-on for the pLSCF method since it starts from the initially estimated modal model by the pLSCF method. Our approach has been optimized to reduce the computation time and the memory requirements. The algorithm is evaluated and compared with two published algorithms by means of Monte-Carlo simulation as well as experimental measurements.

Frequency Domain Estimation and Correction Algorithm of Row Displacement for Scanning PMMW Imaging

Aiming at the random dislocation of data between adjacent rows induced by PMMW imaging scanning, a novel displacement estimation and correction algorithm was proposed based on the correlation feature of the scene and the phase-shift property of the Fourier Transform (SP-DEC). In order to estimate and correct the displacement in the spatial domain, the proposed algorithm fits the low frequency phase difference of adjacent rows by the least-squares method, and compensates the linear phase shift in the frequency domain. A sine/cosine filter and an adaptive method of fitting window selection are used to improve the estimation accuracy of displacement. Experimental results of a visible image and the actual dislocated PMMW image demonstrates that the proposed algorithm can achieve displacement estimation and correction with high precision on sub-pixel level.

Modal parameter estimation by combining stochastic and deterministic frequency-domain approaches

The poly-reference Least squares Complex Frequency-domain (pLSCF) estimator—commercially known as the LMS PolyMAX estimator—is used intensively in modal analysis applications nowadays. pLSCF is non-iterative (deterministic) and relatively accurate modal parameter estimation algorithm. This algorithm has several advantages: it is polyreference, fast, numerically stable for large-bandwidth with high-model order analysis, and yields very clear stabilization diagrams even with highly noisy FRFs measurements. One drawback of the pLSCF-estimator is that it yields a poor damping estimates especially for highly damped and weakly excited modes when the FRFs are very noisy.In this contribution, an approach will be proposed to improve the accuracy of pLSCF estimator and in particular, the damping estimates in case of high noise level. The new proposed approach is a combined stochastic-deterministic frequency-domain algorithm. In this approach, a 2-step procedure is introduced to improve the damping estimates while maintaining the very clear stabilization diagrams. In the first step, a parametric Maximum Likelihood smoothing approach, which is the stochastic part, is used to remove the noise from the data and in the second step, the pLSCF estimator, which is the deterministic part, is applied to the smoothed data resulting in improved (damping) estimates.The presented algorithm is able to maintain the benefits of pLSCF and at the same time leads to an improvement of the damping estimates in highly damped and very noisy cases. In addition, the new procedure properly deals with uncertainty on the measurements where the data variance due to measurement noise is taken into account.The procedure is illustrated and tested by using simulated as well as experimental data. The presented procedure to process a highly damped noisy vibration data leads to very accurate estimates in comparison to the traditional pLSCF estimator.

Derivative-constrained frequency-domain wideband DOA estimation

In this paper, we present a new approach for wideband direction of arrival (DOA) estimation incorporating derivative constraints into the optimization problem. The Taylor series expansion of steering vector with respect to frequency exhibits the dependence of sensor snapshots on the derivatives of the array manifold matrix, suppression of which reduces the data to follow the narrowband data model. Two new formulations following a beamformer framework are developed based on this observation. While the first formulation estimates accurate source directions with apriori knowledge of the signal subspace dimension, the second formulation provides DOA estimates without estimating the number of sources. The coherent averaging at the reference frequency enables the two formulations to handle coherent sources. The effectiveness of the proposed formulations is illustrated with simulations.

Does the Box–Cox transformation help in forecasting macroeconomic time series?

The paper investigates whether transforming a time series leads to an improvement in forecasting accuracy. The class of transformations that is considered is the Box–Cox power transformation, which applies to series measured on a ratio scale. We propose a nonparametric approach for estimating the optimal transformation parameter based on the frequency domain estimation of the prediction error variance, and also conduct an extensive recursive forecast experiment on a large set of seasonal monthly macroeconomic time series related to industrial production and retail turnover. In about a fifth of the series considered, the Box–Cox transformation produces forecasts which are significantly better than the untransformed data at the one-step-ahead horizon; in most cases, the logarithmic transformation is the relevant one. As the forecast horizon increases, the evidence in favour of a transformation becomes less strong. Typically, the naive predictor that just reverses the transformation leads to a lower mean square error than the optimal predictor at short forecast lead times. We also discuss whether the preliminary in-sample frequency domain assessment conducted here provides reliable guidance as to which series should be transformed in order to improve the predictive performance significantly.

A Frequency-Domain Maximum Likelihood Implementation using the modal model formulation

In this paper, a multivariable frequency-domain maximum likelihood estimator based on a modal model formulation is proposed. The proposed approach is mainly introduced to improve the accuracy of the modal parameters estimated by the poly-reference least squares complex frequency-domain (i.e. pLSCF) estimator and to have their confidence intervals as well. In that approach, a 3-step procedure is introduced to improve the estimates accuracy while taking the advantage of the very clear stabilization diagram of pLSCF estimator. The proposed approach has been optimized to reduce the computation time as well as the memory requirements. The algorithm is evaluated and compared with two other published algorithms by means of Monte-Carlo simulations.

Numerically Reliable Frequency-Domain Estimation of Transfer Functions: A Computationally Efficient Methodology

Parametric identification of lightweight motion systems requires solving large weighted least-squares problems. The numerical conditioning of such problems, which determines the solution accuracy, crucially depends on the polynomial basis that is used to formulate the problem. The aim of this paper is to optimize numerical conditioning by constructing a polynomial basis that is orthonormal with respect to a data-dependent inner product. This basis is constructed in a computationally efficient way by exploiting underlying structure of the problem, related to polynomial recurrence relations. Through a confrontation with an industrial system with large dynamical complexity, numerical accuracy and efficiency of the method are confirmed.

Frequency-Domain Carrier Frequency and Symbol Timing Offsets Estimation for Offset QAM Filter Bank Multicarrier Systems in Uplink of Multiple Access Networks

In this paper, we study carrier frequency offset (CFO) and symbol timing offset (STO) estimation in the uplink of multiuser offset QAM filter bank multicarrier (FBMC) communication systems. A low-complexity frequency-domain CFO estimator using periodical training sequence is proposed. Also a good estimate of STO is obtained by maximizing the energy of subcarriers subject to training sequence at the output of analysis filter bank. Furthermore we derive the theoretical MSE for the proposed CFO estimator. Computer simulations show that the derived MSE matches the simulated MSE closely. Compared with state-of-the-art time domain estimator, the proposed estimator achieves better performance with a lower computational complexity.

A frequency domain estimation of wall conduction transfer function coefficients

This article describes a novel method to evaluate the series of wall thermal response factors for multi-layer walls, values which give the surface heat flows at hourly intervals due to a triangular pulse of external temperature (base 2h, height 1K). Here, the pulse is resolved into its Fourier components, each component is linked with the sinusoidal response of the wall at the corresponding frequency and the sums of the products provide the response factors. The approach is conceptually and computationally simple; for high accuracy it entails summation of a large number n of products but when n is large they can be handled in blocks of 200, then 1000,… Response factors can readily be transformed to wall conduction transfer coefficients (TCs) and the method is illustrated through analysis of one of the 41 walls whose transfer coefficients are listed in various editions of the ASHRAE Handbook of Fundamentals. It extends the ASHRAE values (a) by providing more terms and to higher accuracy, so as to remove an anomaly in their presentation, (b) it provides TCs for same-side excitation (additional to the current cross-excitation values), and (c) it demonstrates that such values are appropriate for use with a heat source in the room.

Consistent multi-input modal parameter estimators in the frequency domain

In this paper, consistent multiple-input frequency-domain estimators will be presented based on a right matrix-fraction description of the frequency response function. This matrix-fraction description leads to a fast algorithm in the same way as the least-squares complex frequency-domain estimator (LSCF). The use of multiple inputs simultaneously in the estimation (so-called polyreference estimation) has the advantage that it allows to separate closely spaced modes.The main drawback of the LSCF estimator is that it is theoretically inconsistent, i.e.the estimates do not converge to the true values when the number of measurements increases to infinity. However, the noise information available from most measurements can be used to construct a maximum likelihood-like weighting for the LSCF estimators, giving consistent estimates. The results are fast, polyreference, and consistent weighted generalised total-least-squares (WGTLS) estimators. The iterative quadratic maximum likelihood (IQML) estimator is practically consistent for high signal-to-noise ratios, with the additional advantage that it yields clear stabilisation charts.The performance of the presented WGTLS and IQML estimators is evaluated by means of ground vibration test data and demonstrated on flight flutter test data.