Frequency Response Estimation Research Articles

Turbulent Airwake Estimation from Helicopter–Ship Wind-Tunnel Data

This paper presents a stochastic approach for modeling the turbulent airwake suitable for real-time simulation of the helicopter–ship dynamic interface. This approach relies on the measurements of unsteady loads collected during a wind-tunnel test campaign with a scaled helicopter operating over the deck of simple frigate shape 1. Power spectral densities of the measured aerodynamic loads combined with the estimated frequency response functions are used to find, through an optimization algorithm, a model of airwake spectra over the range of frequencies which mainly affects the pilot workload during shipboard operations. Then, a set of autoregressive filters is designed for every particular rotor position and wind-over-deck condition, so that when driven by white noise, the spectrum of the output will reproduce those obtained from the optimization. This approach is applied to three different tested wind directions and three rotor positions by implementing the autoregressive filters into the multibody model of the experimental rotor. Frequency response analysis of the aerodynamic loads demonstrates that the turbulent airwake model obtained from the experimental data can predict the unsteadiness of loads comparable to those measured in the wind tunnel across the bandwidth of interest for pilot activities. The identified airwake models could be applied to a full-scale model to simulate the unsteady loads effectively experienced by the helicopter during a ship landing flight.

Finite-data nonparametric frequency response evaluation without leakage

The existing nonparametric frequency response estimation methods suffer from leakage. Because of this, these methods do not yield the correct result in case of exact data of a linear time-invariant system. Our main contribution is a time-domain direct data-driven nonparameteric frequency response estimation method that, in case of exact data satisfying standard persistency of excitation condition, eliminates the leakage and has infinite frequency resolution. The method is derived in the behavioral setting. It requires solving a system of linear equations and has no hyper-parameters. In case of noisy data, a modification of the method with preprocessing with low-rank approximation results in a subspace-type method for frequency response estimation.

Estimating frequency response functions by using transient responses of systems to simple excitations

This study develops an efficient method using input–output data on estimating non-parametric and then parametric frequency response functions (FRFs) associated with a dynamic system. Contrary to most existing FRF estimation methods that have been theoretically based on the steady-state or stationary responses, the proposed method uses the transient responses that are induced by simple, such as sinusoidal or two-exponential, excitations instead. Its numerical procedure for obtaining a non-parametric FRF is nothing more than solving a set of linear equations in which the unknown variables are individual components of the sought FRF. Furthermore, from the non-parametric FRF, its corresponding poles and residues are extracted through a procedure that involves a usage of the inverse discrete Fourier transform and the Prony-SS method; afterwards, a partial fraction FRF in terms of poles and residues can be achieved. Three numerical examples, including computer simulations and lab experiment, are provided to demonstrate the superior performance of the developed method.

Bias of anticipated non-parametric closed-loop frequency response for controller gain re-tuning

In data-driven controller re-tuning, when requirements exist for the closed-loop frequency response, it is essential that the estimated closed-loop frequency response for a new controller parameter set, correctly reflects the respective true closed-loop. To quantify the difference between the true and estimated frequency response, this paper presents the bias of the non-parametric closed-loop frequency response estimate for the closed-loop system with updated controller parameters. It is calculated for the case where the estimate of the closed-loop frequency response of the system with an initial controller is used, to estimate the new closed-loop frequency response with an updated controller. Such estimates are useful in the process of gain re-tuning based on closed-loop experiments, where new controller parameters are calculated to satisfy requirements for the closed-loop frequency response. It is shown that the estimate appears similar in structure to the indirect non-parametric plant estimate, and hence the bias is reduced with an increasing excitation-to-noise-ratio for the closed-loop experiment. It is also seen that the bias tends to zero when the change in the controller parameters tends to zero or the feed-forward is increased sufficiently. Simulation results demonstrate the concept for a flight-test-based gain re-tuning of a pitch rate controller for an aircraft.

Signal Calibration and Noise Reduction for Software-Defined Radio-Based GPR

This article studies signal calibration, frequency response estimation, and noise reduction for a software-defined radio (SDRadio)-based ground-penetrating radar (GPR). The radar signal generation utilizes the stepped frequency continuous wave (SFCW) method. The signal calibration takes advantage of the dual-channel structure of the SDRadio and solves the incoherent phase problem caused by phase mismatch between the local oscillators (LOs) in the transmitter and the receiver. The frequency response estimation involves two steps: First, the calibration measures the system’s intrinsic frequency response. Then it measures the frequency response of the target under the ground surface. The noise effect at the receiver is reduced using the ridge regression method. For performance evaluation, outdoor and indoor experiments are conducted, which show that the GPR A-scan waveform and B-scan image qualities can be effectively improved. Compared with the traditional method, the signal-to-clutter ratio (SCR) of the A-scan waveform is improved by around 7 dB and that of the B-scan image is improved by around 13 dB.

Metaheuristic FIR Filter Design with Multi-Objective Atomic Orbital Search Algorithm

In this study, atomic orbital search, one of the newly proposed metaheuristic algorithms, is used to design high-performance and low-order FIR filters in MATLAB. The performance parameters of the designed filter were compared with the given literature. The objective function of filter design includes minimization of pass band ripples and stopband ripples, stop band edge frequency attenuation, square sum of the errors between the estimated frequency response and the ideal filter response. The comparison result shows the proposed method performs better than most algorithms and can be used in practical applications.

The estimation of frequency response of nonlinear quarter car model and bilinear model of damper characteristics

The paper presents proposed and tested methods of estimation of frequency response of nonlinear quarter car suspension model and comparison with method for linear model used for research of vehicle vertical dynamics. Linear quarter car suspension model is widely used for estimation of comfort and safety performance of passive and semiactive suspensions. The real suspension - especially shock absorbers - are non-linear in three aspects: static characteristics, hysteresis and the presence of friction. Testing linear suspension model is possible with the use of analytical transfer function formulas but testing real suspension on a testing stand or even virtual but nonlinear suspension needs to use methods of transfer function estimation. It was necessary to design appropriate input signal allowing to get useful response signals. With the use of obtained frequency responses a method of linear estimation of nonlinear suspension for a given range of working condition was proposed. Also the bilinear model of damper characteristic estimation was proposed and tested proving to be good alternative to nonlinear characteristic.

Contingency reserve estimation of fast frequency response for battery energy storage system

The large-scale renewable energy integration faces a challenge of frequency stability due to low inertia in weak power grids. One solution to mitigate this issue is via the fast frequency response service provided by battery storage systems so that the overall grid response during a large power outage can be improved. The battery power reserve is crucial to ensure the frequency ancillary services provision. However, grid operators currently investigate the contingency reserve of batteries through inefficient processes, such as extensive simulations or trial-and-error methods. Therefore, this paper proposes a semi-analytical methodology to quantitively determine the minimum required battery power reserve for preventing under-frequency load shedding when a severe generation trip occurs. This minimum reserve is derived from the time-variant kinetic energy of a given dispatch case. Case study results of the Mexican network demonstrate that the calculated battery power reserve can provide a cost-effective fast frequency response for a real islanded network. The research outcomes offer valuable insights for battery management and grid ancillary services requirement estimation in the transition to power networks dominated by converter-interfaced renewable energy resources.

A topology optimisation of acoustic devices based on the frequency response estimation with the Padé approximation

We propose a topology optimisation of acoustic devices that work in a certain bandwidth. To achieve this, we define the objective function as the frequency-averaged sound intensity at given observation points, which is represented by a frequency integral over a given frequency band. It is, however, prohibitively expensive to evaluate such an integral naively by a quadrature. We thus estimate the frequency response by the Padé approximation and integrate the approximated function to obtain the objective function. The corresponding topological derivative is derived with the help of the adjoint variable method and chain rule. It is shown that the objective as well as its sensitivity can be evaluated semi-analytically. We present efficient numerical procedures to compute them and incorporate them into a topology optimisation based on the level-set method. We confirm the validity and effectiveness of the present method through some numerical examples.

System Frequency Response Model Considering the Influence of Power System Stabilizers

Frequency stability analysis of large power systems are extremely time consuming, laborious and may even exceed the computational capacity of modern computers. Hence, simplified power system models have being developed in the literature. These models are usually called System Frequency Response (SFR). In SFR models, generators are represented by transfer functions, nonlinearities are generally neglected and the grid is not taken into account. Conventional SFR models only contemplate the mechanical behavior of speed governors, turbines and synchronous machines of generators. This is because, a common simplification is to consider that frequency and voltage can be controlled independently. However, it is demonstrated that there is an interaction between them, so frequency can be affected by the effect of power system stabilizers (PSSs) over excitation system controllers. In this work, a modified SFR model is proposed, considering the influence of generators excitation control on frequency. Simulation results show an improvement of the accuracy in the estimation of frequency response of the power system.

Frequency responses of headphones modulate alpha brain oscillations related to auditory processing

The perception of sound can differ significantly, regardless of its physical properties. The frequency content of a sound can provoke different psychoacoustic effects on humans, and simultaneously, it modulates differently brain oscillations. Audio devices such as headphones are variables that have not been taken into consideration in many studies concerning acoustic therapies, which strongly depend on the transmission means. Headphones become a fundamental key in acoustic treatments since they are responsible for transmitting auditory stimuli. It is known that the frequency response of audio devices can change the frequency content of a signal. However, it is still unknown if their limited (or even inappropriate) functioning could affect acoustic therapy effectiveness. Therefore, the present work aims to analyze alpha (resonance frequency at which neurons decode auditory information) brain oscillations in healthy individuals when listening to the same sound but through different frequency responses of headphones. For this purpose, the frequency responses of three headphone models were firstly obtained: Atvio® supra-aural headphones (ATVIO), Shure® SRH1840 circum-aural headphones (SHURE), and Apple® EarPods® intra-aural headphones (APPLE). The estimated frequency responses showed that ATVIO and APPLE headphones presented a major difference in comparison with an ideal frequency response (same gain at every frequency of the headphone bandwidth, i.e., a flat frequency response). Then, inverse filters on the difference of the responses were implemented. Finally, the alpha brain oscillations of 29 individuals were analyzed while they were listening to pink noise through the filters of the three models. The findings suggested that the three headphones modulated alpha brain oscillations accordingly their frequency response. Namely, mapping of alpha brain oscillations for ATVIO and APPLE headphones reflected lower neural activity associated with decoding of auditory information, possibly due to the loss of gain at different frequencies. In contrast, SHURE headphones, which presented a flatter frequency response, reflected higher neural activity related to decoding and interpretation of acoustic information since frequency response was much less affected.

Optimum DCT type-I based transceiver model and effective channel estimation for uplink NB-IoT system

Single-tone and multi-tone transmissions in the narrowband Internet of Things (NB-IoT) uplink system can be accomplished by employing different orthogonal basis. In this paper, we develop an uplink NB-IoT baseband system model and derive the corresponding analytical signal model based on the discrete cosine transform type-I (DCT-I) domain. Basically, the circular convolution and channel matrix diagonalization issues for designing DCT-based systems are addressed without exploiting any redundancy (a prefix and a suffix sequences, and zero-padding (ZP)) into each transmitted data symbol blocks. In our proposed DCT-I based transceiver, we employ a standard cyclic prefix (CP) and apply discrete Fourier transform (DFT) and inverse DFT (IDFT) operations directly to make the channel matrix circulant and diagonal, resulting in the use of one-tap frequency-domain channel equalizer without incorporating extra front-end prefilter at the receiver. Furthermore, we propose novel least squares (LS) and linear minimum mean square error (LMMSE) channel estimators by considering the energy concentration and spectral compaction properties of DCT-I for the uplink NB-IoT system. The expressions for the DCT-I domain LS and LMMSE estimators are derived for channel frequency response estimation and mean square error computation. Finally, the viability of the proposed CP-DCT-I-NB-IoT uplink system, as well as the channel estimators, are tested compared with the standardized CP-DFT-NB-IoT and ZP-DCT type-2 even based single-carrier frequency-division multiple access (SC-FDMA) systems through rigorous computer simulations.

Comb Type Pilot Based Channel Estimation using Dft Based Interpolation for Spatial Modulated OFDM Systems

An integration of Spatial Modulation with Orthogonal Frequency Division Multiplexing (SM OFDM) is a recently evolved transmission technique. In practical scenarios, channel estimation is significant for detecting transmitted data coherently. Impulse response based interpolation technique that provides channel frequency response estimate with reduction in noise error is proposed for comb type pilot based channel estimation of SM OFDM system along with 1D interpolation techniques under frequency selective channel. This scheme focus on carrying out smoothing and estimation in time domain and transforming output back to the frequency domain. BER performance is investigated for Rayleigh channel employing COST 207 project model on two test urban environments (Typical and Bad) for 4 and 16 QAM SM OFDM systems. Results show that the Least Square estimator with DFT interpolation performs finer compared to all one dimensional interpolation methods with less computational complexity by employing FFT algorithms.

A fast Fourier transform based method to estimate frequency response mismatches in time interleaved systems.

Time interleaving (TI) technique is widely used in acquisition systems to improve the sampling rate. However, as a parallel sampling structure, it inevitably brings in channel mismatches, such as the offset mismatch, gain mismatch, and time mismatch. Moreover, the gain mismatch and time mismatch are frequency-dependent, which means that the gain mismatch and time mismatch will be different when the signal frequency changes. This is because the gain and time mismatches are the special circumstances of frequency response mismatches. In this paper, a frequency response mismatch estimation method in TI acquisition systems is proposed and analyzed. First, the two kinds of mismatch models are compared to find the relationship between frequency response mismatches and the gain and time mismatches. Then, a mismatch estimation method that can estimate mismatches when the analog bandwidth exceeds the sampling rate of a single channel in a time interleaving analog to digital converter is proposed. Sinusoids with different frequencies are utilized to convert the question of estimating frequency response mismatches to acquiring the mismatch coefficients at a series of frequency points. Furthermore, a semi-automatic estimation technique is proposed to reduce the operation time, and a 10 GSPS eight-channel TI system is introduced. Simulations show the accuracy and effectiveness of the proposed method. At last, the frequency response mismatches are calibrated by using the estimated parameters. The calibration improves the performance of an eight-channel TI system from the original spurious free dynamic range of 27.6639 to 56.7029 dB and signal-to-noise ratio of 25.5468 to 32.7667 dB. The calibration result demonstrates the usefulness of the proposed method.

Parametric Model Identification of Axisymmetric MEMS Resonators

This paper proposes a technique for developing parametric models of modally degenerate resonators from stimulus-response data. The technique complements traditional empirical frequency response estimates that are commonly used for testing MEMS resonators, however, the parametric models have distinct advantages when the modal frequency differences are close enough to frustrate estimates of quality factors, natural frequencies and mode orientations. The proposed technique also completely rejects parasitic coupling between the stimulus and pick-off electrodes. It is shown how a modification of the algorithm using demodulated measurement signals greatly reduces storage and computational requirements. [2020-0281]

Accuracy improvement method for dynamic substructuring models in vehicle systems

This study proposes an improved dynamic substructuring model using the estimated frequency response function information at coupling points between substructures. An assembled system generally consists of two or more substructures connected by a bolt. Individual substructure evaluation excluding the effects of other components is important in the development stage of a general mechanical system because the vibro-acoustic performance of the system depends on the specific combination of substructures. Therefore, this study predicted the final coupling system performance using information from the initial evaluation of the individual substructures. Accurate measurements of the joint properties are required to accurately estimate the dynamic assembled system characteristics; however, physical constraints typically limit such measurements at actual coupling points. Accordingly, a method that utilizes generalized coupling properties to estimate the dynamic characteristics of a new coupling system based on the characteristics of an original substructure is proposed. Virtual point transformation is then used to estimate accurate frequency response functions at the coupling points of the assembled system based on convenient measurements. The proposed method was validated using a vehicle suspension that was hard mounted in a test jig and onto an actual vehicle body to estimate the vibration characteristics of the assembled system. The findings of this study contribute to the accurate estimation of the dynamic properties of many real-world bolt-assembled systems.

Topology optimization of acoustic devices based on the frequency response estimation with the Padé approximation

Topology optimization of acoustic devices based on the frequency response estimation with the Padé approximation

Формирование признакового пространства периодических временных зависимостей для систем диагностики состояния динамических объектов на примере сетчатки глаза

The technology of testing dynamically and structurally similar aircraft models for flutter in subsonic wind tunnels using information and The article addresses techniques for setting up the attribute space of informative features of periodic signals recorded at the output of a dynamic object with an unknown structure in response to rectangular testing signals of different frequencies applied to the object input. The attribute space is used in developing expert systems for diagnosing the current state of an operating dynamic object. With a great variety of possible developing faults, the simplest practical techniques involving the use of characteristic points of change in the observed time dependencies yield a limited number of features with large mutual intersection domains. To expand the attribute space, it is proposed to use the expansion of input and output signals into a Fourier series for setting up a base of additional features. The proposed features characterize, depending on the testing conditions, the object’s transferring properties in the frequency domain from changes in its amplitude and phase characteristics. The test pulse frequency and duration serve as such conditions. For the convenience of comparing the object’s frequency responses variation pattern, two special procedures are used. The first procedure allows the observed time dependencies to be reduced to a single pseudo frequency of the test signals. The second procedure uses specially formed windows for subjecting individual fragments of the observed time dependencies to a spectral analysis. It is shown that, depending on the type of the frequency responses being analyzed, the techniques for their polynomial approximation, as well as integral estimates of frequency response individual domains can be useful. The polynomial approximation makes it possible to use the coefficients of the approximating polynomials as additional features, and the integration of individual characteristic domains of the frequency responses makes it possible to introduce dimensionless relative indicators that characterize the degree of change in the frequency responses depending on the experimental conditions. The considered techniques open the possibility to select additional features that can help distinguish both separate groups of faults and individual faults in operating objects. The study results are illustrated by the examples of analyzing the changes in electroretinograms that record changes in the eye retina biopotential in response to light flashes of different frequencies.

Застосування нейронної мережі для оцінювання частотної характеристики багатопроменевого каналу в системах зв’язку з технологією OFDM

In the context of the development of modern technologies, the key role is assigned to the exchange of information. Digital communication systems are at the heart of information technology. To meet the needs of a modern person the requirements for communication systems are constantly increasing. Large information flows require high data rates. At the same time an important task is to reduce the number of errors that occur during data transmission. In OFDM systems, this is achieved by increasing the accuracy of estimating the frequency response of the communication channel. In this paper a neural network of direct propagation is used to estimate the values of the frequency response of the communication channel in OFDM systems. The neural network was designed for conditions when the pilot signals in the OFDM symbol structure are arranged in a combined pattern. Under such conditions the neural network receives noisy values of the frequency response on the pilot subcarriers as input information. Its task is to filter these values from noise and interpolate the values of the frequency response to the data subcarriers. The designed neural network has 32 incoming neurons, 128 outgoing neurons and 2 hidden layers of 8 neurons each. The structure of this neural network was designed with such an approach that the vector of the frequency response of the channel is estimated sequentially by 128 samples with their further combining. The neural network was trained on communication channels with given correlation properties by applying the error backpropagation method. The analysis of the efficiency of the network was carried out by means of statistical modeling using a model example in the Matlab computer-aided design system. The results of estimating the values of the frequency response using a neural network are compared with the results that are given by known methods. The analysis of the efficiency of the neural network showed that it is capable of providing a gain of up to 2 dB in comparison with the method of two-stage estimation of the frequency response estimation for a given model example. The neural network is inferior in the estimation accuracy to the minimum mean square error method, however, it has a lower implementation complexity compared to it.

Two-Stage Method for Joint Estimation of Information Symbols and Channel Frequency Response in OFDM Communication Systems

The optimal and quasi-optimal algorithms of two-stage joint estimation of information symbols and frequency response (FR) of multibeam channels in OFDM-based communication systems have been synthesized. They involve the calculation of a posteriori probability density of estimated processes. At the first stage, the recurrent calculation of joint a posteriori distributions of information symbols and the frequency response is performed from two sides of the measurement vector. At the second stage, a posteriori distributions are combined on each of subcarriers that are obtained as a result of the first stage estimation. Based on the obtained a posteriori distributions, estimates of the information symbol and channel FR are determined by the criteria of a posteriori probability maximum and the average mean squared error minimum, respectively. The performance of synthesized algorithms similar to the well-known MMSE algorithm involves the need of knowledge of statistical properties of communication channel. The device implementing the optimal algorithm is multichannel, each channel of which is matched with the corresponding value of symbol from the modulation constellation. The quasi-optimal algorithm was obtained by using the Gaussian approximation of a posteriori probability density. It should be noted that this algorithm preserves its multichannel structure. The approbation of the presented algorithm was conducted using the computer-aided statistical simulation for different parameters of multibeam communication channels and the comparison of the obtained results with the results obtained by the MMSE and LS algorithms. The simulation results showed that the error probability decreases by about 2 times with a maximum signal propagation delay of 100 μs.