Auto Power Spectral Density Functions Research Articles

Model Parameter Estimation Method on Multichannel Structural Response from Turbulence Flutter Test

Flutter design is important for the design of new aircraft types, for which flutter tests are an important verification measure. Atmospheric turbulence excitation is a common form of excitation in flutter flight tests. The modal parameter estimation of the turbulence response is a key aspect to ensure accurate data processing of flutter test results. Atmospheric turbulence excitation acts on the structural system, and the turbulence response thus simultaneously contains both the randomness of the excitation signal and the determinism of the structure system. In view of the turbulence response characteristics, this paper addresses the incoherence of atmospheric turbulence excitation and the orthogonality of the frequency domain from a multichannel response. The turbulence response is used to perform modal parameter identification in the frequency domain. The power spectral density matrix can be calculated from the multichannel turbulence response using the periodogram method. Singular value decomposition is then performed on the power spectral density matrix at each spectral pin based on the orthogonality of the frequency domain. The maximum singular value of each spectral pin forms a curve over the entire frequency band, which is the autopower spectral density function of the system, the system is directly identified at the frequency domain using the polynomial fitting in the frequency domain, and the modal parameters (frequency, damping ratio) are calculated according to the fitted transfer function. This paper verifies the theoretical feasibility of the proposed method using simulation data. The engineering applicability is verified based on the turbulence response from the flutter flight test of a certain aircraft type.

Simulation of fully non-stationary spatially varying ground motions considering nonlinear soil behavior

Taking the nonlinear soil behavior into consideration, a novel method for simulating fully non-stationary spatially varying earthquake ground motions (SVEGMs) was proposed. Based on the one-dimensional (1D) wave propagation model, time-varying shear modulus and damping ratio were introduced into the classical transfer function model, where the evolution characteristics of soil properties (i.e., shear modulus and damping ratio) during earthquake were obtained by using a two-dimensional (2D) site response analysis. By using an example of application, the out-of-plane and in-plane fully non-stationary SVEGMs on ground surface were simulated. The acceleration and displacement time-histories were observed, and the auto power spectral density functions (PSDFs) and coherency loss functions of simulated motions were compared with corresponding targets, respectively. The normalized time-frequency spectra of simulated motions were presented to exhibit the spectral non-stationarity. It was shown that the evolution tendency of predominant frequency of simulated motions reflected similar characteristics with that of shear modulus of soil, which demonstrated the validness of the proposed method.

Mode identification by eigensystem realization algorithm through virtual frequency response function

Mode identification in civil engineering uses ambient excitation response, where the excitation is assumed to be stationary white noise. However, practical engineering conditions cannot satisfy this assumption of ideal excitation. This paper proposes an innovative method based on eigensystem realization algorithm and a proposed virtual frequency response function. The formulation of the virtual frequency response function is derived from the ratio of the cross-power and autopower spectral density functions of the measurement signals. The impulse responses are calculated by inverse Fourier transform of the product of the virtual frequency response function and the frequency response function of the reference point. After obtaining impulse responses, eigensystem realization algorithm is then performed to identify structural modes. The proposed virtual frequency response function and eigensystem realization algorithm are validated by a numerical example. The results show that the virtual frequency response function and eigensystem realization algorithm can give much a better impulse response than natural excitation technique and identify more precise mode parameters. Finally, the proposed method is applied to a practical engineering bridge, where the results by the virtual frequency response function and eigensystem realization algorithm can also give better results than those given by natural excitation technique and eigensystem realization algorithm.

Modal identification for superstructure using virtual impulse response

In civil engineering, structural modes are identified with the assumption of stationary white noise, which cannot be satisfied in practical engineering. This article proposes a new method, which contains the virtual impulse response and eigensystem realization algorithm. The formulation of virtual impulse response is derived from the inverse Fourier transform of the ratio of the cross-power to auto-power spectral density functions of the measurement responses, which is based on the concept of frequency response function. During the formulation derivation, a single point excitation is only considered. Frequency response function would not change with different excitations and responses, which means that the excitation cannot influence frequency response function. The impulse response is pointed out to only represent the behavior of superstructure. After obtaining impulse responses, eigensystem realization algorithm is then performed to identify the modes of superstructure. The proposed method is validated by a numerical example. The results show that virtual impulse response can have much better free decayed behavior than natural excitation technique and identify very precise modal parameters for superstructure.

Investigation of the reactor heat transfer function between the cold and the hot leg of the primary circuit

In this paper the propagation mechanism of the temperature fluctuations of the coolant is investigated using the measured hot and cold leg temperature signals of the primary loops of a VVER-440 reactor. The aim of the investigation was to provide an estimation of the reactor heat transfer function between the cold and the hot leg of the primary circuit, which was enabled by the finding that the ratio of the auto power spectral density functions of temperature noise of the reactor and the steam generators can be well approximated with the ratio of the spectra of the hot leg and the cold leg temperature noise. It was found that the effect of the control system and the power feedback cannot be neglected up to 0.2 Hz for VVER-440 reactors. The transfer properties of the steam generator were estimated using temperature noise measurements as well.

Between-subject variance in the magnitude of corticomuscular coherence during tonic isometric contraction of the tibialis anterior muscle in healthy young adults

Oscillatory activity of the sensorimotor cortex has been reported to show coherence with muscle activity in the 15- to 35-Hz frequency band (β-band) during weak to moderate intensity of isometric contraction. The present study examined the variance of the magnitude of the corticomuscular coherence across a large number of subjects. We quantified the coherence between EEG over the sensorimotor cortex and rectified electromyogram (EMG) from the tibialis anterior muscle during tonic isometric contraction at 30% of maximal effort in 100 healthy young individuals. We estimated the maximal peak of EEG-EMG coherence (Cohmax) and the ratio of the sum of the autopower spectral density function within the β-band to that of all frequency ranges for both EEG (EEGβ-PSD) and EMG (EMGβ-PSD) signals. The frequency histogram of Cohmax across all subjects showed a broad bell-shaped continuous distribution (range, 0.048-0.816). When the coherence was thresholded at the estimated significance level of P < 0.05 (0.114), 46 out of 100 subjects showed significant EEG-EMG coherence. Cohmax occurred within the β-band in the majority of subjects who showed significant EEG-EMG coherence (n = 43). Furthermore, Cohmax showed significant positive correlations with both EEGβ-PSD (r = 0.575, P < 0.001) and EMGβ-PSD (r = 0.606, P < 0.001). These data suggest that even during simple tonic isometric contraction, the strength of oscillatory coupling between the sensorimotor cortex and spinal motoneurons varies among individuals and is a contributory factor determining muscle activation patterns such as the degree of grouped discharge in muscle activity within the β-band for each subject.

Muscle fatigue-induced enhancement of corticomuscular coherence following sustained submaximal isometric contraction of the tibialis anterior muscle

Oscillatory activity of the sensorimotor cortex shows coherence with muscle activity within the 15- to 35-Hz frequency band (β-band) during weak to moderate sustained isometric contraction. We aimed to examine the acute changes in this corticomuscular coupling due to muscle fatigue and its effect on the steadiness of the exerted force. We quantified the coherence between the electroencephalogram (EEG) recorded over the sensorimotor cortex and the rectified surface electromyogram (EMG) of the tibialis anterior muscle as well as the coefficient of variance of the dorsiflexion force (Force(CV)) and sum of the auto-power spectral density function of the force within the β-band (Force(β-PSD)) during 30% of maximal voluntary contraction (MVC) for 60 s before (prefatiguing task) and after (postfatiguing task) muscle fatigue induced by sustained isometric contraction at 50% of MVC until exhaustion in seven healthy male subjects. The magnitude of the EEG-EMG coherence increased in the postfatiguing task in six of seven subjects. The maximal peak of EEG-EMG coherence stayed within the β-band in both pre- and postfatiguing tasks. Interestingly, two subjects, who had no significant EEG-EMG coherence in the prefatiguing task, showed significant coherence in the postfatiguing task. Additionally, Force(CV) and Force(β-PSD) significantly increased after muscle fatigue. These data suggest that when muscle fatigue develops, the central nervous system enhances oscillatory muscular activity in the β-band stronger coupled with the sensorimotor cortex activity accomplishing the sustained isometric contraction at lower performance levels.

Reliability-based critical earthquake load models. Part 2: nonlinear structures

The problem of determining critical stochastic earthquake excitation models for simple nonlinear systems under single-point or multi-point nonstationary seismic inputs is considered. The earthquake acceleration components are obtained by multiplying known deterministic enveloping functions with zero mean Gaussian stationary random processes with unknown auto-power spectral density functions (for single-point excitations) and power spectral density matrix (for multi-point excitations). The definition of critical earthquake input is based on the notion of a performance function. The system is considered to have failed if the maximum response over a given time interval exceeds specified limits. The critical excitations are defined as those that minimize the Hasofer–Lind reliability index associated with this performance function. The computation of this index, in turn, is based on the use of response surface to model the limit surface near the check point. Here the quantity to be optimally determined is taken to be the unknown input power spectral density function (for single-point excitations) or the input power spectral density matrix (for multi-point excitations). The excitations are taken to satisfy constraints on total average energy, zero crossing rate, lower bounds on entropy rate and other positivity and bounding requirements that are of mathematical nature. The resulting constrained nonlinear optimization problems are solved using the sequential quadratic programming method. Illustrative examples for computing random critical excitations for singly supported and multiply supported oscillators that have cubic force–displacement relations are provided.

Stochastic characteristics of vapor fraction and wall pressure fluctuations in boiling flows

An experimental investigation of the statistical character of boiling flows has been carried out. Two flow field variables, viz. static pressure fluctuations at the test section outer wall and instantaneous chordal-average vapor fraction, were studied in vertical up-flow through concentric annular test sections. Matched piezo-electric pressure transducers were used for the pressure fluctuation measurements, and a linearized dual-beam X-ray system was used for the vapor fraction measurements. Steady state (mean) thermal-hydraulic conditions in the test section were determined by an analytical model and verified to a certain extent by capacitance probe vapor volume fraction measurements. A wide range of local conditions with flow regimes ranging from subcooled bubbly to saturated churn turbulent-slug-annular were investigated. The wall static pressure fluctuation results include: (i) intensity (RMS value). (ii) probability density function: and (iii) autopower spectral density function. The chordal-average vapor fraction results include: (i) probability density function: and (ii) autopower spectral density function. The magnitude of coherence between wall static pressure fluctuations and chordal-average vapor fraction fluctuations are presented as well. It is suggested that diagnosis of flow regimes on the basis of the statistical properties of the two variables studied should be possible.

Noise measurements on the KEMA suspension test reactor (KSTR) and the Dodewaard boiling water reactor

Noise measurements have been performed on the neutron flux and the fuel concentration of the KEMA Suspension Test Reactor. The behaviour of the autopower spectral density function of the neutron flux is given with respect to reactor power and fuel burn up. To investigate the concentration fluctuations the load of the suspension pump has been analysed. Apart from the measurements on the Suspension Test Reactor, noise analysis has been performed on the temperature on the outside of the feed water inlet nozzle and on its thermal sleeve of the Dodewaard Boiling Water Reactor. Temperature distributions indicate the leakage of feed water through the annulus, formed by the nozzle and the thermal sleeve. Amplitude distribution measurements show the magnitude of the circumferential temperature fluctuations on the thermal sleeve. From cross correlation measurements of the temperature fluctuations in nozzle and thermal sleeve the flow pattern in this region has been determined. From the results, temperature fluctuations at the inner radius and the bore of the feed water inlet nozzle can be derived.