Auto Spectral Density Functions Research Articles

Latent space representation method for structural acoustic assessments

When targeting structural acoustic objectives, engineering practitioners face epistemic uncertainties in the selection of optimal geometries and material distributions, particularly during early stages of the design process. Models built for simulating acoustic phenomena generally produce vector-valued output quantities of interest, such as autospectral density and frequency response functions. Given finite compute resources and time we seek computationally parsimonious ways to distill meaningful design information into actionable results from a limited set of model runs, and thus aim to use machine learning to perform model order reduction. Unlike time series data for which recurrent neural networks can learn from prior time steps to inform subsequent steps, frequency-dependent data demands a different machine learning paradigm. We thus evaluate the utility of autoencoders to represent structural acoustic results with a low dimensional latent space to enable such objectives as surrogate modeling for design optimization. We demonstrate the accuracy of autoencoder based methods of constructing a manifold representation for frequency dependent functions of varying modal density and damping, and discuss the predictive capability thereof.

Scaling of cylinder-generated shock-wave/turbulent boundary-layer interactions

Scaling parameters of shock-wave/turbulent boundary-layer interactions generated by a semi-infinite standing cylinder were explored in a combined numerical and experimental effort, consisting of Reynolds-averaged Navier–Stokes simulations and high-speed schlieren imaging. The primary interaction variable, the cylinder diameter (d), and a secondary interaction variable, the boundary-layer thickness ($$\delta $$), were varied to study the effects of the parameter $$d/\delta $$. This was found to be an appropriate scaling parameter for mean features. The characteristic interaction variables (the maximum separation distance, S, and the triple-point height, $$h_\mathrm{tp}$$) followed a linear trend when normalized as $$S/\delta $$ and $$h_\mathrm{tp}/\delta $$; however, when the boundary layer became larger than the cylinder diameter, a power law trend became more representative. The parameter $$d/\delta $$ also determined the role that viscous effects have on the strength of the interaction, where a lower $$d/\delta $$ was characterized by a greater interaction scale and lower surface pressure peaks. Moreover, the high surface pressure on the cylinder leading edge due to the Edney interaction was found to be reduced for $$d/\delta \le 0.45$$, as the boundary layer encompassed the lambda-shock structure. Trends in the shapes or peaks of the auto-spectral density function were not observed based on $$d/\delta $$, but appeared to be dominated by broadband low-frequency ($$f < 1~\hbox {kHz}$$) content. While the position and structure of the interaction may change as a result of varying $$d/\delta $$, the effects on the unsteady dynamics were minimal.

Similitude laws for the structural response of flat plates under a turbulent boundary layer excitation

Similitude laws for scaling the vibration response of flat panels to a turbulent boundary layer excitation are proposed and analyzed in this paper. Their relevance is studied from an analytical, experimental and numerical perspective. It is first shown that a perfect similitude, in terms of vibration response scaling, can theoretically be achieved between plates of proportional sides and of variable thicknesses. Vibration auto-spectral and cross-spectral density functions, measured in a wind-tunnel facility on a set of three plates, are then successfully scaled: the plates dimensions and test flow speeds are a priori defined using the proposed similitude laws. Finally, the applicability of the suggested strategy for different boundary conditions, for different types of materials and properties and for distorted models is also numerically studied and confirmed.

Wind characteristics along a bridge catwalk in a deep-cutting gorge from field measurements

This paper investigates the wind characteristics along the bridge catwalk during construction in a deep-cutting gorge. Five sets of anemometers are installed in the catwalk to collect field measurements. The mean wind characteristics, including wind speed and wind direction, are first investigated. The influence of local topography on the mean wind characteristics is identified. Moreover, it is also found that the recorded wind data obtained from the deep-cutting gorge have strong nonstationary characteristics. Based on the traditional stationary wind speed model and a nonstationary wind speed model, turbulence wind characteristics, such as turbulence intensity, spectral analysis and turbulence length scale, are comprehensively analyzed and compared. The effect of local topography on the turbulence wind characteristics is also examined. Additionally, the change laws of turbulence intensity and turbulence length scale along the bridge catwalk are derived. The estimated auto-spectral density functions of all three turbulence components are in a good agreement with the Von Kármán forms.

On the correlation of chaotic signals generated by multimodal skew tent map

In recent years, a great deal of attention has been devoted to the application of chaos theory in signal processing and communications. Despite the importance of spectral analysis in these domains, there are few works that take an interest in spectral properties of chaotic signals. In this work, we derive analytic expressions for the autocorrelation function and the auto-spectral density function of chaotic signals generated by a multimodal skew tent map. Our results reveal that chaotic signals generated from a multimodal skew tent map have similar spectral properties to those generated from a unimodal skew tent map.

Identification of spatially correlated excitations on a bending plate using the Virtual Fields Method

This paper aims at identifying the autospectral density and spatial correlation functions of random excitations acting on the surface of a thin plate, from its measured vibration response. The general framework is the Virtual Fields Method (VFM), which was previously applied by the authors to the identification of deterministic excitations on plates. In the present paper, the VFM framework is extended to the case of spatially correlated excitations. It is shown that extraction of the loading power spectral density requires measuring power spectral density functions of transverse displacements and bending curvatures, which can be typically derived from contactless Laser Doppler Vibrometry measurements. The paper details the implementation of the VFM for random excitations, presents numerical simulations and experimental results for diffuse acoustic field excitation of a plate.

Signals features extraction in liquid-gas flow measurements using gamma densitometry. Part 2: frequency domain

Knowledge of the structure of a flow is really significant for the proper conduct a number of industrial processes. In this case a description of a two-phase flow regimes is possible by use of the time-series analysis e.g. in frequency domain. In this article the classical spectral analysis based on Fourier Transform (FT) and Short-Time Fourier Transform (STFT) were applied for analysis of signals obtained for water-air flow using gamma ray absorption. The presented method was illustrated by use data collected in experiments carried out on the laboratory hydraulic installation with a horizontal pipe of 4.5 m length and inner diameter of 30 mm equipped with two 241Am radioactive sources and scintillation probes with NaI(Tl) crystals. Stochastic signals obtained from detectors for plug, bubble, and transitional plug – bubble flows were considered in this work. The recorded raw signals were analyzed and several features in the frequency domain were extracted using autospectral density function (ADF), cross-spectral density function (CSDF), and the STFT spectrogram. In result of a detail analysis it was found that the most promising to recognize of the flow structure are: maximum value of the CSDF magnitude, sum of the CSDF magnitudes in the selected frequency range, and the maximum value of the sum of selected amplitudes of STFT spectrogram.

Signals features extraction in liquid-gas flow measurements using gamma densitometry. Part 1: time domain

Knowledge of the structure of a flow is really significant for the proper conduct a number of industrial processes. In this case a description of a two-phase flow regimes is possible by use of the time-series analysis e.g. in frequency domain. In this article the classical spectral analysis based on Fourier Transform (FT) and Short-Time Fourier Transform (STFT) were applied for analysis of signals obtained for water-air flow using gamma ray absorption. The presented method was illustrated by use data collected in experiments carried out on the laboratory hydraulic installation with a horizontal pipe of 4.5 m length and inner diameter of 30 mm equipped with two 241Am radioactive sources and scintillation probes with NaI(Tl) crystals. Stochastic signals obtained from detectors for plug, bubble, and transitional plug – bubble flows were considered in this work. The recorded raw signals were analyzed and several features in the frequency domain were extracted using autospectral density function (ADF), cross-spectral density function (CSDF), and the STFT spectrogram. In result of a detail analysis it was found that the most promising to recognize of the flow structure are: maximum value of the CSDF magnitude, sum of the CSDF magnitudes in the selected frequency range, and the maximum value of the sum of selected amplitudes of STFT spectrogram.

Effects of spatial and temporal resolution of the turbulent inflow on wind turbine performance estimation

AbstractThe effects of spatial and temporal resolution of wind inflows generated using large eddy simulations (LES) on the scales of turbulence present in the wind inflow, and the resulting changes in wind turbine performance were investigated for neutral atmospheric boundary layer conditions. Wind inflows with four different spatial resolutions and five different temporal resolutions were used to produce different turbine responses. An aero‐elastic code assessed the dynamic response of two wind turbines to the different inflows. Auto‐spectral density functions (ASDF) of turbine responses, such as blade deflection and bending moment, that are representative of the turbine response were used to assess the effect of the inflow. The results indicated that, as additional turbulence scales were resolved, the wind turbines showed a similar increased response that was evident in both the ASDF and variance of the different wind turbine performance parameters. As a result, the amount to which turbulence is resolved in the inflow, particularly using tools such as LES, will be important to consider when using these inflows for wind turbine design and performance prediction. Copyright © 2015 John Wiley &amp; Sons, Ltd.

Structural damage identification with power spectral density transmissibility: numerical and experimental studies

This paper proposes a structural damage identification approach based on the power spectral density transmissibility (PSDT), which is developed to formulate the relationship between two sets of auto-spectral density functions of output responses. The accuracy of response reconstruction with PSDT is investigated and the damage identification in structures is conducted with measured acceleration responses from the damaged state. Numerical studies on a seven-storey plane frame structure are conducted to investigate the performance of the proposed damage identification approach. The initial finite element model of the structure and measured acceleration measurements from the damaged structure are used for the identification with a dynamic response sensitivity-based model updating method. The simulated damages can be identified accurately without and with a 5% noise effect included in the simulated responses. Experimental studies on a steel plane frame structure in the laboratory are performed to further verify the accuracy of response reconstruction with PSDT and validate the proposed damage identification approach. The locations of the introduced damage are detected accurately and the stiffness reductions in the damaged elements are identified close to the true values. The identification results demonstrated the accuracy of response reconstruction as well as the correctness and efficiency of the proposed damage identification approach.

Damage Detection of Shear Connectors Based on Power Spectral Density Transmissibility

Damage of shear connectors in slab-on-girder structures will result in shear slippage between slab and girder, which significantly reduces the load-carrying capacity of the bridge. This paper proposes a dynamic damage detection approach to identify the damage of shear connectors in slab-on-girder bridges with power spectral density transmissibility (PSDT). PSDT formulates the relationship between the auto-spectral density functions of two responses. Measured impact force and acceleration responses from hammer tests are analyzed to obtain the frequency response functions at the slab and girder sensor locations by experimental modal analysis. When measurement data from the undamaged structure are available, PSDT from the slab response to the girder response is derived with the obtained frequency response functions. PSDT matrices in the undamaged and damaged states are directly compared to identify the damage of shear connectors. When the measurement data from the undamaged structure are not available, PSDT matrices from measured response at a reference sensor response to those of the slab and girder in the damaged state can also be used to detect the damage of shear connectors. Experimental studies with a concrete slab supported by two steel girders are conducted to investigate the accuracy and efficiency of the proposed approach. Identification results demonstrated that damage of shear connectors can be identified accurately and efficiently with and without measurement data from the undamaged structure.

Implementation of a Probabilistic Structural Health Monitoring Method on a Highway Bridge

This paper describes the application of a probabilistic structural health monitoring (SHM) method to detect global damage in a highway bridge in Connecticut. The proposed method accounts for the variability associated with environmental and operational conditions. The bridge is a curved three-span steel dual-box girder bridge located in Hartford, Connecticut. The bridge, monitored since Fall 2001, experienced a period of settling in the Winter of 2002-2003. While this change was not associated with structural damage, it was observed in a permanent rotation of the bridge superstructure. Three damage measures are identified in this study: the value of fundamental natural frequency determined from peak picking of autospectral density functions of the bridge acceleration measurements; the magnitude of the peak acceleration measured during a truck crossing; the magnitude of the tilt measured at 10-minute intervals. These damage measures, including thermal effects, are shown to be random variables and associatedPvalues are calculated to determine if the current probability distributions are the same as the distributions of the baseline bridge data from 2001. Historical data measured during the settling of the bridge is used to verify the performance of the bridge, and the field implementation of the proposed method is described.

Stochastic and chaotic sub- and superharmonic response of shallow cables due to chord elongations

The paper deals with the non-linear response of shallow cables driven by stochastically varying chord elongations caused by random vibrations of the supported structure. The chord elongation introduces parametric excitation in the linear stiffness terms of the modal coordinate equations, which are responsible for significant internal subharmonic and superharmonic resonances. Under harmonically varying support motions coupled ordered or chaotic in-plane and out-of-plane subharmonic and superharmonic periodic motions may take place. If the harmonically varying chord elongation is replaced by a zero-mean, stationary narrow-band random excitation with the same standard deviation and center frequency, qualitatively and quantitatively completely different modes of vibration are registered no matter how small the bandwidth of the excitation process is. Additionally, the stochastic excitation process tends to enhance chaotic behavior. Based on Monte Carlo simulation on a reduced non-linear two-degree-of freedom system the indicated effects have been investigated for stochastic subharmonic resonance of order 2:1, and stochastic superharmonic resonances of orders 1:2 and 2:3. By analyzing the responses for two chord elongation processes with almost identical auto-spectral density function, but completely different amplitudes, it is shown that the indicated qualitative and quantitative changes of the subharmonic resonance primarily are caused by the slowly varying phase of the stochastic excitation. The superharmonic stochastic responses are dominated by random jumps between a single mode in-plane and a coupled mode attractor, which are caused by the variation of the amplitude of the random excitation. Such jumps do not occur in the subharmonic response, because the single mode in-plane attractor is unstable.

Seepage-Induced Acoustic Emission in Granular Soils

This technical paper presents the results of a study on detecting excessive seepage in granular soils by monitoring the seepage-induced acoustic emission (AE). The laboratory experiments and data analyses were performed using specially designed data acquisition instruments and computer-based data analysis devices. The monitored data were analyzed using three methods, namely, amplitude, time, and frequency domain analyses. The analysis results showed that the seepage-induced AE in the test soils were broadband Gaussian signals which were zero mean, normally distributed, and leptokurtic. All of the measured autospectral density functions showed that the most prominent AE activities occurred within a frequency range of about 0.8 – 10 kHz. Based on acoustic similarity laws and a graphical fitting method, the test results were subjected to dimensional analysis. The results of this analysis provided a relationship between a nondimensional sound pressure level and a nondimensional frequency, in which AE intensity, seepage velocity, soil, and permeant properties were interrelated. This relationship provided a fundamental basis for detecting excessive seepage using the monitored seepage-induced AE intensity.

Time series analysis of electrorheological actuator with double driving discs

An electrorheological(ER) actuator with double driving discs rotating at the same speed in the opposite directions was designed for studying the electrorheological torque experiments. The dynamic model of the disc transmission system consists of the linear part between the output angle and the electric torque, and the nonlinear part between the electric torque and the applied field strength dependent on the ER fluids. Using only the output sampled torque signals, an autoregressive model, the auto-spectral density function, the autoregressive(AR) bispectrum and the slices of the bispectra, taken to analyse the torque dynamic response, are obtained when a zero mean and non-Gaussian white noise interferes with the rotary disc system. The method for AR model order selection based on bispectral cross correlation is proposed and employed to determinate the model order. The experimental and theoretical results show that the time series analysis method and the parametric bispectrum might be helpful to establish the dynamic model of an ER actuator and to quantitatively analyse the torque response.

A spectral density approach for modelling continuous vertical forces on pedestrian structures due to walking

Existing walking models used for vibration serviceability assessment of structures carrying pedestrians are typically based on measurements of single footfalls replicated at precise intervals. This assumed perfect periodicity allows walking forces to be modelled as a Fourier series based on the walking pace and its integer multiples. This paper examines real continuous walking forces obtained from an instrumented treadmill and the effect of their random imperfections through time simulations of structural response and shows that there are significant differences between responses due to the imperfect real walking forces and the equivalent perfectly periodic simulation. These differences are most significant for higher harmonics where the simulated vibration response is overestimated. As a realistic representation of imperfect walking is an auto-spectral density function, the random character naturally leads to a stochastic approach to treatment of pedestrian loading applied in the frequency domain. The approach can be used for single pedestrians as well as crowd loading where correlation between pedestrians as well as statistics of their pacing rates is used.Key words: vibration, coherence, loading, footbridges, gait, floors, pedestrians, spectral density.

Velocity and pressure fluctuations on inclined tube banks submitted to turbulent flow

This paper presents the experimental study of pressure and velocity fluctuations and their interdependence, in the turbulent flow impinging on arrangements of yawed circular cylinders simulating inclined tube banks with square arrangement and a pitch to diameter ratio of 1.26. Measurements were performed with hot-wires and a pressure transducer. Behaviour of fluctuating quantities is described by means of dimensionless autospectral density functions and cross correlations. Experimental results indicates the presence of two different phenomena of vortex generation in inclined tube banks.

Identification of phase propagation of water level in tidal river by spectral analysis

Water levels of the five river stages in the Taipei Basin are analyzed by using spectral analysis in time-frequency domain through one-year hourly data. The autospectral and cross-spectral density function, coherence, phase angle and associated statistic parameters are studied. The semi-diurnal, diurnal and quarter-diurnal tidal components are significant for river stages, which are also apparently related to astronomical tides of M2, S2, N2, S1, O1 and M4, MK4 or MS4 respectively. The time lags versus propagation distance are shown as linear distribution for two stream systems. The time lags are 3.2, 4.0 and 2.5 (h) for semi-diurnal, diurnal and quarter-diurnal components in Tanshui River – Tanhan Stream system, while 3.5, 3.5 and 2.2 (h) in Tanshui River – Hsintien Stream system.

Spectral analysis of water level fluctuations in aquifers

The water level of a seawater gauging station and 18 groundwater wells coupled with atmospheric pressure in southwestern Taiwan are analyzed by using spectral analysis in time and frequency domain. The semidiurnal component is found to be the most significant signal from the measurement of water level and atmospheric pressure, and the diurnal component is less distinctive in part of water level and atmospheric pressure record. Although auto-spectral and cross-spectral density functions are significant in atmospheric pressure and water level, the pressure variations do not significantly affect the seawater and the majority of groundwater level in the study area with amplitude of time series observations. The astronomical tidal components are likely the main factor causing seawater and groundwater level to fluctuate in Pingtung, Taiwan. Time lags are estimated from 20 min to a few hours in aquifers. It concludes that the disturbance on groundwater levels from the effect of oceanic astronomical tide is different from the varying hydrogeological characteristics of aquifer. In this study, the spectral analysis of water level in time and frequency domains gives strong indications of sensitive variations to water level fluctuation.

On the fluctuating wall pressure field in tube banks

This paper presents the experimental analysis of pressure and velocity fluctuations of the cross flow in tube banks, with triangular and square arrangements, and four different aspect ratios. Air is the working fluid, driven by a centrifugal blower, passed by a settling chamber and a set of honeycombs and screens, before reaching the tube bank at an incidence angle of 90°. Both triangular and square arrangements have pitch-to-diameter ratios P/D=1.60, 1.26, 1.16 and 1.05, with Reynolds numbers, calculated with the tube diameter and the velocity of the flow in the narrow gap between the tubes, from Re=4×10 4 to 7×10 4. Velocity and velocity fluctuations were measured by a constant-temperature hot-wire anemometer, while pressure fluctuations were measured by a piezo-resistive pressure transducer mounted inside one of the tubes in the bank. Behavior of fluctuating quantities is described by means of dimensionless root mean square values and autospectral density functions, while their interdependence is discussed based on cross-correlation functions.