Auto Spectral Density Research Articles

Relationship between Casing Pressure and Non-Synchronous Vibration in an Axial Compressor

The relationship between aerodynamic forcing and non-synchronous vibration (NSV) in axial compressors remains difficult to ascertain from experimental measurements. In this work, the relationship between casing pressure and blade vibration was investigated using experimental observations from a 1.5-stage axial compressor under off-design conditions. The wavenumber-dependent auto-spectral density (ASD) of casing pressure was introduced to aid in understanding the characteristics of pressure fluctuations that lead to the aeromechanical response. Specifically, the rotor blade’s natural frequencies and nodal diameters could be directly compared with the pressure spectra. This analysis indicated that the rotating disturbances coincided with the first bending (1B) and second bending (2B) vibration modes at certain frequencies and wavenumbers. The non-intrusive stress measurement system (NSMS) data showed elevated vibration amplitudes for the coincident nodal diameters. The amplitude of the wavenumber-dependent pressure spectra was projected onto the single-degree-of-freedom (SDOF) transfer function and was compared with the measured vibration amplitude. The results showed a near-linear relationship between the pressure and vibration data.

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.

Balancing ensemble averaging and signal stationarity when processing acoustic data recorded during a rocket launch

There are many important details to consider when collecting acoustical data during a rocket launch including system noise floor, dynamic range and transducer sensitivity. In this talk, the choice of signal processing parameters will also be shown to be important. Since the pressures are created by turbulence, ensemble averaging is key to reducing random variation. As such, the use of a Hanning window with 50% overlap would be customary for performing this type of processing. However, as the rocket lifts off, the source location moves, and the data can only be considered stationary for short blocks of time. Therefore, the ability to average is limited by non-stationarity. To balance these competing phenomena, an adjustable windowing function such as the Tukey window may be more appropriate than Hanning. Noise data collected at two different launches will be used to compare of the Hanning window with 50% overlap to that using of the Tukey window with a taper of α = 0.25, which filters 12.5% of the signal at each extremity, with 87.5% overlap. The use of both window types will be compared when estimating auto spectral densities and integrated overall levels. The effect of blocksize will also be determined.

Evaluating a Poroelastic Model via Pore Pressure Signals in Seafloor Sediments

AbstractBelow a certain threshold of wave energy for a given depth, unconsolidated sediment should respond to wave action poroelastically. To this end, a generalized simple poroelastic model was applied to in situ data collected in coastal sediments near Oceanside, California. Pore pressure data were recorded by sensors attached to cylindrical unexploded ordinance surrogates, and water pressure sensors on bottom moorings. Orientation data were collected from inertial motion units attached to the surrogates, which were placed on the seabed and subsequently shallow buried during a high‐energy event on 13 February 2021. The model is characterized by two parameters. A consolidation coefficient controls the depth of diffusive flow, and Skempton's coefficient represents the ratio of the original signal into components transmitted by the sediment matrix and the pore fluid. The model assumes that the pore pressure signal is coherent with the seafloor signal; spectral coherence above 0.75 was used to select the frequency range from 0.05 to 0.2 Hz for the analysis. Spectral analysis methods were then applied to obtain averaged auto spectral densities of the pore pressure and bottom mooring signals over the coherent frequency band. Attenuation between sensor pairs was calculated. The results yielded burial depths over time for the surrogates that agreed with changes in significant wave heights, liquefaction, and recovery depths.

Limit strategy for multi-input multi-output random vibration control

Multi-input multi-output random vibration control combined with limit channels is a commonly used experiment scheme in dynamic environmental testing. This paper proposes a limit control strategy for multi-shaker random vibration tests. Compared to the traditional limit control method, the presented work can alleviate the undertesting phenomenon. The fundamental principles and difficulties in limit control are first formulated and analyzed. It is found that limit auto spectral density can be modified by simultaneously manipulating the control auto and cross spectral density. After that, the proposed limit control strategy is elaborated with a matrix presentation. An intermediate spectral matrix is defined and then it is used to obtain a redefined reference spectral matrix. The multi-input drive signals are generated and updated by the control and limit spectral correction algorithms. A two-input two-output numerical simulation with three limit channels and a tri-axial random vibration experiment are provided. The results from the simulation and experiment show the feasibility and validity of the proposed method.

Optical Diagnostics of Spanwise-Uniform Flows

Aerooptical aberrations along the spanwise direction of a canonical subsonic turbulent boundary layer were measured and studied nonintrusively using a Shack–Hartmann wave front sensor. It was demonstrated that in this case some important fluidic statistics in the wall-normal direction, like the mean velocity profiles, the local skin friction, and the spanwise integral scales, can be directly extracted from aerooptical aberrations. To avoid various spectral contamination in optical data at low frequencies, a model function for the deflection angle autospectral density at low frequencies was proposed. The spectral cross-correlation method and the dispersion method were used to extract the local convective velocities, and the dispersion analysis was demonstrated to be most accurate in computing the velocities. It was shown that it is possible to reconstruct the spectra above the Nyquist frequencies through the newly proposed stacking method. Convective velocities in the log region of the turbulent boundary layer were found to agree well with the direct measurements using a single hot wire. From the convective velocities, the local wall shear stress was nonintrusively extracted, using the Clauser method. Using corrected deflection angle spectra and the convective velocity, the local values of aerooptical aberrations were reconstructed. Finally, using the strong Reynold’s analogy, a wall-normal profile of the spanwise density correlation length was estimated and shown to be in good qualitative agreement with velocity-based spanwise length scales observed in the literature.

Phase-Structure in Conditional Simulation of Spatially Varying Ground Motion and Possible Influence on Structural Demand

Recorded ground motion is nonstationary in both intensity and frequency contents. Two methodologies were reported by the authors elsewhere for generating spatially varying ground motion (SVGM), namely, (i) auto-spectral density (ASD)-based framework, and (ii) evolutionary power-spectral density (EPSD)-based framework. While the former framework imparts nonstationarity through a uniform modulation (that accounts for nonstationarity only in intensities), the latter framework accounts for nonstationarity in both intensity and frequency contents. Reported EPSD-based framework was modeled through a decay function and a random component and was investigated only in the context of horizontal ground motion. Reported EPSD-based framework made two strong assumptions that need further investigation: (i) spatial variation of the random component was assumed to be frequency independent; and (ii) phase-structure of the ground excitation simulated around the reference station (with seed motion) was assumed to be same as that of the seed motion. This paper investigates the possible impact of these two assumptions on the simulated SVGM through appropriately revising the framework and introducing the phase-structure accordingly. Possible effects of the phase-structure on structural demand are investigated through an idealized long-span bridge. Revised EPSD-based framework is next assessed against the vertical recordings of SMART1 array along with the auto-spectral density (ASD) framework. Though spectral representation is nearly identical in both the frameworks, the acceleration time series simulated using the revised EPSD-based framework matches the recorded data better when compared with the ASD-based framework. Possible effect of spatially varying vertical ground motion on the seismic design is investigated through the same idealized bridge model. Significant increase in the demand of axial force in piers and mid-span moment in the deck are observed. Although these inferences are contingent on the idealized example considered for illustration, the spatially varying vertical ground motion is expected to contribute significantly to the seismic design of long-span bridges.

An experimental investigation of a rotationally oscillating cylinder

The flow patterns of the wake region of a rotationally oscillating cylinder were investigated experimentally by using the Particle Image Velocimetry (PIV) technique and dye visualization. The experiments were conducted at Reynolds number Re = 1000 and different values of oscillation amplitude (θA = 60°, 120°, 180°) and frequency ratio (FR = 0.8, 1.7, 3.3, 6.7). Dye visualizations, instantaneous vorticity contours, time-averaged streamlines, vorticity, streamwise and crossflow velocity contours, Reynolds stress correlations, turbulent kinetic energy (<TKE>) and autospectral density contours were analysed. For FR = 0.8, the vortices formation behind the cylinder wake disappeared and the only saddle point formation was observed at θA = 120° and θA = 180°. The maximum and minimum shear stress <u′v′> were obtained at FR = 0.8, θA = 180° and FR = 3.3, θA = 120°, respectively. The turbulent kinetic energy decreased with the increase in the frequency ratio at θA = 180°, and it has been observed that the vortex shedding weakens the interaction between the upper and lower vortices of the cylinder. The maximum decreasing in the drag coefficient of the stationary cylinder was by around 46% at FR = 6.7 θA = 120°. It is concluded that the rotationally oscillating cylinder has a significant effect on the cylinder wake region and changes the wake flow structures and vortex shedding patterns.

A novel framework for conditional simulation of fully nonstationary spatially varying ground motion field

SummaryExisting procedures for conditionally generating the spatially varying ground motion (SVGM) through the coherency‐based methods can be broadly categorized into two approaches: (i) cross‐spectral density (CSD)‐based procedures and (ii) auto‐spectral density (ASD)‐based procedures (reported by the authors elsewhere). CSD‐based procedures consider only the phase variability, whereas ASD‐based procedures account for phase as well as the amplitude variability. However, the ASD‐based framework and most of the CSD‐based frameworks simulate the stationary SVGM, and nonstationarity is imparted through the uniform modulation, ignoring the temporal variation of the frequency content. This paper proposes an evolutionary power spectral density (EPSD)‐based framework for the simulation of nonstationary SVGM. This framework is developed in two steps. First, a new methodology based on Hilbert transform is proposed to compute the nonstationary ground motion given the EPSD, modulating functions, and phase. Second, the ASD‐based framework reported by authors elsewhere is extended to account for the EPSD, and the associated nonstationary ground motion is simulated using the proposed methodology. Nonstationary ground motions thus simulated are assessed against SMART1 array recordings. The close resemblance between the simulated accelerogram and the recorded data indicates that the proposed EPSD based framework accounts not only for the phase and amplitude variabilities but also for the nonstationarity.

Electroadhesion between a flat touchscreen and the human finger with randomly self-affine fractal surface

In this study, the effects of finger roughness on the electrostatic potential, electrostatic field, and average effective squeezing pressure between a human finger and a touchscreen are calculated by the perturbation method. This theory is an extension of an earlier work by Persson. It is found that an additional potential <ϕ(2)> will appear between the solids when the roughness effect is considered in calculating the perturbation potential. This additional potential is still proportional to the distance ū from the bottom surface. Therefore, the effect of the roughness increases the effective potential <ϕ> between the two solids. As a result, the average electrostatic field and average effective squeezing pressure increase. Using the increased effective squeezing pressure, we obtain the contact area, average surface separation, and friction between a human finger and the surface of a touchscreen. The effect of the roughness of the finger skin on the increased average effective squeezing pressure (electroadhesion) increases the contact area and reduces the average surface separation between the finger skin and touchscreen. Therefore, the finger-touchscreen friction increases. The surface topography for the forefinger skin is also measured by atomic force microscopy to obtain more realistic results. The auto spectral density function for the forefinger skin surface is calculated as well.

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.

Spatially correlated vertical ground motion for seismic design

Spatial variation of vertical ground motion may have influence on the response of long span lifeline structures like bridges, pipelines, etc. However, studies specific to the spatial variability of vertical component of ground motion are limited in the literature when compared with the associated horizontal components. Based on the data recorded at SMART1 and LSST arrays, comparison of spatial variability of vertical and horizontal components is explored here using the coherency model reported by the authors elsewhere. Alternatively, Fourier amplitudes of horizontal components are often scaled through an empirical function to estimate that of the vertical components. Ratio of auto-spectral density (ASD) of horizontal to vertical ground accelerations is then investigated using the array recordings. Conditional simulation of spatially varying ground motion (CSSVGM) can be categorized into two different approaches: (i) (evolutionary) cross-spectral density (CSD) based procedures and (ii) auto-spectral density (ASD) based procedure. While the former assumes spatially uniform ASD and accounts only for the phase variability, the latter takes into the account the spatial variability of ASD and thereby accounts for both phase and amplitude variability. These frameworks do not differentiate between horizontal and vertical components. However, the results reported to date by most researchers are based only on the horizontal components. Spatially varying vertical components are next simulated in this paper using both the perspectives and assessed against the array recordings. An attempt has also been made to estimate the SVGM of the vertical components for a future event. Choice of functional form of ASD (of a seed ground motion) on the resulting spatially varying vertical ground motion is also investigated. Finally, empirical forms of vertical to horizontal (V/H) response spectral ratio reported in the prior art do not account for the spatial variability over the footprint of array, which is also investigated here.

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.

On Conditional Simulation of Spatially Varying Rotational Ground Motion

ABSTRACT Authors elsewhere reported two frameworks for conditional simulation of spatially varying translational ground motion, namely, (i) cross-spectral density (CSD) based framework and (ii) auto-spectral density (ASD) based framework. This paper investigates the applicability of both the frameworks for rotational components. Rotational components are extracted here using one of the Single Station Procedures reported in the literature. Spatially varying rotational ground motion for a future event is explored using a coherency model calibrated against a past event and an estimate of ASD of the seed (rotational) ground motion. Choice of representation of ASD is also investigated.

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.

Parameterisation of auto-spectral density of earthquake induced strong ground motions

This paper explores the possibility of a new parametric representation of auto-spectral density (ASD) that enables extraction of several meaningful insights. Recorded translational ground motions are considered first and the resulting parametric model is capable to address the scenario when seismic energy is distributed over multiple frequency bands. A slightly different form is developed to address the rotational ground motion. Variation of ASD over the footprint of seismic arrays, both large (SMART1) and dense (LSST), is studied. The assessment is based on spectral similitude using spectral contrast angles and distance correlation. Possible correlation of the parameters of the proposed ASD model against site and event characteristics is investigated based on selected ground motions from PEER database. Model parameters thus computed are used in synthetically predicting the ASD of ground motions at the LSST array and that shows good resemblance against the recorded events.

Unsteady surface pressure characteristics of asymmetrically beveled trailing edges

The characteristics of unsteady surface pressure (USP) created by turbulent flow over a family of asymmetrically beveled trailing edges were studied experimentally. The geometries had a trailing edge angle $$\theta =25^\circ$$ with a flat lower surface and a rounded upper surface with radii of curvature between zero and ten times the airfoil thickness. The Reynolds number was $$Re=2.1\times 10^6$$ based on chord. A detailed description of the USP and flow field around the trailing edge was obtained using remote microphone probes (RMP) and particle image velocimetry (PIV), respectively. The lower surface exhibited USP auto-spectral density magnitudes that were similar to those of a zero-pressure-gradient turbulent boundary layer at higher frequency. The low-frequency pressure fluctuations were influenced by the turbulent wake, leading to large increases in magnitude closer to the trailing edge. An empirical model of these results is proposed. The beveled upper surface was characterized by a region of favorable pressure gradient, followed by a strong adverse pressure gradient. The cases with smaller radius of curvature were found to exhibit separated flow over the trailing edge. The spectral magnitudes were largest in these regions, and significant attention is given to the proper scaling of these results. The PIV measurements provided the length and velocity scales for this purpose.

Phased array transformation methods to estimate non-compact jet noise source characteristics

This paper reviews the basis of the beamformer and polar correlation phased array methods and shows that these provide different information about axially distributed, non-compact noise sources, which nevertheless satisfy a simple integral relationship. The conventional beamformer method provides an image of the source power or auto spectral density, whereas the polar correlation method yields a ‘source strength’ which is an image of the axial wavenumber transform of the source cross-spectral density. However, the beamformer method can be generalised to provide an image of the source cross-spectral density. At first sight, the generalised beamformer method is therefore more useful for diagnostic purposes but the results presented here suggest that the combined effects of resolution and source convection place serious limitations on the source cross-spectral density image information. For the same reasons, although the source power or auto spectral density axial shape can be obtained with the conventional beamformer method, it cannot yield its absolute level for this type of source. The polar correlation method yields a source strength axial distribution at each ‘reference’ microphone, which when integrated over the source length, yields the far-field power or auto spectral density at that reference microphone. Therefore, the polar correlation source strength is arguably the more relevant quantity to measure when determining what proportion of the sound at a particular microphone position comes from each region of the jet axis, as a function of radiation angle.

Spatial variation and conditional simulation of seismic ground motion

Spatially varying ground motion (SVGM) may have influence on certain civil engineering structures with spatially extended superstructure and/or substructures. Conditional simulation of spatially varying ground motion (CSSVGM) may be viewed from two different perspectives. Most procedures available in the literature neglect the spatial variability in auto-spectral density (ASD) and estimate the SVGM through cross-spectral density (CSD) which was computed using the empirical coherency models. This paper proposes a coherency model that accounts for the spatial variability of ASD. A framework has been developed for the CSSVGM, through the mapping of both proposed coherency model and ASD over the footprint of an array. Current framework (existing in the literature) accounts for only the phase variability of SVGM while proposed framework accounts for both phase and amplitude variability. Ground motion generated from both perspectives is then assessed with the data recorded over SMART1 and LSST arrays. For the purpose of assessment, a definition of target spectrum based on the direction of arrival is explored. The effect of choice of coherency model on the simulated spatially varying ground motion is investigated first. Spectra resulting from both the perspectives are assessed against the target spectrum. An attempt has been made to predict the SVGM for a future event using a coherency model calibrated against a past event and an estimate of ASD of the seed ground motion. Finally, the effect of form of ASD (of a seed ground motion) on SVGM simulated is investigated by considering the ASD in different forms. Simulating SVGM through the mapping of both coherency model and ASD seems to be more appropriate than through CSD.

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.