Spectral Density Function Research Articles

Portable angle-resolved scattering system to measure high spatial frequency roughness for ultra-smooth surfaces

Ultra-smooth surfaces require stringent quality control of their high spatial frequency roughness (HSFR). Angle-resolved scattering (ARS) allows for fast, non-contact roughness measurement that is insensitive to environmental disturbances. However, there is a tradeoff between the roughness measurement bandwidth and the measurement speed for the current ARS methods. We propose a rapid ARS method for HSFR measurement. A prototype instrument is developed using 405 nm laser illumination and a CMOS sensor to capture the scattering distribution. By solving the inverse scattering problem under the Kirchhoff approximation, the power spectral density function can be obtained, from which the root mean square roughness is calculated. The method allows measurement of HSFR from 1 μm−1 to 2.5 μm−1 over a 2 mm area in one minute. Experiments on polished metal flats showed excellent agreement between our method and atomic force microscopy.

Contact mechanics modeling of fractal surface with complex multi-stage actual loading deformation

The contact mechanical behavior of rough surfaces is related to the friction and wear of mechanical components, and also has an important impact on the dynamic performance and force transfer characteristics of assembly surfaces. This paper aims to solve the complex multi-stage mechanical deformation mode of the loading surface, and establishes all multi-stage contact mechanical models involved in the actual loading deformation process from the perspective of the actual deformation and critical deformation of the asperity. Firstly, based on the three-dimensional fractal contact theory, the force deformation relationship of a single asperity during the full deformation stage of loading is constructed. Then, six critical contact areas and four critical deformation quantities of a multi scale asperity are derived. Finally, the complex multi-stage deformation contact mechanical models of three-dimensional fractal surfaces under actual loading are established. The area power spectral density (APSD) function spectrum of rough surface under different fractal parameters, as well as the variation of contact load, contact stiffness, and contact area are analyzed numerically. Compared with several classical models, the rationality of the proposed model is verified. This study can be used as the basis for constructing the overall dynamic model of an assembly system

Analysis of random induced dynamic response of rural roads considering friction effect and nonlocal effect under the load of construction vehicles

Abstract The objective of this paper is to propose a novel computational model for solving the problem of accurately evaluating the randomly induced road vibration response of engineering vehicles traveling on rural roads. The computational model, first, focuses on the unique pavement characteristics of rural roads, constructs a tire grounding function model and innovatively introduces a dynamic friction factor, and successfully develops a coupled stochastic excitation system model for the interaction between the dynamic loads of 1/4 vehicle tires and the pavement of rural roads by applying the power spectral density function of the rural roads and combining it with the elastic roller model of the vehicle tires. Second, considering the nonlocal superposition effect of the soil skeleton of the roadbed, a coupled vibration response model of a 1/4 automobile rural road is successfully developed, and a validation method is given. Finally, the coupled vibration response characteristics of engineering vehicles and rural roads under random excitation at different speeds are analyzed. The analysis results show that the model proposed in this paper can well predict the degree and influence the range of rural road vibration caused by random excitation of construction vehicles traveling at any speed.

Some remarks on compositeness of * *Supported in part by the National Nature Science Foundations of China (12335002, 12375078, 11975028). H.Q. Zheng and Z. Xiao are also Supported by "the Fundamental Research Funds for the Central Universities"

Recently, the LHCb experimental group found an exotic state from the process. A key question is whether it is just a molecule or may have a confined tetraquark ingredient. To investigate this, different methods were used, including a two-channel ( and ) K-matrix unitarization and a single-channel Flatté-like parametrization method analyzed utilizing the pole counting rule and spectral density function sum rule. These analyses demonstrated that is a molecular state, although the possibility that there may exist an elementary ingredient cannot be excluded, according to an approximate analysis of its production rate.

Failure probability estimation of dynamic systems employing relaxed power spectral density functions with dependent frequency modeling and sampling

This work addresses the critical task of accurately estimating failure probabilities in dynamic systems by utilizing a probabilistic load model based on a set of data with similar characteristics, namely the relaxed power spectral density (PSD) function. A major drawback of the relaxed PSD function is the lack of dependency between frequencies, which leads to unrealistic PSD functions being sampled, resulting in an unfavorable effect on the failure probability estimation. In this work, this limitation is addressed by various methods of modeling the dependency, including the incorporation of statistical quantities such as the correlation present in the data set. Specifically, a novel technique is proposed, incorporating probabilistic dependencies between different frequencies for sampling representative PSD functions, thereby enhancing the realism of load representation. By accounting for the dependencies between frequencies, the relaxed PSD function enhances the precision of failure probability estimates, opening the opportunity for a more robust and accurate reliability assessment under uncertainty. The effectiveness and accuracy of the proposed approach is demonstrated through numerical examples, showcasing its ability to provide reliable failure probability estimates in dynamic systems.

A Subject-Specific Attention Index Based on the Weighted Spectral Power.

As an essential cognitive function, attention has been widely studied and various indices based on EEG have been proposed for its convenience and easy availability for real-time attention monitoring. Although existing indices based on spectral power of empirical frequency bands are able to describe the attentional state in some way, the reliability still needs to be improved. This paper proposed a subject-specific attention index based on the weighted spectral power. Unlike traditional indices, the ranges of frequency bands are not empirical but obtained from subject-specific change patterns of spectral power of electroencephalograph (EEG) to overcome the great inter-subject variance. In addition, the contribution of each frequency component in the frequency band is considered different. Specifically, the ratio of power spectral density (PSD) function in attentional and inattentional state is utilized to calculate the weight to enhance the effectiveness of the proposed index. The proposed subject-specific attention index based on the weighted spectral power is evaluated on two open datasets including EEG data of a total of 44 subjects. The results of the proposed index are compared with 3 traditional attention indices using various statistical analysis methods including significance tests and distribution variance measurements. According to the experimental results, the proposed index can describe the attentional state more accurately. The proposed index respectively achieves accuracies of 86.21% and 70.00% at the 1% significance level in both the t-test and Wilcoxon rank-sum test for two datasets, which obtains improvements of 41.38% and 20.00% compared to the best result of the traditional indices. These results indicate that the proposed index provides an efficient way to measure attentional state.

Data-driven and physics-based interval modelling of power spectral density functions from limited data

In stochastic dynamics, ensuring the structural reliability of buildings and structures is of paramount importance, especially when subjected to environmental loads such as wind or earthquakes. To adequately address these loads and the uncertainties associated with them, it is often necessary to utilise advanced load models, frequently expressed using a power spectral density (PSD) function. The construction of these load models becomes challenging when only limited data is available and meaningful statistics cannot be reliably derived. To address this issue, safety bounds are commonly used in load models to account for uncertainties. Many PSD functions, such as the Clough–Penzien model, are described by parameters with a physical background and can therefore reflect the real case. The aim of this work is to expand these physical parameters in order to account for uncertainties. For this purpose, bootstrapping is used to derive more reliable statistics. By introducing a scaling parameter that allows for flexibility, bounds of the data set can be derived. Consequently, suitable PSD models are fitted to the derived bounds. The PSD function is thus represented by intervals for its physical properties instead of relying on discrete values. When applying such a bounded load model to a structure, advanced interval propagation schemes can be utilised to bound the failure probability.

A new probabilistic long-period critical excitation procedure for isolated building structures

The present paper develops a new procedure for finding the most unfavorable long-period excitation for isolated building structures based on the probabilistic critical excitation method. The upper bound of earthquake input energy per unit mass is considered the problem’s constraint, and a modified power spectral density (PSD) function is proposed to conform to the new constraint. It is shown that the new constraint can be used as a criterion to estimate the possible range of input energy of similar earthquakes. In addition, the new PSD function can control the excitation’s intensity. Finally, three base-isolated shear buildings modeled as multi degree of freedom systems with nonproportional damping are considered, and the critical excitations for each model are found based on the proposed method. To examine the reliability of the results, three actual accelerograms with a considerably high level of total input energy are selected as benchmarks and linear dynamic analyses are conducted using these accelerograms along with the generated critical excitations. The results show that the generated long-period excitations can better estimate the structural behavior (i.e., maximum displacement, drift, and absolute acceleration of stories) than the actual benchmark accelerograms.

Site-Specific Aseismic Design of Multi-Storeyed Buildings Using Optimum Tuned Mass Damper Inerter

ABSTRACT The effectiveness of the tuned mass damper inerter (TMDI) in reducing the vibration of building structures under site-specific earthquake excitation is investigated. The site is Guwahati, Assam, which lies in the most severe seismic intensity zone in India. In this paper, the optimization of the TMDI design parameters is carried out for the site-specific input derived for the building site by a modulated Clough-Penzien (C-P) spectrum fitted to the power spectral density function obtained from a strong motion model of the site. All possible topologies of the TMDI, with one terminal of the inerter being connected to the damper mass attached to the top storey of the example buildings, and the other terminal being connected to any other floor, are investigated. The structure-TMDI system is analyzed both in the frequency-domain and in the time-domain. A numerical study is conducted with two example building structures. Optimization of design parameters of the TMDI is carried out using the technique of simulated annealing in the frequency-domain using the site-specific modulated Clough-Penzien spectrum as input. The performance of the optimal TMDI cases is evaluated by subjecting the example structures to 10 site-specific synthetically generated accelerograms. Results indicate that the TMDI is superior to the TMD for all topologies of the TMDI in case of the 3-storieed structure; and for topologies of the TMDI in which the inerter spans more than 4 floors for the 8-storied structure, with improved reductions in top-floor displacement, acceleration, and stroke length.

Gravitational partial-wave absorption from scattering amplitudes

We study gravitational absorption effects using effective on-shell scattering amplitudes. We develop an in-in probability-based framework involving plane- and partial-wave coherent states for the incoming wave to describe the interaction of the wave with a black hole or another compact object. We connect this framework to a simplified single-quantum analysis. The basic ingredients are mass-changing three-point amplitudes, which model the leading absorption effects and a spectral-density function of the black hole. As an application, we consider a non-spinning black hole that may start spinning as a consequence of the dynamics. The corresponding amplitudes are found to correspond to covariant spin-weighted spherical harmonics, the properties of which we formulate and make use of. We perform a matching calculation to general-relativity results at the cross-section level and derive the effective absorptive three-point couplings. They are found to behave as OGNewtons+1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O}\\left({G}_{\ extrm{Newton}}^{s+1}\\right) $$\\end{document}, where s is the spin of the outgoing massive state.

On frequency‐domain estimation of increase in design yield force levels of SDOF structures due to multiplicity of earthquake events

AbstractThe current earthquake design philosophy based on only the most critical earthquake may prove inadequate when the smaller events occurring before this event cause significant damage to the structure and repairs become infeasible. The design force levels may therefore be raised using the modified design force ratio, defined as the ratio of the yield force level for a specified damage level under all the seismic events to the yield force level for the same damage level under only the most critical event. This study considers the updating of the existing frequency‐based approach, using the power spectral density function (PSDF)‐based characterization of design ground motion, for the estimation of modified design force ratio spectrum. First, an empirical expression developed in the companion paper for modifying the damping of the equivalent linear oscillator is used such that the use of the PSDF compatible with 5%‐damping response spectrum leads to correct peak response, even when the equivalent damping ratio exceeds 5%. Next, the frequency‐domain design force ratio estimates are benchmarked in the case of steel and reinforced concrete oscillators by comparing those with the time‐domain estimates of equivalent Bouc–Wen oscillators over various sequences of events and by suitably adjusting the stiffness degradation parameter. It is shown in the case of a hypothetical seismic scenario that the optimal values of this parameter as 2.0 and 1.7 work well for the steel structures and reinforced concrete structures with high stiffness degradation respectively. Also, the proposed approach needs to be improved further for applicability in the case of reinforced concrete structures exhibiting significant pinching behavior.

Dynamic analysis of a highway bridge beam under the passage of compound heavy trucks with multiple trailers

PurposeRealistic composite vehicles with 2, 3, 5 and 9 axles, consisting of a truck with one or two trailers, are addressed in this paper by computational models for vehicle–bridge interaction analysis.Design/methodology/approachThe vehicle–bridge interaction (VBI) models are formed by sets of 2-D rigid blocks interconnected by mass, damping and stiffness elements to simulate their suspension system. The passage of the vehicles is performed at different speeds. Several rolling surface profiles are admitted, considering the maintenance grade of the pavement. The spectral density functions are generated from an experimental database to form the longitudinal surface irregularity profiles. A computational code written in Phyton based on the finite element method was developed considering the Euler–Bernoulli beam model.FindingsSeveral models of composite heavy vehicles are presented as manufactured and currently travel on major roads. Dynamic amplification factors are presented for each type of composite vehicle.Research limitations/implicationsThe VBI models for compound heavy vehicles are 2-D.Social implicationsThis work contributes to improving the safety and lifetime of the bridges, as well as the stability and comfort of the vehicles when passing over a bridge.Originality/valueThe structural response of the bridge is affected by the type and size of the compound vehicles, their speed and the conservative grade of the pavement. Moreover, one axle produces vibrations that can be superposed by the vibrations of the other axles. This effect can generate not usual dynamic responses.

Testing serial independence of object-valued time series

Summary We propose a novel method for testing serial independence of object-valued time series in metric spaces, which are more general than Euclidean or Hilbert spaces. The proposed method is fully nonparametric, free of tuning parameters and can capture all nonlinear pairwise dependence. The key concept used in this paper is the distance covariance in metric spaces, which is extended to the autodistance covariance for object-valued time series. Furthermore, we propose a generalized spectral density function to account for pairwise dependence at all lags and construct a Cramér–von Mises-type test statistic. New theoretical arguments are developed to establish the asymptotic behaviour of the test statistic. A wild bootstrap is also introduced to obtain the critical values of the nonpivotal limiting null distribution. Extensive numerical simulations and two real data applications on cumulative intraday returns and human mortality data are conducted to illustrate the effectiveness and versatility of our proposed test.

Offshore Triceratops With Elliptical Legs Under Postulated Failure of Tethers

Offshore Triceratops are classified as form-dominant structures possessing the novelty of counteracting the lateral loads with material strength and geometric form. The deck is supported by the buoyant legs, which are positioned on the seabed using taut-moored tethers. Ball joints connect the legs with the deck and help partially isolate the deck to remain horizontal under waves and wind. While offshore structures commonly have tubular legs, the current study investigates Triceratops with elliptical legs under the postulated failure of tethers. Detailed dynamic analysis under postulated failure conditions is carried out using ANSYS AQWA, while the LIBRIUM analysis is used to obtain the equilibrium position of the platform under intact and postulated failure conditions. Results show that under postulated failure conditions, the peaks of the power spectral density function of the pitch response are seen closer to its natural frequency and the input wave frequency. Ball joints restrain this rotation from transferring to the deck, conforming to one of the advantages of its existence. The fatigue life of tethers calculated for different load cases under intact and postulated failure conditions helps understand the stability conditions of the platform.

Vibration characteristic analysis of three-dimensional sandwich cylindrical shell based on the Spectro-Geometric method

This paper presents the numerical investigations on the free and random vibration properties of thick cylindrical shells under the three-dimensional (3-D) elasticity theory. The analysis of these properties is conducted using the Rayleigh-Ritz method in conjunction with the Spectro-Geometric method (SGM). The cylindrical shell considered in this study is composed of fiber-reinforced composite and functionally graded porous graphene platelet reinforced composites (FGP-GPLRC). To simulate different boundary conditions, an artificial spring technique is utilized. The displacement components, as determined by SGM, are incorporated into the energy expression of the cylindrical shell. By applying the Rayleigh-Ritz method, the intrinsic frequencies and vibration modes of the cylindrical shell are obtained. Additionally, the power spectral density (PSD) function of the cylindrical shell under random excitation is obtained by the Pseudo-Excitation method (PEM). The accuracy and effectiveness of the present method are verified through comparative studies with existing literature and finite element method (FEM). Furthermore, an investigation on the effects of various parameters on the intrinsic frequency and random response of the cylindrical shell is conducted.

Multi-Wavelength Angle-Resolved Scattering of Randomly Rough Surfaces Based on the Scalar Diffraction Theory

Angle-resolved scattering was measured for four samples of silicon exhibiting different surface roughnesses. The measurements were performed for three wavelengths: 457.9 nm, 514.5 nm, and 647.1 nm. Three approaches were used to evaluate the experimental data. The first approach corresponds to the exact formula derived using the scalar diffraction theory. This formula is quite complicated, and numerical methods must be used for its evaluation. For this reason, another two approaches representing approximations by much simpler formulae were considered. The use of several wavelengths allowed us not only to recover the power spectral density function in a limited interval of spatial frequencies but also to determine the total rms values of the heights, which represent the quantity of roughness for all spatial frequencies. The possibility of recovering the total rms values of the heights using the multi-wavelength approach is the most important result of this work. The results obtained from the scattering experiment and atomic force microscopy are compared.

Advanced morphological characterization of DC sputtered copper thin films

In this paper, Cu thin films were successfully deposited on glass substrates using DC magnetron sputtering at varying deposition times. The deposition time was varied as 5, 9, 11 and 17[Formula: see text]min. The obtained Cu thin films were analyzed for morphology and topography using atomic force microscopy (AFM). The size of the surface structures/grains was seen to evolve with deposition time. The conventional/statistical, fractal and multifractal analyses were carried out on AFM images using existing imaging algorithms. The arithmetic roughness and interface width parameters were seen to evolve with the sputtering time. The autocorrelation and height–height correlation functions revealed that the surfaces of all the Cu thin films exhibited self-affine character, but were not mounded properties. The fractal dimensions computed using box counting and power spectral density functions revealed that larger dimensions were associated with larger surface features. The lacunarity coefficients were too small indicating that the surfaces were generally deficient in porosity and other defects. The multifractal analyses revealed that spatial roughness does not exhibit linear relationship with the deposition time. The study reveals that surface evolution and nanoscale behavior is significantly influenced by the deposition time although a linear relationship is not established.

Developmental changes in endogenous testosterone have sexually-dimorphic effects on spontaneous cortical dynamics.

The transition from childhood to adolescence is associated with an influx of sex hormones, which not only facilitates physical and behavioral changes, but also dramatic changes in neural circuitry. While previous work has shown that pubertal hormones modulate structural and functional brain development, few of these studies have focused on the impact that such hormones have on spontaneous cortical activity, and whether these effects are modulated by sex during this critical developmental window. Herein, we examined the effect of endogenous testosterone on spontaneous cortical activity in 71 typically-developing youth (ages 10-17 years; 32 male). Participants completed a resting-state magnetoencephalographic (MEG) recording, structural MRI, and provided a saliva sample for hormone analysis. MEG data were source-reconstructed and the power within five canonical frequency bands (delta, theta, alpha, beta, and gamma) was computed. The resulting power spectral density maps were analyzed via vertex-wise ANCOVAs to identify spatially specific effects of testosterone and sex by testosterone interactions, while covarying out age. We found robust sex differences in the modulatory effects of testosterone on spontaneous delta, beta, and gamma activity. These interactions were largely confined to frontal cortices and exhibited a stark switch in the directionality of the correlation from the low (delta) to high frequencies (beta/gamma). For example, in the delta band, greater testosterone related to lower relative power in prefrontal cortices in boys, while the reverse pattern was found for girls. These data suggest testosterone levels are uniquely related to the development of spontaneous cortical dynamics during adolescence, and such levels are associated with different developmental patterns in males and females within regions implicated in executive functioning.

Chemical Exchange Rate Study by NMR CPMG Method

Analysis of the NMR CPMG method is presented that enables direct sampling of the spectral-density function of the chemical exchange processes. The approach is demonstrated on a solution of sucrose in water. The result confirms that the method can provide insight into the details of the dynamics of molecular conformations beyond a single-parameter description by an exchange rate. The results of the method are not limited to a single exchange process but can be of advantage if a large and potentially unknown number of exchange processes is contributing to the dynamics of a spin system.

Comparing CMIP6 Climate Model Simulations of Annual Global Mean Temperatures to a New Combined Data Product

AbstractA new statistical approach to validating climate models is introduced. First, five observational estimates of global mean surface temperature with estimated standard errors are combined into one data product, latent observed annual global temperature anomalies for the years 1880–2014, using a Bayesian hierarchical statistical approach. Summarizing these observed anomalies, estimates of smooth trend, levels of warming, and residual dependence as summarized by the spectral density function, are provided with simultaneous 95% credible bands. Then, corresponding estimates of smooth trend, levels of warming, and residual dependence are produced for sixth Climate Model Intercomparison Project (CMIP6) historical simulations analyzed at the annual global temperature anomaly scale, and compared to these bands. Among our results, we find that 93 out of the 318 CMIP6 historical model runs contain trends fitting inside the simultaneous bands for the smooth trend constructed from the data products, and for residual temporal dependence 69 out of 318 model runs contain spectral density functions that are within the corresponding data‐product‐based‐bands. We estimate the mean global temperature increase from 1995–2014 relative to 1880–1899, from the data product, to be 0.896°C with a 95% credible interval of between 0.877 and 0.915. We find that 14 CMIP6 model runs agree with this interval, 197 model runs lead to a smaller temperature increase globally, and 107 model runs lead to a larger temperature increase.