Power Spectrum Density Function Research Articles

Numerical investigation of chaotic flow in a 2D closed-loop pulsating heat pipe

In the present study, investigation of chaotic flow in a two-dimensional closed-loop pulsating heat pipe has been carried out numerically. Constant temperature boundary conditions have been applied for the heating (evaporator) and the cooling (condenser) sections. The width of the tube was 3 mm and water was used as working fluid. Structured meshing configuration has been used and Volume of Fluid (VOF) method has been employed for two-phase flow simulation. The investigated temperature ranges for the evaporator and the condenser were 100–180 °C and 20–50 °C, respectively. The range of filling ratio was from 30 to 80%. Volume fraction of liquid and vapor in the pulsating heat pipe was investigated for different operating conditions. Time series analysis of the adiabatic wall temperature, correlation dimension, power spectrum density, Lyapunov exponent and autocorrelation function were used to investigate chaos in the pulsating heat pipe. Chaotic behavior was observed under several operating conditions. It was found that the time series has complicated, irregular and aperiodic behavior. Absence of dominating peaks in the power spectrum density curves denoted the existence of chaos in the pulsating heat pipe. It was observed that by increasing the filling ratio and evaporator temperature, the correlation dimension increases. Positive values of Lyapunov exponent were obtained for temperatures between 140 and 180 °C at filling ratio of 30%. At filling ratio of 75%, all of the Lyapunov exponents were positive for the temperature interval between 120 and 180 °C.

Fluid-Elastic Instability Tests on Parallel Triangular Tube Bundles with Different Mass Ratio Values under Increasing and Decreasing Flow Velocities

To study the effects of increasing and decreasing flow velocities on the fluid-elastic instability of tube bundles, the responses of an elastically mounted tube in a rigid parallel triangular tube bundle with a pitch-to-diameter ratio of 1.67 were tested in a water tunnel subjected to crossflow. Aluminum and stainless steel tubes were tested, respectively. In the in-line and transverse directions, the amplitudes, power spectrum density functions, response frequencies, added mass coefficients, and other results were obtained and compared. Results show that the nonlinear hysteresis phenomenon occurred in both tube bundle vibrations. When the flow velocity is decreasing, the tubes which have been in the state of fluid-elastic instability can keep on this state for a certain flow velocity range. During this process, the response frequencies of the tubes will decrease. Furthermore, the response frequencies of the aluminum tube can decrease much more than those of the stainless steel tube. The fluid-elastic instability constants fitted for these experiments were obtained from experimental data. A deeper insight into the fluid-elastic instability of tube bundles was also obtained by synthesizing the results. This study is beneficial for designing and operating equipment with tube bundles inside, as well as for further research on the fluid-elastic instability of tube bundles.

General AltBOC Modulation with Adjustable Power Allocation Ratio for GNSS

Alternative Binary Offset Carrier (AltBOC) modulation signal has the constraint of an equal power allocation scheme. Thus, it is not flexible enough to meet different requirements. To solve this problem, we propose a General AltBOC (GAltBOC) modulation. The proposed technique can achieve the same function as AltBOC. Meanwhile, its power allocation ratio can be adjusted when required. The detailed derivation of the GAltBOC modulation is presented, and three representative cases as well as the signal properties are discussed. To further improve the combination efficiency, we develop the Interlacing GAltBOC (IGAltBOC) modulation based on the GAltBOC modulation. The Power Spectrum Density (PSD) and correlation functions of the proposed signals are verified by simulation. The code tracking error and implementation complexities are analysed and compared with existing methods. Results show the proposed signals indeed enhance the flexibility of power allocation ratio with the same level code tracking accuracy. Compared with AltBOC modulation, the proposed signal can reach a higher combination efficiency at the expense of relatively higher implementation complexity. Compared with Asymmetric Constant Envelope Double-sideband (ACED) modulation, the proposed signals have significantly lower complexity of signal generation, which is helpful in simplifying the signal generation in the payload transmitter.

Singularity power spectrum distribution

Fractal and multifractal signal processing are hot topics in current studies. At present, the research mainly concentrates in fractal dimension, multifractal spectrum and time-singularity spectrum distribution, which are based on differentiability of fractal subsets, however fail to reflect the energy and power measurement of fractal singular subset. Therefore, singularity power spectrum distribution (SPSD) is proposed in this paper, based on the traditional power spectrum density function and multifractal spectrum. In theory, basic concept of SPSD is put forward based on the related singularity measure, the theoretical expression of SPSD is deduced, and the compatibility between SPSD and conventional power spectrum analysis is proved. In algorithm, the discrete approximation algorithm of SPSD for discrete fractal time series is introduced. Simulation based on the multifractal Brownian motion (mFBM) and actual sea clutter indicates that SPSD can reveal effectively the singular power distribution of sea clutter and mFBM, and identify fractal signals, even for those with approximate multifractal spectra or approximate power spectra. The SPSD will provide application prospect of multifractal signal processing, detection and distinguishing of multifractal time series.

Dynamic responses of a continuous beam railway bridge under moving high speed train with random track irregularity

This paper addresses the dynamic response of a continuous beam bridge with different levels of track irregularities under a single, moving high-speed train. The train is modeled as one-foot sprung masses. The bridge is described as an Euler-Bernoulli beam supported by several hinged supports. Rayleigh damping coefficients of the bridge are calculated by using the modal damping ratio. Random track irregularities are generated by power spectrum density functions. The interaction equation of motion is derived and then solved by using the Newmark-beta method combined with the Newton-Raphson method. The dynamic impact factors of a single-span simply supported bridge and a five-span continuous beam bridge under the same train are calculated and compared for verification. Additionally, a three-span continuous beam bridge with various damping ratios and track irregularities under a Korea Train Express (KTX) train is used as an example to investigate the dynamic impact factors at the midpoints of different bridge spans in both downward and upward directions, the deck rotations at the bridge supports, and the average maximum acceleration of the train bodies under different conditions.

Wu Guang High-Speed Rail Track Irregularity Power Spectrum Analysis

Irregularity is the locomotive and the main excitation source of vibration, is directly related to the smooth running of the train, safety and comfort, is to control the maximum operating speed of the train one of the main factors. The statistic specimen was collected by track geometry inspection car from Wuhan-Guangzhou high-speed rail. Based on the stationarity test of the specimen, Fast Fourier Transform (FFT) method was used to evaluate the spectrum of the whole specimen space. The power spectrum density (PSD) and related functions of track irregularity were obtained by MATLAB program. We analyzed it by comparing the fitting curve of the national speed lines and fitting curve of Qinhuangdao-Shenyang dedicated passenger railway line, by comparison, the Wuhan-Guangzhou high-speed railway track irregularity is much better than the national speed lines and Qinhuangdao-Shenyang dedicated passenger railway line. The parameter values of PSD fitting curve for track irregularity are obtained by the nonlinear curve-fitting algorithm in the least-squares sense, which has referencing value to maintenance high-speed rail.

Measurements and analysis of track irregularities on high speed maglev lines

Track irregularities have an obvious effect on the running stability and ride quality of maglev trains traveling at high speeds. We developed a measurement principle and data processing method which were applied to the high speed maglev line operating. The method, which includes partial filtering, integration, resampling of signal, and a low pass Butterworth filter, was used to calculate the irregularities of the maglev line. The spectra of the sample space were evaluated. A 7-parameter power spectrum density (PSD) function of line irregularities was fitted, based on the measured data. Analysis of the results showed that the maglev stator plane irregularities were better than conventional railway vertical rail irregularities when the wavelength was 5–100 m, and worse when the wavelength was 1–5 m. The PSD of maglev guidance plane irregularities was similar to that of cross level GRSHL (German railway spectra of high irregularity) when the wavelength was 10–100 m. The irregularities were clearly worse than cross level rail irregularities in a conventional railway when the wavelength was 1–10 m. This suggests that short-wavelength track irregularities of a maglev line caused by deviation and inclination of the stator plane should be minimized by strictly controlling the machining error of functional components during construction and maintenance.

An Improved Road Roughness Simulation Method Based on Trigonometric Series Method

Accurate road data is critical to vehicle ride comfort research. Trigonometric series (TS) method is widely used in road roughness construction, but the accuracy of the road data in time domain is not high and the power spectrum density (PSD) exits poor convergence problem. To solve the above problems, this paper has made two improvements: generate random frequency in each band using the local PSD function, optimize phase angle using the principle of minimum energy. The simulation results show that the improved method has higher precise and better convergence of PSD.

Spatially Varying Ground Motion Effects on Seismic Response of Adjacent Structures considering Soil-Structure Interaction

Spatial variation of seismic ground motions is caused by incoherence effect, wave passage, and local site conditions. This study focuses on the effects of spatial variation of earthquake ground motion on the responses of adjacent reinforced concrete (RC) frame structures. The adjacent buildings are modeled considering soil-structure interaction (SSI) so that the buildings can be interacted with each other under uniform and non-uniform ground motions. Three different site classes are used to model the soil layers of SSI system. Based on fast Fourier transformation (FFT), spatially correlated non-uniform ground motions are generated compatible with known power spectrum density function (PSDF) at different locations. Numerical analyses are carried out to investigate the displacement responses and the absolute maximum base shear forces of adjacent structures subjected to spatially varying ground motions. The results are presented in terms of related parameters affecting the structural response using three different types of soil site classes. The responses of adjacent structures have changed remarkably due to spatial variation of ground motions. The effect can be significant on rock site rather than clay site.

Modelling line edge roughness in periodic line-space structures by Fourier optics to improve scatterometry

In the present paper, we propose a 2D-Fourier transform method as a simple and efficient algorithm for stochastical and numerical studies to investigate the systematic impacts of line edge roughness on light diffraction pattern of periodic line-space structures. The key concept is the generation of ensembles of rough apertures composed of many slits, to calculate the irradiance of the illuminated rough apertures far away from the aperture plane, and a comparison of their light intensities to those of the undisturbed, ’non-rough’ aperture. We apply the Fraunhofer approximation and interpret the rough apertures as binary 2D-gratings to compute their diffraction patterns very efficiently as the 2D-Fourier transform of the light distribution of the source plane. The rough edges of the aperture slits are generated by means of power spectrum density (PSD) functions, which are often used in metrology of rough geometries. The mean efficiencies of the rough apertures reveal a systematic exponential decrease for higher diffraction orders if compared to the diffraction pattern of the unperturbed aperture. This confirms former results, obtained by rigorous calculations with computational expensive finite element methods (FEM) for a simplified roughness model. The implicated model extension for scatterometry by an exponential damping factor for the calculated efficiencies allows to determine the standard deviation σr of line edge roughness along with the critical dimensions (CDs), i.e., line widths, heights and other profile properties in the sub-micrometer range. First comparisons with the corresponding roughness value determined by 3D atomic force microscopy (3D AFM) reveal encouraging results.

Experimental Study on Fan-Induced Airflow Evaluation by Comparing the Power Spectrum, Turbulence Intensity and Draught Rate Methods

In hot climates a comfortable indoor environment is important. Mechanical fans are often introduced to cool the indoor air. However, it has been found that the airflow from such fans is not comfortable, especially compared with natural wind. Artificial airflow in an enclosure has been known to disturb hair, irritate eyes, and distract occupants. This paper presents the result of an experimental study on the characteristics of household airflow inducing appliances. The details of experiments carried out in the laboratory are described. Four kinds of common appliances were tested and two operating conditions were chosen. The power spectrum density function was used to evaluate the airflow dynamic characteristics.The preliminary conclusion shows that the power spectrum exponent is determined by the mean air velocity and the intermittence of the air velocity profiles. However, even mechanical airflow with dynamic characteristics such as shift and intermittence cannot exactly replicate natural wind. A small ratio of height to width of the fan airflow outlets is required so that more surrounding air can be involved in the flow, and more comfortable airflow is available for occupants.

Small damage detection of real steel bridge by using local excitation method

By using a piezoelectric actuator, a real steel bridge can be accelerated locally to detect the effect of small damage like fatigue crack and connection damage as a response to change of vibration. Power spectrum density (PSD) function of the response can give us the indication of the extent of damage before and after the damage. Detailed analysis of PSD before and after damage can give us the location and size (area) of damage. This paper shows the experimental result of damage detection by using local excitation method on a real bridge.

Wavelet-Based Evolutionary Response of Multispan Structures Including Wave-Passage and Site-Response Effects

Stochastic seismic wavelet-based evolutionary response of multispan structures including wave-passage and site-response effects is formulated in this paper. A procedure to estimate site-compatible parameters of surface-to-bedrock frequency response function (FRF) by using finite-element analysis of the supporting soil medium is proposed. The earthquake energy content is represented by a composite power spectrum density function contributed by the surface-to-bedrock FRF and bedrock power spectra. A long span multisupport structure is subjected to spatially varying differential support motions where the spatial-variability is represented by bedrock parametric coherency models and time-lags. In addition to the time-lags from wave-passage effects, the site-response effects from different soil conditions at the supports are characterized by frequency-dependent time-lags. In an illustrative case study, a three-span, two-dimensional hangar frame is analyzed using the proposed formulations. The time-lags resulting from site-response effects and computed by different FRFs show different variation in trends and frequency content. The site-response effect is found to introduce additional frequency nonstationarity and leads to an increase in the frame responses but with slower attenuation in time.

Random Response Analysis of a Large-Size Cooling Tower Subjected to the Stationary Earthquake Motion

The response of a large-size cooling tower with 250m high subjected to the seismic action are investigated by both random vibration theory and response spectrum method. Shell element is taken to model the tower body, and beam element is used for the circular foundation and supporting columns. The earthquake motion input is a colored filtered white noise model and mode superposition method is adopted to analyze the random response of the large-size cooling tower. The paper presents the power spectrum density functions (PDF) and standard deviation of the displacement of the top and characteristic node, and the analysis results indicate that the results of the stationary random vibration theory and the response spectrum method are the same order of magnitude. The power spectrum density function of the bottom node stress is obviously bigger than the one at the top and the throat, and the random response of meridonal stress is dominated at the top. In addition, the peak frequency position of the power spectrum density function is different from the corresponding stress.

Power Spectrum of Generalized Fractional Gaussian Noise

Recently, we introduced a type of autocorrelation function (ACF) to describe a long-range dependent (LRD) process indexed with two parameters, which takes standard fractional Gaussian noise (fGn for short) as a special case. For simplicity, we call it the generalized fGn (GfGn). This short paper gives the power spectrum density function (PSD) of GfGn.

One-dimensional autocorrelation and power spectrum density functions of irregular regions

Scanning probe microscopy (SPM) can be effectively used for evaluation of nanoscale roughness of surfaces obtained by different technological processes. Spectral properties of surface roughness can be evaluated using algorithms based on Fast Fourier Transform (FFT). For data that are not rectangular, this approach, however fails. In this paper we describe a modification of SPM data evaluation algorithms enabling to use FFT based approach even for irregular and non-continuous data. This opens novel possibilities in analysis of local surface roughness in many fields, e.g. on nanoparticles, semiconductor structures or any other nanostructured samples prepared using nanotechnology methods. Together with theoretical description of proposed method we present benchmarks for its performance and typical results of its application on different samples.

Cauchy‐Matern Model of Sea Surface Wind Speed at the Lake Worth, Florida

We study the Cauchy‐Matern (CM) process with long‐range dependence (LRD). The closed form of its power spectrum density (PSD) function is given. We apply it to model the autocovariance function (ACF) and the PSD of the sea surface wind speed (wind speed for short) observed in the Lake Worth, Florida, over the 1984–2006 period. The present results exhibit that the wind speed at the Lake Worth over 1984–2006 is of LRD. The present results exhibit that the CM process may yet be a novel model to fit the wind speed there.

Synthesis of Equivalent Load Conditions for Military Vehicles

The aim of this paper was the identification of the load conditions to consider during the design and assessment of military vehicles. This meant identifying test tracks and their corresponding ground speeds and track lengths, and to define their combinations that are useful to simulate the load spectrum representing the system/component life in an accelerated way. The result of this activity was the development of a formulation for the synthesis of a single power spectrum density function (PSD) representing multiple load conditions expressed by a set of PSD functions. This function is equivalent in terms of damage to the given PSD functions set. Another important result was the definition of a virtual test ring, equivalent to those defined in standards for equipment and supplies, but useful for the virtual check of the military vehicle integrity. This new formulation and the proposed test ring intend to supply tools that would be very useful in the early phases of vehicle design and assessment. In order to verify these results, numerical and experimental analyses of a generic military vehicle were undertaken. Results demonstrated the validity of the load synthesis formulation and the load combination that are useful for the assessment of military vehicle durability.

Viewing Sea Level by a One‐Dimensional Random Function with Long Memory

Sea level fluctuation gains increasing interests in several fields, such as geoscience and ocean dynamics. Recently, the long‐range dependence (LRD) or long memory, which is measured by the Hurst parameter, denoted by H, of sea level was reported by Barbosa et al. (2006). However, reports regarding the local roughness of sea level, which is characterized by fractal dimension, denoted by D, of sea level, are rarely seen. Note that a common model describing a random function with LRD is fractional Gaussian noise (fGn), which is the increment process of fractional Brownian motion (fBm) (Beran (1994)). If using the model of fGn, D of a random function is greater than 1 and less than 2 because D is restricted by H with the restriction D = 2 − H. In this paper, we introduce the concept of one‐dimensional random functions with LRD based on a specific class of processes called the Cauchy‐class (CC) process, towards separately characterizing the local roughness and the long‐range persistence of sea level. In order to achieve this goal, we present the power spectrum density (PSD) function of the CC process in the closed form. The case study for modeling real data of sea level collected by the National Data Buoy Center (NDBC) at six stations in the Florida and Eastern Gulf of Mexico demonstrates that the sea level may be one‐dimensional but LRD. The case study also implies that the CC process might be a possible model of sea level. In addition to these, this paper also exhibits the yearly multiscale phenomenon of sea level.

Numerical Study of Dynamic Response of Steel Deck Pavement under Traveling Random Vehicle Load

The steel deck pavement on long-span steel bridges is subjected to the heavy impact load imposed by the passage of millions of trucks during the several decades of its service life, and severe premature failures of steel deck pavement have appeared, especially the cracking. The irregularity of the pavement surface was simulated according to the power spectrum density function, and the random load was calculated according to the vehicle vibrating equation. Finite Element Method was used to build the vehicle-pavement coupling model. The effects of vehicle speed on the dynamic response of pavement were studied. Research results have proved that the maximum transversal tensile stress related to the cracking firstly increases and then decreases with the increase of vehicle speed.