Spectrum Representation Method Research Articles

Accurate Spectrum Map Construction for Spectrum Management Through Intelligent Frequency-Spatial Reasoning

Spectrum maps are of crucial importance for realizing efficient spectrum management in the sixth-generation (6G) wireless communication networks. However, existing spectrum map construction schemes mainly depend on spatial interpolation or just simply exploit the frequency correlation and cannot accurately construct the spectrum map when measurement data at the target frequency are not available. To overcome this challenge, we propose two accurate spectrum map construction schemes using different intelligent frequency-spatial reasoning methods. The frequency correlation among different spectrum maps at different frequencies is fully exploited to construct highly accurate spectrum maps of the frequencies without spectrum data by combining the joint frequency-spatial spectrum representation method with deep learning data-driven techniques. Specifically, a joint three-dimensional spectrum representation model is established and both a novel autoencoder network and a novel conditional generative adversarial network suitable for processing the three-dimensional spectrum data are proposed to realize the intelligent frequency-spatial reasoning. Simulation results demonstrate that our proposed schemes are superior to the benchmark schemes in terms of the spectrum map construction accuracy. Moreover, simulation results demonstrate that our proposed neural networks have a fast convergence speed, which achieves a better tradeoff between the computation efficiency and the construction accuracy.

Simulation of fully nonstationary random processes using generalized harmonic wavelets

Simulation of nonstationary random processes plays an important role to probabilistic response analysis of structures and systems under stochastic excitations via Monte Carlo methods. Based on the evolutionary spectral representation theory, this article proposes a novel approach to simulate one-dimensional nonstationary random processes by using generalized harmonic wavelet (GHW). According to the explicit relationship between the evolutionary power spectral density (EPSD) and GHW coefficients, the samples of a random process can be generated by superposing GHWs with stochastic phase angles. The attractive features of the proposed approach are (1) the sample time histories obtained by the proposed method can accurately match the target EPSD and reflect the evolutionary probabilistic characteristics of the random process, (2) the number of GHWs used in the simulation is fixed due to the constraint relationship between the frequency and time resolutions of GHWs, and (3) the proposed method has better computational efficiency than the classical spectrum representation method (SRM). To demonstrate the accuracy and efficiency of the proposed GHW-based approach, three case studies involving the generation of time history samples from a given EPSD model, the simulation of an actual earthquake record, and a comparison between the proposed method and the SRM are presented respectively.

Dynamic reliability assessment of nonlinear structures using extreme value distribution based on L-moments

In this paper, an efficient method using the linear moments (L-moments) is proposed for dynamic reliability assessment of nonlinear structures subjected to non-stationary ground motions. The proposed method comprises three main steps. First, the extrema of structural responses are obtained from the random function-spectral representation model (RFSRM) and nonlinear time history analysis, in which the principal points are first combined with the RFSRM and a sampling strategy is suggested to determine the final samples of extrema by deleting close values. Second, after the samples of extrema are obtained, the first four L-moments can be estimated from their definitions. Finally, using the first four L-moments of extrema of structural responses, the probability distribution of extrema is approximated by a cubic normal distribution based on the L-moments and the corresponding failure probability of a nonlinear structure is calculated. Three numerical examples are presented to demonstrate the efficiency, accuracy, and usefulness of the proposed method for the dynamic reliability assessment of nonlinear structures, and the conventional spectrum representation method and subset simulation method are used for comparison.

Wheel–rail stochastic dynamics and rail wear analysis of small radius curved sections of a tram line based on generalized probability density evolution

Compared with ordinary railways, the curve radius of tram lines tends to be smaller, with minimum values of only 30 m. Therefore, wheel–rail interaction is more intense and complicated in sections of small radius tram line curves. Using a stochastic variable sample set based on a generalized probability density evolution method, the stochastic variable–spectrum representation method was used to generate a time-domain sample set of stochastic track irregularities. By inputting the stochastic set of track irregularities into a tram-track coupled dynamic system model, the stochastic dynamic response of the coupled dynamic system can be obtained. Moreover, by substituting the stochastic dynamic system response into the generalized probability density evolution formula, the process of probability density evolution of each evaluation index can be obtained by the finite difference method. Finally, the dynamic response of the tram-track coupled dynamic system can be evaluated by the probability distribution of each index. By setting a series of specific groove rail wear values, a tram-track coupled dynamic analysis was carried out, and compared with the specification requirements, vehicle safety limits under different wear values were obtained. This research has great engineering value for guiding the routine maintenance of small radius curve sections of trams.

Rapid and simultaneous determination of physical and chemical properties of asphalt by ATR-FTIR spectroscopy combined with a novel calibration-free method

Determining wax content, softening point, and penetration of asphalt products by traditional methods is too time-consuming to meet the instant need in practice. Although infrared spectroscopy combined with multivariate calibration may realize rapid determination of asphalt, its modeling and maintenance are very labor-intensive and challenging. In this paper, a novel method combining attenuated total reflectance-Fourier transform infrared spectroscopy (ATR-FTIR) with a fast algorithm of spectrum representation (SR) was proposed to rapidly and expediently determine the properties. The proposed method achieves calibration-free, effectively overcoming the drawback of the modeling methods. The feasibility of the new method was demonstrated using 431 asphalt samples produced by different kinds of crude oil. The root mean standard error of prediction (RMSEP) of wax content, softening point, and penetration by SR method are 0.14%, 0.55 °C and 4.71 (0.1 mm), respectively. Each of them is below the reproducibility of corresponding standard test method. Moreover, the new method is compared with other two commonly used methods, partial least squares regression (PLS) and local modeling by densification (LMD), in detail. The results show that the new method not only can solve the disadvantages of PLS modeling effectively, but also is remarkably superior to LMD method, in repeatability and speed, and robustness for predicting the sample in the region with lower density and unreasonable distribution of the samples in data bank.

Effects of fundamental factors on coupled vibration of wind-rail vehicle-bridge system for long-span cable-stayed bridge

In a wind-vehicle-bridge (WVB) system, there are various interactions among wind, vehicle and bridge. The mechanism for coupling vibration of wind-vehicle-bridge systems is explored to demonstrate the effects of fundamental factors, such as mean wind, fluctuating wind, buffeting, rail irregularities, light rail vehicle vibration and bridge stiffness. A long cable-stayed bridge which carries light rail traffic is regarded as a numerical example. Firstly, a finite element model is built for the long cable-stayed bridge. The deck can generally be idealized as three-dimensional spine beam while cables are modeled as truss elements. Vehicles are modeled as mass-spring-damper systems. Rail irregularities and wind fluctuation are simulated in time domain by spectrum representation method. Then, aerodynamic loads on vehicle and bridge deck are measured by section model wind tunnel tests. Eight vertical and torsional flutter derivatives of bridge deck are identified by weighting ensemble least-square method. Finally, dynamic responses of the WVB system are analyzed in a series of cases. The results show that the accelerations of the vehicle are excited by the fluctuating wind and the track irregularity to a great extent. The transverse forces of wheel axles mainly depend on the track irregularity. The displacements of the bridge are predominantly determined by the mean wind and restricted by its stiffness. And the accelerations of the bridge are enlarged after adding the fluctuating wind.

Analysis and Optimisation of Wind-Induced Vibration Control for High-Rise Chimney Structures

Wind is a key factor when determining the safety of high-rise structures, such as buildings, chimneys, or towers. Using dampers to control wind-induced vibration is a safe, effective, and economical method for high-rise structures to employ. In this paper, viscoelastic dampers (VEDs) were used to reduce the dynamic responses of a 75-metre-high chimney. First, a simulation method for the stochastic wind field, based on the modified Fourier spectrum, was proposed. The method provided the accurate data of the wind velocity time history, which then simulated wind pressure through the use of a numerical wind tunnel. Then, the finite element model for the Madagascar chimney structure was built, and a wind-induced vibration analysis of the structure with and without VEDs was carried out under the simulated wind excitation. The optimisation – method, based on the genetic algorithm, was used to optimise the location of the VEDs. It was concluded that the accuracy of the modified Fourier spectrum method (MFSM) was greatly improved, when compared to the spectrum representation method of simulating the stochastic wind field. VEDs can effectively reduce the dynamic responses of chimney towers, especially for the displacement responses. In addition, the proposed optimisation method quickly determined the optimum positions and necessary quantities of VEDs to use, which yielded effective vibration mitigation.

Anisotropic dynamics of optical vortex-beam propagating in biaxial crystals: a numerical method based on asymptotic expansion

One difficulty of angular spectrum representation method in studying optical propagation inside anisotropic crystals is to calculate the double integrals containing highly oscillating functions. In this paper, we introduce an accuracy and numerically cheap method based on asymptotic expansion theory to overcome this difficulty, which therefore allows to compute optical fields with arbitrary incident beam and is not restricted to the paraxial limit. This numerical method is benchmarked against the analytical solutions in uniaxial crystals and excellent agreements between them are obtained. As an application, we adopt it to investigate the propagation of a Gaussian vortex-beam in a biaxial crystal. The general features of anisotropic dynamics and power conversion between field components are revealed. The numerical results is interpreted by making appropriate analytical approximation to the wave equations.

Rotational Turbulent Wind Field Simulation of Wind Turbine

In order to accurately obtain the influence of rotational effect on fluctuating component of turbulent wind acted on wind turbine, rotational Fourier spectrum with considering rotational effect of rotor was deduced. Physical nature of the rotational Fourier spectrum embodied by coherence function and phase lag was indicated. Auto power spectral density and cross power spectral density of rotational Fourier spectrum with introducing phase lag were proposed. The spectrum matrix constructed by the module of rotational Fourier spectrum was decomposed with Cholesky's method, according to the spectrum representation method with introducing phase lag, the random turbulent wind speed field was generated by superposing a set of cosine functions. Finally, an example involving simulation of the longitudinal turbulent wind velocity time series of a 1.5 MW three-bladed pitch regulated wind turbine was investigated. The target spectrum and simulated spectrum were compared. The result shows that the proposed algorithm is more accurate to simulate the fluctuating wind velocity of rotational blade.

Study on dynamic routing and spectrum assignment in bitrate flexible optical networks

The exponential growth of Internet traffic necessitates high-capacity optical networks and has also highlighted the importance of bandwidth-flexible and multi-granularity transport platforms. Improving both transport capacity and bandwidth flexibility is a significant challenge in optical networks. A bitrate flexible network architecture that is based on orthogonal frequency division multiplexing has been proposed as a promising solution for meeting this challenge. In the current study, we focus on the online routing and spectrum assignment problems in the aforementioned network architecture and introduce a general solution for dynamic bitrate flexible traffic in distributed environments. A novel spectrum representation method based on continuous spectrum segments is introduced into the networks. Segment-based routing and signaling mechanisms provide general solutions that support both the conventional slot-based networks and the ideal fully gridless networks. The routing algorithms and spectrum selection approaches are demonstrated and compared in a simulation. Performance estimation indicates that random spectrum segment assignment achieves the lowest capacity blocking rate in light traffic, whereas the adaptive routing plus minimum residual spectrum scheme obtains the lowest capacity blocking rate under heavy traffic.

Simulation of stochastic wind field for large complex structures based on modified Fourier spectrum

Simulation for stochastic wind field is very important in analyzing dynamic responses of large complex structures due to strong wind. The typical simulation method is the spectrum representation method (SRM), but the SRM has drawbacks of inferior precision in lower frequency and slow calculating speed. In view of this, the modified Fourier spectrum method (MFSM) is introduced into the simulation of stochastic wind field in this paper. In this method, phase information of wind velocity time history is determined by cross power spectral density (CPSD) between adjacent points, and the wind velocity time history with time and space correlation is generated by iterative modification for CPSD considering auto power spectral density (APSD). Simulation of the wind field for a long-span bridge is undertaken to verify the effectiveness of the MFSM. Simulation results of the SRM and the MFSM are compared. It can be concluded that the MFSM is more accurate and has higher calculation speed than the SRM.

Modulation of optical focusing by using optimized zone plate structures

The focusing properties of the optimized zone plate structures which have upper and lower zones with different thicknesses are studied by the three-dimensional finite-difference time-domain method. Two kinds of materials are chosen, including silver representing metal and BK7 glass representing dielectric. An optimization algorithm is applied to tune the parameters of zone plate structures. Several optimized zone plate structures with smaller circular-shape focus are presented. By using the angular spectrum representation method, we found that the cases with smaller focal sizes have larger high-k components; however, the intensities of side lobes also become larger in comparison with the main beam. It is also found that the phase differences between different spatial field components can have the influences on focusing properties. A special case with two focuses is shown by changing the cost function of the same optimization algorithm. Our findings suggest that the optimized zone plate structures can reconstruct the light intensity distribution and have a great potential for the applications in imaging, lithography, and data storage.

Analytical vectorial structure of controllable dark-hollow beams close to the source

By means of the vector angular spectrum representation method and mathematical techniques, the analytical vectorial structure of the controllable dark-hollow beam (CDHB) close to the source is derived without any approximation. Analytical expressions of the energy flux for the TE term, the TM term, and the CDHB are presented in the source region, respectively. Energy flux distributions of the TE term, the TM term, and the CDHB close to the source are illustrated with numerical examples. The influences of the beam parameters on energy flux distributions are analyzed, and the dependence of the area of the central dark region for a CDHB on the three beam parameters is also discussed.