A Realistic 3D Non-Stationary Channel Model for UAV-to-Vehicle Communications Incorporating Fuselage Posture

Considering the unmanned aerial vehicle(UAV) three-dimensional(3D) posture, a novel 3D non-stationary geometry-based stochastic model(GBSM) is proposed for multiple-input multipleoutput(MIMO) UAV-to-vehicle(U2V) channels. It consists of a line-of-sight(Lo S) and non-line-of-sight(NLo S) components. The factor of fuselage posture is considered by introducing a time-variant 3D posture matrix. Some important statistical properties, i.e.the temporal autocorrelation function(ACF) and spatial cross correlation function(CCF), are derived and investigated. Simulation results show that the fuselage posture has significant impact on the U2V channel characteristic and aggravate the non-stationarity. The agreements between analytical, simulated, and measured results verify the correctness of proposed model and derivations. Moreover, it is demonstrated that the proposed model is also compatible to the existing GBSM without considering fuselage posture.

Modeling Rainfall Intensity-Duration-Frequency (IDF) and Establishing Climate Change Existence in Uyo-Nigeria Using Non-Stationary Approach

This study aims at establishing if climate change exists in the Niger Delta environment using non-stationary rainfall Intensity-Duration-Frequency (IDF) modelling incorporating time-variant parameters. To compute the intensity levels, the open-access R-studio software was used based on the General Extreme Value (GEV) distribution function. Among the four linear parameter models adopted for integrating time as a covariate, the fourth linear model incorporating scale and location with the shape function constant produced the least corrected Akaike Information Criteria (AICc), varying between 306.191 to 101.497 for 15 and 1440 minutes, respectively, selected for calibration of the GEV distribution equation. The non-stationary intensities yielded higher values above those of stationary models, proving that the assumption of stationary IDF models underestimated extreme events. The difference of 13.71 mm/hr (22.71%) to 14.26 mm/hr (17.0%) intensities implies an underestimation of the peak flood from a stationary IDF curve. The statistical difference at a 95% confidence level between stationary and non-stationary models was significant, confirming evidence of climatic change influenced by time-variant parameters. Consequently, emphasis should be on applying shorter-duration storms for design purposes occurring with higher intensities to help reduce the flood risk and resultant infrastructural failures.

Enhanced Fourier Transform Using Wavelet Packet Decomposition

Many domains, including communication, signal processing, and image processing, use the Fourier Transform as a mathematical tool for signal analysis. Although it can analyze signals with steady and transitory properties, it has limits. The Wavelet Packet Decomposition (WPD) is a novel technique that we suggest in this study as a way to improve the Fourier Transform and get beyond these drawbacks. In this experiment, we specifically considered the utilization of Daubechies level 4 for the wavelet transformation. The choice of Daubechies level 4 was motivated by several reasons. Daubechies wavelets are known for their compact support, orthogonality, and good time-frequency localization. By choosing Daubechies level 4, we aimed to strike a balance between preserving important transient information and avoiding excessive noise or oversmoothing in the transformed signal. Then we compared the outcomes of our suggested approach to the conventional Fourier Transform using a non-stationary signal. The findings demonstrated that the suggested method offered a more accurate representation of non-stationary and transient signals in the frequency domain. Our method precisely showed a 12% reduction in MSE and a 3% rise in PSNR for the standard Fourier transform, as well as a 35% decrease in MSE and an 8% increase in PSNR for voice signals when compared to the traditional wavelet packet decomposition method.

A Novel 3D Non-Stationary UAV-MIMO Channel Model and Its Statistical Properties

The wireless communication systems based on Unmanned Aerial Vehicles(UAVs) have found a wide range of applications recently. In this paper, we propose a new three-dimensional(3 D) non-stationary multiple-input multiple-output(MIMO) channel model for the communication links between the UAV and mobile terminal(MT). The new model originates the traditional geometry-based stochastic models(GBSMs) but considers the non-stationary propagation environment due to the rapid movements of the UAV, MT, and clusters. Meanwhile, the upgrade time evolving algorithms of time-variant channel parameters, i.e., the path number based on birth-death processes of clusters, path delays, path powers, and angles of arrival and departure, are developed and optimized. In addition, the statistical properties of proposed GBSM including autocorrelation function(ACF), cross-correlation function(CCF), and Doppler power spectrum density(DPSD) are investigated and analyzed. Simulation results demonstrate that our proposed model provides a good agreement on the statistical properties with the corresponding derived theoretical ones, which indicates its usefulness for the performance evaluation and validation of the UAV based communication systems.

A REDUCED MFE FORMULATION BASED ON POD FOR THE NON-STATIONARY CONDUCTION-CONVECTION PROBLEMS

In this article, a reduced mixed finite element （MFE） formulation based on proper orthogonal decomposition （POD） for the non-stationary conduction-convection problems is presented. Also the error estimates between the reduced MFE solutions based on POD and usual MFE solutions are derived. It is shown by numerical examples that the results of numerical computation are consistent with theoretical conclusions. Moreover, it is shown that the reduced MFE formulation based on POD is feasible and efficient in finding numerical solutions for the non-stationary conduction-convection problems.

NON-STATIONARY EFFECTS IN HYPERSONIC NONUNIFORM DUSTY-GAS FLOW PAST A BLUNT BODY

In the framework of the two-fluid model, a hypersonic flow of a nonuniform dusty gas with low inertial (non-depositing) particles around a blunt body is considered. The particle mass concentration is assumed to be small, so that the effect of particles on the carrier phase is significant only inside the boundary layer where the particles accumulate. Stepshaped and harmonic nonuniformities of the particle concentration ahead of the bow shock wave are considered and the corresponding nonstationary distributions of the particle concentration in the shock layer are studied. On the basis of numerical study of nonstationary two-phase boundary layer equations derived by the matched asymptotic expansion method, the effects of free-stream particle concentration nonuniformities on the thermal flux, and the friction coefficient in the neighborhood of stagnation point are investigated, in particular, the most “dangerous” nonuniformity periods are found.

The maxima and sums of multivariate non-stationary Gaussian sequences

Let {Xkl,…, Xkp, k≥ 1} be a p-dimensional standard （zero-means, unit-variances）non-stationary Gaussian vector sequence. In this work, the joint limit distribution of the maximaof {Xkl,…, Xkp, k 〉 1}, the incomplete maxima of those sequences subject to random failureand the partial sums of those sequences are obtained.

Estimation of extreme wind speed in SCS and NWP by a non-stationary model

In offshore engineering design, it is considerably significant to have an adequately accurate estimation of marine environmental parameters, in particular, the extreme wind speed of tropical cyclone （TC） with different return periods to guarantee the safety in projected operating life period. Based on the 71-year （1945-2015） TC data in the Northwest Pacific （NWP） by the Joint Typhoon Warning Center （JTWC） of US, a notable growth of the TC intensity is observed in the context of climate change. The fact implies that the traditional stationary model might be incapable of predicting parameters in the extreme events. Therefore, a non-stationary model is proposed in this study to estimate extreme wind speed in the South China Sea （SCS） and NWP. We find that the extreme wind speeds of different return periods exhibit an evident enhancement trend, for instance, the extreme wind speeds with different return periods by non- stationary model are 4.1%-4.4% higher than stationary ones in SCS. Also, the spatial distribution of extreme wind speed in NWP has been examined with the same methodology by dividing the west sea areas of the NWP 0°-45°N, 105°E-130°E into 45 subareas of 5° × 5°, where oil and gas resources are abundant. Similarly, remarkable spacial in-homogeneity in the extreme wind speed is seen in this area： the extreme wind speed with 50-year return period in the subarea （15°N-20°N, 115°E-120°E） of Zhongsha and Dongsha Islands is 73.8 m/s, while that in the subarea of Yellow Sea （30°N-35°N, 120°E-125°E） is only 47.1 m/s. As a result, the present study demonstrates that non-stationary and in-homogeneous effects should be taken into consideration in the estimation of extreme wind speed.

Feature Extraction Techniques of Non-Stationary Signals for Fault Diagnosis in Machinery Systems

Previously, fault diagnosis of fixed or steady state mechanical failures (e.g., pumps in nuclear power plant turbines, engines or other key equipment) applied spectrum analysis (e.g., fast Fourier transform, FFT) to extract the frequency features as the basis for identifying the causes of failure types. However, mechanical equipment for increasingly instant speed variations (e.g., wind turbine transmissions or the mechanical arms used in 3C assemblies, etc.) mostly generate non-stationary signals, and the signal features must be averaged with analysis time which makes it difficult to identify the causes of failures. This study proposes a time frequency order spectrum method combining the short-time Fourier transform (STFT) and speed frequency order method to capture the order features of non-stationary signals. Such signal features do not change with speed, and are thus effective in identifying faults in mechanical components under non-stationary conditions. In this study, back propagation neural networks (BPNN) and time frequency order spectrum methods were used to verify faults diagnosis and obtained superior diagnosis results in non-stationary signals of gear-rotor systems.

Fluctuations and pseudo long range dependence in network flows: A non-stationary Poisson process model

In the study of complex networks （systems）, the scaling phenomenon of flow fluctuations refers to a certain powerlaw between the mean flux （activity） （Fi） of the i-th node and its variance σi as σi α （Fi）α Such scaling laws are found to be prevalent both in natural and man-made network systems, but the understanding of their origins still remains limited. This paper proposes a non-stationary Poisson process model to give an analytical explanation of the non-universal scaling phenomenon： the exponent α varies between 1/2 and 1 depending on the size of sampling time window and the relative strength of the external/internal driven forces of the systems. The crossover behaviour and the relation of fluctuation scaling with pseudo long range dependence are also accounted for by the model. Numerical experiments show that the proposed model can recover the multi-scaiing phenomenon.

Simulation of non-stationary ground motion processes(I)

This paper proposes a method for simulation of non-stationary ground motion processes having the identical statistical feature, time-dependent power spectrum, with a given ground motion record, on the basis of review of simulation of non-stationary ground motion processes. The method has the following advantages: the sample processes are non-stationary both in amplitude and frequency, and both the amplitude and frequency non-stationarity depend on the target power spectrum; the power spectrum of any sample process does not necessarily accord with the target power spectrum, but statistically, it strictly accords with the target power spectrum. Finally, the method is verified by simulation of one acceleration record in Landers earthquake.

A modified method for simulating non-stationary multi-point earthquake ground motion

A spectral-representation-based algorithm is proposed to simulate non-stationary and stochastic processes with evolutionary power,according to a prescribed non-stationary cross-spectral density matrix. Non-stationary multi-point seismic ground motions at different locations on the ground surface are generated for use in engineering applications. First,a modified iterative procedure is used to generate uniformly modulated non-stationary ground motion time histories which are compatible with the prescribed power spectrum. Then,ground motion time histories are modeled as a non-stationary stochastic process with amplitude and frequency modulation. The characteristic frequency and damping ratio of the Clough-Penzien acceleration spectrum are considered as a function of time in order to study the frequency time variation. Finally,two numerical examples are presented to validate the efficiency of the proposed method,and the results show that this method can be effectively applied to the dynamic seismic analysis of long and large scale structures.

Reduced finite difference scheme and error estimates based on POD method for non-stationary Stokes equation

The proper orthogonal decomposition （POD） is a model reduction technique for the simulation Of physical processes governed by partial differential equations （e.g., fluid flows）. It has been successfully used in the reduced-order modeling of complex systems. In this paper, the applications of the POD method are extended, i.e., the POD method is applied to a classical finite difference （FD） scheme for the non-stationary Stokes equation with a real practical applied background. A reduced FD scheme is established with lower dimensions and sufficiently high accuracy, and the error estimates are provided between the reduced and the classical FD solutions. Some numerical examples illustrate that the numerical results are consistent with theoretical conclusions. Moreover, it is shown that the reduced FD scheme based on the POD method is feasible and efficient in solving the FD scheme for the non-stationary Stokes equation.

An Intelligent Optimization Approach to Non-stationary Interference Suppression for Wireless Networks

In this paper, we propose a new technique to effectively suppress non-stationary interference signal for wireless networks. This technique combines a new scheme of interference signal estimation with the intelligent optimization projection. In order to capture interference signal's subspace, a time-varying method is used to estimate the non-stationary interference.Orthogonal polynomials are used for the basis function instead of the power of the time to reduce the computational complexity.The interference is then removed from the corrupted signal by subspace projection, resulting in less distortion to the desired signal. The performance of this approach is validated by computer simulation.

Non-stationary Buffeting Response Analysis of Long Span Suspension Bridge Under Strong Wind Loading

The non-stationary buffeting response of long span suspension bridge in time domain under strong wind loading is computed. Modeling method for generating non-stationary fluctuating winds with probabilistic model for non-stationary strong wind fields is first presented. Non-stationary wind forces induced by strong winds on bridge deck and tower are then given a brief introduction. Finally,Non-stationary buffeting response of Pulite Bridge in China,a long span suspension bridge,is computed by using ANSYS software under four working conditions with different combination of time-varying mean wind and time-varying variance. The case study further confirms that it is necessity of considering non-stationary buffeting response for long span suspension bridge under strong wind loading,rather than only stationary buffeting response.

MODIS-Derived Nighttime Arctic Land-Surface Temperature Nascent Trends and Non-Stationary Changes

Arctic nighttime land-surface temperatures derived by the Moderate Resolution Imaging Spectroradiometer (MODIS) sensors onboard the NASA Terra and Aqua satellites are investigated. We use the local equator crossing times of 22:30 and 01:30, respectively, in the analysis of changes, trends and variations on the Arctic region and within 120° sectors. We show increases in the number of days above 0°C and significant increase trends over their decadal periods of March 2000 through 2010 (MODIS Terra) and July 2002 through 2012 (MODIS Aqua). The MODIS Aqua nighttime Arctic land-surface temperature change, +0.2°C ± 0.2°C with P-value of 0.01 indicates a reduction relative to the MODIS Terra nighttime Arctic land-surface temperature change, +1.8°C ± 0.3°C with P-value of 0.01. This reduction is a decadal non-stationary component of the Arctic land-surface temperature changes. The reduction is greatest, -1.3°C ± 0.2°C with P-value of 0.01 in the Eastern Russia— Western North American sector of the Arctic during the July 2002 through 2012.

Simulation of non-stationary ground motion processes (II)

This paper proposes a method for simulation of non-stationary ground motion processes having the identical statis-tical feature, time-dependent power spectrum, with a given ground motion record, on the basis of review of simu-lation of non-stationary ground motion processes. The method has the following advantages: the sample processes are non-stationary both in amplitude and frequency, and both the amplitude and frequency non-stationarity depend on the target power spectrum; the power spectrum of any sample process does not necessarily accord with the tar-get power spectrum, but statistically, it strictly accords with the target power spectrum. Finally, the method is veri-fied by simulation of one acceleration record in Landers earthquake.

A STABILIZED CRANK-NICOLSON MIXED FINITE VOLUME ELEMENT FORMULATION FOR THE NON-STATIONARY PARABOLIZED NAVIER-STOKES EQUATIONS

A time semi-discrete Crank-Nicolson （CN） formulation with second-order time accuracy for the non-stationary parabolized Navier-Stokes equations is firstly established. And then, a fully discrete stabilized CN mixed finite volume element （SCNMFVE） formu- lation based on two local Gaussian integrals and parameter-free with the second-order time accuracy is established directly from the time semi-discrete CN formulation so that it could avoid the discussion for semi-discrete SCNMFVE formulation with respect to spatial wriables and its theoretical analysis becomes very simple. Finally, the error estimates of SCNMFVE solutions are provided.

Structural Strength Degradation Model Based on Non-stationary Gamma Process

Strength degradation is a stochastic and irreversible process.Gamma process is an independent nonnegative increment process which can be used to describe the characteristics of strength degradation.It is unreasonable to choose a linear function to describe the strength degradation trend considering that the degradation rate may change over time.So,a non-linear power law is proposed to describe the strength degradation trend based on preliminary work.It is more general compared with the linear one and the inadequacy of strict linear assumption is overcome.Then,the model parameters of non-stationary Gamma process are estimated based on the maximum likelihood method.Finally,it is proved that the non-stationary Gamma process can accurately reflect the strength degradation law through comparative analysis of a real example.

Discrete Time-Frequency Signal Analysis and Processing Techniques for Non-Stationary Signals

This paper presents the methodology, properties and processing of the time-frequency techniques for non-stationary signals, which are frequently used in biomedical, communication and image processing fields. Two classes of time-frequency analysis techniques are chosen for this study. One is short-time Fourier Transform (STFT) technique from linear time-frequency analysis and the other is the Wigner-Ville Distribution (WVD) from Quadratic time-frequency analysis technique. Algorithms for both these techniques are developed and implemented on non-stationary signals for spectrum analysis. The results of this study revealed that the WVD and its classes are most suitable for time-frequency analysis.