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.

TVAR Time-frequency Analysis for Non-stationary Vibration Signals of Spacecraft

Predicting the time-varying auto-spectral density of a spacecraft in high-altitude orbits requires an accurate model for the non-stationary random vibration signals with densely spaced modal frequency. The traditional time-varying algorithm limits prediction accuracy, thus affecting a number of operational decisions. To solve this problem, a time-varying auto regressive （TVAR） model based on the process neural network （PNN） and the empirical mode decomposition （EMD） is proposed. The time-varying system is tracked on-line by establishing a time-varying parameter model, and then the relevant parameter spectrum is obtained. Firstly, the EMD method is utilized to decompose the signal into several intrinsic mode functions （IMFs）. Then for each IMF, the PNN is established and the time-varying auto-spectral density is obtained. Finally, the time-frequency distribution of the signals can be reconstructed by linear superposition. The simulation and the analytical results from an example demonstrate that this approach possesses simplicity, effectiveness, and feasibility, as well as higher frequency resolution.

非平稳随机地震激励下多层框架-摇摆墙结构的响应分析

框架-摇摆墙是一种可有效提高建筑抗震性和韧性的组合自复位结构,为充分了解其在地震下的随机响应特性,构建多自由度框架-摇摆墙结构的简化非线性方程,并利用等效线性化,基于响应的伪谐波行为假设,构建含时变参数的等效线性动力方程;基于随机平均的原理,得出控制响应幅值概率密度函数(PDF)的时间演变形式的福克-普朗克-科尔莫哥洛夫(FPK)方程,最终得出随机响应时间相关方差的一阶微分方程;并以某教学楼一榀框架为样本构建算例模型进行验证。结果表明:近似解析方法具有优异的精确度,在保证随机响应时间相关方差准确性的前提下,相对于传统的蒙特卡罗模拟(MCS)方法可提高分析的效率;在可分离形式和不可分离形式的非平稳地震动功率谱模型的结果中,随机响应方差曲线趋势与随机地震激励的形式相关,且在分段式调制非平稳谱作用下其分段点表现出很明显的不平滑现象;不同类型的随机地震激励扰动下的结果证明了此方法优异的适用性。

一种高斯-重尾切换分布鲁棒卡尔曼滤波器

为降低实际应用中由强未知干扰和仪器故障对观测造成的影响,减轻随机和未建模干扰对系统的侵蚀,从而提升系统在非高斯噪声环境下的状态估计精度,提高滤波器的鲁棒性能,提出了一种基于高斯-重尾切换分布的鲁棒卡尔曼滤波器(Gaussian-heavy-tailed switching distribution based robust Kalman filter,GHTSRKF)。首先,通过自适应学习高斯分布和一种重尾分布之间的切换概率将噪声建模为GHTS(Gaussian-heavy-tailed switching)分布,所设计的GHTS分布可以通过在线调整高斯分布和新的重尾分布之间的切换概率来对非平稳重尾噪声进行建模,具有虚拟协方差的高斯分布用于处理协方差矩阵不准确的高斯噪声。其次,引入两个分别服从Categorical分布与伯努利分布的辅助参数将GHTS分布表示为一个分层高斯形式,进一步利用变分贝叶斯方法推导了GHTSRKF。最后,利用一个仿真场景对几种不同的RKFs(robust Kalman filters)进行了对比验证。结果表明,所提出的GHTSRKF算法的估计精度对初始状态的选取不敏感,精度优于其他RKFs,它的RMSEs最接近噪声信息准确的KFTNC(KF with true noise covariances)的RMSEs(root mean square errors),且当系统与量测噪声是未知时变高斯噪声时,相比于现有的滤波器,GHTSRKF具有更好的估计性能,从而验证了GHTSRKF的有效性。

采用非稳相偏振滤波的DAS-VSP数据P/S波分离方法及其应用

分布式光纤声学传感(DAS)因成本低、易布设以及高密度采样等优势正成为重要的地震观测技术,尤其是越来越多地与垂直地震剖面(VSP)结合,用于主动地震勘探或被动地震监测.DAS传感器通过感知弹性波场产生的轴向应变或应变速率来观测地震波场振动.然而,目前单分量DAS-VSP数据未完整地记录地下弹性波场的三维矢量振动信号,因此如何从中分离出P波或S波用于后续地震成像与参数反演是重要且很有挑战的课题.以弹性波传播理论为基础,本文根据P波和S波的频散关系估算接收点处各自的偏振方向,通过随频率和空间位置变化的偏振滤波实现DAS-VSP数据的P/S波分离.理论模型合成数据与东海实际DAS-VSP数据实验结果表明,该方法能有效地将P波和S波信号从单分量DAS-VSP数据中分离出来,可为后续纵横波速度反演、PP与PS波成像提供关键的数据预条件处理.

MULTIPLE STATIONARY SOLUTIONS OF EULER-POISSON EQUATIONS FOR NON-ISENTROPIC GASEOUS STARS

The motion of the self-gravitational gaseous stars can be described by the Euler-Poisson equations. The main purpose of this paper is concerned with the existence of stationary solutions of Euler-Poisson equations for some velocity fields and entropy functions that solve the conservation of mass and energy. Under different restriction to the strength of velocity field, we get the existence and multiplicity of the stationary solutions of Euler-Poisson system.

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.

考虑时变特性的车-桥耦合系统非平稳振动频域方法研究

当列车行驶经过桥梁时,由于车辆在桥上的位置随时间不断变化,车-桥耦合系统具有时变特性,即使假设轨道不平顺为平稳激励,车辆和桥梁的振动仍然是一种非平稳的随机过程。本研究旨在提出一种非平稳频域分析方法,以高效分析受轨道不平顺激励的车-桥耦合系统的非平稳随机振动问题。首先推导了单节列车通过单跨简支桥的耦合系统时变频响传递函数(FRF),据此描述线性时变系统的动力特性。该函数满足一组变系数微分方程,可采用摄动法求解该函数,从而提高计算效率。随后,结合PRIESTLEY的演化谱理论,推导非平稳随机响应的演化功率谱密度函数(EPSD)。基于非平稳频域分析方法,计算响应时变均值和方差,结合3σ准则来估计非平稳响应的极值。研究结果表明,由于轨道不平顺的影响,车辆振动表现出平稳随机过程的特性,但其方差较大,表现出更大的离散性;而桥梁的振动则呈现出明显的非平稳特性,但方差较小,响应具有较小的随机性。极值分析表明,轨道不平顺激励对车辆振动具有显著影响,其均方根对极值响应起主导作用。而轨道不平顺激励对桥梁振动的影响较小,桥梁振动则主要受移动质量影响,其响应的极值主要受均值的影响。此外,相较于系统位移响应,车速对加速度响应的影响更为显著,例如车身加速度响应最大值随车速的增加可增大至3倍左右。

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.

Ng-Perron单位根检验在径流序列非平稳性分析中的应用

在全球气候变化和高强度人类活动的共同影响下,许多流域天然水循环过程受到破坏。径流序列呈现明显的非平稳特性,给水资源规划、管理、预测和调控带来一定的挑战。揭示径流序列的非平稳特性可以有效应对全球气候变化下的复杂水问题,对降低水文分析难度和提高径流预测精度具有十分重要的意义。研究以汾河上游兰村站为研究对象,分析该站1958-2016年年径流和月径流序列是否平稳。首先从随机水文学角度,采用Mann-Kendall检验法和小波分析法识别径流序列的趋势、突变和周期特征。在此基础上,从统计水文学角度引入Ng-Perron单位根检验方法。通过Mann-Kendall趋势检验和散点图法选择合适的检验方程,对径流序列进行广义最小二乘法(Generalized Least Squares,GLS)退势,并利用修正的信息准则(Modified information criterion,MIC)计算最优时间滞后阶数,判别径流序列是否具有非平稳性。结果显示,径流序列存在趋势、突变和周期成分,为非平稳径流序列。同时Ng-Perron单位根检验表明,该站年、月径流序列在1%显著性水平上具有非平稳特性。相较传统单位根检验方法,Ng-Perron单位根检验采用更为稳健的修正检验统计量,显著调整小样本情况下水平扭曲的现象,具有更好检验水平和功效,因而可以得到更合理的检验结果。研究成果为径流序列非平稳性检验理论的进一步改进及径流预测模型发展与应用提供参考。

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.

Tunnelling effect of the non-stationary Kerr black hole

Extending Parikh and Wilczek＇s work to the non-stationary black hole, we study the Hawking radiation of the non-stationary Kerr black hole by the Hamilto-Jacobi method. The result shows that the radiation spectrum is not purely thermal and the tunnelling probability is related to the change of Bekenstein Hawking entropy, which gives a correction to the Hawking thermal radiation of the black hole.

NON-EQUILIBRIUM STATIONARY STATE IN CHEMICAL REACTION OF SiO_2/Fe AT INTERFACE OF SLAG/METAL AND ITS STABILITY DURING ARC WELDING

For characteristics of open and far from thermodynamic equilibrium in welding chemical reaction, a new kind of quantitative method, which is used to analyze direction and extent for chemical reaction of SiO2/Fe during quasi-steady state period, is introduced with the concept of non-equilibrium stationary state. The main idea is based on thermodynamic driving forces, which result in non-zero thermodynamic fluxes and lead to chemical reaction far away from thermodynamic equilibrium. There exists certain dynamic equilibrium relationship between rates of diffusion fluxes in liquid phase of reactants or products and the rate equation of chemical reaction when welding is in quasi-steady state. As result of this, a group of non-linear equations containing concentrations of all substances at interface of slag/liquid-metal may be established. Moreover the stability of this non-equilibrium stationary state is discussed using dissipative structure theory and it is concluded theoretically that this non-equilibrium stationary state for welding chemical reaction is of stability.

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.

The Study of a New Method for Forecasting Non-stationary Series

A new method for forecasting non stationary series is developed. Its steps are as follows: Step 1. Data delaminating. Non stationary series is delaminated into several multi scale steady data layers and one trend layer. Step 2. Modeling and forecasting each stationary data layer. Step 3. Imitating trend layer using polynomial. Step 4. Combining the forecasting layers and imitating layer into one series. The EMD (Empirical Mode Decomposition) method suitable to process non stationary series is selected to delaminate data, while ARMA (Auto Regressive Moving Average) model is employed to model and forecast stationary data layer and least square error method for trend layer regression. Aiming at forecasting length, forecasting orientation and selective method, experiments are performed for SAR (Synthetic Aperture Radar) images. Finally, an example is provided, in which the whole SAR image is restored via the method proposed by this paper.

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.

THE STATIONARY VALUE PROPERTY OF HAMILTON'S PRINCIPLE IN NON-HOLONOMIC SYSTEMS

This paper proves that Hanlilton's prmciple of both using the Appell-Chetaevcondition and not using the Appell-CHETAEV conditiion is the variational principle of stationary action.The relevant problems are discussed