A microbial growth kinetics model driven by hybrid stochastic colored noises in the water environment

This study develops three microbial growth models in the sewage biodegradation process driven by white noise, colored noise and hybrid noises, respectively. The proposed models are more universal in reflecting the impact of uncertainty on microbial systems, compared with the previous efforts. An improved Box–Mueller algorithm is used to solve the model. The modeling results show that the different noise types have remarkable effects on microbial growth kinetics. To better understanding the insights of various noises affecting the system, the growth process of microbial in the sewage biodegradation process is discussed under different conditions with varied noise properties (i.e. intensity and correlation time). The results indicate that the effect of noise on the microbial growth kinetics decreases with the reduction of the noise intensity and the correlation time. Therefore, a known noise can be relieved by changing the noise intensity or the correlation time. As the model driven by noises is capable of addressing the system’s uncertainty, it is useful in supporting stochastic simulation, risk analysis, and process design of a sewage biological treatment system. Future works may focus on the development of more effective statistical-inference methods for the noises based on observed data.     

基于有色噪声模型的GPS速度场精度与时间序列长度相关性研究

利用2010—2015年陆态网络GPS连续观测站的三维站坐标时序资料, 在采用最大似然估计MLE方法计算得到云南地区GPS基准站三维站坐标分量最优噪声模型的基础上, 进一步定量对比分析了有色噪声和白噪声模型下陆态网络GPS连续站速度场稳定性与时间序列长度的关系。 结果表明: 在闪烁噪声模型下, 中国大陆大部分地区GPS连续站1 a时段的速度不确定度大。 而随着时间的逐年累积, 闪烁噪声模型下的速度不确定度与同时段白噪声模型下的差异逐步减小, 闪烁噪声模型下3～4 a时段的速度不确定度与同时段白噪声模型的差异小于0.2 mm。 研究说明在有色噪声模型下要获得高精度的速度场需要3～4 a的观测数据, 白噪声模型下GPS速度场精度可靠可信的前提是采用不少于3～4 a的数据。     

Comparative study of monthly inflow prediction methods for the Three Gorges Reservoir

Due to the complexity of influencing factors and the limitation of existing scientific knowledge, current monthly inflow prediction accuracy is unable to meet the requirements of various water users yet. A flow time series is usually considered as a combination of quasi-periodic signals contaminated by noise, so prediction accuracy can be improved by data preprocess. Singular spectrum analysis (SSA), as an efficient preprocessing method, is used to decompose the original inflow series into filtered series and noises. Current application of SSA only selects filtered series as model input without considering noises. This paper attempts to prove that noise may contain hydrological information and it cannot be ignored, a new method that considerers both filtered and noises series is proposed. Support vector machine (SVM), genetic programming (GP), and seasonal autoregressive (SAR) are chosen as the prediction models. Four criteria are selected to evaluate the prediction model performance: Nash–Sutcliffe efficiency, Water Balance efficiency, relative error of annual average maximum (RE_max) monthly flow and relative error of annual average minimum (RE_min) monthly flow. The monthly inflow data of Three Gorges Reservoir is analyzed as a case study. Main results are as following: (1) coupling with the SSA, the performance of the SVM and GP models experience a significant increase in predicting the inflow series. However, there is no significant positive change in the performance of SAR (1) models. (2) After considering noises, both modified SSA-SVM and modified SSA-GP models perform better than SSA-SVM and SSA-GP models. Results of this study indicated that the data preprocess method SSA can significantly improve prediction precision of SVM and GP models, and also proved that noises series still contains some information and has an important influence on model performance.     

Estimation for rainfall-runoff modeled as a partially observed Markov process

Abstract: Linear continuous time stochastic Nash cascade conceptual models for runoff are developed. The runoff is modeled as a simple system of linear stochastic differential equations driven by white Gaussian and marked point process noises. In the case of d reservoirs, the outputs of these reservoirs form a d dimensional vector Markov process, of which only the dth coordinate process is observed, usually at a discrete sample of time points. The dth coordinate process is not Markovian. Thus runoff is a partially observed Markov process if it is modeled using the stochastic Nash cascade model. We consider how to estimate the parameters in such models. In principle, maximum likelihood estimation for the complete process parameters can be carried out directly or through some form of the EM (estimation and maximization) algorithm or variation thereof, applied to the observed process data. In this research we consider a direct approximate likelihood approach and a filtering approach to an algorithm of EM type, as developed in Thompson and Kaseke (1994). These two methods are applied to some real life runoff data from a catchment in Wales, England. We also consider a special case of the martingale estimating function approach on the runoff model in the presence of rainfall. Finally, some simulations of the runoff process are given based on the estimated parameters.     

结构平稳随机地震反应时域分析:方法

给出了三种常用的随机地震地面运动过程模型,即理想白噪声模型、金井清模型、改进金井清模型的相关函数表达式.引入状态向量,在状态空间中建立地震地面运动激励下的结构振动方程,并求解出结构的复模态特性和复模态反应.利用复模态叠加法推导出线性时不变多自由度体系在这三种随机地震动激励下的平稳协方差反应的解析式,可在时域内直接计算结构随机反应的统计特征.该方法物理概念清晰,结论简便明确,可作为实际工程结构平稳随机地震反应的实用分析方法.     

ATTENUATION DES MULTIPLES EN SISMIQUE MARINE PAR ANTIMOYENNE*

A satisfactory attenuation of the multiples in marine seismic may be obtained by the application of the principle of “Antiaveraging”. This principle in a first step consists in getting the model of the organized noise, which one tries to eliminate by using an averaging method, and in a second step to subtract that model from the initial information. Obviously the elimination of the model should not simultaneously cause the elimination of useful signals. The model may be obtained if the considered organized noise keeps a constant shape or if its time-space deformation is known. Besides one has to assume the time-distance curve of the organized noise can be determined. Thus noise arrivals may be detected on the records. The “antiaveraging” is very often efficient when organized noises are stronger than signals or when a signal, once identified, exploited and then considered as an organized noise, can be attenuated in order to make the detection of the other signals easier.     

连续GPS观测中的相关噪声分析

分析了中国地壳运动观测网络GPS基准站位置时间序列中相关噪声的特性.利用最大似然估计反演了幂指数噪声的谱指数;考察了多种噪声模型,发现除闪烁噪声之外,约50%台站的东分量中的相关噪声可用"随机漫步噪声+一阶高斯-马尔可夫噪声"模型来描述,与其它分析机构产出的全球解并不一致,显示出处理策略的不同能够造成相关噪声的差异.白噪声和闪烁噪声的大小存在明显的地理分异,东南沿海台站的噪声要大于西北内陆台站.考虑相关噪声时,各站的速率估计方差要增大一个数量级以上,水平分量多在1mm/a以内,而垂向分量则较大.     

基于FFT-MA谱模拟的快速随机反演方法研究

虽然基于地质统计学的随机反演方法能够有效融合测井资料中的高频信息,但计算效率低,占用内存大,限制了它在实际资料中的应用.本文在保留传统随机反演方法优点的基础上,创造性地引入傅里叶滑动平均(Fast Fourier Transform-Moving Average,FFT-MA)谱模拟进行频率域的地质统计模拟,并利用逐步变形算法(Gradual Deformation Method,GDM)确保模拟结果与实际地震数据的匹配,构建了基于FFT-MA谱模拟的新的快速随机反演方法.与常规随机反演相比,新方法不仅分辨率高,而且能够使反演解得到快速收敛,有效提高计算效率,减少内存占用.模型试算获得了与理论模型吻合度较好的高分辨率反演结果.实际资料分析也表明新方法所得到的高分辨率反演结果能够对薄互储层进行良好的展示,为薄储层的识别提供高效可靠的技术支持.     

利用FG5绝对重力仪观测数据确定重力垂直梯度

本文建立了利用FG5实测数据求解重力垂直梯度的数据处理模型与算法.通过对多次自由落体实验的下落距离拟合残差叠加求均值,发现下落距离观测量中存在明显的有色噪声.通过对有色噪声的建模,并以剩余残差为依据选取可靠的下落时段,解算测站点的重力垂直梯度.利用本文所提出的数据处理方法分别对FG5-214绝对重力仪在两个测站上的观测数据进行处理,以相对重力仪测量的重力垂直梯度结果为参考值,本文处理得到的重力垂直梯度结果相比于未考虑有色噪声并依据经验选取下落时段的解算方法得到了显著改善.     

An eddifying Stommel model: fast eddy effects in a two-box ocean

ABSTRACT

A system of stochastic differential equations is formulated describing the heat and salt content of a two-box ocean. Variability in the heat and salt content and in the thermohaline circulation between the boxes is driven by fast Gaussian atmospheric forcing and by ocean-intrinsic, eddy-driven variability. The eddy forcing of the slow dynamics takes the form of a colored, non-Gaussian noise. The qualitative effects of this non-Gaussianity are investigated by comparing to two approximate models: one that includes only the mean eddy effects (the “averaged model”), and one that includes an additional Gaussian white-noise approximation of the eddy effects (the “Gaussian model”). Both of these approximate models are derived using the methods of fast averaging and homogenisation. In the parameter regime where the dynamics has a single stable equilibrium the averaged model has too little variability. The Gaussian model has accurate second-order statistics, but incorrect skew and rare-event probabilities. In the parameter regime where the dynamics has two stable equilibria the eddy noise is much smaller than the atmospheric noise. The averaged, Gaussian, and non-Gaussian models all have similar stationary distributions, but the jump rates between equilibria are too small for the averaged and Gaussian models.     

基于EM算法的运行模态参数识别

结合随机状态空间方程和极大似然法的期望最大EM算法进行了结构运行模态分析。EM算法以迭代的方式更新模型参数,进而得到状态空间方程的极大似然估计。模态参数通过状态空间模型参数求得。应用了平方根卡尔曼滤波方程提高EM迭代过程的计算稳健性。考虑到状态空间方程中激励噪声和测量噪声的相关性,建立了更完善的参数化状态空间方程。通过数值模拟对比分析,结果表明：考虑噪声相关性的EM算法比假设噪声不相关的EM算法具有更高的识别精度,EM算法在采样数据较少的情况下比随机子空间方法更有优势。     

Discrimination between stochastic dynamics patterns of ambient noises (Case study for Oni seismic station)

Investigation of complex dynamics of ambient seismic noise remains as an important scientific research challenge. In this work we investigated dynamical features of the ambient noises at Oni seismic station, Georgia. We used stochastic model reconstruction method from measured data sets. Seismic records for different time periods around Oni seismic station have been analysed. It was shown that the dynamics of fluctuations of seismic noise vertical component undergoes essential changes for considered time period from 2005 to 2012. These changes are more noticeable for time periods of preparation and aftershock activity of strong M6.0 earthquake occurred in 2009 in the vicinity of Oni seismic station.     

On low-frequency errors of uniformly modulated filtered white-noise models for ground motions

Low-frequency errors of a commonly used non-stationary stochastic model (uniformly modulated filtered white-noise model) for earthquake ground motions are investigated. It is shown both analytically and by numerical simulation that uniformly modulated filter white-noise-type models systematically overestimate the spectral response for periods longer than the effective duration of the earthquake, because of the built-in low-frequency errors in the model. The errors, which are significant for low-magnitude short-duration earthquakes, can be eliminated by using the filtered shot-noise-type models (i.e. white noise, modulated by the envelope first, and then filtered).     

检测地震勘探微弱同相轴的混沌振子算法

针对地震勘探资料湮没在随机噪声中的微弱同相轴问题提出基于混沌理论的混沌振子检测算法. 利用修正的Duffing_Holmes方程建立检测微弱同相轴的混沌振子系统,之后经过对同相轴的扫描处理,构成新子波等时间间隔序列W(t),与此同时对随机噪声也进行相同的截断. 截断的随机噪声在混沌振子系统中可以具有与周期信号相同的表现;经过大量仿真实验确定出满足通常地震勘探子波延续时间的使混沌振子检测子波不呈现周期相态的随机噪声截断时间范围. 选用与松辽盆地T1、T2反射层类似的子波函数并构成待检微弱周期信号,经过MATLAB仿真试验成功地检测出该弱信号,信噪比达到约-103dB.     

平稳随机地震地面运动过程模型及其统计特征

地震地面运动过程具有强烈的随机性,应用随机理论对实际工程结构进行地震可靠性分析和抗震设计与加固时都需要建立合理的随机地震地面运动模型,本文选择3种典型的随机地震动模型,即理想白噪声模型、金井清模型和改进的金井消模型,分析了它们的物理概念、频域特征以及适用范围。引入状态向量,建立状态方程．通过复振型叠加法分析了地震地面运动过程的时域统计特性,推导出3种随机地震动模型的相关函数的解析表达式．这些结果可为结构随机地震反应时域分析和抗震可靠性评估提供基础。     

Simulation of orthogonal horizontal ground motion components for specified earthquake and site characteristics

A method for generating an ensemble of orthogonal horizontal ground motion components with correlated parameters for specified earthquake and site characteristics is presented. The method employs a parameterized stochastic model that is based on a time‐modulated filtered white‐noise process with the filter having time‐varying characteristics. Whereas the input white‐noise excitation describes the stochastic nature of the ground motion, the forms of the modulating function and the filter and their parameters characterize the evolutionary intensity and nonstationary frequency content of the ground motion. The stochastic model is fitted to a database of recorded horizontal ground motion component pairs that are rotated into their principal axes, a set of orthogonal axes along which the components are statistically uncorrelated. Model parameters are identified for each ground motion component in the database. Using these data, predictive equations are developed for the model parameters in terms of earthquake and site characteristics and correlation coefficients between parameters of the two components are estimated. Given a design scenario specified in terms of earthquake and site characteristics, the results of this study allow one to generate realizations of correlated model parameters and use them along with simulated white‐noise processes to generate synthetic pairs of horizontal ground motion components along the principal axes. The proposed simulation method does not require any seed recorded ground motion and is ideal for use in performance‐based earthquake engineering. Copyright © 2011 John Wiley & Sons, Ltd.