Non-stationary Approach Research Articles

Modeling and mitigating natural hazards: Stationarity is immortal!

AbstractEnvironmental change is a reason of relevant concern as it is occurring at an unprecedented pace and might increase natural hazards. Moreover, it is deemed to imply a reduced representativity of past experience and data on extreme hydroclimatic events. The latter concern has been epitomized by the statement that “stationarity is dead.” Setting up policies for mitigating natural hazards, including those triggered by floods and droughts, is an urgent priority in many countries, which implies practical activities of management, engineering design, and construction. These latter necessarily need to be properly informed, and therefore, the research question on the value of past data is extremely important. We herein argue that there are mechanisms in hydrological systems that are time invariant, which may need to be interpreted through data inference. In particular, hydrological predictions are based on assumptions which should include stationarity. In fact, any hydrological model, including deterministic and nonstationary approaches, is affected by uncertainty and therefore should include a random component that is stationary. Given that an unnecessary resort to nonstationarity may imply a reduction of predictive capabilities, a pragmatic approach, based on the exploitation of past experience and data is a necessary prerequisite for setting up mitigation policies for environmental risk.

Non-stationary nonparametric inference of river-to-groundwater travel-time distributions

The travel-time distribution between rivers and groundwater observation points and the mixing of freshly infiltrated river water with groundwater of other origin is of high relevance in riverbank filtration. These characteristics usually are inferred from the analysis of natural-tracer time series, typically relying on a stationary input–output relationship. However, non-stationarity is a significant feature of the riparian zone causing time-varying river-to-groundwater transfer functions. We present a non-stationary extension of nonparametric deconvolution by performing stationary deconvolution with windowed time series, enforcing smoothness of the determined transfer function in time and travel time. The nonparametric approach facilitates the identification of unconventional features in travel-time distributions, such as broad peaks, and the sliding-window approach is an easy way to accommodate the method to dynamic changes of the system under consideration. By this, we obtain time-varying signal-recovery rates and travel-time distributions, from which we derive the mean travel time and the spread of the distribution as function of time. We apply our method to electric-conductivity data collected at River Thur, Switzerland, and adjacent piezometers. The non-stationary approach reproduces the groundwater observations significantly better than the stationary one, both in terms of overall metrics and in matching individual peaks. We compare characteristics of the transient transfer function to base flow which indicates shorter travel times at higher river stages.

Nonstationary magnetotelluric data processing with instantaneous parameter

Nonstationarity in electromagnetic data affects the computation of Fourier spectra and therefore the traditional estimation of the magnetotelluric (MT) transfer functions (TF). We provide a TF estimation scheme based on an emerging nonlinear, nonstationary time series analysis tool, called empirical mode decomposition (EMD) and show that this technique can handle nonstationary effects with which traditional methods encounter difficulties. In contrast to previous works that employ EMD for MT data processing, we argue the advantages of a multivariate decomposition, highlight the possibility to use instantaneous parameters, and define the homogenization of frequency discrepancies between data channels. Our scheme uses the robust statistical estimation of transfer functions based on robust principal component analysis and a robust iteratively reweighted least squares regression with a Huber weight function. The scheme can be applied with and without aid of any number of available remote reference stations. Uncertainties are estimated by iterating the complete robust regression, including the robust weight computation, with a bootstrap routine. We apply our scheme to synthetic and real data (Southern Africa) with and without nonstationary character and compare different processing techniques to the one presented here. As a conclusion, nonstationary noise can heavily affect Fourier‐based MT data processing but the presented nonstationary approach is nonetheless able to extract the impedances.

A novel nonstationary deconvolution method based on spectral modeling and variable-step sampling hyperbolic smoothing

Abstract Deconvolution is an important part of seismic processing tool for improving the resolution. One of the key assumptions made in most deconvolutional methods is that the seismic data is stationary. However, due to the anelastic absorption, the seismic data is usually nonstationary. In this paper, a novel nonstationary deconvolution approach is proposed based on spectral modeling and variable-step sampling (VSS) hyperbolic smoothing. To facilitate our method, firstly, we apply the Gabor transform to perform a time-frequency decomposition of the nonstationary seismic trace. Secondly, we estimate the source wavelet amplitude spectrum by spectral modeling. Thirdly, smoothing the Gabor magnitude spectrum of seismic data along hyperbolic paths with VSS can obtain the magnitude of the attenuation function, and can also eliminate the effect of source wavelet. Fourthly, by assuming that the source wavelet and attenuation function are minimum phase, their phases can be determined by Hilbert transform. Finally, the estimated two factors are removed by dividing them into the Gabor spectrum of the trace to estimate the Gabor spectrum of the reflectivity. An inverse Gabor transform gives the time-domain reflectivity estimate. Tests on synthetic and field data show that the presented method is an effective tool that not only has the advantages of stationary deconvolution, but also can compensate for the energy absorption, without knowing or estimating the quality factor Q.

Failures of cranes due to wind induced vibrations

Self-excited vibrations with large amplitudes in natural wind may occur at slender structural elements with low damping. Because of the different designs (e. g. using solid sections today instead of cables for tension elements in the past) the susceptibility to wind induced oscillations has increased. Those wind induced vibrations of profiles with specific cross section geometry which are motion induced and therefore self-exciting are called “galloping vibrations”. Especially systems with elements that are highly tensile loaded and undamped, like hangers of bridges or tension bars of cranes, are sensitive to wind induced vibrations. Therefore more and more fatigue problems caused by galloping oscillations have occurred in the 1990s. This paper describes exemplary the collapses of two modern cranes of different design and manufacturers. During standstill periods, both cranes suffered from wind induced vibrations of the tension bars, which bear up the counterweights. The failure analysis process to identify and explain the fatigue fractures as well as the comparative experiments and simulation to verify that they were caused by wind induced galloping-vibrations is described. It is shown, which parameters led to galloping-vibrations of the tension bars and how their onset wind speed and the amplitudes can be estimated with more accuracy by a non-linear and non-stationary approach. Furthermore it is shown that such dynamic stresses caused fatigue failure of the tension bars for the counter weights and subsequently collapsing of the cranes.For loss prevention knowledge and results gained by these investigations should be put at disposal to engineers working on this field of design. In the meantime, a contribution to development of appropriate technical standards on structural steelwork was given by the research works on galloping. Although new standards were introduced, which consider wind induced vibrations, such failures still occur. (Reference to the paper “Fatigue crack in railway bridge hanger due to wind induced vibrations – failure analysis, measures and remaining service life estimation” in this same Special Issue “A tribute to A. Martens” 2014).

Multiple stationary–non-stationary object-tracking approach in real-time applications through an extendable RGB modelling framework

The main contribution of the present research arises from developing standard object tracking approaches by considering a number of available research works in the area of multiple-object tracking approaches in real-time applications. An automatic robust algorithm is proposed in this investigation, which is able to track multiple synchronized stationary and/or non-stationary objects in high performance quality. The proposed approach is realized based upon an efficient extendable RGB (red/green/blue) modelling framework. This means that the investigated results are easily applicable to tracking the desirable number of objects to be chosen, i.e. the approach is flexible enough to reorganize to track the stationary/non-stationary objects in all frames of the video sequences. This proposed idea unique in that we plan to track all the chosen objects, in a synchronized manner, without a lengthy processing time. In fact, the proposed approach is realized in association with a desirable number of sub-systems, each of them needing to be enabled in parallel. The investigated results indicate that the present approach is now applicable in real-time applications by running a robust estimator to predict the new position of the tracked objects, since the objects are in the presence of long-term environmental problems – situations that are usually too difficult to deal with through standard object tracking algorithms.

Covariance structure of spatial and spatiotemporal processes

An important aspect of statistical modeling of spatial or spatiotemporal data is to determine the covariance function. It is a key part of spatial prediction (kriging). The classical geostatistical approach uses an assumption of isotropy, which yields circular isocorrelation curves. However, this is inappropriate for many applications, and several nonstationary approaches have been developed. Adding the temporal aspect, there is often interaction between time and space, requiring classes of nonseparable covariance structures. WIREs Comput Stat 2013, 5:279–287. doi: 10.1002/wics.1259This article is categorized under: Data: Types and Structure > Image and Spatial Data Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data

Macrokinetic grounds for a model of microbial growth on a substrate with a single major component

The dependency of experimental microbial growth data on the concentration of a major substrate component in phase space follows the law of a deformed bell curve and, until now, has not had a widely accepted rational. In the present work, a theoretical equation of this dependency at a fixed time was derived from the equation of the dependency of growth on time for a single concentration of a major component, which was previously obtained using a non-stationary non-equilibrium approach. The validity of the equation was established by comparison to experimental data from an independent source. The equation allows one to find intervals in the phase space of the dependency of growth on the initial concentration of the major component of the substrate that qualitatively vary by sign (plus or minus) and direction (increasing or decreasing) of the change of: a) growth, b) rates, and c) acceleration of its change in response to the change in the concentration of a major component of the substrate.

Effect of topography and accessibility on vegetation dynamic pattern in Mountain-hill Region

Knowledge of both vegetation distribution pattern and phenology changes is very important. Their complicated relationship with elevation and accessibility were explored through a geographically weighted regression (GWR) framework in Fujian province, China. The 16-day time series of 250 m Moderate Resolution Imaging Spectroradiometer (MODIS) Enhanced Vegetation Index (EVI) dataset from 2000 to 2010 was applied. Wavelet transform method was adopted to decompose the original time series and construct the annual maximum EVI and amplitude of the annual phenological cycle (ΔEVI). Candidate explaining factors included topographic conditions, accessibility variables and proportions of primary vegetation types. Results revealed very strong positive influence from parameters of elevation and accessibility to big rivers and negative effect from accessibility to resident on both maximum EVI and phenological magnitude through ordinary linear least square (OLS) regression analysis. GWR analysis revealed that spatially, the parameters of topography and accessibility had a very complex relationship with both maximum EVI and phenology magnitude, as a result of the various combinations of environmental factors, vegetation composition and also intensive anthropogenic impact. Apart from the continuously increasing trend of phenology magnitude with increasing altitude, the influence of topography and accessibility on maximum EVI and phenological magnitude generally decreased, even from strongly positive to negative, with increasing altitude or distance. Specially, the most rapid change of correlation coefficient between them was observed within a low elevation or close distance; less variation was discovered within a certain range of medium altitude or distance and their relationship might change above this range. Non-stationary approaches are needed to better characterize the complex vegetation dynamic pattern in Mountain-hill Region.

Challenging Traditional Risk Models by a Non-Stationary Approach with Nonparametric Heteroscedasticity

In this paper we analyze an econometric model for non-stationary asset returns. Volatility dynamics are modelled by nonparametric regression; consistency and asymptotic normality of a symmetric and of a one-sided kernel estimator are outlined with remarks on the bandwidth decision. Further attention is paid to asymmetry and heavy tails of the return distribution, involved by the framework for innovations. We survey the practicability and automatization of the implementation. For simulated price processes and a multitude of financial time series we observe a satisfying model approximation and good short-term forecasting abilities of the univariate approach. The non-stationary regression model outperforms parametric risk models and famous ARCH-type implementations.

Investigation of solute transport in nonstationary unsaturated flow fields

Abstract. Most theoretical work on analyzing plume spreading at the field scale in a partially saturated heterogeneous formation assumes weak stationarity of velocity field. While this assumption is not applicable to the case of a bounded flow domain, the nonstationarity in fluctuations of unsaturated velocity fields is induced through the presence of the boundary conditions in the flow domain. In this work, we attempt to quantify the large-time macrodispersion in nonstationary unsaturated velocity fields caused by the presence of a fixed head boundary condition. Application of the perturbation-based nonstationary spectral approach leads to an analytical expression for the macrodispersion describing the field-scale dispersive solute flux in terms of the statistical moments of two formation parameters: the Gardener's parameter (α) and the saturated hydraulic conductivity (Ks). The results predicted from the expression indicate that the enhanced unsaturated plume spreading can arise from a larger correlation scale of ln Ks or ln α fields. In addition, the α-parameter takes the role in reducing the field-scale plume spreading.

Uncertainty in hydrologic modelling for estimating hydrologic response due to climate change (Santiam River, Oregon)

AbstractThis paper explores the predicted hydrologic responses associated with the compounded error of cascading global circulation model (GCM) uncertainty through hydrologic model uncertainty due to climate change. A coupled groundwater and surface water flow model (GSFLOW) was used within the differential evolution adaptive metropolis (DREAM) uncertainty approach and combined with eight GCMs to investigate uncertainties in hydrologic predictions for three subbasins of varying hydrogeology within the Santiam River basin in Oregon, USA. Predictions of future hydrology in the Santiam River include increases in runoff in the fall and winter months and decreases in runoff for the spring and summer months. One‐year peak flows were predicted to increase whereas 100‐year peak flows were predicted to slightly decrease. The predicted 10‐year 7‐day low flow decreased in two subbasins with little groundwater influences but increased in another subbasin with substantial groundwater influences. Uncertainty in GCMs represented the majority of uncertainty in the analysis, accounting for an average deviation from the median of 66%. The uncertainty associated with use of GSFLOW produced only an 8% increase in the overall uncertainty of predicted responses compared to GCM uncertainty. This analysis demonstrates the value and limitations of cascading uncertainty from GCM use through uncertainty in the hydrologic model, offers insight into the interpretation and use of uncertainty estimates in water resources analysis, and illustrates the need for a fully nonstationary approach with respect to calibrating hydrologic models and transferring parameters across basins and time for climate change analyses. Copyright © 2012 John Wiley & Sons, Ltd.

Modeling of reflection of detonation and shock waves from a rigid wall in mixtures of a reactive gas and chemically inert particles

An algorithm of approximate calculation of the reflection of detonation waves in mixtures of a reactive gas and chemically inert microparticles has been proposed. Consideration has been given to the case where the gas behind the wave front is in chemical equilibrium (D → D reflection). It has been shown that the presence of the condensed phase can substantially decrease the parameters of the reflected wave (its velocity, pressure, and temperature). Within the framework of a one-dimensional nonstationary approach and with allowance for the detailed kinetics of chemical reactions, the evolution of the shock wave in a stoichiometric hydrogen-oxygen mixture with sand particles in its reflection from a rigid wall has been calculated. The limiting particle concentration below which the reflected wave is of the detonation type and above which it is of the shock type has been found.

Stationarity of the transition probabilities in the Markov chain formulation of owner payments on projects

Stationarity of the transition probabilities in the Markov chain formulation of owner payments on projects

Macrokinetic grounds for a soil microbial growth model

The law of microbial growth in soil following a bell-shaped experimental curve has, until now, had no widely accepted justification. An equation was deduced relating microbial growth dynamics in soils to the initial concentration of the leading component of substrate in the framework of a nonstationary nonequilibrium approach. This equation becomes identical with the equation published by the authors earlier when the initial concentration of the leading substrate component is invariable. This equation is helpful in the identification and discrimination of microbial growth phases and stages of response to chemical action.

Hurst-Kolmogorov Dynamics and Uncertainty1

The nonstatic, ever changing hydroclimatic processes are often described as nonstationary. How- ever, revisiting the notions of stationarity and nonstationarity, defined within stochastics, suggests that claims of nonstationarity cannot stand unless the evolution in time of the statistical characteristics of the process is known in deterministic terms, particularly for the future. In reality, long-term deterministic predictions are dif- ficult or impossible. Thus, change is not synonymous with nonstationarity, and even prominent change at a mul- titude of time scales, small and large, can be described satisfactorily by a stochastic approach admitting stationarity. This ''novel'' description does not depart from the 60- to 70-year-old pioneering works of Hurst on natural processes and of Kolmogorov on turbulence. Contrasting stationary with nonstationary has important implications in engineering and management. The stationary description with Hurst-Kolmogorov stochastic dynamics demonstrates that nonstationary and classical stationary descriptions underestimate the uncertainty. This is illustrated using examples of hydrometeorological time series, which show the consistency of the Hurst- Kolmogorov approach with reality. One example demonstrates the implementation of this framework in the planning and management of the water supply system of Athens, Greece, also in comparison with alternative nonstationary approaches, including a trend-based and a climate-model-based approach. (KEY TERMS: climate variability; climate change; Hurst-Kolmogorov dynamics; planning; stationarity; stochastic models; uncertainty analysis.)

Load distribution performance of super-node based peer-to-peer communication networks: A nonstationary Markov chain approach

Voice over Internet protocol (VoIP) services using peer-to-peer (P2P) technology have become popular in recent years. In P2P-based VoIP networks such as Skype and P2P session initiation protocol (P2PSIP), super nodes are chosen from among all ordinary end-user nodes and handle particular tasks such as the management of user information, call establishment, and traffic relay. Future communication networks based on P2P technology must support a huge number of user nodes. A fundamental analysis of the load distribution in decentralized user-information management is needed to develop efficient and robust communication networks. In this paper, we analyze the performance of the P2P-based dynamic load distribution. In our analytical model, new nodes join the network according to a nonstationary Poisson process, and the stochastic behavior of the number of online nodes is analyzed approximately with an M($t$)/M/$\infty$ queue. We focus on two performance measures that significantly affect the quality of service (QoS) provided to the users: the churn rate and the load of super nodes. Numerical examples show that the performance of the P2P-based VoIP networks is sensitive to the sojourn time of super nodes and the maximum number of nodes managed by a super node.

Development of Diagnosis System for Machine Tool Shaft Inspection

Aiming at reducing cost and time of repair, condition-based shaft faults diagnosis is considered an efficient strategy for machine tool community. While the shaft with faults is operating, its vibration signals normally indicate nonlinear and non-stationary characteristics but Fourier-based approaches have shown limitations for handling this kind of signals. The methodology proposed in this research is to extract the features from shaft faults related vibration signals, from which the corresponding fault condition is then effectively identified. With an incorporation of empirical mode decomposition (EMD) method, the model applied in this research embraces some characteristics, like zero-crossing rate and energy, of intrinsic mode functions (IMFs) to represent the feature of the shaft condition.

Numerical modeling of the coal-and-gas outburst gasdynamics

The article discusses the problem of coal outbursts into mined-out space based on the nonstationary and nonequilibrium velocity and temperature approach of the mechanics of inhomogeneous media, presents the math models with and without taking account of intergranular pressure of solid particles, and compares the new assessment with the available calculation and experimental references. Based on the analysis of the mixture flow behavior, the authors have found some rules in the relationships of depression waves, shock waves, initial concentration and diameter of particles in coal-and-gas mixtures.

Estimativa da probabilidade do evento extremo de precipitação de janeiro de 2000 no Vale do Paraíba, baseada na distribuição generalizada de pareto

Um evento extremo de precipitacao ocorreu na primeira semana do ano 2000, de 1o a 5 de janeiro, no Vale do Paraiba, parte leste do Estado de Sao Paulo, Brasil, causando enorme impacto socioeconomico, com mortes e destruicao. Este trabalho estudou este evento em 10 estacoes meteorologicas selecionadas que foram consideradas como aquelas tendo dados mais homogeneos do Que outras estacoes na regiao. O modelo de distribuicao generalizada de Pareto (DGP) para valores extremos de precipitacao de 5 dias foi desenvolvido, individualmente para cada uma dessas estacoes. Na modelagem da DGP, foi adotada abordagem nao-estacionaria considerando o ciclo anual e tendencia de longo prazo como co-variaveis. Uma conclusao desta investigacao e que as quantidades de precipitacao acumulada durante os 5 dias do evento estudado podem ser classificadas como extremamente raras para a regiao, com probabilidade de ocorrencia menor do que 1% para maioria das estacoes, e menor do que 0,1% em tres estacoes.