Second-moment Analysis Research Articles

Investigating the Number of Monte Carlo Simulations for Statistically Stationary Model Outputs

The number of random fields required to capture the spatial variability of soil properties and their impact on the performance of geotechnical systems is often varied. However, the number of random fields required to obtain higher-order statistical moments of model outputs has not yet been studied. This research aims to investigate the number of Monte Carlo simulations needed to achieve stationary higher-order statistics of a pore pressure head in an unsaturated soil slope under steady-state infiltration. The study recommends using at least 500 Monte Carlo samples for the probabilistic analysis of geotechnical engineering models. A more conservative choice for up to second-moment analysis is 1000 samples. The analysis reveals significant variations in skewness, which become stationary for all mesh grids when the number of samples exceeds 15,000. Kurtosis stabilizes only when the number of samples reaches 25,000. The pore pressure head in the unsaturated zone is less uncertain. Additionally, the probability density function of the pore pressure head follows a leptokurtic distribution.

Uncertainty Quantification for Aircraft Noise Emission Simulation: Methods and Limitations

Implementing measures for the reduction of aircraft noise impact, such as optimization of flight paths and aircraft, requires sophisticated simulation capabilities. These tools have to incorporate simulation of aircraft noise generation at the source (i.e., emission) and account for prevailing sound propagation effects to ultimately predict noise levels as received on the ground. Obviously, understanding the associated uncertainties is crucial when aiming at a reliable and meaningful assessment. It also becomes essential when comparing different technologies, mixing experimental and numerical data, or using simulation methods of different fidelity (e.g., semi-empirical and first-order methods). This research focuses on quantifying uncertainties in the first step in aircraft noise simulation (i.e., the prediction of the emission situation). The quantified uncertainties reflect imperfections of models for different aircraft noise sources and variability of model input parameters at different operating conditions. A general framework is presented, which also accounts for limited knowledge of the underlying data distributions, and quantitative comparisons of different uncertainty methods are provided. In particular, the first-order second-moment analysis is compared to higher-order polynomial chaos methods, and the advantages and disadvantages of the different methods are discussed.

A reduced modal subspace approach for damped stochastic dynamic systems

A novel method for characterising and propagating system uncertainty in structures subjected to dynamic actions is proposed, whereby modal shapes, frequencies and damping ratios constitute the random quantities. The latter, defined in the modal subspace rather than the full geometrical space, reduce the number of the random variables and the size of the dynamic problem. A numerical procedure is presented for their identification by calibrating their probabilistic definition in line with the geometrical space. A high-order perturbation technique is proposed for the multi-fidelity response quantification by means of an ad hoc extension of the conventional perturbation method. The approach involves a set of auxiliary deterministic differential equations to be adaptively solved with the piecewise exact method, and moment-cumulant relationships are employed to approximate high-order moments. Finally, a polynomial chaos expansion approach is adopted to complement the second-moment analysis for spectral quantification with the modal subspace reduction. Demonstrated on a multi-storey steel frame with semi-rigid connections and a simply supported bridge subjected to a moving load, the proposed variants exhibit improved performance with respect to the conventional second-order and improved perturbation, as well as increased flexibility, enabling the analyst to decide, on-demand, the level of fidelity, balancing accuracy and computational effort.

A solid-state 1H-NMR study of the dynamic structure of ZIF-8 and its role in the adsorption of bulky molecules

In order to clarify the adsorption mechanism of the zeolitic imidazolate framework, ZIF-8, for bulky molecules larger than its aperture diameter, the local structure of ZIF-8 and its host–guest interactions were studied by adsorption kinetics, potential energy analysis, and solid-state 1H nuclear magnetic resonance (1H-NMR) spectroscopy. Adsorption kinetics measurements lead to apparent diffusion coefficients for CS2, CDCl3, and CCl4 in ZIF-8 that provide residence times for each molecule in the ZIF-8 micropores. Potential energy analyses using van der Waals pairwise interactions reveal two kinds of feasible sites for bulky molecules in the ZIF-8 micropores, where there are minimal intermolecular interactions between an adsorbate and the pore wall. Each site lies on one of the four diagonal axes of the cubic lattice of the ZIF-8 unit cell. One set of sites corresponds to the side of the micropore where methyl groups form a bottleneck, and the other to the side where CH moieties form the bottleneck. Second-moment analysis of the 1H-NMR resonance line reveals that the 2-methylimidazolate rings undergo flip motions, with flip angles of ~55°, in addition to the rapid axial rotations of their methyl groups. Temperature-dependent spin–lattice relaxation time analyses indicate that adsorptions of these molecules reduce the motions of the 2-methylimidazolate rings. In particular, steric hindrance from bulky molecules such as CDCl3 and CCl4 significantly lowers the flipping frequency of the 2-methylimidazolate ring. The flipping of the 2-methylimidazolate ring results in instantaneous aperture expansion that enables bulky molecules to pass through the ZIF-8 aperture.

Comparison of methods for non-stationary hydrologic frequency analysis: Case study using annual maximum daily precipitation in Taiwan

Future climatic conditions likely will not satisfy stationarity assumption. To address this concern, this study applied three methods to analyze non-stationarity in hydrologic conditions. Based on the principle of identifying distribution and trends (IDT) with time-varying moments, we employed the parametric weighted least squares (WLS) estimation in conjunction with the non-parametric discrete wavelet transform (DWT) and ensemble empirical mode decomposition (EEMD). Our aim was to evaluate the applicability of non-parameter approaches, compared with traditional parameter-based methods. In contrast to most previous studies, which analyzed the non-stationarity of first moments, we incorporated second-moment analysis. Through the estimation of long-term risk, we were able to examine the behavior of return periods under two different definitions: the reciprocal of the exceedance probability of occurrence and the expected recurrence time. The proposed framework represents an improvement over stationary frequency analysis for the design of hydraulic systems. A case study was performed using precipitation data from major climate stations in Taiwan to evaluate the non-stationarity of annual maximum daily precipitation. The results demonstrate the applicability of these three methods in the identification of non-stationarity. For most cases, no significant differences were observed with regard to the trends identified using WLS, DWT, and EEMD. According to the results, a linear model should be able to capture time-variance in either the first or second moment while parabolic trends should be used with caution due to their characteristic rapid increases. It is also observed that local variations in precipitation tend to be overemphasized by DWT and EEMD. The two definitions provided for the concept of return period allows for ambiguous interpretation. With the consideration of non-stationarity, the return period is relatively small under the definition of expected recurrence time comparing to the estimation using the reciprocal of the exceedance probability of occurrence. However, the calculation of expected recurrence time is based on the assumption of perfect knowledge of long-term risk, which involves high uncertainty. When the risk is decreasing with time, the expected recurrence time will lead to the divergence of return period and make this definition inapplicable for engineering purposes.

Reliability of sight distance at stop-control intersections

The American Association of State Highway and Transportation Officials presents guidelines for intersection sight distance (ISD) based on extreme values of the component design variables such as speed and time gap. The guidelines for a stopped vehicle at a stop-control intersection on a minor road assume that the component design variables are deterministic. This paper presents a reliability method that considers the design variables as random. The method uses the means and variances of the probability distributions of the random variables and accounts for their correlations. A safety margin is defined as the difference between available and required ISD. Relationships for the mean and standard deviation of the safety margin are developed based on first-order second-moment analysis. The proposed method is useful for ISD design of a new intersection or redesign of an existing intersection for a desired reliability level. For single-unit trucks, the obstruction clearances from the minor- and major-road pavement edges are approximately 10% higher than those for passenger cars. The proposed method should be of interest to highway engineers involved in road safety and management.

Temperature Determination by EPR at 275 GHz and the Detection of Temperature Jumps in Aqueous Samples.

Second-moment analysis along two dimensions of continuous-wave EPR spectra of nitroxides enables EPR thermometry in a broad temperature range. Simulations show that the temperature can be derived in both the slow-motion and the fast-motion regime, which is experimentally verified at 275 GHz for H2O/glycerol (50/50% by volume) and pure water. We demonstrate that this tool allows the calibration of temperature jumps induced by infrared laser irradiation of a submicroliter sample in the single-mode cavity of a 275 GHz spectrometer, which prepares for kinetic studies of processes involving paramagnetic species.

Shallow foundation response variability due to soil and model parameter uncertainty

Geotechnical uncertainties may play crucial role in response prediction of a structure with substantial soil-foundation-structure-interaction (SFSI) effects. Since the behavior of a soil-foundation system may significantly alter the response of the structure supported by it, and consequently several design decisions, it is extremely important to identify and characterize the relevant parameters. Moreover, the modeling approach and the parameters required for the modeling are also critically important for the response prediction. The present work intends to investigate the effect of soil and model parameter uncertainty on the response of shallow foundation-structure systems resting on dry dense sand. The SFSI is modeled using a beam-on-nonlinear-winkler-foundation (BNWF) concept, where soil beneath the foundation is assumed to be an assembly of discrete, nonlinear elements composed of springs, dashpots and gap elements. The sensitivity of both soil and model input parameters on shallow foundation responses are investigated using first-order second-moment (FOSM) analysis and Monte Carlo simulation through Latin hypercube sampling technique. It has been observed that the degree of accuracy in predicting the responses of the shallow foundation is highly sensitive soil parameters, such as friction angle, Poisson’s ratio and shear modulus, rather than model parameters, such as stiffness intensity ratio and spring spacing; indicating the importance of proper characterization of soil parameters for reliable soilfoundation response analysis.

Antiferromagnetic Potts Model on the Erdős-Rényi Random Graph

We study the antiferromagnetic Potts model on the Poissonian Erdős-Rényi random graph. By identifying a suitable interpolation structure and an extended variational principle, together with a positive temperature second-moment analysis we prove the existence of a phase transition at a positive critical temperature. Upper and lower bounds on the temperature critical value are obtained from the stability analysis of the replica symmetric solution (recovered in the framework of Derrida-Ruelle probability cascades) and from an entropy positivity argument.

Probabilistic Assessment for Seismic Performance of Pile-Supported Wharves

The main objective of this study is to investigate the influence of uncertainties associated with the material properties on the seismic performance of pile-supported wharves. For this purpose a two-dimensional finite difference model, representing typical pile-supported wharf structures from western United States has been constructed using software FLAC2D. Incremental dynamic analysis has been applied to evaluate the response of wharf structure under different levels of seismic loading. The uncertainties at both structural and geotechnical parameters have been investigated using a tornado diagram and a Wrst-Order Second-Moment (FOSM) analysis. It has been found that the uncertainties at the dead load of structure, friction angle of rock fill and the porosity of rock fill contribute most to the variability of the displacement ductility factor of the pile- supported wharf structures. Based on the results, design considerations have been provided.

Reliability Analysis of Minimum Pedestrian Green Interval for Traffic Signals

AbstractThe current method of computing the minimum pedestrian green interval for intersection signal timing assumes that the component variables are deterministic. This paper presents a probabilistic method in which the pedestrian start-up time and walking speed are random variables. To establish pedestrian characteristics, data were collected at 14 intersections in downtown, suburban, and tourist areas. The method is based on a safety margin that is defined as the difference between the supplied and demanded green intervals, where the demanded green interval is a random variable. Relationships for the mean and standard deviation of the safety margin of the demanded green interval are developed on the basis of the first-order second-moment analysis. A closed-form solution for the minimum supplied green interval is then derived as a function of the relevant variables, including the vehicular intergreen interval and its component variables. A procedure for establishing the walk and the flashing “don’t walk...

Uncertainty and sensitivity analysis techniques for hydrologic modeling

Formal uncertainty and sensitivity analysis techniques enable hydrologic modelers to quantify the range of likely outcomes, likelihood of each outcome and an assessment of key contributors to output uncertainty. Such information is an improvement over standard deterministic point estimates for making engineering decisions under uncertainty. This paper provides an overview of various uncertainty analysis techniques that permit mapping model input uncertainty into uncertainty in model predictions. These include Monte Carlo simulation, first-order second-moment analysis, point estimate method, logic tree analysis and first-order reliability method. Also presented is an overview of sensitivity analysis techniques that permit identification of those parameters that control the uncertainty in model predictions. These include stepwise regression, mutual information (entropy) analysis and classification tree analysis. Two case studies are presented to demonstrate the practical applicability of these techniques. The paper also discusses a systematic framework for carrying out uncertainty and sensitivity analyses.

Real-Time Demand Estimation and Confidence Limit Analysis for Water Distribution Systems

A real-time estimation of water distribution system state variables such as nodal pressures and chlorine concentrations can lead to savings in time and money and provide better customer service. While a good knowledge of nodal demands is prerequisite for pressure and water quality prediction, little effort has been placed in real-time demand estimation. This study presents a real-time demand estimation method using field measurement provided by supervisory control and data acquisition systems. For real-time demand estimation, a recursive state estimator based on weighted least-squares scheme and Kalman filter are applied. Furthermore, based on estimated demands, real-time nodal pressures and chlorine concentrations are predicted. The uncertainties in demand estimates and predicted state variables are quantified in terms of confidence limits. The approximate methods such as first-order second-moment analysis and Latin hypercube sampling are used for uncertainty quantification and verified by Monte Carlo simulation. Application to a real network with synthetically generated data gives good demand estimations and reliable predictions of nodal pressure and chlorine concentration. Alternative measurement data sets are compared to assess the value of measurement types for demand estimation. With the defined measurement error magnitudes, pipe flow data are significantly more important than pressure head measurements in estimating demands with a high degree of confidence.

Evaluating height structure in Scots pine forests using marked point processes

In this study, the second-moment analysis of marked spatial point processes is applied to the characterization of the tree height distribution in two Scots pine ( Pinus sylvestris L.) forests in the Central Mountain Range of Spain. The cumulative function Lm(d) weighted by the normalized mark variance is proposed to analyse the second-order properties of marked point patterns. The empirical Lm(d) was compared with two null models to assess the relationship between the spatial distribution of the trees and the tree height correlations: the first null model was used to characterize the spatial clustering of the trees and was derived from the complete spatial randomness model used with Ripley’s K(d) function. The second null model, which is derived from the random labelling model used with the intertype second-moment measure K12(d) (type 1 intensity conditioned to the type 2 intensity and vice versa), allows us to identify the mark correlations. The performance of the technique was assessed through simulated marked point patterns. The second-moment analysis showed that most of the analysed Scots pine stands have a uniform height distribution at small scale and greater heterogeneity at large scales, with the exception of an upper altitudinal stand, which exhibited heterogeneity at short distances. These results demonstrate the utility of second-moment analysis of marked point processes for characterizing height structure in forest stands and the interaction between the height and the spatial pattern of the trees.

Probabilistic assessment for seismic performance of port structures

Past experience has shown that ports are often susceptible to severe damage during earthquakes. From field damage data of 1995 Kobe earthquake, it is observed that the seismic behavior of port structures shows significant variability. In this study, a 2D numerical model, representing PC1 berth located in Port Island, Kobe and damaged in the 1995 Kobe earthquake, has been developed and used to simulate seismic behavior. It has been found that the uncertainties in the friction angle and the shear modulus of reclaimed soil contribute most to the variability of the residual horizontal displacement (RHD) response of the quay wall of port structures. To investigate the propagation of uncertainties of soil–structure system to the quay wall, a tornado diagram and a first-order second-moment analysis are used. Uncertainty of ground motions has also been investigated. Based on the results, design considerations have been provided.

Job Displacement Risk and the Cost of Business Cycles

This paper analyzes the welfare costs of business cycles when workers face uninsurable job displacement risk. The paper uses a simple macroeconomic model with incomplete markets to show that cyclical variations in the long-term earnings losses of displaced workers can generate arbitrarily large cost of business cycles even if the variance of individual income changes is constant over the cycle. In addition to the theoretical analysis, this paper conducts a quantitative study of the cost of business cycles using empirical evidence on the long-term earnings losses of US workers. The quantitative analysis shows that realistic variations in job displacement risk generate sizable costs of business cycles, even though a second-moment analysis would suggest negligible costs. (JEL E21, E24, E32, J63)

Conformation of a Peptide Encompassing the Proton Translocation Channel of Vacuolar H +-ATPase

The structural properties of a crucial transmembrane helix for proton translocation in vacuolar ATPase are studied using double site-directed spin-labeling combined with electron spin resonance (ESR) (or electron paramagnetic resonance) and circular dichroism spectroscopy in sodium dodecyl sulfate micelles. For this purpose, we use a synthetic peptide derived from transmembrane helix 7 of subunit a from the yeast Saccharomyces cerevisiae vacuolar proton-translocating ATPase that contains two natural cysteine residues suitable for spin-labeling. The interspin distance is calculated using a second-moment analysis of the methanethiosulfonate spin-label ESR spectra at 150 K. Molecular dynamics simulation is used to study the effect of the side-chain dynamics and backbone dynamics on the interspin distance. Based on the combined results from ESR, circular dichroism, and molecular dynamics simulation we conclude that the peptide forms a dynamic α-helix. We discuss this finding in the light of current models for proton translocation. A novel role for a buried charged residue (H729) is proposed.

Simultaneous near-field and far-field imaging of the11.9‐nmNi-likeSnsoft-x-ray laser

We report on two-dimensional near-field imaging experiments of the 11.9-nm Sn x-ray laser that were performed with a set of Mo/Y multilayer mirrors having reflectivities of up to {approx}45% at normal and at 45{sup o} incidence. Second-moment analysis of the x-ray laser emission was used to determine values of the x-ray beam propagation factor M{sup 2} for a range of irradiation parameters. The results reveal a reduction of M{sup 2} with increasing prepulse amplitude. The spatial size of the output is a factor of {approx}2 smaller than previously measured for the 14.7-nm Pd x-ray laser, while the distance of the x-ray emission with respect to the target surface remains roughly the same.

Simultaneous imaging of the near- and far-field intensity distributions of the Ni-like Sn X-ray laser

We report two-dimensional near-field imaging experiments of the 11.9-nm Sn X-ray laser that were performed with a set of novel Mo/Y multilayer mirrors having reflectivities of up to ∼40% at normal and at 45° incidence. Second-moment analysis of the X-ray laser emission was used to determine values of the X-ray beam propagation factor M2 for a range of irradiation parameters. The results reveal a reduction of M2 with increasing prepulse intensity. The spatial size of the output is a factor of ∼2 smaller than previously measured for the 14.7-nm Pd X-ray laser, while the distance of the X-ray emission with respect to the target surface remains roughly the same .

Stochastic equations of rigid-thermo-viscoplasticity in metal forming process

Stochastic rigid-thermo-viscoplastic metal forming process is described and discussed. The theoretical formulation for stochastic equations in rigid-thermo-viscoplasticity is presented. It is based on the combination of the second-order perturbation technique and second-moment analysis. The principle allows incorporation of system uncertainties into finite-element equations. Probabilistic distributions for temperatures and strains taking into account random initial and boundary conditions are given. Example of stochastic analysis in shell nosing process is shown.