A stochastic model for localized disturbances and its applications

A stochastic model for local disturbances, particularly for a temporal harmonic with random modulations in amplitude and/or phase, is proposed in this paper. Results for the second moment responses of a linear single-degree-of-freedom system to this type of stochastic loading demonstrate a significant change in response characteristics due to a small uncertainty. A local phenomenon may last much longer and resonance may be smeared to a broad range. Integrated with wavelet transform, the proposed approach may be used to model a random process with non-stationary frequency content. Especially, it can be effectively used for Monte Carlo simulation to generate large size of samples that have similar characteristics in time and frequency domains as a pre-selected mother sample has. The technique has a great potential for the case where uncertainty study is warranted but the available samples are limited.     

Probabilistic analysis of a static frame model

This paper describes our efforts during our participation in the Sandia Validation Workshop. The focus of the paper is the calibration of material models and simulation of random fields to characterize the variations of material properties across spatial field. Both parametric and non-parametric methods were used to represent uncertainty. Part of the challenge of this problem is the small amount of data that is available for the necessary probabilistic analyses in support of calibration, validation, accreditation and prediction activities. The analysis methods and corresponding results are described.     

Response level crossing rate of a linear system excited by a partially specified Gaussian load process

The problem of determining the maximum mean response level crossing rate of a linear system driven by a partially specified Gaussian load process has been considered. The partial specification of the load is given only in terms of its total average energy. The critical input power spectral (PSD) function, which maximizes the mean response level crossing rate, is obtained. The critical input PSD turns out to be highly narrow-banded which fails to capture the erratic nature of the excitation. Consequently, the trade-off curve between the maximum mean response level crossing rate and the maximum disorder in the input process, quantified in terms of its entropy rate, has been generated. The method of Pareto optimization is used to tackle the conflicting objectives of the simultaneous maximization of the mean response level crossing rate and the input entropy rate. The non-linear multi-objective optimization has been carried out using a recently developed multi-criteria genetic algorithm scheme. Illustrative example of determining the critical input of an axially vibrating rod, excited by a partially specified stationary Gaussian load process, has been considered.     

Comparison of finite element reliability methods

The spectral stochastic finite element method (SSFEM) aims at constructing a probabilistic representation of the response of a mechanical system, whose material properties are random fields. The response quantities, e.g. the nodal displacements, are represented by a polynomial series expansion in terms of standard normal random variables. This expansion is usually post-processed to obtain the second-order statistical moments of the response quantities. However, in the literature, the SSFEM has also been suggested as a method for reliability analysis. No careful examination of this potential has been made yet. In this paper, the SSFEM is considered in conjunction with the first-order reliability method (FORM) and with importance sampling for finite element reliability analysis. This approach is compared with the direct coupling of a FORM reliability code and a finite element code. The two procedures are applied to the reliability analysis of the settlement of a foundation lying on a randomly heterogeneous soil layer. The results are used to make a comprehensive comparison of the two methods in terms of their relative accuracies and efficiencies.     

Sensitivity of generation reserve requirements in deregulated power systems

Since demand for power exhibits great variability the amount of firm energy to be purchased to meet real time demand based on forecasts is usually different from the realized demand for that period. The role of generation reserves is to meet the real time fluctuations of power demand. The predictable part of the demand is met through purchases of firm energy. In this paper a model is presented to determine optimal quantities of firm energy and generation reserves to meet random demands. The model is then parameterized introducing a set of factors to perform a sensitivity study. A full factorial experiment is designed to study the impact of five factors on the response variable (i.e., proportion of generation reserves on the total purchased quantity). An example consisting of 640 simulations corresponding to 2⁵ treatment combinations evaluated over 20 randomly generated mean demands is used to identify significant factors on the response variable. Results from the experiment suggest that generation reserve requirements should be adjusted considering changes in significant factors and in the mean demand over the dispatch interval.     

Extremes of random fields over arbitrary domains with application to concrete rupture stresses

To find the exact probability distribution of the global maximum or minimum of a random field within a bounded domain is a pending problem even for Gaussian fields. Except for very special examples of fields, recourse must be taken to approximate reasoning or asymptotic considerations to be judged with respect to accuracy by simulations. In this paper, the problem is addressed through a functional equation that leads to the definition of a class of distribution functions that depend solely on process or field characteristics and domain quantities that can be calculated explicitly. This distribution function class is studied for Gaussian processes in earlier works by the author and it has been obtained explicitly for Gaussian fields on rectangular domains in the plane. Simulation studies show that rather good predictions are obtained for sufficiently smooth wide band Gaussian processes and fields. In this paper, the distribution function is obtained in general for Gaussian fields over arbitrary bounded domains with piecewise continuous and differentiable boundaries, and as in earlier works the distribution function is tested against empirical distribution functions obtained by simulation of sample functions of a smooth approximately Gaussian field, herein called a broken line Hino field. For completeness this particular field type is defined in appendix a and appendix b. The paper concludes with a statistical application on data for plain concrete tensile strength.     

羰基铁类随机混合吸波材料等效电磁参数的计算

本文为计及多重散射偶极子间的相互作用，引入参量εｈ和μｈ，导得一组公式。它不仅能计算铁氧体类也能计算羰基铁类的随机混合吸波材料的等效电磁参数，均与实验结果吻合良好。     

Random Vibration of Systems with Viscoelastic Memory

The equation of motion of linear dynamic systems with viscoelastic memory is usually expressed in a integrodifferential form, and its numerical solution is computationally heavy. In two recent papers, the writers suggested that the system memory be accounted for through the introduction of a number of additional internal variables. Following this approach, the motion of the system is governed by a set of first-order, linear differential equations, whose solution is quite easy. In this paper, the approach is extended to single-degree-of-freedom systems subjected to random, nonstationary excitation. The equations governing the time variation of the second-order statistics are derived, and an effective step-by-step solution procedure is proposed. Numerical example shows the accuracy of the procedure for white and nonwhite excitations.     

Critical building separation distance in reducing pounding risk under earthquake excitation

A separation distance between adjacent buildings is provided to reduce the risk of pounding of adjacent buildings under seismic excitations. It should be recognized that the evaluation of the critical separation distance is a one-sided barrier crossing problem while the problem of structural design under seismic excitations is a two-sided crossing problem. A procedure for assessing the required separation distance with or without considering possible uncertainty in structural properties was presented based on the reliability methods and random vibration theory. The procedure was used to carry out parametric analyses. It is shown that use of the complete quadratic combination (CQC) rule with the modal responses employed for designing structures may over- or underestimate the critical separation distance, depending on the damping ratios and the closeness of the natural vibration periods of adjacent buildings. This is due to not only one-sided versus two-sided crossing problem but also the approximation in the CQC rule. Further, the effect of the uncertainty in structural properties on the estimated separation is investigated. The results indicate that this uncertainty tends to increase the required critical separation distance.     

Microstress estimate of stochastically heterogeneous structures by the functional perturbation method: A one dimensional example

A new functional perturbation method (FPM) for calculating the probabilistic response of stochastically heterogeneous, linear elastic structures is developed. The method is based on treating the governing differential operator as well as the unknown displacement function as a functional of material modulus field. By executing a functional perturbation around the homogeneous case, a set of successive differential equations is obtained and solved, from which the average and variance of any local parameter (displacements, stresses, strains) can be found. For a linear problem, the equations to be solved in each approximation order differ from the one for the homogeneous case by a pseudo external loading (right hand side) part only. Thus, only the Green function for the homogeneous case is needed for an analytical solution of the corresponding heterogeneous problem. A one dimensional stochastically heterogeneous rod embedded in a uniform shear resistant elastic medium is solved as an example. The statistical variance of displacements and stresses are found analytically, including the edge regions. Morphological (grain size) and material (modulus) effects on the stochastic response are demonstrated. The above results are essential for estimating the stochastic features of local stress concentrations, which are the source for many strength-related macro properties of materials. Extensive usage of generalized functions (Dirac operator and its derivatives) is needed for the analysis.