Statistics for Spatial Data.

Recently there has been a growing interest in designing efficient methods for the solution of ordinary/partial differential equations with random inputs. To this end, stochastic Galerkin methods appear to be superior to other nonsampling methods and, in many cases, to several sampling methods. However, when the governing equations take complicated forms, numerical implementations of stochastic Galerkin methods can become nontrivial and care is needed to design robust and efficient solvers for the resulting equations. On the other hand, the traditional sampling methods, e.g., Monte Carlo methods, are straightforward to implement, but they do not offer convergence as fast as stochastic Galerkin methods. In this paper, a high-order stochastic collocation approach is proposed. Similar to stochastic Galerkin methods, the collocation methods take advantage of an assumption of smoothness of the solution in random space to achieve fast convergence. However, the numerical implementation of stochastic collocation is trivial, as it requires only repetitive runs of an existing deterministic solver, similar to Monte Carlo methods. The computational cost of the collocation methods depends on the choice of the collocation points, and we present several feasible constructions. One particular choice, based on sparse grids, depends weakly on the dimensionality of the random space and is more suitable for highly accurate computations of practical applications with large dimensional random inputs. Numerical examples are presented to demonstrate the accuracy and efficiency of the stochastic collocation methods.

High-Order Collocation Methods for Differential Equations with Random Inputs

OR/MS research in disaster operations management


 The spectral ratio between horizontal and vertical components (H/V ratio) of microtremors measured at the ground surface has been used to estimate fundamental periods and amplification factors of a site, although this technique lacks theoretical background. The aim of this article is to formulate the H/V technique in terms of the characteristics of Rayleigh and Love waves, and to contribute to improve the technique. The improvement includes use of not only peaks but also troughs in the H/V ratio for reliable estimation of the period and use of a newly proposed smoothing function for better estimation of the amplification factor. The formulation leads to a simple formula for the amplification factor expressed with the H/V ratio. With microtremor data measured at 546 junior high schools in 23 wards of Tokyo, the improved technique is applied to mapping site periods and amplification factors in the area.

Ground Motion Characteristics Estimated from Spectral Ratio between Horizontal and Verticcl Components of Mietremors.

http://www.ukm.my/kamal3/psm/pfpstochastics.pdf

The stochastic finite element method: Past, present and future

With the aid of the finite element method, the present paper deals with the problem of structural response variability resulting from the spatial variability of material properties of structures, when they are subjected to static loads of a deterministic nature. The spatial variabilities are modeled as two‐dimensional stochastic fields. The finite element discretization is performed in such a way that the size of each element is sufficiently small. Then, the present paper takes advantage of the Neumann expansion technique in deriving the finite element solution for the response variability within the framework of the Monte Carlo method. The Neumann expansion technique permits more detailed comparison between the perturbation and Monte Carlo solutions for accuracy, convergence, and computational efficiency. The result from such a Monte Carlo method is also compared with that based on the commonly used perturbation method. The comparison shows that the validity of the perturbation method is limited to the c...

Neumann Expansion for Stochastic Finite Element Analysis

A method by which sample fields of a multidimensional non‐Gaussian homogeneous stochastic field can be generated is developed. The method first generates Gaussian sample fields and then maps them into non‐Gaussian sample fields with the aid of an iterative procedure. Numerical examples indicate that the procedure is very efficient and generated sample fields satisfy the target spectral density and probability distribution function accurately. The proposed method has a wide range of applicability to engineering problems involving stochastic fields where the Gaussian assumption is not appropriate.

Digital Generation of Non‐Gaussian Stochastic Fields

Synthetic aperture radar (SAR) is remarkable for its capability to record the backscattering coefficient, the physical value of the earth’s surface, regardless of weather condition or sun illumination. Therefore, SAR is a powerful tool that can be utilized to develop a universal method to comprehend damaged areas in disasters such as earthquakes, forest fires, and floods. We performed a feasibility study on backscattering characteristics of damaged areas in the 1995 Hyogoken-Nanbu (Kobe), Japan, earthquake using the preand post-event ERS images, revealing that the backscattering coefficient and intensity correlation between the two attained values were significantly lowered in hard-hit areas. The evaluation, however, was performed without speckle noise reduction. We also investigated the effects of speckle noise reduction and pixel-window size in evaluating building damage using the difference in the backscattering coefficient and correlation coefficient of the pre- and post-event ERS images. From the analysis, an optimum window size for the damage evaluation was obtained. It was also found that the accuracy of damage detection is not significantly improved for speckle-reduction filtering of window size larger than 21321 pixels. We developed an automated method to detect hard-hit areas based on the discriminant analysis, and compared the detected distribution with a damage survey result. [DOI: 10.1193/1.1774182]

Use of Satellite SAR Intensity Imagery for Detecting Building Areas Damaged Due to Earthquakes

SUMMARY Fragility curves express the probability of structural damage due to earthquakes as a function of ground motion indices, e.g., PGA, PGV. Based on the actual damage data of highway bridges from the 1995 Hyogoken-Nanbu (Kobe) earthquake, a set of empirical fragility curves was constructed. However, the type of structure, structural performance (static and dynamic) and variation of input ground motion were not considered to construct the empirical fragility curves. In this study, an analytical approach was adopted to construct fragility curves for highway bridge piers of speciCc bridges. A typical bridge structure was considered and its piers were designed according to the seismic design codes in Japan. Using the strong motion records from Japan and the United States, non-linear dynamic response analyses were performed, and the damage indices for the bridge piers were obtained. Using the damage indices and ground motion indices, fragility curves for the bridge piers were constructed assuming a lognormal distribution. The analytical fragility curves were compared with the empirical ones. The proposed approach may be used in constructing the fragility curves for highway bridge structures. Copyright ? 2001 John Wiley & Sons, Ltd.

Effect of earthquake ground motions on fragility curves of highway bridge piers based on numerical simulation

Fragility curves are found to be useful tools for predicting the extent of probable damage. They show the probability of highway structure damage as a function of strong motion parameters, and they allow the estimation of a level of damage probability for a known ground motion index. In this study, an analytical approach was adopted to develop the fragility curves for highway bridges based on numerical simulation. Four typical RC bridge piers and two RC bridge structures were considered, of which one was a non-isolated system and the other was an isolated system, and they were designed according to the seismic design code in Japan. From a total of 250 strong motion records, selected from Japan, the United States, and Taiwan, non-linear time history analyses were performed, and the damage indices for the bridge structures were obtained. Using the damage indices and ground motion parameters, fragility curves for the four bridge piers and the two bridge structures were constructed assuming a lognormal distribution. It was found that there was a significant effect on the fragility curves due to the variation of structural parameters. The relationship between the fragility curve parameters and the over-strength ratio of the structures was also obtained by performing a linear regression analysis. It was observed that the fragility curve parameters showed a strong correlation with the over-strength ratio of the structures. Based on the observed correlation between the fragility curve parameters and the over-strength ratio of the structures, a simplified method was developed to construct the fragility curves for highway bridges using 30 non-isolated bridge models. The simplified method may be a very useful tool to construct the fragility curves for non-isolated highway bridges in Japan, which fall within the same group and have similar characteristics. Copyright © 2003 John Wiley & Sons, Ltd.

Fumio Yamazaki

Papers

Neumann Expansion for Stochastic Finite Element Analysis

Digital Generation of Non‐Gaussian Stochastic Fields

Use of Satellite SAR Intensity Imagery for Detecting Building Areas Damaged Due to Earthquakes

Effect of earthquake ground motions on fragility curves of highway bridge piers based on numerical simulation

A simplified method of constructing fragility curves for highway bridges