Masanobu Shinozuka

A Framework to Quantitatively Assess and Enhance the Seismic Resilience of Communities

This paper presents a conceptual framework to define seismic resilience of communities and quantitative measures of resilience that can be useful for a coordinated research effort focusing on enhancing this resilience. This framework relies on the complementary measures of resilience: “Reduced failure probabilities,” “Reduced consequences from failures,” and “Reduced time to recovery.” The framework also includes quantitative measures of the “ends” of robustness and rapidity, and the “means” of resourcefulness and redundancy, and integrates those measures into the four dimensions of community resilience—technical, organizational, social, and economic—all of which can be used to quantify measures of resilience for various types of physical and organizational systems. Systems diagrams then establish the tasks required to achieve these objectives. This framework can be useful in future research to determine the resiliency of different units of analysis and systems, and to develop resiliency targets and detailed analytical procedures to generate these values.

Digital simulation of random processes and its applications

Abstract Efficient methods are presented for digital simulation of a general homogeneous process (multidimensional or multivariate or multivariate-multidimensional) as a series of cosine functions with weighted amplitudes, almost evenly spaced frequencies, and random phase angles. The approach is also extended to the simulation of a general non-homogeneous oscillatory process characterized by an evolutionary power spectrum. Generalized forces involved in the modal analysis of linear or non-linear structures can be efficiently simulated as a multivariate process using the cross-spectral density matrix computed from the spectral density function of the multidimensional excitation process. Possible applications include simulation of (i) wind-induced ocean wave elevation, (ii) spatial random variation of material properties, (iii) the fluctuating part of atmospheric wind velocities and (iv) random surface roughness of highways and airport runways.

Simulation of multivariate and multidimensional random processes

Efficient and practical methods of simulating multivariate and multidimensional processes with specified cross‐spectral density are presented. When the cross‐spectral density matrix of an n‐variate process is specified, its component processes can be simulated as the sum of cosine functions with random frequencies and random phase angles. Typical examples of this type are the simulation, for the purpose of shaker test, of a multivariate process representing six components of the acceleration (due to, for example, a booster engine cutoff) measured at the base of a spacecraft and the simulation of horizontal and vertical components of earthquake acceleration. A homogeneous multidimensional process can also be simulated in terms of the sum of cosine functions with random frequencies and random phase angles. Examples of multidimensional processes considered here include the horizontal component f0(t,x) of the wind velocity perpendicular to the axis (x axis) of a slender structure, the vertical gust velocity f...

Monte Carlo Solution of Structural Dynamics

Abstract The recent advent of high speed digital computers has made it not only possible but also highly practical to apply the Monte Carlo techniques to a large variety of engineering problems. In this paper a technique of digital simulation of multivariate and/or multidimensional Gaussian random processes (homogeneous or nonhomogeneous) which can represent physical processes germane to structural engineering is presented. The paper also describes a method of digital simulation of envelope functions. Such simulations are accomplished in terms of a sum of cosine functions with random phase angles and used as the basic tool in a general Monte Carlo method of solution of a wide class of problems in structural engineering. Most important problems for which the method is found extremely useful includes (a) numerical analysis of dynamic response of nonlinear structures to random excitations, (b) time domain analysis of linear structures under random excitations performed for the purpose of obtaining a kind of information, such as first excursion probability and time history of a sample function, that is not obtainable from the standard frequency domain analysis, (c) numerical solution of structural problems involving randomly nonhomogeneous material property such as wave propagation through random medium, and (d) dynamic analysis of extremely complex systems such as those involving structure-fluid interaction. Numerical examples of some of these problems are presented.

Simulation of Multi-Dimensional Gaussian Stochastic Fields by Spectral Representation

The subject of this paper is the simulation of multi-dimensional, homogeneous, Gaussian stochastic fields using the spectral representation method. Following this methodology, sample functions of the stochastic field can be generated using a cosine series formula. These sample functions accurately reflect the prescribed probabilistic characteristics of the stochastic field when the number of terms in the cosine series is large. The ensemble-averaged power spectral density or autocorrelation function approaches the corresponding target function as the sample size increases. In addition, the generated sample functions possess ergodic characteristics in the sense that the spatially-averaged mean value, autocorrelation function and power spectral density function are identical with the corresponding targets, when the averaging takes place over the multi-dimensional domain associated with the fundamental period of the cosine series. Another property of the simulated stochastic field is that it is asymptotically Gaussian as the number of terms in the cosine series approaches infinity. The most important feature of the method is that the cosine series formula can be numerically computed very efficiently using the Fast Fourier Transform technique. The main area of application of this method is the Monte Carlo solution of stochastic problems in structural engineering, engineering mechanics and physics. Specifically, the method has been applied to problems involving random loading (random vibration theory) and random material and geometric properties (response variability due to system stochasticity).

Measuring Improvements in the Disaster Resilience of Communities

This paper demonstrates the concept of disaster resilience through the development and application of quantitative measures. As the idea of building disaster-resilient communities gains acceptance, new methods are needed that go beyond estimating monetary losses and that address the complex, multiple dimensions of resilience. These dimensions include technical, organizational, social, and economic facets. This paper first proposes resilience measures that relate expected losses in future disasters to a communitys seismic performance objectives. It then demonstrates these measures in a case study of the Memphis, Tennessee, water delivery system. An existing earthquake loss estimation model provides a starting point for quantifying resilience. The analysis compares two seismic retrofit strategies and finds that only one improves community resilience over the status quo. However, it does not raise resilience to an adequate degree. The exercise demonstrates that the resilience framework can be valuable for guiding mitigation and preparedness efforts. However, to fully implement the concept, new research on resilience is needed that goes beyond loss estimation modeling.

Random fields and stochastic finite elements

Abstract This state of the art paper identifies as the distinguishing feature of stochastic finite element analysis that it involves the discretization of the parameter space of a random field of material properties and / or loads. This discretization implies that the stochastic input consists of a vector of random variables whose covariance matrix depends on the finite element mesh. The paper provides an overview of basic concepts underlying random field theory, describes specific analytical tools to convey first- and second-order information about homogeneous random fields, and surveys available information on the space-time variation of random loads and material properties encountered in structural engineering. Stochastic finite element formulations covering a wide range of applications to both static and dynamic problems in structural engineering are examined, and a parallel approach to stochastic finite difference analysis is outlined.

Integrating Transportation Network and Regional Economic Models to Estimate the Costs of a Large Urban Earthquake

In this paper we summarize an integrated, operational model of losses due to earthquake impacts on transportation and industrial capacity, and how these losses affect the metropolitan economy. The procedure advances the information provided by transportation and activity system analysis techniques in ways that help capture the most important ecomonic implications of earthquakes. Network costs and origin-destination requirements are modeled endogenously and consistently. Indirect and induced losses associated with direct impacts on transportation and industrial capacity are distributed across zones and ecomonic sectors. Preliminary results are summarized for a magnitude 7.1 earthquake on the Elysian Park blind thrust fault in Los Angeles. Copyright 2001 BlackwellPublishers

Identification of Nonlinear Structural Dynamic Systems

This paper studies methods of parameter estimation for linear multi-degree-of-freedom structural dynamic systems, based on observed records of the external forces and the structural responses. The auto-regressive and moving-average (ARMA) model is used for this purpose. It is found that the ARMA model is a convenient model representing linear multi-degree-of-freedom structural dynamic systems and that the model is highly compatible with the instrumental variable method and the maximum likelihood method of identification. In order to check the accuracy of the estimation methods, analytical simulation studies are performed on the basis of simulated data dealing with the aerodynamic coefficient matrices that appear in the equations of motion of a two-dimensional model of a suspension bridge. Then, these methods are applied to the same equations to identify the coefficient matrices using the field measurement data yielding good estimates of the system parameters even under large output noise conditions.

Probabilistic earthquake scenarios : Extending risk analysis methodologies to spatially distributed systems

This paper proposes a methodology by which probabilistic risk analysis methods can be extended to the assessment of urban lifeline systems. Probabilistic hazard information is commonly used for site-specific analysis. However, for such systems as highway networks, electric power grids, and regional health care delivery systems, the spatial correlation between earthquake ground motion across many sites is important in determining system functionality. The methodology developed in this paper first identifies a limited set of deterministic earthquake scenarios and evaluates infrastructure system-wide performance in each. It then assigns hazard-consistent probabilities to the scenarios in order to approximate the regional seismicity. The resulting probabilistic scenarios indicate the likelihood of exceeding various levels of system performance degradation. A demonstration for the Los Angeles study area highway network suggests that there is roughly a 50% probability of exceedance of Northridge-level disruption in 50 years. This methodology provides a means for selecting representative earthquake scenarios for response or mitigation planning.