THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

This paper presents a polynomial dimensional decomposition (PDD) method for global sensitivity analysis of stochastic systems subject to independent random input following arbitrary probability distributions. The method involves Fourier-polynomial expansions of lower-variate component functions of a stochastic response by measure-consistent orthonormal polynomial bases, analytical formulae for calculating the global sensitivity indices in terms of the expansion coefficients, and dimension-reduction integration for estimating the expansion coefficients. Due to identical dimensional structures of PDD and analysis-of-variance decomposition, the proposed method facilitates simple and direct calculation of the global sensitivity indices. Numerical results of the global sensitivity indices computed for smooth systems reveal significantly higher convergence rates of the PDD approximation than those from existing methods, including polynomial chaos expansion, random balance design, state-dependent parameter, improved Sobol’s method, and sampling-based methods. However, for non-smooth functions, the convergence properties of the PDD solution deteriorate to a great extent, warranting further improvements. The computational complexity of the PDD method is polynomial, as opposed to exponential, thereby alleviating the curse of dimensionality to some extent. Mathematical modeling of complex systems often requires sensitivity analysis to determine how an output variable of interest is influenced by individual or subsets of input variables. A traditional local sensitivity analysis entails gradients or derivatives, often invoked in design optimization, describing changes in the model response due to the local variation of input. Depending on the model output, obtaining gradients or derivatives, if they exist, can be simple or difficult. In contrast, a global sensitivity analysis (GSA), increasingly becoming mainstream, characterizes how the global variation of input, due to its uncertainty, impacts the overall uncertain behavior of the model. In other words, GSA constitutes the study of how the output uncertainty from a mathematical model is divvied up, qualitatively or quantitatively, to distinct sources of input variation in the model [1].

Reliability Engineering and System Safety

The increasing complexity of engineering systems has sparked increasing interest in multidisciplinary optimization (MDO). This paper presents a survey of recent publications in the field of aerospace where interest in MDO has been particularly intense. The two main challenges of MDO are computational expense and organizational complexity. Accordingly the survey is focused on various ways different researchers use to deal with these challenges. The survey is organized by a breakdown of MDO into its conceptual components. Accordingly, the survey includes sections on Mathematical Modeling, Design- oriented Analysis, Approximation Concepts, Optimization Procedures, System Sensitivity, and Human Interface. With the authors'' main expertise being in the structures area, the bulk of the references focus on the interaction of the structures discipline with other disciplines. In particular, two sections at the end focus on two such interactions that have recently been pursued with a particular vigor: Simultaneous Optimization of Structures and Aerodynamics, and Simultaneous Optimization of Structures Combined With Active Control.

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Multidisciplinary Aerospace Design Optimization: Survey of Recent Developments

Review on modeling and simulation of interdependent critical infrastructure systems

A Glimpse at Set Theory. The Real Numbers. The Topology of Cartesian Spaces. Convergence. Continuous Functions. Functions of One Variable. Infinite Series. Differentiation in RP Integration in RP.

The elements of real analysis (2nd edition), by Robert G. Bartle. Pp xv, 480. £10. 1976. SBM 0 471 05464 X (Wiley)

During the last decade, critical infrastructure systems such as electric power, water distribution, transportation and telecommunications have been stressed by significant natural hazards and human errors leading to malfunction. Earthquakes, blackouts and satellite failures have evidenced the vulnerability of these growing networked systems threatening the continuity of the United States' economy. The potential for malicious perturbations to these systems is also an important current concern. However, the underlying susceptibility of these networks to disruptive events is in large part due to the increasingly complex pattern of interdependencies that tie these civil infrastructures together. This paper mainly investigates the effect of seismic disruptions on the performance of real interdependent networks. Maintenance-induced malfunctions and coordinated attacks are also studied for completeness. Several degrees of interconnectedness are explored. Interdependent network fragility curves are introduced to display the effect of these different strengths of coupling. Characterization of the performance displayed by the networks is utilized to propose mitigation actions and study propagation of their effects. It is shown that minimal strategic interventions propagated through the network can generate a more resilient interdependent entity. Copyright © 2006 John Wiley & Sons, Ltd.

Seismic response of critical interdependent networks

Continuous functionality of critical infrastructure systems is essential to support the social and economic organization of productive sectors within a country. Electric power, potable water, natural gas, telecommunications, and transportation are examples of these critical systems, whose nature makes them suitable for network analysis. This study presents the topological characterization of two interdependent small-sized real networks. The same properties are calculated for ideal models of comparable size to the real networks. Selected topological properties are monitored for these interdependent systems when subjected to external or internal disruptions (e.g., deliberate attacks, malfunction due to aging, or lack of maintenance). This study introduces a simple rule to establish interdependencies among network elements based upon geographical proximity. The effect of the degree of coupling between networks is investigated with a tunable parameter that drives the networks from independence to complete interdependence. Network detrimental responses are observed to be larger when interdependencies are considered after disturbances. Effective mitigation actions could take advantage of the same network interconnectedness that facilitates cascading failures.

Interdependent Response of Networked Systems

Seismic fragility analysis of low-rise unreinforced masonry structures

Metamodel-based regional vulnerability estimate of irregular steel moment-frame structures subjected to earthquake events

The static energy absorption behavior of graphite epoxy composite cor rugated (sine wave) webs loaded in axial compression is reported in this paper. Tests have been conducted to study the effects ...

James I. Craig

Papers

Seismic response of critical interdependent networks

Interdependent Response of Networked Systems

Seismic fragility analysis of low-rise unreinforced masonry structures

Metamodel-based regional vulnerability estimate of irregular steel moment-frame structures subjected to earthquake events

Energy Absorption Behavior of Graphite Epoxy Composite Sine Webs