© Hindawi Publishing Corp. STOCHASTIC LINEARIZATION OF NONLINEAR POINT DISSIPATIVE SYSTEMS

Stochastic linearization produces a linear system with the same covariance kernel as the original nonlinear system. The method passes from factorization of finite-dimensional covariance kernels through convergence results to the final input/output operator representation of the linear system. 2000 Mathematics Subject Classification: 34K23, 93B18. 1. Introduction. Linearizatio

Stochastic linearization of nonlinear point dissipative systems

Stochastic linearization produces a linear system with the same covariance kernel as the original nonlinear system. The method passes from factorization of finite-dimensional covariance kernels through convergence results to the final input/output operator representation of the linear system

Vehicle design decomposition under uncertainty and risk

The automotive vehicle design process is a complex undertaking due to the large number of disciplines and associated interdisciplinary couplings, the size and type of manpower concurrently involved in the process, and accompanying computational tasks. Traditionally, the vehicle design process has been handled within mathematical optimization, which has been strengthened by considerations of design robustness and reliability in the presence of uncertainty. In this paper, we develop a new paradigm for vehicle design which not only follows on prior research efforts but integrates recent design trends for comprehensive uncertainty management in engineering systems design. The proposed approach unifies technical vehicle design, manufacturing, and management concerns into broadly understood engineering design in a space of common uncertainties and offers the capability of active uncertainty management in the sense that designers and managers can exercise decisions as circumstances warrant. The process of vehicle development is viewed as an interactive decision process between a management team charged with the exploitation of an economic opportunity, which includes management of the development of a vehicle design, supply, manufacturing, distribution, and marketing chains, and investments in those chains, and a design team charged with producing a vehicle design meeting requirements of the management team and regulatory agencies while minimizing performance risk. Assessment models for the management team and design models for the design team are based on normal random fields defined over the space of uncertainties. A modeling and decision-making methodology is presented for rationalizing the development process including consideration of communication between the two teams. 2. Keywords: vehicle design, uncertainty, risk, decomposition, coordination 3

The generalized Airy diffusion equation

Solutions of a generalized Airy diffusion equation and an associated nonlinear partial differential equation are obtained. Trigonometric type functions are derived for a third order generalized radial Euler type operator. An associated complex variable theory and generalized Cauchy-Euler equations are obtained. Further, it is shown that the Airy expansions can be mapped onto the Bessel Calculus of Bochner, Cholewinski and Haimo

Complex system design decomposition under uncertainty and risk

We propose a new modeling and decision-making framework for engineering design of complex systems operating under uncertainty and risk. The framework goes beyond the conventional optimization-based scheme and follows upon emerging ideas calling for the inclusion of comprehensive uncertainty management into engineering systems design, and thus providing options for design flexibility and robustness. The complex system development process is decomposed into a assessment process and design process, which operate in the same space of uncertainties but from two different knowledge bases, interact with each other, and are further decomposable into simpler components. Decomposition of each of the two processes into components is based on managers ’ or designers ’ experience and knowledge while computational models of the components use normal random fields defined over the common space of uncertainties. The assessment process is decomposed into interacting criteria that evaluate overall designs produced by the design process. The design process is decomposed into interacting tasks to be performed by the system and the associated design team is charged with finding methods (partial designs) meeting the requirements specified in the assessment process. A methodology to coordinate the two processes is proposed. System performance in the entire space of uncertainties is measured by risk that is modeled as system performance variance and a function of the uncertainties treated as independent variables. Using stochastic and multi-criteria analyses, the methodology creates and evaluates design options, thus calculating the value of engineering flexibility. System robustness as its ability to perform satisfactorily over the space of uncertainties is also addressed. 2. Keywords: design, complex systems, decomposition, uncertainty, ris