Jaroslaw Sobieszczanski-Sobieski

Sensitivity of Complex, Internally Coupled Systems

A method is presented for computing sensitivity derivatives with respect to independent (input) variables for complex, internally coupled systems, while avoiding the cost and inaccuracy of finite differencing performed on the entire system analysis. The method entails two alternative algorithms: the first is based on the classical implicit function theorem formulated on residuals of governing equations, and the second develops the system sensitivity equations in a new form using the partial (local) sensitivity derivatives of the output with respect to the input of each part of the system. A few application examples are presented to illustrate the discussion.

Bilevel Integrated System Synthesis for Concurrent and Distributed Processing

A new version is introduced of the bilevel integrated system synthesis method intended for optimization of engineering systems conducted by distributed specialty groups working concurrently in a multiprocessor computing environment. The method decomposes the overall optimization task into subtasks associated with disciplines or subsystems, where the local design variables are numerous and a single, system-level optimization whose design variables are relatively few. The subtasks are fully autonomous as to their inner operations and decision making. Their purpose is to eliminate the local design variables and generate a wide spectrum of feasible designs whose behavior is represented by response surfaces to be accessed by a system-level optimization. It is shown that, if the problem is convex, the solution of the decomposed problem is the same as that obtained without decomposition. A simplie ed example of an aircraft design shows the method working as intended. A discussion of the method merits and demerits as well as recommendations for further research is included.

Multidisciplinary design optimisation - some formal methods, framework requirements, and application to vehicle design

A vehicle is an engineering system whose successful design requires harmonisation of a number of objectives and constraints that, in principle, can be modelled as a constrained optimisation in the space of design variables. However, dimensionality of such optimisation and the complexity and expense of the underlying analysis suggest a decomposition approach to enable concurrent execution of smaller and more manageable tasks. In order to preserve the couplings that naturally occur among the elements of the whole problem, such optimisation by various types of decomposition must include a degree of coordination at the system level. Multidisciplinary Design Optimisation (MDO) is a body of methods and techniques for performing the above optimisation so as to balance the design considerations at the system and detail levels. The paper is an overview of a few MDO methods selected for their applicability to vehicle systems.

NON-HIERARCHIC SYSTEM DECOMPOSITION IN STRUCTURAL OPTIMIZATION

Decomposition methods provide a systematic approach for decoupling large engineering systems into smaller, coupled subsystems identified by disciplines or by engineering tasks. The paper develops a general decomposition approach for multidisciplinary optimization that is applicable for non-hierarchic systems in which a distinct system hierarchy is difficult to identify. The approach is implemented in a structural synthesis problem for verification purposes. The optimal design of a ten-bar truss for minimum weight subject to displacement and stress constraints is considered. Subsystems are defined in terms of sizing and space variables. The approach allows for implementation of specialized methods for analysis in each subsystem and the ability to incorporate human intervention and decision making. Results demonstrate that the Concurrent Subspace Optimization approach is a versatile method that potentially offers exceptional computational as well as data management advantages.

Multidisciplinary design optimization - An emerging new engineering discipline

This paper attempts to define the Multidisciplinary Design Optimization (MDO) as a new field of research endeavor and as an aid in the design of engineering systems. It examines the MDO conceptual components in relation to each other and defines their functions.

Sensitivity analysis and multidisciplinary optimization for aircraft design - Recent advances and results

Optimization by decomposition, complex system sensitivity analysis, and a rapid growth of disciplinary sensitivity analysis are some of the recent developments that hold promise of a quantum jump in the support engineers receive from computers in the quantitative aspects of design. Review of the salient points of these techniques is given and illustrated by examples from aircraft design as a process that combines the best of human intellect and computer power to manipulate data.

Structural sizing by generalized, multilevel optimization

Developments of a general multilevel optimization capability and results for a three-level structural optimization are described. The latter is considered a major stage in the method development because the addition of more levels beyond three does not introduce any new qualitative elements. Therefore, a three-level implementation is, qualitatively, the equivalent to a multilevel implementation. The method partitions a structure into a number of substructurin g levels where each substructure corresponds to a subsystem. The method is illustrated by a portal framework that decomposes into individual beams. Each beam is a box that can be further decomposed into stiffened plates. Consequently, substructuring for this example spans three levels: the bottom level of finite elements representing the plates, an intermediate level of beams treated as substructures, and the top level for the assembled structure. This example is an extension of a previously presented case that was limited to two levels.

Sensitivity of control-augmented structure obtained by a system decomposition method

The verification of a method for computing sensitivity derivatives of a coupled system is presented. The method deals with a system whose analysis can be partitioned into subsets that correspond to disciplines and/or physical subsystems that exchange input-output data with each other. The method uses the partial sensitivity derivatives of the output with respect to input obtained for each subset separately to assemble a set of linear, simultaneous, algebraic equations that are solved for the derivatives of the coupled system response. This sensitivity analysis is verified using an example of a cantilever beam augmented with an active control system to limit the beams dynamic displacements under an excitation force. The verification shows good agreement of the method with reference data obtained by a finite difference technique involving entire system analysis. The usefulness of a system sensitivity method in optimization applications by employing a piecewise-linear approach to the same numerical example is demonstrated. The methods principal merits are its intrinsically superior accuracy in comparison with the finite difference technique, and its compatibility with the traditional division of work in complex engineering tasks among specialty groups.

Application of global sensitivity equations in multidisciplinary aircraft synthesis

The present paper investigates the applicability of the Global Sensitivity Equation (GSE) method in the multidisciplinary synthesis of aeronautical vehicles. The GSE method provides an efficient approach for representing a large coupled system by smaller subsystems and accounts for the subsystem interactions by means of first-order behavior sensitivities. This approach was applied in an aircraft synthesis problem with performance constraints stemming from the disciplines of structures, aerodynamics, and flight mechanics. Approximation methods were considered in an attempt to reduce problem dimensionality and to improve the efficiency of the optimization process. The influence of efficient constraint representations, the choice of design variables, and design variable scaling on the conditioning of the system matrix was also investigated. 10 refs.

Bilevel integrated system synthesis with response surfaces

Two variants of the BLISS method are proposed for multidisciplinary design optimization (MDO). These variants utilize experimental design methods and response surfaces to reduce the number of expensive system analysis required for solution of the MDO problem. BLISS is an MDO method for decomposition-based optimization of engineering systems that involves system optimization with a relatively small number of design variables and a number of subsystem optimizations that could each have a large number of local variables. In BLISS, the optimum sensitivity analysis data are used to relate the subsystem optimization solutions with the system optimizations. Instead, with the proposed variants, polynomial response surface approximations using either the system analysis or the subsystem optimization results are used. Additionally, the response surface construction process is well suited for computing in a concurrent processing environment. The proposed variants are implemented and evaluated on a conceptual-level aircraft and ship design problem.