Prabhat Hajela

NEUROBIOLOGICAL COMPUTATIONAL MODELS IN STRUCTURAL ANALYSIS AND DESIGN

Abstract This paper examines the role of neural computing strategies in structural analysis and design. A principal focus of the work resides in the use of neural networks to represent the force-displacement relationship in static structural analysis. Such models provide computationally efficient capabilities for reanalysis, and appear to be well suited for application in numerical optimum design. The paper presents an overview of the neural computing approach, with special emphasis on supervised learning techniques adopted in the present work. Special features of such learning strategies which have a direct bearing on numerical accuracy and efficiency, are examined in the context of representative structural optimization problems.

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.

Immune network simulations in multicriterion design

A modification to the genetic algorithm (GA) based search procedure, based on the modeling of a biological immune system, is proposed as an approach to solving the multicriterion design problem. Such problems have received considerable attention, given that decisions in engineering design practice typically require allocation of resources to satisfy multiple, and frequently conflicting requirements. The approach is particularly amenable to problems with a mix of continuous, discrete, and integer design variables, where the GA has been shown to perform in an effective manner. The approach considered in the present work is based on the concept of converting the multicriterion problem into one with a scalar objective through the use of the utility function. The strength of the approach is in its ability to generate the Pareto-Edgeworth front of compromise solutions in a single execution of the GA. A characteristic feature of biological immune systems which allows for the generation of multiple specialist antibodies, is shown to be an effective approach to facilitate the generation of the Pareto-Edgeworth front. Solutions to problems in structural design are presented in support of the proposed approach.

Parallel Genetic Algorithm Implementation in Multidisciplinary Rotor Blade Design

Abstract : The present paper describes an adaptation of genetic algorithms in the design of large-scale multidisciplinary optimization problems. A hingeless composite rotor blade is used as the test problem, where the formulation of the objective and constraint functions requires the consideration of disciplines of aerodynamics, performance, dynamics, and structures. A rational decomposition approach is proposed for partitioning the large-scale multidisciplinary design problem into smaller, more tractable subproblems. A design method based on a parallel implementation of genetic algorithms is shown to be an effective strategy, providing increased computational efficiency, and a natural approach to account for the coupling between temporarily decoupled subproblems. A central element of the proposed approach is the use of artificial neural networks for identifying a topology for problem decomposition and for generating global function approximations for use in optimization. (AN)

Genetic Algorithms in Structural Topology Optimization

The present paper describes the use of a stochastic search procedure that is the basis of genetic algorithms (GA), in developing near-optimal topologies of load bearing truss structures. The problem addressed is one wherein the structural geometry is created from a specification of load conditions and available support points in the design space. The development of this geometry must satisfy kinematic stability requirements in addition to the usual requirements of structural strength and stiffness. The approach is an adaptation of the ground-structure method of topology optimization, and is implemented in a two-level GA based search. In this process, the kinematic stability constraints are imposed at one level, followed by the treatment of response constraints at a second level of optimization. Singular value decomposition is used to assess the kinematic stability constraint at the first level of design, and results in the creation of a finite number of increasing weight, stable topologies. Member sizing is then introduced at a second level of design, where minimal weight and response constraints are simultaneously considered. At this level, the only admissible topologies are those identified during the first stage and any stable combinations thereof. The design variable representation scheme allows for both the removal and addition of structural members during optimization.

Nongradient Methods in Multidisciplinary Design Optimization-Status and Potential

A number of multidisciplinary design optimization (MDO) problems are characterized by the presence of discrete and integer design variables, over and beyond the more traditional continuous variable problems. In continuous variable design problems, the design space may be nonconvex or even disjointed. Furthermore, the number of design variables and constraints may be quite large. The use of conventional gradient-based methods in such problems is fraught with hazards. First, these gradient-based methods cannot be used directly in the presence of discrete variables. Their use is facilitated by creating multiple equivalent continuous variable problems; in the presence of high dimensionality, the number of such problems to be solved can be quite large. Second, these methods have a propensity to converge to a relative optimum closest to the starting point, and this is a major weakness in the presence of multimodality in the design space. This paper primarily focuses on the use of nontraditional optimization methods in such problems, broadly classified today as soft computing strategies. These methods include techniques such as simulated annealing, genetic algorithms, Tabu search, and rule-based expert systems. It also examines issues pertinent to using these methods in MDO problems.

Constrained genetic search via schema adaptation: An immune network solution

Genetic search derives its computational advantage from an intrinsic pattern recognition capability. Patterns or schemata associated with a high level of fitness are rapidly identified and reproduced at a near-exponential growth rate through generations of simulated evolution. This highly exploitative search process has been shown to be extremely effective in searching for schema that represent an optimum, requiring only that an appropriate measure of fitness be defined. This exploitative pattern recognition process is also at work in another biological system-the immune system which recognizes antigens foreign to the system and generates antibodies to combat the growth of these antigens. The present paper describes key elements of how the functioning of the immune system can be modeled in the context of genetic search, and its applicability for handling constrained genetic search. Results from this simulation are compared with those obtained from the more traditional approach of handling constraints in genetic search, viz. through the use of a penalty function formulation.

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.

GA BASED SIMULATION OF IMMUNE NETWORKS APPLICATIONS IN STRUCTURAL OPTIMIZATION

Genetic algorithms have received considerable recent attention in the optimal design of structural systems. These algorithms derive a computational leverage from an intrinsic pattern recognition capability, whereby patterns or schemata associated with a high level of fitness are identified and evolved at a near-exponential growth rate through generations of simulated evolution. This highly exploitative search process has been shown to be extremely effective in searching for schema that represent an optimum, requiring only that an appropriate measure of fitness be defined. This exploitative pattern recognition process is also at work in another biological system - the immune system responsible for recognizing antigens foreign to the system and generating antibodies to combat the growth of these antigens. The paper describes key elements of how the functioning of the immune system can be modelled in the context of genetic search. It then provides an overview of the implications of this model in improving th...