Ravindra V. Tappeta

Trust region model management in multidisciplinary design optimization

A common engineering practice is the use of approximation models in place of expensive computer simulations to drive a multidisciplinary design process based on nonlinear programming techniques. The use of approximation strategies is designed to reduce the number of detailed, costly computer simulations required during optimization while maintaining the pertinent features of the design problem. This paper overviews the current state of the art in model management strategies for approximate optimization. Model management strategies coordinate the interaction between the optimization and the fidelity of the approximation models so as to ensure that the process converges to a solution of the original design problem. Approximations play an important role in multidisciplinary design optimization (MDO) by offering system behavior information at a relatively low cost. Most approximate MDO strategies are sequential, in which an optimization of an approximate problem subject to design variable move limits is iteratively repeated until convergence. The move limits or trust region are imposed to restrict the optimization to regions of the design space in which the approximations provide meaningful information. In order to insure convergence of the sequence of approximate optimizations to a Karush–Kuhn–Tucker solution, a trust region model management or move limit strategy is required. In this paper recent developments in approximate MDO strategies and issues of trust region model management in MDO are reviewed.

Interactive Physical Programming: Tradeoff Analysis and Decision Making in Multicriteria Optimization

This research focuses on multiobjective system design and optimization. The goal is to develop and test an interactive multi-objective optimization algorithm that takes into account the designers preferences during the design process. The Physical Programmingi (PP) methodology has been extended to develop an Interactive Physical Programming (IPP) framework which allows for design exploration by the designer or the Decision Maker (DM) at a given Pareto design. The IPP framework provides the DM with Pareto sensitivity information, a Pareto surface approximation and a formal decision making strategy for efficient design (or Pareto surface) exploration around a given Pareto design. The IPP has been successfully applied to two test problems. The first problem consists of a set of simple analytical expressions for its objectives and con

INTERACTIVE MULTIOBJECTIVE OPTIMIZATION PROCEDURE

This research focuses on multiobjective system design and optimization. The primary goal is to develop and test a mathematically rigorous and efficient interactive multiobjective optimization algorithm that takes into account the designers preferences during the design process. In this research, an interactive multiobjective optimization procedure (IMOOP) that uses an aspiration-level approach to generate Pareto points is developed. This method provides the designer or the decision maker (DM) with a formal means for efficient design exploration around a given Pareto point. More specifically, the procedure provides the DM with the Pareto sensitivity information and the Pareto surface approximation at a given Pareto design for decision making and tradeoff analysis. The IMOOP has been successfully applied to two test problems. The first problem consists of a set of simple analytical expressions for its objective and constraints. The second problem is the design and sizing of a high-performance and low-cost 10-bar structure that has multiple objectives. The results indicate that the Pareto designs predicted by the Pareto surface approximation are reasonable and the performance of the second-order approximation is superior compared to that of the first-order approximation. Using this procedure a set of new aspirations that reflect the DMs preferences are easily and efficiently generated, and the new Pareto design corresponding to these aspirations is close to the aspirations themselves. This is important in that it builds the confidence of the DM in this interactive procedure for obtaining a satisfactory final Pareto design in a minimal number of iterations.

An interactive multiobjective optimization design strategy for decision based multidisciplinary design

This research focuses on Multidisciplinary Design and Optimization (MDO) of large scale systems that have multiple objective functions. The primary goal is to develop and test an interactive multi-objective optimization algorithm for multidisciplinary system design that takes into account the Decision Makers (DMs) preferences during the design process. An interactive Multi-Objective Optimization Design Strategy (iMOODS) developed in Tappeta and Renaud [1-3] has been modified in this research to include a MDO algorithm to address both the multiobjective and multidisciplinary issues involved in system design. This interactive strategy (iMOODS with MDO capability) provides the DM with a formal means for efficient design exploration around a given Pareto point. The strategy has been successfully applied to two design problems which are multidisciplinary in nature and have multiple objective functions. The first problem is the design of an autonomous hovercraft system that has four complexly coupled disciplines or contributing analyses (CAs) and two objective functions. The second problem is an aircraft concept sizing problem that has three disciplines and three objective functions. The results indicate that the strategy is effective and efficient in capturing the DMs preferences and arriving at the optimum design.

MONTE CARLO SIMULATION IN RELIABILITY BASED OPTIMIZATION APPLIED TO MULTIDISCIPLINARY SYSTEM DESIGN

The work presented in the paper deals with the incorporation of Monte Carlo Simulation (MCS) techniques in Reliability Based Optimization (RBO). The main criteria used to select the suitable MCS techniques are the ease of obtaining analytical sensitivities and the smoothness of the probability of failure estimates with changes in design. The MCS techniques that best suit these criteria are Conditional Expectation MCS techniques that consist of the Directional Simulation and Axis-Orthogonal Simulation techniques. Details of obtaining probability of failure estimates and its sensitivities using these simulation techniques for component reliability and series system reliability are presented. A strategy for performing RBO using the axis-orthogonal simulation is presented. This strategy was applied to two multidisciplinary test problems. The first test problem is a simple analytic problem that is used for demonstration purposes. The second test problem is a control-augmented structure problem that has been used in various Multidisciplinary Design Optimization (MDO) studies. The MCS based RBO converged for both test problems and substantial improvements from initial designs, obtained using First Order Reliability Method based RBO, were observed for both

TURBINE BLADE RELIABILITY-BASED OPTIMIZATION USING A VARIABLE- COMPLEXITY METHOD

This paper investigates the application and implementation of an aircraft engine turbine blade reliability-based optimization (RBO). The turbine blade is designed to be minimum volume while satisfying component reliability-based constraints on displacement and stress. Design variables consist of computer aided design (CAD) shape parameters. Uncertainty is introduced via random variable models of material and load parameters. A sequential qaudratic programming (SQP) technique is used in conjunction with first-order reliability theory to design the blade. State-of-the-art CAD techniques are employed to automate and coordinate the necessary finite element analyses required by the optimization and reliability algorithms. Three RBO constraint evaluation techniques are examined: the mean-value (MV) firstorder reliability method, the Hasofer-Lind RackwitzFiessler first-order reliability method (FORM), and a variable-complexity (VC) approach. Computational costs of the different RBO strategies and a discussion of implementation issues are presented.

Application of Approximate Optimization to Turbine Blade Design In a Network -Centric Environment

A trust region based approximate optimization strategy has been implemented within a network centric environment. The strategy sequentially builds response surface approximations of the objective and constra ints based on current and previous design data. These approximations are optimized subject to move limits that are updated depending on the trust region ratio (the trust region ratio measures the goodness of approximations. The strategy has been applied to turbine blade design and optimization. The results indicate that the strategy has good convergence properties and is able to converge quickly compared to traditional optimization.