Victor Perez

Adaptive Experimental Design for Construction of Response Surface Approximations

Sequential Approximate Optimization (SAO) is a class of methods available for the multidisciplinary design optimization (MDO) of complex systems that are composed of several disciplines coupled together. One of the approaches used for SAO, is based on a quadratic response surface approximation, where zero and first order information are required. In these methods, designers must generate and query a database of order O(n2) in order to compute the second order terms of the quadratic response surface approximation. As the number of design variables grows, the computational cost of generating the required database becomes a concern. In this paper, we present an new approach in which we require just O(ri) parameters for constructing a second order approximation. This is accomplished by transforming the matrix of second order terms into the canonical form. The method periodically requires an order O(n2) update of the second order approximation to maintain accuracy. Results show that the proposed approach is practical and convenient for engineering design problems by dramatically reducing the total number of calls to the simulation tools.

Investigation of reliability method formulations in DAKOTA/UQ

Reliability methods are probabilistic algorithms for quantifying the effect of simulation input uncertainties on response metrics of interest. In particular, they compute approximate response function distribution statistics (probability, reliability and response levels) based on specified input random variable probability distributions. In this paper, a number of algorithmic variations are explored for both the forward reliability analysis of computing probabilities for specified response levels (the reliability index approach (RIA)) and the inverse reliability analysis of computing response levels for specified probabilities (the performance measure approach (PMA)). These variations include limit state linearizations, probability integrations, warm starting and optimization algorithm selections. The resulting RIA/PMA reliability algorithms for uncertainty quantification are then employed within bi-level and sequential reliability-based design optimization approaches. Relative performance of these uncertainty quantification and reliability-based design optimization algorithms are presented for a number of computational experiments performed using the DAKOTA/UQ software.

CONSTRUCTING VARIABLE FIDELITY RESPONSE SURFACE APPROXIMATIONS IN THE USABLE FEASIBLE REGION

The use of Response Surface Approximation (RSA) within an approximate optimization framework for the design of complex systems has increased as designers are challenged to develop better designs in reduced times. Traditionally, statistical sampling techniques (i. e., experimental design) have been used for constructing RSAs. These statistical sampling techniques are designed to be space filling, so that the response surface approximations are predictive across the range of the design sample space. When used in sequential approximate optimization strategies, a portion of the samples can be in the infeasible and/or ascent regions of the design space. These samples can bias the resulting RSA and make it less predictive in the usable feasible region where the optimization takes place. In the response surface based concurrent subsace optimization approach the design sampling strategy for RSA construction is optimization based. This optimization based sampling has proved to be effective due to the fact it samples in the linearized usable feasible region. In the present research, an experimental design strategy for projecting data points in the linearized usable feasible region is developed for constructing RSAs. The technique is implemented in a Sequential Approximate Optimization framework and tested in application to two multidisciplinary design optimization (MDO) test problems. Results show that the proposed technique pro

Reduced sampling for construction of quadratic response surface approximations using adaptive experimental design

Purpose – To reduce the computational complexity per step from O(n2) to O(n) for optimization based on quadratic surrogates, where n is the number of design variables.Design/methodology/approach – Applying nonlinear optimization strategies directly to complex multidisciplinary systems can be prohibitively expensive when the complexity of the simulation codes is large. Increasingly, response surface approximations (RSAs), and specifically quadratic approximations, are being integrated with nonlinear optimizers in order to reduce the CPU time required for the optimization of complex multidisciplinary systems. For evaluation by the optimizer, RSAs provide a computationally inexpensive lower fidelity representation of the system performance. The curse of dimensionality is a major drawback in the implementation of these approximations as the amount of required data grows quadratically with the number n of design variables in the problem. In this paper a novel technique to reduce the magnitude of the sampling f...

Parallel Processing in Sequential Approximate Optimization

The paper presents a first level of coarse-grained parallelization in a sequential approximate optimization framework. A sequential approximate optimization framework builds local approximations of the system every iteration by evaluating a set of design points around the current design. In this research the database is generated by distributing the data sampling process among several processors in a cluster. Two test problems are implemented in a 32 processor cluster. Communications and process control is performed using a message passing interface (MPI) implementation called LAM (Local area multicomputer). The MPI application sends to each processor a set of points to evaluate during the database generation step. Results demonstrate that the use of a cluster of computers to perform the optimization reduces significantly the overall computational time.

DEVELOPMENT AND VERIFICATION OF A MATLAB DRIVER FOR THE SNOPT OPTIMIZATION SOFTWARE

The MATLAB program and computing language has seen increased usage both in industry and academia in recent years. This is due to the ease in which it handles matrices and numerical computations. This computing environment also has an array of toolboxes for different mathematical and engineering tasks (e.g., controls, optimization). These toolboxes provide a general suite of numerical tools within a specific discipline for the user. The toolbox codes are general tools and are not typically as robust or as efficient as state of the art numerical codes develop by advanced users in a given discipline. In this research a MATLAB driver which links an existing robust and efficient optimization program SNOPT is developed and tested. The resulting program and driver have proved to be more efficient than the existing MATLAB toolbox codes for optimization.