Adaptive experimental design for construction of response surface approximations

2001 ◽  
Author(s):  
Victor Perez ◽  
John Renaud ◽  
Layne Watson
Keyword(s):  
Experimental Design ◽  
Response Surface ◽  
Response Surface Approximations ◽  
Adaptive Experimental Design

Adaptive Experimental Design for Construction of Response Surface Approximations

AIAA Journal ◽  
2002 ◽  
Vol 40 (12) ◽  
pp. 2495-2503 ◽  
Author(s):  
Victor M. Perez ◽  
John E. Renaud ◽  
Layne T. Watson
Keyword(s):  
Experimental Design ◽  
Response Surface ◽  
Response Surface Approximations ◽  
Adaptive Experimental Design

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

2008 ◽  
Vol 25 (8) ◽  
pp. 764-782 ◽  
Author(s):  
Victor M. Pérez ◽  
John E. Renaud ◽  
Layne T. Watson
Keyword(s):  
Response Surface ◽  
Optimization Algorithm ◽  
Hessian Matrix ◽  
Major Drawback ◽  
Content Type ◽  
Response Surface Approximations ◽  
Design Variables ◽  
Multidisciplinary Systems ◽  
Time Required ◽  
Adaptive Experimental Design

PurposeTo 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/approachApplying 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 from O(n2) to O(n) is presented.FindingsThe technique uses prior information to approximate the eigenvectors of the Hessian matrix of the RSA and only requires the eigenvalues to be computed by response surface techniques. The technique is implemented in a sequential approximate optimization algorithm and applied to engineering problems of variable size and characteristics. Results demonstrate that a reduction in the data required per step from O(n2) to O(n) points can be accomplished without significantly compromising the performance of the optimization algorithm.Originality/valueA reduction in the time (number of system analyses) required per step from O(n2) to O(n) is significant, even more so as n increases. The novelty lies in how only O(n) system analyses can be used to approximate a Hessian matrix whose estimation normally requires O(n2) system analyses.

scholarly journals Modeling and Sensitivity Analysis of the Forward Osmosis Process to Predict Membrane Flux Using a Novel Combination of Neural Network and Response Surface Methodology Techniques

Membranes ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 70
Author(s):  
Jasir Jawad ◽  
Alaa H. Hawari ◽  
Syed Javaid Zaidi
Keyword(s):  
Response Surface Methodology ◽  
Experimental Design ◽  
Response Surface ◽  
Forward Osmosis ◽  
Feed Solution ◽  
Operating Conditions ◽  
Ann Model ◽  
Membrane Flux ◽  
Input Variables ◽  
Rsm Model

The forward osmosis (FO) process is an emerging technology that has been considered as an alternative to desalination due to its low energy consumption and less severe reversible fouling. Artificial neural networks (ANNs) and response surface methodology (RSM) have become popular for the modeling and optimization of membrane processes. RSM requires the data on a specific experimental design whereas ANN does not. In this work, a combined ANN-RSM approach is presented to predict and optimize the membrane flux for the FO process. The ANN model, developed based on an experimental study, is used to predict the membrane flux for the experimental design in order to create the RSM model for optimization. A Box–Behnken design (BBD) is used to develop a response surface design where the ANN model evaluates the responses. The input variables were osmotic pressure difference, feed solution (FS) velocity, draw solution (DS) velocity, FS temperature, and DS temperature. The R2 obtained for the developed ANN and RSM model are 0.98036 and 0.9408, respectively. The weights of the ANN model and the response surface plots were used to optimize and study the influence of the operating conditions on the membrane flux.

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