# Single and Multiresponse Adaptive Design of Experiments with Application to Design Optimization of Novel Heat Exchangers

##### 抄録

Engineering design optimization often involves complex computer simulations.
Optimization with such simulation models can be time consuming and sometimes
computationally intractable. In order to reduce the computational burden, the use of
approximation-assisted optimization is proposed in the literature. Approximation
involves two phases, first is the Design of Experiments (DOE) phase, in which
sample points in the input space are chosen. These sample points are then used in a
second phase to develop a simplified model termed as a metamodel, which is
computationally efficient and can reasonably represent the behavior of the simulation
response. The DOE phase is very crucial to the success of approximation assisted
optimization.
This dissertation proposes a new adaptive method for single and multiresponse
DOE for approximation along with an approximation-based framework for multilevel
performance evaluation and design optimization of air-cooled heat exchangers.
The dissertation is divided into three research thrusts. The first thrust presents a new
adaptive DOE method for single response deterministic computer simulations, also
called SFCVT. For SFCVT, the problem of adaptive DOE is posed as a bi-objective
optimization problem. The two objectives in this problem, i.e., a cross validation error
criterion and a space-filling criterion, are chosen based on the notion that the DOE
method has to make a tradeoff between allocating new sample points in regions that
are multi-modal and have sensitive response versus allocating sample points in
regions that are sparsely sampled. In the second research thrust, a new approach for
multiresponse adaptive DOE is developed (i.e., MSFCVT). Here the approach from
the first thrust is extended with the notion that the tradeoff should also consider all
responses. SFCVT is compared with three other methods from the literature (i.e.,
maximum entropy design, maximin scaled distance, and accumulative error). It was
found that the SFCVT method leads to better performing metamodels for majority of
the test problems. The MSFCVT method is also compared with two adaptive DOE
methods from the literature and is shown to yield better metamodels, resulting in
fewer function calls.
In the third research thrust, an approximation-based framework is developed for
the performance evaluation and design optimization of novel heat exchangers. There
are two parts to this research thrust. First, is a new multi-level performance evaluation
method for air-cooled heat exchangers in which conventional 3D Computational
Fluid Dynamics (CFD) simulation is replaced with a 2D CFD simulation coupled
with an e-NTU based heat exchanger model. In the second part, the methods
developed in research thrusts 1 and 2 are used for design optimization of heat
exchangers. The optimal solutions from the methods in this thrust have 44% less
volume and utilize 61% less material when compared to the current state of the art
microchannel heat exchangers. Compared to 3D CFD, the overall computational
savings is greater than 95%.

University of Maryland, College Park, MD 20742-7011 (301)314-1328.

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