Optimization Under Uncertainty Applied to Heat Sink Design

Abstract

Optimization under uncertainty (OUU) is a powerful methodology used in design and optimization to produce robust, reliable designs. Such an optimization methodology, employed when the input quantities of interest are uncertain, yields output uncertainties that help the designer choose appropriate values for input parameters to produce safe designs. Apart from providing basic statistical information, such as mean and standard deviation in the output quantities, uncertainty-based optimization produces auxiliary information, such as local and global sensitivities. The designer may thus decide the input parameter(s) to which the output quantity of interest is most sensitive, and thereby design better experiments based on just the most sensitive input parameter(s). Another critical output of such a methodology is the solution to the inverse problem, i.e., finding the allowable uncertainty (range) in the input parameter(s), given an acceptable uncertainty (range) in the output quantities of interest. We apply optimization under uncertainty to the problem of heat transfer in fin heat sinks with uncertainties in geometry and operating conditions. The analysis methodology is implemented using DAKOTA, an open-source design and analysis kit. A response surface is first generated which captures the dependence of the quantity of interest on inputs. This response surface is then used to perform both deterministic and probabilistic optimization of the heat sink, and the results of the two approaches are compared.

Manifold microchannel heat sink design using optimization under uncertainty

“…The models are described only briefly here, and a detailed discussion on the UQ and OUU methodology employed may be found in Bodla et al [15]. In the present study, two sets of computations are performed.…”

“…Further details may be found in [18] and in the comprehensive review by Eldred [25]. The utility of such a non-intrusive gPC approach in the design of electronics cooling equipment such as pin-fin heat sinks, and its advantages compared to an intrusive approach, were demonstrated recently by Bodla et al [15].…”

“…The PDFs of the response R may be computed by sampling the space of input random variables using random sampling algorithms such as Monte Carlo or Latin Hypercube sampling. Output response statistics, such as PDFs, and the mean and standard deviation of the outputs, may then be readily computed [15].…”

“…An improved alternative strategy is to adopt a probabilistic optimization approach using the optimization under uncertainty (OUU) method which combines the optimization procedure with uncertainty quantification (UQ) [15] . Optimization under uncertainty is a powerful approach that ensures reliable design of systems by considering the input uncertainties as part of the design process.…”

“…In this model, the microchannel heat sink is represented as a porous medium with equivalent porosity and permeability [17], so as to reduce computational complexity. After validating the numerical model, an OUU analysis is performed by using a nested approach as discussed in detail in [15]. In this approach, uncertainty quantification is performed in an inner loop, which is nested within an outer optimization loop, as described in section 3.2.…”