Validation of Simplified Rack Boundary Conditions for Numerical Data Center Models

As cloud computing and computational needs grow, data centers will continue to become a larger part of our energy load. Proper design and layout is crucial to efficient energy use in data centers. Modeling the rack is one of critical pieces in this design. Often this is done as a black box rather than modeling the rack in detail. Modeling a computer rack as a black box has been done in numerous data center studies, but rarely has it been validated against experimental temperature and velocity data. This study looks at two simplified rack models and compares them against a rack composed of four 10U server simulators. The first model is an open box model that has a heating and fan plate and allows air to flow through the rack. The second model is a black box model that allows no flow through the rack and imposes a constant pressure boundary across the inlet and exhaust. The model adds the proportion of the rack load to the upwind cells at the rack inlet plate to generate the exhaust temperature profile. The models were tested across a range of airflows and rack loads. Agreements were found to be within 3°C and 0.2 m/s on average over all experiments. An interesting finding of this study was the importance of correctly capturing the boundary conditions at the perforated floor tile. Modeling the perforated floor tile as a nozzle using the momentum method described in ASHRAE RP-1009 was found to produce acceptable results for airflow from the perforated floor tile

Online and Offline Approximations for Population based Multi-objective Optimization

The high computational cost of population based optimization methods has been preventing applications of these methods to realistic engineering design problems. The main challenge is to devise approaches that can significantly reduce the number of function (or simulation) calls required in such optimization methods. This dissertation presents some new online and offline approximation approaches for design optimization. In particular, it presents new DOE and metamodeling techniques for Genetic Algorithm (GA) based multi-objective optimization methods along four research thrusts. The first research thrust is called: Online Metamodeling Assisted Fitness Evaluation. In this thrust, a new online metamodeling assisted fitness evaluation approach is developed that aims at significantly reducing the number of function calls in each generation of a Multi-Objective Genetic Algorithm (MOGA) for design optimization. The second research thrust is called: DOE in Online Metamodeling. This research thrust introduces a new DOE method that aims at reducing the number of generations in a MOGA. It is shown that the method developed under the second research thrust can, compared to the method in the first thrust, further reduce the number of function calls in the MOGA. The third research thrust is called: DOE in Offline Metamodeling. In this thrust, a new DOE method is presented for sampling points in the non-smooth regions of a design space in order to improve the accuracy of a metamodel. The method under the third thrust is useful in approximation assisted optimization when the number of available function calls is limited. Finally, the fourth research thrust is called: Dependent Metamodeling for Multi-Response Simulations. This research thrust presents a new metamodeling technique for an engineering simulation that has multiple responses. Numerous numerical and engineering examples are used to demonstrate the applicability and performance of the proposed online and offline approximation techniques

Robust Optimization and Sensitivity Analysis with Multi-Objective Genetic Algorithms: Single- and Multi-Disciplinary Applications

Uncertainty is inevitable in engineering design optimization and can significantly degrade the performance of an optimized design solution and/or even change feasibility by making a feasible solution infeasible. The problem with uncertainty can be exacerbated in multi-disciplinary optimization whereby the models for several disciplines are coupled and the propagation of uncertainty has to be accounted for within and across disciplines. It is important to determine which ranges of parameter uncertainty are most important or how to best allocate investments to partially or fully reduce uncertainty under a limited budget. To address these issues, this dissertation concentrates on a new robust optimization approach and a new sensitivity analysis approach for multi-objective and multi-disciplinary design optimization problems that have parameters with interval uncertainty. The dissertation presents models and approaches under four research thrusts. In the first thrust, an approach is presented to obtain robustly optimal solutions which are as best as possible, in a multi-objective sense, and at the same time their sensitivity of objective and/or constraint functions is within an acceptable range. In the second thrust, the robust optimization approach in the first thrust is extended to design optimization problems which are decomposed into multiple subproblems, each with multiple objectives and constraints. In the third thrust, a new approach for multi-objective sensitivity analysis and uncertainty reduction is presented. And in the final research thrust, a metamodel embedded Multi-Objective Genetic Algorithm (MOGA) for solution of design optimization problems is presented. Numerous numerical and engineering examples are used to explore and demonstrate the applicability and performance of the robust optimization, sensitivity analysis and MOGA techniques developed in this dissertation. It is shown that the obtained robust optimal solutions for the test examples are conservative compared to their corresponding optimal solutions in the deterministic case. For the sensitivity analysis, it is demonstrated that the proposed method identifies parameters whose uncertainty reduction or elimination produces the largest payoffs for any given investment. Finally, it is shown that the new MOGA requires a significantly fewer number of simulation calls, when used to solve multi-objective design optimization problems, compared to previously developed MOGA methods while obtaining comparable solutions