Date of Award
Doctor of Philosophy (PhD)
Many problems in engineering and science can be framed as decision problems in which we choose values for decision variables that lead to desired outcomes. Notable examples include maximizing lift in airplane wing design, improving the efficiency of a power plant, or identifying processing protocols resulting in structural materials with desired mechanical properties. These problems typically involve a significant degree of uncertainty about the often-complex underlying relationships between the decision variables and the outcomes. Solving such decision problems involves the use of computational models or physical experimentation to generate data to make predictions and test hypotheses. As a result, both approaches incur costs in terms of data generation and collection that must be considered when assessing the trade-off between the benefits of these data and the cost of generating it. This is especially true when there is variability in the generated results. This variability requires multiple measurements to characterize the outcome statistically, further increasing the costs. This can often result in suboptimal solutions because the optimization process is prematurely stopped due to the high costs incurred.
To overcome these challenges, we develop a value-based data-driven optimization framework to solve such complex decision problems efficiently. Typically, the computational or physical experiments needed to solve these problems are spread over the entire design space to explore it or focused on subregions to exploit them and find an optimum. Since the experimentation costs are high, these costs need to be considered during optimization. One way to accomplish this is by taking advantage of the fact that in many problems, simultaneously performing multiple experiments incurs less total cost than when performed individually. Another way to accomplish it is to choose to collect data, whether computational or physical, that maximize the expected value gained from them. This balances the exploration and exploitation and allows the framework to identify the solution efficiently. The developed framework starts with design space exploration and gradually transitions to an exploitation stage as the framework gains a better understanding of the problem. This is achieved by incrementally performing experiments and using their results to help choose the next set of experiments while considering the associated expenses. This iterative approach leads to a multistage stochastic programming method, allowing for a guided and targeted experimentation approach that improves the overall efficiency of the optimization framework.
We develop the framework in the context of materials design efforts, specifically the Laser-Powder Bed Fusion (L-PBF) additive manufacturing process. We adopt the view that materials design entails deciding on the processing conditions that optimize the engineering properties of the manufactured materials systems. Materials design is chosen as the application of interest because traditional design methods are inefficient and time-consuming, as they rely on trial-and-error experimentation. More specifically, the motivating design problem considered in this work is to identify the laser process parameters for L-PBF to achieve a combination of mechanical properties that maximize the value to the user, customer, or manufacturer.
We test the framework using a series of synthetic profiles to quantify and compare its performance with currently used optimization algorithms for L-PBF. The synthetic profiles vary differently within the design space and are considered to represent the trends of the mechanical properties in the space. These synthetic profiles are combined to yield outcome surfaces of the material value with varying degrees of complexity. Simulation results show that the framework follows a balanced exploration-exploitation optimization scheme. Additionally, comparison with currently used optimization methods for L-PBF shows that the framework outperforms the latter method. The framework requires fewer experiments to identify a material with a better material value.
Applying the framework to complex problems in materials design and other fields leads to many benefits, opening new research avenues and possibilities for optimization in practice. The framework can yield materials with enhanced properties when applied to the L-PBF process and many other materials synthesis and processing techniques with several design variables. The framework improves the search efficiency for an optimal solution by identifying an optimal outcome using less time and experimentation resources. This makes the framework a valuable tool for addressing a wide range of real-world challenges, where complex relationships exist between decision variables and outcomes and where solving these challenges requires resource-intensive approaches.
Alghalayini, Maher, "A Value-Based Sequential Optimization Framework for Efficient Materials Design Considering Uncertainty and Variability" (2023). All Dissertations. 3323.
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