Evaluation of Multi-Dimensional Optimization Methods for Maximizing Segmented Thermoelectric Unicouple Performance
Authors: Lehrer Caroline , Riley Shane P. , Gassler Carter D. , Rossetti Cara R. , Fleurial Jean-Pierre , Durka Michael J. , Nesmith Bill J. , Barry Matthew M. 
Published: January 2025

Abstract
To further enable future NASA deep-space and sub-surface missions, the use of alternative radioisotopes (e.g., Am-241, Cm-244, Po-210, Sr-90), heat source configurations (e.g., General Purpose Heat Source in the STEP-1 and STEP-2 configurations, Compact Heat Source, etc.), and thermoelectric materials (e.g., La3-xTe4 and 14-1-11 Zintl, skutterudites, and PbTe/TAGs, etc.) comprising a radioisotope thermoelectric generator (RTG) in either a legacy or novel form-factor piques interest. Evaluating and optimizing alternative designs that meet electrical and/or thermal performance requirements necessitates improved RTG design and optimization methods. Several independent design variables can constitute the design space, including those mentioned above and thermoelectric converter geometry, such as n- and p-type cross-sectional areas (An and Ap) and high-temperature segment lengths, total unicouple height, externally applied load resistance (Rload), desired output voltage, and expected cold-side temperature. Naive search methods are computationally intractable, and the imposition of system response constraints nullifies simple optimization methods (e.g., gradient-based algorithms, such as hill climb and particle swarm). Prior work compared optimization methods over a representative design space (Rload, An and Ap, and length fractions) and identified methods that decreased computational time, as measured by number of solver calls. This work expands upon prior studies by accounting for the solution space shape and identifying exploitable trends that allow for the use of faster methods, such as Multi-dimensional (MD) Section Search (SS), Nested Section Search (NSS), and Grid Search (GS) schemes. MD SS was done three ways, considering a 5D-SS, a 4D+1D-NSS, and a 2D+2D+1D-NSS. The GS was paired with Successive Refinement (SR) and then SR and NSS simultaneously. The results and computational time of MD SS, NSS, GS+SR, and GS+SR-NSS optimization methods were compared to and benchmarked against known global solutions and the number of solver calls (Ncalls), respectively. With these methods, Ncalls can be reduced by six orders of magnitude while remaining within 1.0% relative difference from the “true” solution, as determined from an exhaustive parametric study. Using pure GS+SR methods, the most significant attainable speedup (Ncalls of the exhaustive parametric study per Ncalls of the proposed method) was 154,787; GS+SR methods are the most robust and have the slightest deviation from the “true” solution. MD SS methods failed to find a design configuration within 1% of the “true” solution. Using NSS methods, the maximum speedup obtained was 552,827; these methods are susceptible to the SS fraction and the shape of the design. Combining GS and NSS methods, the GS+SR-NSS method had a maximum speedup of 316,185. With the demonstration and validation of less computationally expensive optimization methods, it is possible to identify additional optimal mission-satisfying RTG designs. Furthermore, using these methods, multiple designs that meet design requirements were found, some with more favorable geometries and operating points (i.e., fewer unicouples required and lower segment interfacial temperatures).