Computationally Efficient Imprecise Uncertainty Propagation

Modeling uncertainty through probabilistic representation in engineering design is common and important to decision making that considers risk. However, representations of uncertainty often ignore elements of “imprecision” that may limit the robustness of decisions. Furthermore, current approaches that incorporate imprecision suffer from computational expense and relatively high solution error. This work presents a method that allows imprecision to be incorporated into design scenarios while providing computational efficiency and low solution error for uncertainty propagation. The work draws on an existing method for representing imprecision and integrates methods for sparse grid numerical integration, resulting in the computationally efficient imprecise uncertainty propagation (CEIUP) method. This paper presents details of the method and demonstrates the effectiveness on both numerical case studies, and a thermocouple performance problem found in the literature. Results for the numerical case studies, in most cases, demonstrate improvements in both computational efficiency and solution accuracy for varying problem dimension and variable interaction when compared to optimized parameter sampling (OPS). For the thermocouple problem, similar behavior is observed when compared to OPS. The paper concludes with an overview of design problem scenarios in which CEIUP is the preferred method and offers opportunities for extending the method.

Computationally Efficient Imprecise Uncertainty Propagation in Engineering Design and Decision Making

Modeling uncertainty through probabilistic representation in engineering design is common and important to decision making that considers risk. However, representations of uncertainty often ignore elements of “imprecision” that may limit the robustness of decisions. Further, current approaches that incorporate imprecision suffer from computational expense and relatively high solution error. This work presents the Computationally Efficient Imprecise Uncertainty Propagation (CEIUP) method which draws on existing approaches for propagation of imprecision and integrates sparse grid numerical integration to provide computational efficiency and low solution error for uncertainty propagation. The first part of the paper details the methodology and demonstrates improvements in both computational efficiency and solution accuracy as compared to the Optimized Parameter Sampling (OPS) approach for a set of numerical case studies. The second half of the paper is focused on estimation of non-dominated design parameter spaces using decision policies of Interval Dominance and Maximality Criterion in the context of set-based sequential design-decision making. A gear box design problem is presented and compared with OPS, demonstrating that CEIUP provides improved estimates of the non-dominated parameter range for satisfactory performance with faster solution times. Parameter estimates obtained for different risk attitudes are presented and analyzed from the perspective of Choice Theory leading to questions for future research. The paper concludes with an overview of design problem scenarios in which CEIUP is the preferred method and offers opportunities for extending the method.