Uncertainty management in the design of multiscale systems

Abstract

In this thesis, a framework is laid for holistic uncertainty management for simulation-based design of multiscale systems. The work is founded on uncertainty management for microstructure mediated design (MMD) of material and product, which is a representative example of a system over multiple length and time scales, i.e., a multiscale system. The characteristics and challenges for uncertainty management for multiscale systems are introduced context of integrated material and product design. This integrated approach results in different kinds of uncertainty, i.e., natural uncertainty (NU), model parameter uncertainty (MPU), model structure uncertainty (MSU) and propagated uncertainty (PU). We use the Inductive Design Exploration Method to reach feasible sets of robust solutions against MPU, NU and PU. MMD of material and product is performed for the product autonomous underwater vehicle (AUV) employing the material in-situ metal matrix composites using IDEM to identify robust ranged solution sets. The multiscale system results in decision nodes for MSU consideration at hierarchical levels, termed as multilevel design. The effectiveness of using game theory to model strategic interaction between the different levels to facilitate decision making for mitigating MSU in multilevel design is illustrated using the compromise decision support problem (cDSP) technique. Information economics is identified as a research gap to address holistic uncertainty management in simulation-based multiscale systems, i.e., to address the reduction or mitigation of uncertainty considering the current design decision and scope for further simulation model refinement in order to reach better robust solutions. It necessitates development of an improvement potential (IP) metric based on value of information which suggests the scope of improvement in a designer's decision making ability against modeled uncertainty (MPU) in simulation models in multilevel design problem. To address the research gap, the integration of robust design (using IDEM), information economics (using IP) and game theoretic constructs (using cDSP) is proposed. Metamodeling techniques and expected value of information are critically reviewed to facilitate efficient integration. Robust design using IDEM and cDSP are integrated to improve MMD of material and product and address all four types of uncertainty simultaneously. Further, IDEM, cDSP and IP are integrated to assist system level designers in allocating resources for simulation model refinement in order to satisfy performance and robust process requirements. The approach for managing MPU, MSU, NU and PU while mitigating MPU is presented using the MMD of material and product. The approach presented in this article can be utilized by system level designers for managing all four types of uncertainty and reducing model parameter uncertainty in any multiscale system.