Metamodeling Uncertainty Quantification And Sequential Sampling In Multi-level System Design

With the rapid development of modern industry, complex system design often involves a multitude of decision variables and factors. In the traditional “All-In-One” design paradigm, all the design variables are optimized simultaneously, leading to unaffordable computational complexity and cost. To mitigate the computational burden, manage the complexity, and achieve concurrent analysis and design in complex system design process, systems are oftentimes decomposed into several subsystems(also called submodels) with a hierarchical(multi-level) manner according to their functional attributes and physical scales etc. With such decomposition strategy, each subsystem in the hierarchy can be analyzed and designed independently and concurrently. Metamodeling techniques are widely used in hierarchical system analysis and design to replace the original time-consuming simulation models, like finite element simulation, molecular dynamics simulation etc., to future reduce computational burden. However, due to the limited sample points from simulation models, metamodel may contain metamodeling uncertainty at sites with no sample point. Such metamodeling uncertainty may have significant influence on performance analysis and design optimization of complex systems.A variety of metamodeling techniques and sampling strategies have been proposed in the past few decades. However, reducing metamodeling uncertainty and improving fidelity of metamodels for multi-level systems are rarely reported. With the aim of improving the global fidelity of metamodels in multi-level system analysis and design, this thesis devotes to investigate a metamodeling uncertainty quantification method and a sequential sampling strategy. The specific contributions of this thesis contain:(1) Deriving the analytical mathematical express of the metamodeling uncertainty of top-level response as a function of lower level metamodeling uncertainties. In the analysis and design of a multi-level system, the metamodeling uncertainty raised from metamodels across the entire hierarchy will propagate from lower levels to upper levels, and eventually impact the top-level response. A metamodeling uncertainty quantification(MUQ) method for multi-level systems is proposed to provide analytical formulations for computing the mean and variance of the top-level response at any un-sampled sites.(2) Developing a computational efficient numerical integration algorithm to relieve the computational cost in quantifying metamodeling uncertainty. The aforementioned metamodeling uncertainty quantification method will be computationally unaffordable if the number of submodels increases. Alternatively, the Gauss-Hermite quadrature is tailored to compute the mean and variance of the top-level response at un-sampled sites. As demonstrated in our comparative study, the proposed algorithm outperforms others numerical integration methods in our specific problem.(3) Proposing a new sequential sampling strategy to improve the global fidelity of metamodels for the analysis and design of a multi-level system. Most reported sequential sampling methods only consider to increase the fidelity of a single level metamodel. These methods are unable to directly apply to multi-level systems as they ignore the metamodeling uncertainty propagation in hierarchy. To address this issue, a new sequential sampling method which takes account of metamodeling uncertainties in multiple levels of a system is proposed. The proposed method chooses the sample site which has the greatest influence on average uncertainty of the top-level response as the next new sample site, and uses the sample from simulation model to update the corresponding metamodels. As exemplified in numerical examples and a case study, with the same amount of limited samples, the new sequential sampling method is superior to the existing sequential sampling methods in terms of improving the global fidelity of metamodels for multi-level systems.