From Materials to Missions. Assess-Predict-Optimize: A Computational Approach to Adaptive Design

摘要

We develop an Assess-Predict-Optimize (APO) strategy for the adaptive design of optimal missions for critical components and systems. We first assess the system through non-destructive inverse procedures for evaluating the system characteristics of interest: this yields the many possible realizations of the system. We then Predict future behavior of the system through various modeling and computational procedures: this translates the uncertainties in system characterization into ranges of performance. Finally, we Optimize the system mission through mathematical programming methods: this provides the best possible configuration and deployment schedule relative to the design objectives and now-identified (but uncertain) system characteristics. The essential mathematical ingredients of our approach are twofold. First, we employ Reduced- Basis Output Bound Methods: dimension reduction the rational construction of highly efficient ('real-time' response) system-specific approximation spaces that reflect the low-dimensional parametric manifold on which a component 'evolves' during design and operation; and apostertori error estimation relaxations of the classical error-residual equality that provide inexpensive bounds for the prediction error. Second, we employ Mathematical Programming Methods: techniques which incorporate our reduced-basis output bounds for efficient minimization of objective functions with strict adherence to constraints even in the presence of uncertainty.