Computer simulations are routinely executed to predict the behavior of complex systems in many fields of engineering and science. These computer-aided predictions involve the theoretical foundation, numerical modeling, and supporting experimental data, all of which come with their associated errors. A natural question then arises concerning the validity of computer model predictions, especially in cases where these models are executed in support of high-consequence decision making. This article lays out a methodology for quantifying the degrading effects of incompleteness and inaccuracy of the theoretical foundation, numerical modeling, and experimental data on the computer model predictions. Through the method discussed in this paper, the validity of model predictions can be judged and communicated between involved parties in a quantitative and objective manner.
The concept of partitioning a complex engineering problem into smaller, manageable components and investigating each individual component autonomously has been in use for many decades. Such partitioning approaches, however, rely on strong and occasional unwarranted assumptions regarding the interactions among different engineering components. Fluid and structure interaction, soil and structure interaction, and human and structure interaction are but a few of the many such partitioned analyses commonly needed in civil engineering applications. Recently, there has been a growing interest in combining the expertise developed separately in traditionally distinct fields to obtain a holistic treatment of engineering problems. Such holistic treatment would ultimately yield not only more realistic and accurate analyses of coupled systems but also improved optimality in engineering designs. This growing interest has resulted in development of mathematical coupling procedures for conjoining multiple, separately developed, single-solver numerical models along their interfaces. The present manuscript contributes to the field of partitioned analysis by introducing a novel mathematical coupling procedure based on the minimization of an objective function consisting of coupling conditions. The authors' approach to coupling implements optimization techniques and is observed to eliminate the divergence issues that may be encountered with iterative coupling methods. The proposed optimization-based coupling scheme is compared against the well-known block Gauss-Seidel (BGS) iteration method and considers two aspects: the accuracy of the coupled model predictions and the convergence of the coupled parameters. The comparison is completed for three case studies with increasing complexity: a linear set of equations, polynomials with random coefficients, and a linear dynamic system.
The present study develops an integrated coupling and uncertainty quantification framework for strongly coupled models that explicitly considers the propagation of uncertainty and bias inherent in model prediction between constituents during the iterative coupling process. Utilizing optimization techniques, three distinct configurations are formulated that differ in sequence of coupling and uncertainty quantification campaigns. Focusing on a controlled structural dynamics problem, the systematic biases from the constituents are quantified, from which the critical components of the model that require further improvement can be identified to aid in the prioritization of future code development efforts.
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