Multifidelity

Optimization or reliability assessment often require repeated calls to expensive simulations (e.g., finite element analysis, CFD, etc). To lighten the burden associated with repeated function calls, multifidelity approaches, whereby a hierarchy of model fidelities is used, have proven to be quite efficient. Fidelity qualifies the ability of a model to reproduce accurately, spatially and temporally, a phenomenon (e.g., aeroelastic behavior). An example of low-fidelity model would be a response approximation such as a metamodel, while a high-fidelity model would be a highly accurate and computationally expensive.

In the context of classification-based approaches and EDSD in particular,  it has been realized that multifidelity can be used in an elegant manner: Consider a low and a high fidelity model, LF and HF, respectively. We wish to construct an SVM boundary (using the EDSD adaptive sampling) separating failure and safe spaces according to HF using information from LF with the objective of reducing the number of calls to the HF model. This is made possible because of the fact that ``away" from the HF boundary, both models will predict the same class (class, not function value). This is represented in the Figure 1.

Figure 1: Basic idea of the multifidelity approach: Define an envelope (bounded by green lines) beyond which the low fidelity model can be trusted.

Of course, the question is: How far is "away"? The proposed algorithm, initially described in Dribusch and Missoum (2010) and subsequently refined in Dribusch and Missoum (2012), uses a "margin" that is iteratively updated based on how inconsistent the HF and LF model are. This methodology has been applied to analytical and aeroelasticity problems. Figure 2 gives an example of how much reduction in the number of HF function calls can be obtained with the approach.

Figure 2:     Example of difference of the number of high fidelity calls with and without multifidelity approach (red and blue curves respectively).

Traditional approaches for reliability analysis rely on regression methods to model the limit state functions by approximating the underlying computationally heavy simulation models. Our work, on the other hand, emphasise the binary (failure/safe) nature of the limit state function and proposes an approach to perform realiability analysis with the above described classifcation based multifidelity framework. To this end, we developed an adaptive sampling technique which iteratively adds samples in the locations with high probability of inconsistency between HF and LF models. This approach is applied to a Shell and Tube Heat Exchanger reliability problem.

References:

Dribusch, C., Missoum, S., and Beran, P., “A multifidelity approach for the construction of explicit decision boundaries: application to aeroelasticity”, Structural and Multidisciplinary Optimization, vol. 42, 2010, pp. 693-705.

Dribusch, C., and Missoum, S., “Construction of Aeroelastic Stability Boundaries Using a Multi-Fidelity Approach”, Proceedings of the 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, 2012.

Pidaparthi, B., Missoum, S., and Li, P., “A Multi-Fidelity Approach for the Reliability Assessment of Shell and Tube Heat Exchangers”, Proceedings of the ASME International Mechanical Engineering Congress and Exposition, Virtual Conference: American Society of Mechanical Engineers, 2020.