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Abstract:
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Finite element models (FEMs) are mathematical models that approximate the behavior of a diverse set of complex structures from jet wings to cardiovascular implants. Given the FEM's role in assessing structural vibration, validating FEM accuracy is key. Validation is done by placing sensors on prototype structures and comparing estimated vibration properties from the sensor data to the theoretical FEM. A critical question is the number and location of sensors needed for estimation. Current approaches for optimal sensor placement (OSP) assume the FEM is correct and sequentially add/remove sensors using criteria such as residual kinetic energy or effective independence. While these approaches have similarities to optimal design problems, there has been little research done by the statistical community in this area. Moreover, few OSP approaches are directly tied to the statistical properties of estimators resulting from the sensor data. This talk presents the OSP problem from a statistical perspective, detailing advantages and disadvantages of current approaches, and proposing new statistically motivated directions. We also describe a new OSP approach that combines existing methods.
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