Optimal Sensor Placement for Reliable Virtual Sensing Using Modal Expansion and Information Theory.

Area of Science:

• Structural Dynamics
• Information Theory
• Optimization

Background:

• Virtual sensing enables predicting structural responses at unmeasured locations.
• Output-only vibration measurements are common but pose challenges for traditional methods.
• Uncertainties in structural models and measurements can significantly impact prediction accuracy.

Purpose of the Study:

• To develop a framework for optimal sensor placement (OSP) for virtual sensing using output-only vibration data.
• To maximize the expected information gain for reducing uncertainties in predicted quantities of interest (QoI).
• To ensure the OSP design is robust to various sources of uncertainty.

Main Methods:

• Utilizing modal expansion techniques and information/utility theory for OSP.
• Maximizing a utility function that quantifies expected information gain.
• Extending the utility function to incorporate robustness against structural model uncertainties and modeling errors.
• Employing approximate methods to solve the resulting multidimensional optimization problem.

Main Results:

• A novel framework for OSP in virtual sensing under output-only vibration measurements.
• The utility function effectively quantifies information gain and accounts for uncertainties.
• Analytical expressions for the utility function were derived by exploiting the Gaussian nature of response QoI.
• The study thoroughly investigated the impact of various errors and uncertainties on sensor configuration selection.

Conclusions:

• The proposed framework provides an effective approach for optimal sensor placement in virtual sensing.
• Accounting for robustness to errors and uncertainties is crucial for reliable sensor configuration.
• The method is applicable to output-only vibration measurements and can handle complex uncertainties.