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

Tulay Ercan¹, Costas Papadimitriou¹

¹Department of Mechanical Engineering, University of Thessaly, Pedion Areos, 383 34 Volos, Greece.

Sensors (Basel, Switzerland)

|June 2, 2021

Summary

This study presents a robust framework for optimal sensor placement (OSP) for virtual sensing using vibration data. It maximizes information gain to reduce prediction uncertainty, even with model errors.

Keywords:

Bayesian inference Kullback-Leibler divergence information gain relative entropy response predictions

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Data Acquisition Protocol for Determining Embedded Sensitivity Functions

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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.