Publications

This paper develops a novel method for reconstructing the full-field response of structural dynamic systems using sparse measurements. The singular value decomposition is applied to a frequency response matrix relating the structural response to physical loads, base motion, or modal loads. The left singular vectors form a non-physical reduced basis that can be used for response reconstruction with far fewer sensors than existing methods. The contributions of the singular vectors to measured response are termed singular-vector loads (SVLs) and are used in a regularized Bayesian framework to generate full-field response estimates and confidence intervals. The reconstruction framework is applicable to the estimation of single data records and power spectral densities from multiple records. Reconstruction is successfully performed in configurations where the number of SVLs to identify is less than, equal to, and greater than the number of sensors used for reconstruction. In a simulation featuring a seismically excited shear structure, SVL reconstruction significantly outperforms modal FRF-based reconstruction and successfully estimates full-field responses with as few as two uniaxial accelerometers. SVL reconstruction is further verified in a simulation featuring an acoustically excited cylinder. Finally, response reconstruction and uncertainty quantification are performed on an experimental structure with three shaker inputs and 27 triaxial accelerometer outputs.

The frequency response function (FRF) is an essential means by which dynamic systems are qualified. In recent years, local modeling approaches have been extensively researched and shown to significantly outperform traditional FRF estimators. However, the standard local modeling approach assumes a perfectly-known system input, which results in biased FRF estimates in the presence of input noise. This paper derives a simple adjustment that can be used to improve FRF estimation for systems subjected to random excitation with noisy input data. This improvement can be implemented with little modification to standard local modeling algorithms and with little additional computational burden. The adjustment is coupled with a model selection procedure to avoid underfitting and overfitting. The methods presented in this paper are validated on a simulation, and they are shown to reduce bias due to input noise.

Accurate measurement of frequency response functions is essential for system identification, model updating, and structural health monitoring. However, sensor noise and leakage cause variance and systematic errors in estimated FRFs. Low-noise sensors, windowing techniques, and intelligent experiment design can mitigate these effects but are often limited by practical considerations. This chapter is a guide to implementation of local modeling methods for FRF estimation, which have been extensively researched but are seldom used in practice. Theoretical background is presented, and a procedure for automatically selecting a parameterization and model order is proposed. Computational improvements are discussed that make local modeling feasible for systems with many input and output channels. The methods discussed herein are validated on a simulation example and two experimental examples: a multi-input, multi-output system with three inputs and 84 outputs and a nonlinear beam assembly. They are shown to significantly outperform the traditional H1 and HSVD estimators.