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Fast Stochastic Subspace Identification of Densely Instrumented Bridges Using Randomized SVD

Elisa Tomassini, Enrique García-Macías, Filippo Ubertini

Abstract

The rising number of bridge collapses worldwide has compelled governments to introduce predictive maintenance strategies to extend structural lifespan. In this context, vibration-based Structural Health Monitoring (SHM) techniques utilizing Operational Modal Analysis (OMA) are favored for their non-destructive and global assessment capabilities. However, long multi-span bridges instrumented with dense arrays of accelerometers present a particular challenge, as the computational demands of classical OMA techniques in such cases are incompatible with long-term SHM. To address this issue, this paper introduces Randomized Singular Value Decomposition (RSVD) as an efficient alternative to traditional SVD within Covariance-driven Stochastic Subspace Identification (CoV-SSI). The efficacy of RSVD is also leveraged to enhance modal identification results and reduce the need for expert intervention by means of 3D stabilization diagrams, which facilitate the investigation of the modal estimates over different model orders and time lags. The approach's effectiveness is demonstrated on the San Faustino Bridge in Italy, equipped with over 60 multiaxial accelerometers.

Fast Stochastic Subspace Identification of Densely Instrumented Bridges Using Randomized SVD

Abstract

The rising number of bridge collapses worldwide has compelled governments to introduce predictive maintenance strategies to extend structural lifespan. In this context, vibration-based Structural Health Monitoring (SHM) techniques utilizing Operational Modal Analysis (OMA) are favored for their non-destructive and global assessment capabilities. However, long multi-span bridges instrumented with dense arrays of accelerometers present a particular challenge, as the computational demands of classical OMA techniques in such cases are incompatible with long-term SHM. To address this issue, this paper introduces Randomized Singular Value Decomposition (RSVD) as an efficient alternative to traditional SVD within Covariance-driven Stochastic Subspace Identification (CoV-SSI). The efficacy of RSVD is also leveraged to enhance modal identification results and reduce the need for expert intervention by means of 3D stabilization diagrams, which facilitate the investigation of the modal estimates over different model orders and time lags. The approach's effectiveness is demonstrated on the San Faustino Bridge in Italy, equipped with over 60 multiaxial accelerometers.

Paper Structure

This paper contains 13 sections, 24 equations, 15 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Theoretical background and methodology
  3. Covariance-drive Stochastic Subspace Identification (CoV-SSI)
  4. Randomized Singular Value Decomposition (RSVD)
  5. 3D Stabilization diagrams
  6. Numerical results and discussion
  7. Theoretical 10-DOFs case study
  8. Parametric analysis: rank selection
  9. 2D and 3D stabilization diagrams including the RSVD
  10. Real case study: the San Faustino Bridge
  11. Computational efficiency
  12. Continuous RSVD-CoV-SSI modal identification
  13. Conclusions

Figures (15)

  • Figure 1: Flowchart for the construction of 3D stabilization diagrams considering pole stability across various model orders and time lag values.
  • Figure 2: Sketch of the 10-DOFs dynamic system (a), sampled accelerations with signal-to-noise ratio (SNR) of 20 dB (b), and corresponding power spectral density (PSD) spectrum (c).
  • Figure 3: Results of the parametric analysis for the 10-DOFs dynamic system. The dots represent the experimental minimum percentage ranks $\overline{k}$ for different SNR values.
  • Figure 4: Stabilization diagrams extracted by CoV-SSI using SVD and RSVD. In the background, the first three singular values of the spectral density matrix are plotted for reference.
  • Figure 5: Stability analysis of the 10DOFs system after the first stage of clustering.
  • ...and 10 more figures