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Transfer learning via interpolating structures

T. A. Dardeno, A. J. Hughes, L. A. Bull, R. S. Mills, N. Dervilis, K. Worden

Abstract

Despite recent advances in population-based structural health monitoring (PBSHM), knowledge transfer between highly-disparate structures (i.e., heterogeneous populations) remains a challenge. The current work proposes that heterogeneous transfer may be accomplished via intermediate structures that bridge the gap in information between the structures of interest. A key aspect of the technique is the idea that by varying parameters such as material properties and geometry, one structure can be continuously morphed into another. The approach is demonstrated via a case study involving the parameterisation of (and transfer between) simulated heterogeneous bridge designs (Case 1). Transfer between simplified physical representations of a 'bridge' and 'aeroplane' is then demonstrated in Case 2, via a chain of finite-element models. The facetious question 'When is a bridge not an aeroplane?' has been previously asked in the context of predicting positive transfer based on structural similarity. While the obvious answer to this question is 'Always,' the results presented in the current paper show that, in some cases, positive transfer can indeed be achieved between highly-disparate systems.

Transfer learning via interpolating structures

Abstract

Despite recent advances in population-based structural health monitoring (PBSHM), knowledge transfer between highly-disparate structures (i.e., heterogeneous populations) remains a challenge. The current work proposes that heterogeneous transfer may be accomplished via intermediate structures that bridge the gap in information between the structures of interest. A key aspect of the technique is the idea that by varying parameters such as material properties and geometry, one structure can be continuously morphed into another. The approach is demonstrated via a case study involving the parameterisation of (and transfer between) simulated heterogeneous bridge designs (Case 1). Transfer between simplified physical representations of a 'bridge' and 'aeroplane' is then demonstrated in Case 2, via a chain of finite-element models. The facetious question 'When is a bridge not an aeroplane?' has been previously asked in the context of predicting positive transfer based on structural similarity. While the obvious answer to this question is 'Always,' the results presented in the current paper show that, in some cases, positive transfer can indeed be achieved between highly-disparate systems.
Paper Structure (22 sections, 11 equations, 17 figures, 8 tables)

This paper contains 22 sections, 11 equations, 17 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Research aims of the current work
  3. Paper layout
  4. Related work
  5. Transfer learning
  6. Domain adaptation
  7. Gradual domain adaptation
  8. Geometric and topological approaches to transfer learning
  9. Novelty and contribution
  10. Background theory
  11. A geometric framework for PBSHM
  12. Geodesics and geodesic flows
  13. Geodesic flow kernel (GFK)
  14. Case 1: Transfer between heterogeneous bridges
  15. Generation of finite element models
  16. ...and 7 more sections

Figures (17)

  • Figure 1: Schematic of geometrical model of PBSHM in terms of a fibre bundle.
  • Figure 2: A geodesic (red curve) on a sphere, with tangent spaces (planes) shown at successive points along the path. The blue arrows show the tangent directions evolving continuously along the geodesic, illustrating the geodesic flow.
  • Figure 3: Geodesic flow kernel, adapted from Boqing2012.
  • Figure 4: Two-span source (a) and three-span target bridges (b) in the damaged state.
  • Figure 5: Schematic of model generation process. The first support remained fixed while the second support moved to the right and materialised as $\alpha$ increased.
  • ...and 12 more figures