Identifiability of Viscoelastic Mechanical Systems

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Claim: a spring–dashpot network is locally identifiable iff the number of non‑monic coefficients equals the number of parameters, and global identifiability requires unique polynomial factorizations. Method: rewrite stress–strain laws as linear differential operators, reduce series/parallel assemblies to a shape factorization problem, and study the resulting polynomial coefficient map. Tools: counting, factorization of monic polynomials, and invertibility of a submatrix (a Sylvester matrix) to prove finiteness. Examples: Maxwell, Voigt and Burgers models (4 parameters → 4 coefficients) are identifiable; ambiguous assemblies are only locally identifiable.

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" chapters (20)

1. 0:00Intro
2. 0:17Structural Identifiability
3. 2:19Viscous Material
4. 2:52Viscoelastic material
5. 3:25Application to cardiovascular modeling
6. 5:27Viscoelastic (VE) System
7. 8:54Identifiability problem
8. 11:28Main result
9. 13:14Local Identifiability
10. 15:33Generalize process of combining in Series/Parallel
11. 16:25Series connection
12. 17:18Parallel connection
13. 17:44Types of viscoelastic models
14. 19:57Shape factorization problem for a quadruple of shapes
15. 21:20Example cont'd
16. 21:39Solving shape factorization problem
17. 23:04Global identifiability
18. 23:40Real Example (Dietrich 1998)
19. 24:10Summary
20. 24:43References