Model Structures and Structural Identifiability: What? Why? How?

Whyte, Jason M.

doi:10.1007/978-3-030-62497-2_10

Cited by 2 publications

(4 citation statements)

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“…An extension of Uncontrolled_Lin_Comp_Fig to suit controlled LTI structures will require modifications to include the influence of inputs on states. Certain complexities in the testing of controlled structures (see [18,Section 4]) will necessitate substantial changes to how our interactive application processes arguments. For example, it may be desirable to consider an SGI test where output is available for (the often realistic case of) a limited number of inputs that do not permit us to obtain the structure's invariants.…”

Section: Discussionmentioning

confidence: 99%

“…However, given an ULTI structure having finitelyvalued parameters (a physically realistic assumption), each component of x or y is a sum of exponentials with finite exponents which depend linearly on t. As such, the Laplace transform does exist on some domain of convergence, the specific nature of which is unimportant for our purposes here. (We direct the reader interested in details to Sections 2.3.1 and 3.1 of Whyte [18]. )…”

Section: The Transfer Function Methods Of Testing Uncontrolled Lti St...mentioning

confidence: 99%

“…Definition 2 (From Whyte [18,Definition 7]). Suppose we have a structure of uncontrolled state-space systems M , having parameter set Θ (an open subset of R p , p ∈ N), and time set T ⊆ [0, ∞).…”

Section: Structural Identifiability Of Uncontrolled Structuresmentioning

confidence: 99%

“…Definition 3 (Whyte [18,Definition 8]). Suppose that structure M satisfies Conditions 1 and 2 of Definition 2.…”

Section: Structural Identifiability Of Uncontrolled Structuresmentioning

confidence: 99%

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Branching out into Structural Identifiability Analysis with Maple: Interactive Exploration of Uncontrolled Linear Time-Invariant Structures

Whyte

2021

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Suppose we wish to predict the behaviour of a physical system. We may choose to represent the system by model structure S (a set of related mathematical models defined by parametric relationships between system variables), and a parameter set Θ. Each parameter vector in Θ is associated with a completely specified model in S. We use S with system observations in estimating the "true" (unknown) parameter vector. Inconveniently, multiple parameter vectors may cause S to approximate the data equally well. If we cannot distinguish between such alternatives, and these lead to dissimilar predictions, we cannot confidently use S in decision making. This result may render efforts in data collection and modelling fruitless. This outcome occurs when S lacks the property of structural global identifiability (SGI). Fortunately, we can test various classes of structures for SGI prior to data collection. A non-SGI result may guide changes to our structure or experimental design towards obtaining a better outcome. We aim to assist the testing of structures for SGI through bespoke Maple 2020 procedures. We consider continuous-time, uncontrolled, linear timeinvariant state-space structures. Here, the time evolution of the statevariable vector x is modelled by a system of constant-coefficient, ordinary differential equations. We utilise the "transfer function" approach, which is also applicable to the "compartmental" subclass (mass is conserved). Our use of Maple's "Explore" enables an interactive consideration of a parent structure and its variants, obtained as the user changes which components of x are observed, or have non-zero initial conditions. Such changes may influence the information content of the idealised output available for the SGI test, and hence, its result. Our approach may inform the interactive analysis of structures from other classes.

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Section: Discussionmentioning

confidence: 99%

Section: The Transfer Function Methods Of Testing Uncontrolled Lti St...mentioning

confidence: 99%

Section: Structural Identifiability Of Uncontrolled Structuresmentioning

confidence: 99%

“…Definition 3 (Whyte [18,Definition 8]). Suppose that structure M satisfies Conditions 1 and 2 of Definition 2.…”

Section: Structural Identifiability Of Uncontrolled Structuresmentioning

confidence: 99%

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