Extended space method for parameter identifiability of DAE systems

Area of Science:

• Mathematical modeling
• Systems analysis
• Parameter identification

Background:

• Mathematical models are crucial for physical systems, requiring parameter identification from data.
• Parameter identifiability analysis is essential but underexplored for differential algebraic equation (DAE) systems.
• Existing methods for ordinary differential equation (ODE) systems are not always suitable for DAEs.

Purpose of the Study:

• To propose a novel method for analyzing parameter identifiability specifically for DAE systems.
• To address the limitations of traditional methods when applied to DAEs, particularly when the prime ideal condition is not met.

Main Methods:

• The proposed method utilizes the concept of space extension to decouple algebraic and differential variables in DAE systems.
• It transforms the DAE system into an equivalent, inherent, low-dimensional, regular ODE system.
• Identifiability analysis is then performed on the derived ODE system using established differential algebraic (DA) methods.

Main Results:

• The method successfully decouples variables, enabling the derivation of a simpler, equivalent ODE system.
• Theoretical analysis supports the validity and applicability of the proposed space extension technique.
• Demonstrated effectiveness through two examples: a simplified interaction model and an isothermal reactor system.

Conclusions:

• The novel space extension method provides an effective approach for parameter identifiability analysis in DAE systems.
• This technique overcomes limitations of existing methods and offers a robust alternative for complex systems.
• The findings facilitate more reliable parameter estimation in physical systems modeled by DAEs.