Structural Identifiability of Series-Parallel LCR Systems

TL;DR

This paper investigates the conditions under which parameters of series-parallel LCR circuits can be uniquely identified from their equations, revealing key roles of equation types and limitations in general cases.

Contribution

It establishes criteria for identifiability in two-class LCR networks and classifies types of constitutive equations in general series-parallel circuits, highlighting the complexity of the problem.

Findings

Parameters are identifiable if the number of non-monic coefficients matches the number of parameters.

22 types of constitutive equations can arise in general series-parallel LCR circuits.

A basic classification method is insufficient for general circuits' identifiability.

Abstract

We consider the identifiability problem for the parameters of series-parallel LCR circuit networks. We prove that for networks with only two classes of components (inductor-capacitor (LC), inductor-resistor (LR), and capacitor-resistor (RC)), the parameters are identifiable if and only if the number of non-monic coefficients of the constitutive equations equals the number of parameters. The notion of the "type" of the constitutive equations plays a key role in the identifiability of LC, LR, and RC networks. We also investigate the general series-parallel LCR circuits (with all three classes of components), and classify the types of constitutive equations that can arise, showing that there are 22 different types. However, we produce an example that shows that the basic notion of type that works to classify identifiability of two class networks is not sufficient to classify the identifiability of general series-parallel LCR circuits.