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A frequency-domain approach for estimating continuous-time diffusively coupled linear networks

Desen Liang, E. M. M., Kivits, Maarten Schoukens, Paul M. J. Van den Hof

TL;DR

A three-step frequency-domain identification method for linear CT DCNs that allows to accurately recover all the physical component values of the network while exploiting the particular symmetric structure in a DCN model is developed.

Abstract

This paper addresses the problem of consistently estimating a continuous-time (CT) diffusively coupled network (DCN) to identify physical components in a physical network. We develop a three-step frequency-domain identification method for linear CT DCNs that allows to accurately recover all the physical component values of the network while exploiting the particular symmetric structure in a DCN model. This method uses the estimated noise covariance as a non-parametric noise model to minimize variance of the parameter estimates, obviating the need to select a parametric noise model. Moreover, this method is extended to subnetworks identification, which enables identifying the local dynamics in DCNs on the basis of partial measurements. The method is illustrated with an application from In-Circuit Testing of printed circuit boards. Experimental results highlight the method's ability to consistently estimate component values in a complex network with only a single excitation.

A frequency-domain approach for estimating continuous-time diffusively coupled linear networks

TL;DR

A three-step frequency-domain identification method for linear CT DCNs that allows to accurately recover all the physical component values of the network while exploiting the particular symmetric structure in a DCN model is developed.

Abstract

This paper addresses the problem of consistently estimating a continuous-time (CT) diffusively coupled network (DCN) to identify physical components in a physical network. We develop a three-step frequency-domain identification method for linear CT DCNs that allows to accurately recover all the physical component values of the network while exploiting the particular symmetric structure in a DCN model. This method uses the estimated noise covariance as a non-parametric noise model to minimize variance of the parameter estimates, obviating the need to select a parametric noise model. Moreover, this method is extended to subnetworks identification, which enables identifying the local dynamics in DCNs on the basis of partial measurements. The method is illustrated with an application from In-Circuit Testing of printed circuit boards. Experimental results highlight the method's ability to consistently estimate component values in a complex network with only a single excitation.

Paper Structure

This paper contains 29 sections, 2 theorems, 64 equations, 6 figures, 4 tables.

Table of Contents

  1. INTRODUCTION
  2. DIFFUSIVELY COUPLED NETWORKS
  3. Continuous-time model
  4. Frequency-domain model
  5. FREQUENCY-DOMAIN IDENTIFICATION
  6. Step 1: non-parametric identification
  7. Step 2: structured polynomial matrix identification
  8. Step 3: reduce bias with structured MLE estimation
  9. Full network identification algorithm
  10. FREQUENCY-DOMAIN SUBNETWORK IDENTIFICATION FOR DIFFUSIVELY COUPLED NETWORKS
  11. The immersed network
  12. The subnetwork identification procedure
  13. Subnetwork identification algorithm
  14. SIMULATION EXPERIMENTS
  15. Full network identification experiments
  16. ...and 14 more sections

Key Result

Proposition 1

The DCN is identifiable if the following conditions are satisfied according to lizan and lizanidentifibility:

Figures (6)

  • Figure 1: A 10-node RLC circuit with inductors ($L_{jk}$), resistors ($R_{jk}$), capacitors ($C_{jk}$), and ground nodes($GND_{j}$).
  • Figure 2: Boxplot of the RMSE of the coefficients of the components for each experimental set (full network identification).
  • Figure 3: Relative parameters errors for the 10-node defect model.
  • Figure 4: A seven-node RLC network circuit with inductors ($L_{jk}$), resistors ($R_{jk}$), capacitors ($C_{jk}$) and ground nodes($GND_{j}$).
  • Figure 5: Boxplot of the RMSE of the coefficients of the components for each experimental set (subnetwork identification).
  • ...and 1 more figures

Theorems & Definitions (15)

  • Definition 1
  • Remark 1
  • Definition 2
  • Remark 2
  • Proposition 1
  • Remark 3
  • Remark 4
  • Remark 5
  • Remark 6
  • Definition 3
  • ...and 5 more