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Event-Triggered Data Selection for Online Frequency-Domain Identification

Enrico Dozzi, Tom Oomen, Rodrigo González

arXiv:2610.21968v1eess.SYcs.SYeess.SP

TL;DR

Changing system dynamics can make offline frequency-response estimates outdated, while sending every high-rate measurement from distributed sensors imposes growing communication demands. The paper locally selects periodically acquired measurements using uncertainty and model mismatch, then transmits selected samples for remote identification. In simulation, it reports comparable FRF performance with about 90% fewer transmissions and faster adaptation after a dynamics change.

  • Problem

    Changing dynamics can make offline FRF estimates stale, while transmitting all high-rate measurements across subsystems increases communication and computational demands.

    Source: §1 · p. 1

  • Method

    A local recursive frequency-domain estimator supports a trigger that selects periodically acquired samples using information gain and model mismatch for remote identification.

    Source: §2 · p. 3, §3.1 · p. 3, §6 · p. 8

  • Results

    About 90% fewer transmissions achieved essentially the same FRF estimation performance as full transmission, with faster adaptation after an abrupt dynamics change.

    Source: §5 · p. 7

  • Takeaways & Limitations

    The trigger allocates more transmissions during initial learning and after dynamics changes, then reduces the rate as the estimator adapts.

    Source: §5 · p. 7

    For λ < 1, σ^2P_N no longer has the exact covariance interpretation used in Lemma 1.

    Source: §3.2 · p. 5

Abstract

from arXiv · show

Online identification of frequency response functions is increasingly relevant for control and monitoring of high-performance systems whose dynamics may change during operation. In modern machines, however, continuously transmitting all locally acquired measurements to a central unit for identification can impose substantial communication demands, particularly as sensing rates and the number of subsystems increase. This paper develops an event-triggered data-selection approach for remote frequency-domain identification, in which periodically acquired measurements are evaluated locally and transmitted only when relevant. The selection mechanism combines information about the current estimation uncertainty with evidence of model mismatch, reducing communication while preserving identification accuracy and responsiveness to changes in the dynamics.

1. INTRODUCTION

Because system dynamics can change, an offline frequency response estimate may become stale, while transmitting every high-rate measurement from many subsystems strains communication and computation. The paper proposes locally selecting informative measurements for remote online identification, combining information gain and model mismatch to retain responsiveness while reducing data transmission.

1. INTRODUCTION

  • Changing operating conditions, degradation, or faults can make an offline FRF cease to represent current dynamics, motivating online tracking across locally sensed subsystems.High-rate transmission also grows in communication and computation demands with sampling rate and subsystem count.Source: §1 · p. 1

1.1 Contribution

  • The framework evaluates periodically acquired measurements locally and transmits only those that offer new FRF information or reveal model mismatch.A recursive local estimator summarizes previously selected data; the retained measurements support remote identification and adaptation to abrupt changes.Source: §1 · p. 1, §1.1 · p. 2

1.2 Related Work

  • The uncertainty-based trigger assesses each measurement’s incremental identification information and also uses prediction discrepancy to respond to changes.This differs from variance-based state-estimation triggering, where uncertainty concerns the predicted measurement.Source: §1.2 · p. 2
  • Unlike related identification work on fixed-dynamics finite-dimensional models, this work targets online nonparametric frequency-domain identification under abrupt changes.It selects from conventional periodic sensing rather than requiring event-based acquisition hardware, and evaluates candidate measurements online rather than designing the sampling pattern offline.Source: §1.2 · p. 2

2. PROBLEM FORMULATION

The problem is to identify the frequency response of a periodically measured system whose dynamics may change abruptly, while selecting a smaller informative dataset for remote estimation. A local trigger evaluates each candidate using the information accumulated from previously selected samples and transmits it when its score reaches a threshold.

2. PROBLEM FORMULATION

  • The formulation considers a continuous-time SISO system with piecewise-LTI dynamics that may change at unknown instants.The output is described as noise-free in the system model, while sampled measurements are separately subject to additive Gaussian noise.Source: §2 · pp. 2–3
  • The system is excited by a multisine input and its output is measured periodically, with independent, zero-mean Gaussian measurement noise of variance σ^2.The input is continuously available; measurements are acquired at sampling period Ts.Source: §2 · pp. 2–3
  • A candidate sample is transmitted and added to the remote identification dataset when its local triggering functional reaches threshold η.The trigger uses information available immediately before observing the candidate; the objective is accurate FRF estimation and timely adaptation to abrupt changes.Source: §2 · p. 3

3. EVENT-TRIGGERED DATA SELECTION FOR ONLINE FREQUENCY-DOMAIN IDENTIFICATION

The section develops a local recursive estimator and event trigger for selecting periodically acquired measurements for remote frequency-domain identification. The trigger combines potential uncertainty reduction with evidence of mismatch between observations and the current model.

3.1 Recursive Frequency-Domain Estimator

  • A complex-valued, exponentially weighted recursive least-squares estimator updates the FRF using only event-selected measurements.Its compact estimate and uncertainty state summarize previously selected data without storing the complete measurement history.Source: §3.1 · pp. 3–4
  • Forgetting is indexed by selected measurements, preserving estimator memory without events while allowing faster replacement of past-regime information as event rates rise.With λ < 1, the estimator’s uncertainty matrix no longer has the exact covariance interpretation used in the predictive-surprise lemma.Source: §3.1 · p. 3, §3.2 · p. 5

3.2 Event-Triggering Rule

  • Predictive surprise separates potential uncertainty reduction from unexpected output, so a candidate can be informative through either mechanism.The uncertainty component uses information available before observing the candidate output; the mismatch component reflects its deviation from the model prediction.Source: §3.2 · p. 5
  • The trigger selects a candidate measurement when its uncertainty score plus weighted, averaged mismatch evidence reaches a threshold.The uncertainty score ranks candidate directions by potential information gain; averaging mismatch evidence helps avoid sensitivity to isolated noise-induced outliers.Source: §3.2 · p. 5

4. INFORMATION PROPERTIES OF EVENT-TRIGGERED DATA SELECTION

The section gives two information-theoretic properties of the trigger: its uncertainty score matches incremental D-optimal information gain, and persistent excitation ensures selected data retain a uniformly positive information level.

  • U_k ranks candidate measurements exactly by incremental D-optimal information gain, making uncertainty a sequential counterpart to offline D-optimal sampling.Source: §4 · pp. 5–6
  • Under uniformly persistent excitation, event-triggered selection keeps the retained information matrix uniformly positive definite, so uncertainty cannot grow arbitrarily large.Source: §4 · p. 6
  • The retention guarantee requires persistent excitation of candidate regressors; mismatch-driven selections may add measurements but are not required for that guarantee.Source: §4 · p. 6

5. SIMULATION RESULTS

In simulation, event-triggered selection retained estimation performance with substantially fewer transmissions than full periodic transmission, and adapted faster than uniform downsampling after an abrupt dynamics change.

5. SIMULATION RESULTS

  • The evaluation used a mass-spring-damper-mass system with an abrupt coupling-stiffness change at T1 = 5000 s and periodically acquired measurements selected for transmission by condition (10).Simulation parameters are summarized in Table 1; the system was excited by a multisine input and estimated online at the excited frequencies.Source: §5 · pp. 6–7, Table 1 · p. 7
  • The central unit used the same RLS estimator for evaluation so performance differences reflected the transmitted measurements; with exponential forgetting, estimation error was not expected to vanish asymptotically.The evaluation considered steady-state accuracy and adaptation following the dynamics change; in practice, the central unit could use another identification method based on the same FRF regression model.Source: §5 · p. 7
  • About 10% of candidate measurements preserved essentially the same FRF estimation performance as full transmission, including adaptation after the abrupt change, while reducing transmissions by approximately 90%.Figure 3 compares the two strategies during initial convergence and after the dynamics change.Source: Figure 3 · p. 7, §5 · p. 7
  • After convergence, event-triggered selection and uniform downsampling attained comparable estimation error, but event-triggered selection adapted substantially faster after the dynamics change.The inter-event time fell to the candidate sampling period, Ts, immediately after the change, then increased as the estimator adapted.Source: Figure 4 · p. 7, §5 · p. 7, Figure 5 · p. 8

6. CONCLUSION

The paper presents an event-triggered data-selection approach for online frequency-domain identification. Its uncertainty and model-mismatch criteria support informative measurement selection, with simulations showing reduced communication while maintaining accuracy and adapting to abrupt changes.

6. CONCLUSION

  • The event trigger combines uncertainty about FRF information gain with model mismatch to select locally acquired measurements for remote identification.The uncertainty component ranks candidates by incremental D-optimal information gain and guarantees a uniformly positive definite retained information matrix despite selection and exponential forgetting.Source: §6 · p. 8
  • Simulation results showed that the method can substantially reduce communication while maintaining estimation accuracy and adapting quickly to abrupt dynamics changes.Source: §6 · p. 8
  • The proposed approach is designed for online frequency-domain identification in distributed sensing architectures.Source: §6 · p. 8
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