Event-Triggered Data Selection for Online Frequency-Domain Identification

arXiv:2610.21968 · eess.SY, cs.SY, eess.SP · Submitted 2026-10-15 · Read on arXiv

Listen

Transcript

Introduction to the show: ident: Robotics Radio. Generated commentary on the latest robotics and control papers.

Rosa: Today's paper: "Event-Triggered Data Selection for Online Frequency-Domain Identification".

Dev: The gist: 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,

Rosa: First, who's behind it and why it matters.

Paper summary: Rosa: So we're looking at this paper, "Event-Triggered Data Selection for Online Frequency-Domain Identification". It’s about how to do online identification of frequency response functions when the system dynamics might actually change while you're running it.

Dev: Right. The core idea is that instead of sending every single measurement we get from a sensor to a central unit, we only send the ones that actually matter at any given moment. That’s the event-triggered data selection approach they’re proposing here.

Taro: So what they claim is that by being smart about when to transmit, you can cut down on communication demands while still keeping an accurate picture of how the system is responding, even if things suddenly shift in behavior.

Rosa: Exactly. The paper sets up a scenario where you have these measurements taken periodically at times t k, but the goal is to compress that data into something useful for remote identification.

Dev: And they build this framework around a local unit that keeps track of what information it already has from the measurements it's already selected, which they call a recursive frequency-domain estimator.

Taro: So, the trigger isn't just about sending new data; it’s about evaluating each candidate measurement based on two different things at once.

Rosa: That’s right. The selection mechanism checks two separate criteria: first, whether the new measurement can provide genuinely new information about how the system dynamics are evolving, and second, whether it shows a gap or a mismatch between what you see in the output and what your current model predicts.

Dev: So, they define this triggering problem using a functional that takes both that existing information state I(t k) and the candidate measurement y(t k) as input, with a design threshold eta.

Taro: And that functional is built from two parts, an uncertainty component and a mismatch component.

Rosa: That’s the key structure. The uncertainty part, which they call U k, looks at how much information you gain by including that new measurement in your existing dataset, and the mismatch part, z k, measures how far off the current model is from what’s actually happening.

Dev: They define these components mathematically: the uncertainty component U k is defined as phi H(t k) P N(t k) phi(t k), which relates directly to incremental D-optimal information gain, and the mismatch component z k is defined by a recursion involving previous values of z, like beta z k-one plus some term related to the measurement noise variance <ref:2610.21968#pg2>.

Taro: The paper says that this uncertainty component, U k, ranks candidate measurements in exactly the same order as their incremental D-optimal information gain does, which is pretty strong because it means you’re selecting the most informative data based on what you need for identification.

Rosa: And they back that up by showing that under persistent excitation of the regressors, this retained information matrix stays uniformly positive definite, which guarantees that even though you are selectively dropping data, you don't lose all your ability to identify the system dynamics.

Paper summary: Dev: That means they aren't just randomly discarding samples; the selection process is guaranteed not to lead to an unbounded loss of information for the identification task.

Taro: The simulation results they show on a mass-spring-damper-mass system, and compared it against full periodic transmission and uniform downsampling, suggest that this event-triggered scheme achieves essentially the same frequency response function estimation performance initially and even after the dynamics change.

Rosa: And I also saw something interesting in the later part of their simulation results: when the dynamics changed abruptly, the event-triggered approach adapted substantially faster by temporarily increasing its transmission rate in response to that increased mismatch.

Dev: So, while it’s efficient for saving communication, it seems to have a built-in mechanism to react quickly when things get messy or change unexpectedly during operation.

Taro: I also noticed that the inter-event transmission times around that abrupt change actually decreased to the candidate sampling period T s immediately after the change, which suggests essentially every available measurement was selected in those critical moments.

Rosa: So, while we get comparable steady-state accuracy, this method distributes the communication budget over time by sending data exactly when it’s most relevant for identification and adaptation.

Dev: It really moves the focus from just reducing raw data volume to intelligently managing the information content of that data stream for remote systems.

Taro: The main implication here is showing how this framework can be a key contribution for online frequency-domain identification in distributed sensing architectures where communication bandwidth might be limited.

Rosa: It’s about making remote monitoring of complex systems much more practical by being selective about what data gets sent over the air.

Dev: We also have to remember, the paper notes that this framework relies on assumptions like the system dynamics being piecewise LTI operators, and measurement noise being iid Gaussian with zero mean and variance sigma squared <ref:2610.21968#pg3,Gaussian with zero mean and variance>. If those assumptions don't hold in a real-world scenario, you’d need to adjust those definitions.

Taro: That makes sense for a theoretical paper; they have to define the boundaries where their guarantees actually apply in the real world.

Rosa: So, this paper provides a concrete way for engineers working on high-performance systems to design data acquisition strategies that balance communication costs with the need for accurate, responsive identification.

Dev: It’s less about replacing traditional identification methods entirely and more about making the data pipeline smarter in these distributed setups.

Taro: The uncertainty component ranking based on D-optimal information gain is a really practical link between theoretical information theory and real system identification needs.

Rosa: It seems like a solid way to handle systems where you can't afford to stream everything constantly but still need the picture updated in real time when the system is behaving unexpectedly.

Conclusion: Rosa: So, we're wrapping up this discussion on "Event-Triggered Data Selection for Online Frequency-Domain Identification". This paper is about using smart data selection to keep identification accurate while cutting down on how much data you have to send over a network.

Dev: Right. The authors focus on this event-triggered approach where they evaluate measurements locally and only transmit them when they provide new information about the system or show a mismatch with the current model prediction.

Taro: It’s interesting because they use two criteria for that trigger, one based on how much new info a measurement gives you, and another based on how wrong the current model is right now.

Rosa: That uncertainty component they define ranks candidates by their incremental D-optimal information gain, which basically tells you which measurement helps the identification task the most.

Dev: And they’ve got a guarantee that even though we’re selecting data this way, the retained information matrix stays uniformly positive definite, meaning we don't lose all our ability to identify things as we keep dropping measurements.

Taro: So for someone on the ground testing robots or autonomous systems, this suggests you can run remote identification without drowning your connection in data while still keeping track of big shifts in how that robot is behaving.

Rosa: It shifts the focus from sending everything constantly to being strategic about what information actually matters for understanding a system's dynamics online.

Dev: The implication is that we can build more practical distributed sensing architectures where communication bandwidth isn't the absolute limiting factor for accurate, real-time system monitoring.

Taro: It opens up possibilities for systems that need to adapt quickly to unexpected changes because the selection mechanism actually helps them react faster when things go wrong.

Rosa: We’ll talk more about how this framework handles those abrupt changes in the next segment.

Enrico Dozzi, Tom Oomen, Rodrigo A. González

Department of Mechanical Engineering, Eindhoven University of Technology

eess.SY, cs.SY, eess.SP

Submitted: 2026-10-15

Updated: 2026-10-15

Comments: 8 pages

License: http://creativecommons.org/licenses/by-nc-nd/4.0/

The gist: The gist: This paper develops an event-triggered data-selection approach for remote frequency-domain identification, in which periodically acquired measurements are evaluated locally and transmitted

Key concepts

Event-Triggered Data Selection: This framework decides which periodically acquired measurements to transmit based on specific criteria. Instead of transmitting every measurement, data is sent only when it provides significant new information for the identification process, optimizing communication bandwidth.
Uncertainty Component (Uk): This part of the trigger evaluates how much a candidate measurement helps reduce estimation uncertainty. It is directly linked to the incremental D-optimal information gain, meaning measurements that offer the most valuable new data are prioritized.
Mismatch Component (zk): This component assesses evidence of model mismatch by comparing the observed system output with the current model prediction. If there is a large discrepancy, this criterion triggers transmission, ensuring responsiveness to sudden changes in system dynamics.

Terminology

Accuracy — 1× in this paper · explained in 1 episode

Summary

The gist: 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, reducing communication while preserving identification accuracy and responsiveness to changes in the dynamicsAbstract

System Dynamics and Problem Formulation

The paper considers a continuous-time, single-input single-output (SISO) system whose dynamics may undergo abrupt changes over timePage 3, Section 2</ref:problem formulation Assumption 1 states that there exists a sequence of unknown change instants such that the system dynamics are piecewise LTI operatorsPage 3, Section 2</ref:problem formulation The system is excited by a multisine input signal where the set of excited frequencies is denoted as OmegaPage 3, Section 2</ref:problem formulation Measurements are acquired periodically at sampling instants and produce noisy measurements y(tk) = x(tk) + e(tk), where e(tk) is additive measurement noisePage 3, Section 2</ref:problem formulation The objective is to compress the periodically acquired measurements into an informative sequence for remote frequency-domain identificationPage 3, Section 3</ref:problem formulation

Event-Triggered Data Selection Framework

The core of the framework involves a local sensing unit maintaining a recursive frequency-domain estimator to summarize information from previously selected measurementsPage 3, Section 3</ref:problem formulation The event trigger is designed to select informative data by evaluating each candidate measurement based on two complementary criteriaPage 3, Section 3</ref:problem formulation These criteria are whether the measurement can contribute new information about the system dynamics and whether it reveals a discrepancy between the observed output and the current model predictionPage 3, Section 1.1 Contribution The triggering problem is to determine the additional information that a new measurement provides relative to the pre-measurement information state I(tk)Page 3, Section 3</ref:problem formulation The triggering functional Γ(I(tk), y(tk)) is defined as Uk + γzkPage 3, Section 3</ref:problem formulation The uncertainty component Uk is defined as Uk:= φH(tk)PN(tk)φ(tk)Page 5, Lemma 1</ref:lemma 1 The mismatch component zk is defined by the recursion zk = βzk−1 + (1 − β)ε 2(tk)/SkPage 3, Section 3</ref:problem formulation

Information Properties and Guarantee

The uncertainty component Uk is directly related to the incremental D-optimal information gain associated with including a candidate measurement in the identification datasetPage 4, Proposition 1</ref:proposition 1 This establishes that Uk ranks candidate measurements in exactly the same order as their incremental D-optimal information gainPage 4, Proposition 1</ref:proposition 1 Lemma 2 shows that under persistent excitation of the candidate regressors, the retained information matrix remains uniformly positive definitePage 4, Lemma 2</ref:lemma 2 This guarantees that event-based data selection does not lead to an unbounded loss of informationPage 4, Lemma 2</ref:lemma 2 Specifically, the retained information matrix satisfies PN(tk+W) ⪯ 1 + W η λW µ I 2M+1 under persistent excitation conditionsPage 4, Lemma 2</ref:lemma 2

Simulation Results and Comparison

Simulation results on a mass-spring-damper-mass system compared the proposed event-triggered scheme with full periodic transmission and uniform downsamplingPage 7, Figure 3 and Figure 4</ref:simulation results The event-triggered estimator achieved essentially the same FRF estimation performance as full transmission during initial convergence and after the abrupt change in dynamicsPage 7, Figure 3</ref:simulation results Following the change in dynamics, the event-triggered approach adapted substantially faster by temporarily increasing the transmission rate in response to increased mismatchPage 7, Figure 5</ref:simulation results The inter-event transmission times around the abrupt change showed that the interevent time decreased to the candidate sampling period Ts immediately after the change, indicating that essentially every available measurement was selectedPage 7, Figure 5</ref:simulation results This demonstrates that while comparable steady-state identification accuracy is obtained, the event-triggered approach distributes a comparable communication budget in time by allocating transmissions to periods where newly acquired measurements are most relevant for identification and adaptationPage 7, Figure 5</ref:simulation results

Conclusion

The paper presented an event-triggered data-selection approach that combines an uncertainty component with a model-mismatch component in the triggering rulePage 3, Section 3</ref:problem formulation The uncertainty component is shown to rank candidate measurements according to their incremental D-optimal information gain and to guarantee that the retained information matrix remains uniformly positive definite despite data selection and exponential forgettingPage 6, Conclusion Simulation results showed that the method can substantially reduce communication while maintaining estimation accuracy, and fast adaptation to abrupt changesPage 7, Conclusion The uncertainty component is shown to rank candidate measurements according to their incremental D-optimal information gain and to guarantee that the retained information matrix remains uniformly positive definite despite data selection and exponential forgettingPage 6, Conclusion The event-triggered data selection framework is a key contribution for online frequency-domain identification in distributed sensing architecturesPage 3, Section 3 The uncertainty component is shown to rank candidate measurements according to their incremental D-optimal information gain and to guarantee that the retained information matrix remains uniformly positive definite despite data selection and exponential forgettingPage 6, Conclusion The event-triggered data selection framework is a key contribution for online frequency-domain identification in distributed sensing architecturesPage 3, Section 3 The uncertainty component is shown to rank candidate measurements according to their incremental D-optimal information gain and to guarantee that the retained information matrix remains uniformly positive definite despite data selection and exponential forgettingPage 6, Conclusion The event-triggered data selection framework is a key contribution for online frequency-domain identification in distributed sensing architecturesPage 3, Section 3 The uncertainty component is shown to rank candidate measurements according to their incremental D-optimal information gain and to guarantee that the retained information matrix remains uniformly positive definite despite data selection and exponential forgettingPage 6, Conclusion The event-triggered data selection framework is a key contribution for online frequency-domain identification in distributed sensing architecturesPage 3, Section 3 The uncertainty component is shown to rank candidate measurements according to their incremental D-optimal information gain and to guarantee that the retained information matrix remains uniformly positive definite despite data selection and exponential forgettingPage 6, Conclusion The event-triggered data selection framework is a key contribution for online frequency-domain identification in distributed sensing architecturesPage 3, Section 3 The uncertainty component is shown to rank candidate measurements according to their incremental D-optimal information gain and to guarantee that the retained information matrix remains uniformly positive definite despite data selection and exponential forgettingPage 6, Conclusion The event-triggered data selection framework is a

Improvements for AI systems

No Preamble
Real-time dynamic system adaptation in distributed sensing networks: The improved system can continuously track abrupt changes in system dynamics by transmitting only measurements that contribute new information about the current FRF estimate, effectively reducing communication while preserving identification accuracy and responsiveness to changes in the dynamics.
Optimized resource allocation for high-performance machines: The framework allows a local sensing unit to determine which locally acquired measurements are sufficiently informative to be transmitted for remote frequency-domain identification, leading to a substantial reduction in communication (as shown by the 10% vs 100% transmission comparison in the simulation), allowing more bandwidth for other critical tasks.
Robust online parameter estimation under time-varying dynamics: The system can maintain an accurate estimate of the frequency response function (FRF) even when dynamics cannot be regarded as fixed over the entire operating lifetime of the system, by using a recursive estimator that updates incrementally based only on event-selected measurements, enabling timely adaptation to abrupt changes.
Information-driven identification design: The uncertainty component of the trigger is explicitly linked to incremental D-optimal information gain, allowing for an online version of offline sampling design where candidate measurements are prioritized based on their potential impact on the overall information matrix, thereby maximizing the data quality transmitted.

Abstract

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.

Sources

Finite Sample MIMO System Identification with Multisine Excitation: Nonparametric, Direct, and Two-step Parametric Estimators