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Cited by 3Structural Health Monitoring TechniquesBladed Disk Vibration DynamicsControl Systems and Identification

On the Effect of Intra- and Inter-Node Sampling Variability on Operational Modal Parameters in a Digital MEMS-Based Accelerometer Sensor Network for SHM: A Preliminary Numerical Investigation

Open access
Brambilla, Matteo, Chiariotti, Paolo, Cigada, Alfredo·2025·Sensors
DOI 10.3390/s25165044PMC PMC12390391
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Abstract

Reliable estimation of operational modal parameters is essential in structural health monitoring (SHM), particularly when these parameters serve as damage-sensitive features. Modern distributed monitoring systems, often employing digital MEMS accelerometers, must account for timing uncertainties across sensor networks. Clock irregularities can lead to non-deterministic sampling, introducing uncertainty in the identification of modal parameters. In this paper, the effects of timing variability throughout the network are propagated to the final modal quantities through a Monte-Carlo-based framework. The modal parameters are identified using the covariance-driven stochastic subspace identification (SSI-COV) algorithm. A finite element model of a steel cantilever beam serves as a test case, with timing irregularities modeled probabilistically to simulate variations in sensing node clock stability. The results demonstrate that clock variability at both intra-node and inter-node levels significantly influences mode shape estimation and introduces systematic biases in the identified natural frequencies and damping ratios. The confidence intervals are calculated, showing increased uncertainty with greater timing irregularity. Furthermore, the study examines how clock variability impacts damage detection, offering metrological insights into the limitations of distributed vibration-based SHM systems. Overall, the findings offer guidance for designing and deploying monitoring systems with independently timed nodes, aiming to enhance their reliability and robustness.

AI snapshot

Written from the paper’s full text.

TL;DR

This preliminary numerical study propagates intra- and inter-node sampling variability in a digital MEMS accelerometer network to operational modal parameters using a Monte Carlo framework and SSI-COV. It finds that mode shapes degrade sharply even at small timing variability, natural frequencies are biased low, and damping ratios are biased high, with consequences for damage detection.

Key findings

  • Mode shapes are highly sensitive to non-deterministic sampling: MAC values are around 0.8 at αx = 0.01%, decline sharply at low αx, and at αx = 3% the mode shapes become “completely unrecognizable and unusable.”
  • Natural frequencies are systematically underestimated as αx increases, while damping ratios are overestimated; the normalized mean shows natural frequencies are more stable than damping ratios.
  • Identification success rate ηj varies by resonance: for j = 2 and j = 3 it drops to a minimum between αx = 1.4% and 2.0%, while for j = 5 it drops to zero, making j = 5 the most sensitive resonance.
  • In damage scenarios, sampling variability can mask stiffness reduction: for d1 at αx = 3.0%, damaged and undamaged natural-frequency confidence intervals overlap up to damage severity 3, and damping intervals overlap even at severe stiffness reduction; for d2 at αx = 1%, sampling variability outweighs the stiffness-reduction effect for both frequency and damping.

Methods

  • A 5 m steel cantilever beam was modeled in Abaqus as a 2D linear FE structure: rectangular cross-section 0.012 m × 0.006 m, mass density 7800 kg/m³, E = 210 GPa, Poisson’s coefficient 0.3, 49 B12 elements, 50 nodes, and six virtual accelerometers; damping was proportional with γ = 0.05 s⁻¹ and β = 3.5 × 10⁻⁵ s.
  • Operational modal parameters were identified with covariance-driven stochastic subspace identification (SSI-COV), using τ = 2 s, εcluster = 4 Hz, fixed Kc = 100 samples per chunk, and T = 240 s; resonance j = 1 was excluded, so analysis covered j = 2 to j = 5.
  • Non-deterministic sampling was modeled probabilistically as Gaussian ODR variability with coefficient of variation αx; Monte Carlo simulations used M = 10³ iterations after convergence was observed at M = 10³, with 51 datasets for αx from 0.01% to 10% in the undamaged case and 69 additional datasets for damage cases d1, d2, and d3 at αx = 1.0%, 2.0%, and 3.0%.

Limitations

  • The paper states that the results refer to a specific test case and are not intended to be universally generalized; it also states that the Monte Carlo method has a key limitation in computational cost, requiring significant resources for statistically meaningful datasets.
  • The paper states that the framework fixes, simplifies, or neglects modal complexity, environmental and operational variables, sensor placement, and signal-to-noise ratio; EOVs are assumed constant and low SNR is not treated as a source of variability.
  • Evident from the text: this is a numerical, preliminary investigation without experimental validation on a real MEMS sensor network, uses only one identification algorithm (SSI-COV), assumes fixed chunk size with no data-loss events, and tests only two nominal ODRs (500 and 833 samples/s).

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.3390/s25165044

Cites

37 of 37 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

1 of 37 cited sources checked · 1 supported · 0 flagged

  • Findingown data

    Confidence intervals show increased uncertainty with greater timing irregularity.

    “The confidence intervals are calculated, showing increased uncertainty with greater timing irregularity.”
    Quote in the paperSubstantial claim
  • Findingown data

    Clock variability at both intra-node and inter-node levels introduces systematic biases in the identified natural frequencies and damping ratios.

    “The results demonstrate that clock variability at both intra-node and inter-node levels significantly influences mode shape estimation and introduces systematic biases in the identified natural frequencies and damping ratios.”
    Quote in the paperSubstantial claim
  • Findingown data

    Clock variability at both intra-node and inter-node levels significantly influences mode shape estimation.

    “The results demonstrate that clock variability at both intra-node and inter-node levels significantly influences mode shape estimation and introduces systematic biases in the identified natural frequencies and damping ratios.”
    Quote in the paperSubstantial claim
  • Findingown data

    At low-frequency resonances j=2 and j=3, ηj drop to a minimum between αx=1.4% and αx=2.0%.

    “focusing on low-frequency resonances, at both j=2 (Figure 7a, Figure 8a and Figure 9a) and j=3 (Figure 7b, Figure 8b and Figure 9b), ηj drop to a minimum between αx=1.4% and αx=2.0%.”
    Quote in the paperNot a substantial claim
  • Findingown data

    As αx increases, the sample mean of natural frequency μ^ωj/2π(αx) decreases.

    “At the same time, the sample mean μ^ωj/2π(αx) shows the opposite trend.”
    • Also stated in: § 5.2. Confidence Intervals in Presence of a Structural Alteration Under Non-Deterministic Sampling · plain
      “the confidence interval Δωj/2π decreases in terms of mean value μ^ωj/2π and becomes wider in terms of standard deviation σ^ωj/2π”
    Quote in the paperSubstantial claim
  • May combine two claims. 16
  • Classified as probably not a substantial claim. 20

  • May combine two claims.

    Premisecitation

    D'Emilia et al. found significant variability in actual sampling rates among 25 MEMS-based sensors from the same production batch and noticeable deviations from the nominal rate specified by the manufacturer.

    “The results revealed significant variability in the actual sampling rates among the sensors, as well as noticeable deviations from the nominal rate specified by the manufacturer.”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites [6] D’Emilia, G., Gaspari, A., Natale, E., Prato, A., Mazzoleni, F., and Schiavi, A. (2021, January 7–9). Managing the sampling rate variability of digital MEMS accelerometers in dynamic calibration. Proceedings of the 2021 IEEE International Workshop on Metrology for Industry 4.0 & IoT (MetroInd4.0 & IoT), Rome, Italy. source

  • May combine two claims.

    Findingreasoning

    At resonance j=5, confidence intervals lose statistical significance when ηj drops to zero, and are completely unavailable once η5 has dropped to zero.

    “At resonance j=5, consistently with the previous analysis on ηj, confidence intervals lose statistical significance when ηj drops to zero, and they are completely unavailable once after η5 has dropped to zero.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    For increasing αx, different ηj trends are observed across resonances, meaning that the number of times the j-th resonance is identified by SSI-COV is not uniform.

    “For increasing αx, different ηj (Equation (19)) trends are observed across resonances, meaning that the number of times the j-th resonance is identified by SSI-COV is not uniform”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The trend of increasing standard deviation and decreasing mean of natural frequency with αx is confirmed at both ODRnl and in all resonances j=2 to j=5.

    “This trend is confirmed at both ODRnl and in all resonances: j=2 (Figure 7a, Figure 8a and Figure 9a), j=3 (Figure 7b, Figure 8b and Figure 9b), j=4 (Figure 7c, Figure 8c and Figure 9c), and j=5 (Figure 7d, Figure 8d and Figure 9d).”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    At αx=0.2%, the physical phase relationship at resonance j=3 is lost for ODRnl=500 samples/s but retained for ODRnl=833 samples/s.

    “For instance, for αx=0.2%, the physical phase relationship at resonance j=3 is lost in case of ODRnl=500 samples/s (Figure 14g), but is retained in case of ODRnl=833 samples/s (Figure 15g)”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The specific values of ηj differ for ODRnl=500 samples/s and ODRnl=833 samples/s, but the same trend is recognizable.

    “The specific values assumed by ηj are different for ODRnl=500 samples/s and ODRnl=833 samples/s; nevertheless, the same trend is recognizable”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    For all resonances, both the sampling mean and the sampling standard deviation of damping ratio increase for increasing αx.

    “All resonances show that both the sampling mean μ^ζj and the sampling standard deviation μ^ζj increase for increasing αx—see, as example, resonance j=2 in Figure 8a, Figure 9a and Figure 10a.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    At αx=0.4%, the physical phase relationship at resonance j=2 is preserved for ODRnl=500 samples/s but becomes unreliable for ODRnl=833 samples/s.

    “conversely, the physical phase relationship at resonance j=2 for αx=0.4% is preserved at ODRnl=500 samples/s (Figure 14c) but becomes unreliable at ODRnl=833 samples/s (Figure 15c).”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S4 (based).

    Interpretationnone given

    When a common time reference cannot be shared among sensors belonging to the same network, the physical phase relationship among the sensorized DOFs is lost.

    “When a common time reference cannot be shared among sensors belonging to the same network, the physical phase relationship among the sensorized DOFs is lost.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Previous works using different identification strategies arrived at the same conclusions: synchronization errors significantly affect mode shape estimation but have limited impact on frequency and damping estimates.

    “Notably, previous works based on different identification strategies, such as [12] (using ARMAV models) and [13] (using SSI with corrective actions), arrived at the same conclusions: synchronization errors significantly affect mode shape estimation but have limited impact on frequency and damping estimates.”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [12] Lei, 2005, Algorithms for time synchronization of wireless structural monitoring sensors, Earthq. Eng. Struct. Dyn. source
    • cites [13] Bernal, 2018, Analytical minimization of synchronicity errors in stochastic identification, Mech. Syst. Signal Process. source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Recent works have emphasized that uncertainty quantification is central to ensuring safety and reliability when data volatility is high.

    “Moreover, recent works [22,23] have emphasized that uncertainty quantification is not optional in SHM; it is central to ensuring safety and reliability when data volatility is high.”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [22] Wang, 2023, Towards high-accuracy data modelling, uncertainty quantification and correlation analysis for SHM measurements during typhoon events using an improved most likely heteroscedastic Gaussian process, Smart Struct. Syst. source
    • cites [23] Wang, 2024, Data interpretation and forecasting of SHM heteroscedastic measurements under typhoon conditions enabled by an enhanced Hierarchical sparse Bayesian Learning model with high robustness, Measurement source

  • May combine two claims.

    Interpretationreasoning

    Loss of the physical phase relationship can cause operational modal parameters to deviate from baseline even under undamaged conditions, leading to false alarms or masking structural alterations.

    “Consequently, operational modal parameters can deviate from baseline even under undamaged conditions, leading to false alarms or masking structural alterations, resulting in missed detections.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Uncertainty, measured through modelling errors and confidence intervals, increases significantly under extreme wind and traffic conditions.

    “Uncertainty, measured through modelling errors and confidence intervals, increases significantly under extreme wind and traffic conditions.”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [22] Wang, 2023, Towards high-accuracy data modelling, uncertainty quantification and correlation analysis for SHM measurements during typhoon events using an improved most likely heteroscedastic Gaussian process, Smart Struct. Syst. source
    • cites [23] Wang, 2024, Data interpretation and forecasting of SHM heteroscedastic measurements under typhoon conditions enabled by an enhanced Hierarchical sparse Bayesian Learning model with high robustness, Measurement source

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation

    Prior findings indicate that natural frequencies remain reasonably unaffected, while damping values tend to be significantly overestimated.

    “Their findings indicate that natural frequencies remain reasonably unaffected, while damping values tend to be significantly overestimated.”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [12] Lei, 2005, Algorithms for time synchronization of wireless structural monitoring sensors, Earthq. Eng. Struct. Dyn. source
    • cites [18] Zhu, 2017, Spectral characteristics of asynchronous data in operational modal analysis, Struct. Control Health Monit. source

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation

    Frequency Domain Decomposition is known for robustness in low SNR conditions, while SSI-COV can outperform FDD and data-driven SSI in terms of speed if properly tuned.

    “Among them, Frequency Domain Decomposition (FDD) is known for robustness in low SNR conditions, while covariance-driven stochastic subspace identification (SSI-COV) can outperform FDD and data-driven SSI in terms of speed if properly tuned [32].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [32] Jahangiri, G., Nabavian, S.R., Davoodi, M.R., Neya, B.N., and Mostafavian, S. (2020). Effect of noise on output-only modal identification of beams. arXiv. source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    The confidence interval metric for modal parameters estimated under stochastic conditions has been well established for aligned and properly sampled data.

    “The confidence interval metric for modal parameters estimated under stochastic conditions has been well established for aligned and properly sampled data in [19,20,21].”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites [19] Pintelon, 2007, Uncertainty calculation in (operational) modal analysis, Mech. Syst. Signal Process. source
    • cites [20] Reynders, 2008, Uncertainty bounds on modal parameters obtained from stochastic subspace identification, Mech. Syst. Signal Process. source
    • cites [21] Mevel, 2013, Efficient multi-order uncertainty computation for stochastic subspace identification, Mech. Syst. Signal Process. source

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Interpretationnone given

    The results presented refer to a specific test case and are not intended to be universally generalized.

    “The results presented refer to a specific test case and are not intended to be universally generalized.”
    Quote in the paperNot a substantial claim

  • Classified as probably not a substantial claim.

    Interpretationnone given

    At the intra-node level, multiple clock sources or instability of non-quartz-based clock sources results in data records sampled at non-constant time intervals.

    “At the intra-node level, i.e., within a single digital node, the presence of multiple clock sources (e.g., in the ADC and MCU) or the instability of non-quartz-based clock sources results in data records sampled at non-constant time intervals.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Lei et al. found that non-simultaneous sampling primarily affects mode shape identification rather than natural frequencies and damping ratios.

    “Lei et al. [12] examined time delays caused by different triggering times, radio transmission interference, and internal sensor clock errors, highlighting that non-simultaneous sampling primarily affects mode shape identification rather than natural frequencies and damping ratios.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [12] Lei, 2005, Algorithms for time synchronization of wireless structural monitoring sensors, Earthq. Eng. Struct. Dyn. source

  • May combine two claims.

    Premisecitation

    Mode shapes are the modal quantities most affected by lack of synchronization and require corrections for reliable use in SHM applications.

    “Mode shapes are the modal quantities most affected by lack of synchronization and require corrections for reliable use in SHM applications.”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [12] Lei, 2005, Algorithms for time synchronization of wireless structural monitoring sensors, Earthq. Eng. Struct. Dyn. source
    • cites [18] Zhu, 2017, Spectral characteristics of asynchronous data in operational modal analysis, Struct. Control Health Monit. source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Environmental factors, particularly temperature, are known to affect the reliability of OMA-based damage detection because they influence the modal parameters of undamaged structures.

    “Environmental factors—particularly temperature—are known to affect the reliability of OMA-based damage detection, as they influence the modal parameters of undamaged structures [24].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [24] Sohn, 2007, Effects of environmental and operational variability on structural health monitoring, PHilosophical Trans. R. Soc. A Math. Phys. Eng. Sci. source

  • Classified as probably not a substantial claim.

    Study design and conductown data

    The number of Monte Carlo simulations in the main analysis was fixed at M=10^3.

    “Based on this observation, the number of Monte Carlo simulations in the main analysis was fixed at M=103.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Premisecitation

    Previous studies [12,18] pointed out that even a tiny time misalignment is sufficient to lose the physical phase relationship between sensorized DOFs.

    “As already mentioned, previous studies [12,18] pointed out that even a tiny time misalignment is sufficient to lose the physical phase relationship between sensorized DOFs.”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [12] Lei, 2005, Algorithms for time synchronization of wireless structural monitoring sensors, Earthq. Eng. Struct. Dyn. source
    • cites [18] Zhu, 2017, Spectral characteristics of asynchronous data in operational modal analysis, Struct. Control Health Monit. source

  • Classified as probably not a substantial claim.

    Study design and conductreasoning

    The numerical model was used as a reference model with EOVs and algorithmic input parameters fixed to isolate the effect of non-deterministic sampling variability on operational modal parameters.

    “Second, it serves as a reference model in which EOVs and algorithmic input parameters (Table 2) remain fixed so that the effect of non-deterministic sampling variability on the operational modal parameters can be isolated and assessed.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The Monte Carlo framework assumes invariance in EOVs, firmware configuration, sensor placement, and the identification algorithm.

  • Probably not a substantial claim: may not pass S4 (based).

    Premisenone given

    Inter-node asynchronism arises because each sensor node generates its asynchronous time base independently, in the absence of a shared master clock.

    “Inter-node asynchronism arises because each sensor node generates its asynchronous time base independently, in the absence of a shared master clock.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisecitation

    SSI-COV integrates seamlessly into a Monte Carlo framework; it is computationally efficient, robust, and well suited for automation, making it ideal for reproducible modal parameter extraction.

    “In addition, SSI-COV integrates seamlessly into a Monte Carlo framework. It is computationally efficient, robust, and well suited for automation, making it ideal for reproducible modal parameter extraction [20,33,34,35].”
    Quote in the paperSubstantial claim0 of 3 sources checked
    • cites [20] Reynders, 2008, Uncertainty bounds on modal parameters obtained from stochastic subspace identification, Mech. Syst. Signal Process. source
    • cites [33] Cunha, 2009, Online automatic identification of the modal parameters of a long span arch bridge, Mech. Syst. Signal Process. source
    • cites [34] Cheynet, E. (2020). Operational modal analysis with automated SSI-COV algorithm. Zenodo. source

  • Classified as probably not a substantial claim.

    Premisecitation

    Previous works [12,13] suggested that natural frequencies and damping ratios are generally more robust to sampling variability.

    “Since previous works [12,13] suggested that natural frequencies and damping ratios are generally more robust to sampling variability, convergence analysis on those parameters is reported in Figure 6.”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [12] Lei, 2005, Algorithms for time synchronization of wireless structural monitoring sensors, Earthq. Eng. Struct. Dyn. source
    • cites [13] Bernal, 2018, Analytical minimization of synchronicity errors in stochastic identification, Mech. Syst. Signal Process. source

  • Classified as probably not a substantial claim.

    Premisereasoning

    When the structure undergoes a stiffness reduction, natural frequencies are expected to decrease with increasing damage severity.

    “At the same time, when the structure undergoes a stiffness reduction (see Equation (3)), the natural frequencies are expected to decrease with increasing damage severity.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationown data

    Early-stage damage is not clearly detectable from resonance j=2 under αx=3.0%, and damage becomes distinguishable only at higher damage severity.

    “This suggests that early-stage damage is not clearly detectable from resonance j=2 under such a non-deterministic sampling variability level, and the damage becomes distinguishable only at higher damage severity.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Previous findings in the literature [12,13] attribute such degradation to the loss of physical phase consistency between sensor nodes.

    “This trend aligns with previous findings in the literature [12,13], which attribute such degradation to the loss of physical phase consistency between sensor nodes.”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [12] Lei, 2005, Algorithms for time synchronization of wireless structural monitoring sensors, Earthq. Eng. Struct. Dyn. source
    • cites [13] Bernal, 2018, Analytical minimization of synchronicity errors in stochastic identification, Mech. Syst. Signal Process. source

  • Classified as probably not a substantial claim.

    Study design and conductnone given

    Intra- and inter-node sampling variability are modeled via a statistical distribution calibrated with vendor-provided information, from nominal ODR to actual sampling rate variability.

    “Intra- and inter-node sampling variability are modeled via a statistical distribution calibrated with vendor-provided information, from nominal ODR (ODRnl) to actual sampling rate variability (αx).”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The Monte Carlo framework assumes invariance in EOVs, firmware configuration, sensor placement, and the identification algorithm.

  • May combine two claims.

    Interpretationreasoning

    Confidence intervals derived under healthy conditions may not extend to altered states, limiting their effectiveness for SHM.

    “Confidence intervals derived under healthy conditions may not extend to altered states, limiting their effectiveness for SHM.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S4 (based).

    Study design and conductnone given

    Monte Carlo simulations require significant resources to generate statistically meaningful datasets.

    “Monte Carlo simulations require significant resources to generate statistically meaningful datasets.”
    Quote in the paperNot a substantial claim
33 of 33

  • The paper relies on this without support.

    OMA requires the target system to be linear, the natural excitation to be stochastic, and the output acceleration data records to be collected synchronously.

    “OMA requires the target system to be linear, the natural excitation g(t) stochastic, and the output acceleration data records to be collected synchronously.”

  • The authors state this as an assumption.

    Environmental and operational variables are constant, and the same stochastic excitation is applied across all cases.

    “In this study, EOVs are assumed constant, and the same stochastic excitation is applied across all cases.”

  • The authors state this as an assumption.

    Systematic clock drift errors are reasonably compensated by state-of-the-art resynchronization strategies.

    “Assuming that systematic clock drift errors are reasonably compensated by state-of-the-art resynchronization strategies—such as those based on network time protocol (NTP) [38] or global positioning system (GPS)—the non-deterministic component of ODR fluctuations remains.”

  • The authors state this as an assumption.

    The number of samples per chunk Kc is constant during acquisition.

    “The assumption of a constant Kc during acquisition is justified by the fact that the firmware architecture is based on interrupt requests, meaning that data chunk transmission is triggered once the FIFO buffer is filled.”

  • The paper relies on this without support.

    State-of-the-art modal identification algorithms assume data to be collected with constant sampling intervals.

    “State-of-the-art algorithms assume data to be collected with constant sampling intervals.”

  • The authors state this as an assumption.

    The Monte Carlo framework assumes invariance in EOVs, firmware configuration, sensor placement, and the identification algorithm.

    “It assumes invariance in EOVs, firmware configuration, sensor placement, and the identification algorithm.”

  • The paper relies on this without support.

    In realistic scenarios, non-deterministic sampling variability can only be approximately known.

    “The considered range is expressed relative to the nominal output data rate (ODRnl) to reflect a realistic scenario in which non-deterministic sampling variability can only be approximately known.”

  • The paper relies on this without support.

    The nominal output data rates of 500 samples/s and 833 samples/s can be easily found among commercially available digital MEMS modules.

    “These values can be easily found among commercially available digital MEMS modules.”
8 of 8

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

Each contradiction between two passages listed here was confirmed by an independent check.

  • Damping-ratio figure cited as natural-frequency evidence

    Minor

    The text cites Figure 8a as evidence for a trend in natural frequency, but elsewhere identifies Figure 8 as showing damping ratios.

  • Damping-ratio standard deviation is labeled as a mean

    Minor

    The paper defines σ^ as the sample standard deviation, but this sentence labels the damping-ratio standard deviation μ^ζj, the same symbol it uses for the mean.

2 of 2

Cites

Flagged first, then by citations

Research works printed but not linked: 3

  1. Wang, 2023, Towards high-accuracy data modelling, uncertainty quantification and correlation analysis for SHM measurements during typhoon events using an improved most likely heteroscedastic Gaussian process, Smart Struct. Syst., 32, 267
  2. Allemang, R., and Brown, D. (1982, January 8–10). A correlation coefficient for modal vector analysis. Proceedings of the 1st International Modal Analysis Conference, Orlando, FL, USA.
  3. Chang, F.K., Guemes, A., and Farhangdoust, S. (2023, January 12–14). Exploring Crowdsensing Potentials for Structural Health Monitoring Applications: Challenges and Opportunities. Proceedings of the 14th International Workshop on Structural Health Monitoring (IWSHM), Stanford, CA, USA.

Cited by

Sorted by citations

Related

Authors
Brambilla, M., Chiariotti, P., & Cigada, A.
Affiliations
Politecnico di Milano (IT)
Corresponding author
Chiariotti, Paolo
ORCID
Venue
Sensors
Publisher
MDPI AG
Published
2025-08-14
Volume
25
Issue
16
Pages
5044
ISSN
1424-8220 (ISSN-L)
DOI
10.3390/s25165044
PMC
PMC12390391
OpenAlex
W4413971052
Semantic Scholar
59c3995d8142f9e6d20f586acdc315b7d8edb9fa
Cited by
3
References
3
Citations by year
2026: 3
FWCI
1.18
Type
journal article
Language
en
Open access
Licence
Locations
  • Sensors (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • Virtual Community of Pathological Anatomy (University of Castilla La Mancha) (submittedVersion, cc-by)
  • Europe PMC (PubMed Central) (submittedVersion, cc-by)
  • PubMed Central (submittedVersion, cc-by)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
Topics
  • Physical Sciences › Engineering › Civil and Structural Engineering › Structural Health Monitoring Techniques
  • Physical Sciences › Engineering › Civil and Structural Engineering › Bladed Disk Vibration Dynamics
  • Physical Sciences › Engineering › Control and Systems Engineering › Control Systems and Identification
Keywords
operational modal analysis, structural health monitoring, MEMS accelerometer, sensor networks, sampling uncertainty, stochastic subspace identification, mode shape identification, natural frequency estimation, damping ratio estimation, damage detection, cantilever beam, metrology

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