Variable input observer for nonstationary high-rate dynamic systems

Hong, Jonathan; Laflamme, Simon; Cao, Liang; Dodson, Jacob; Joyce, Bryan

doi:10.1007/s00521-018-3927-x

Cited by 19 publications

(24 citation statements)

References 37 publications

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“…into Equation 10 and noting thatθ =θ −θ = −θ yieldṡ V = e T P T PAe + s T PÃX −θΓ −1 θ (Γ θ s T PQX) = e T P T PAe + s T PÃX − s T PÃX = e T P T PAe (13) showing the stability of the adaptation rule (Equation 12) under persistent excitation. 23,24 In the discrete time form, Equation 12 becomes:…”

Section: Model Adaptationmentioning

confidence: 96%

“…[9][10][11] A solution is to leverage iterative procedures and simplified models that are more applicable in real-time, yet at the cost of lower accuracy. 12,13 Here, the physical surrogate is a simplified representation of the monitored system that is constructed based on a given DSN configuration. The performance of the DSN is quantified using the probability of detection (POD) metric, 14,15 which allows assessing the capability of a DSN to quantify damage in an uncertain environment.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Model-assisted validation of a strain-based dense sensor network

Jin

Laflamme

Leifsson

et al. 2019

Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2019

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Recent advances in sensing are empowering the deployment of inexpensive dense sensor networks (DSNs) to conduct structural health monitoring (SHM) on large-scale structural and mechanical systems. There is a need to develop methodologies to facilitate the validation of these DSNs. Such methodologies could yield better designs of DSNs, enabling faster and more accurate monitoring of states for enhancing SHM. This paper investigates a model-assisted approach to validate a DSN of strain gauges under uncertainty. First, an approximate physical representation of the system, termed the physics-driven surrogate, is created based on the sensor network configuration. The representation consists of a state-space model, coupled with an adaptive mechanism based on sliding mode theory, to update the stiffness matrix to best match the measured responses, assuming knowledge of the mass matrix and damping parameters. Second, the physics-driven surrogate model is used to conduct a series of numerical simulations to map damages of interest to relevant features extracted from the synthetic signals that integrate uncertainties propagating through the physical representation. The capacity of the algorithm at detecting and localizing damages is quantified through probability of detection (POD) maps. It follows that such POD maps provide a direct quantification of the DSNs' capability at conducting its SHM task. The proposed approach is demonstrated using numerical simulations on a cantilevered plate elastically restrained at the root equipped with strain gauges, where the damage of interest is a change in the root's bending rigidity.

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Section: Model Adaptationmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Model-assisted validation of a strain-based dense sensor network

Jin

Laflamme

Leifsson

et al. 2019

Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…By incorporating physical knowledge, the algorithm can be designed to converge more efficiently, therefore preserving a leaner or less complex architecture, and thus favoring faster computing. Of interest, the authors have proposed in [ 32 ] a purely on-the-edge learning wavelet neural network that exhibited good convergence properties by varying its input space as a function of the extracted local dynamic characteristics of the time series. This information on the time series data structure was based on Takens’ embedding theorem [ 33 ] which constituted the physical information fed to the wavelet network.…”

Section: Introductionmentioning

confidence: 99%

“…The objective of this paper is to investigate the performance of a physics-informed deep learning method in predicting sensor measurements enabling HRSHM, inspired by the authors’ prior work in [ 32 ]. Instead of a time-varying input space, the algorithm uses an ensemble of RNNs, each using a different delay vector to represent distinct local data structures in the dynamics.…”

Section: Introductionmentioning

confidence: 99%

Multi-Time Resolution Ensemble LSTMs for Enhanced Feature Extraction in High-Rate Time Series

Barzegar

Laflamme

et al. 2021

Sensors

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Systems experiencing high-rate dynamic events, termed high-rate systems, typically undergo accelerations of amplitudes higher than 100 g-force in less than 10 ms. Examples include adaptive airbag deployment systems, hypersonic vehicles, and active blast mitigation systems. Given their critical functions, accurate and fast modeling tools are necessary for ensuring the target performance. However, the unique characteristics of these systems, which consist of (1) large uncertainties in the external loads, (2) high levels of non-stationarities and heavy disturbances, and (3) unmodeled dynamics generated from changes in system configurations, in combination with the fast-changing environments, limit the applicability of physical modeling tools. In this paper, a deep learning algorithm is used to model high-rate systems and predict their response measurements. It consists of an ensemble of short-sequence long short-term memory (LSTM) cells which are concurrently trained. To empower multi-step ahead predictions, a multi-rate sampler is designed to individually select the input space of each LSTM cell based on local dynamics extracted using the embedding theorem. The proposed algorithm is validated on experimental data obtained from a high-rate system. Results showed that the use of the multi-rate sampler yields better feature extraction from non-stationary time series compared with a more heuristic method, resulting in significant improvement in step ahead prediction accuracy and horizon. The lean and efficient architecture of the algorithm results in an average computing time of 25 μμs, which is below the maximum prediction horizon, therefore demonstrating the algorithm’s promise in real-time high-rate applications.

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“…Work directly addressing the problem of high-rate state estimation, or system identification is limited. In previous work, the authors have proposed an adaptive sequential neural network with a self-adapting input space enabling fast learning of nonstationary signals from high-rate systems [3]. Although the data-based technique showed great promise at high rate state estimation, it did not provide insight into the system's physical characteristics, as it is generally the case with data-based techniques.…”

Section: Introductionmentioning

confidence: 99%

A Comparison of Time-Frequency Methods for Real-Time Application to High-Rate Dynamic Systems

et al. 2020

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High-rate dynamic systems are defined as engineering systems experiencing dynamic events of typical amplitudes higher than 100 gn for a duration of less than 100 ms. The implementation of feedback decision mechanisms in high-rate systems could improve their operations and safety, and even be critical to their deployment. However, these systems are characterized by large uncertainties, high non-stationarities, and unmodeled dynamics, and it follows that the design of real-time state-estimators for such purpose is difficult. In this paper, we compare the promise of five time-frequency representation (TFR) methods at conducting real-time state estimation for high-rate systems, with the objective of providing a path to designing implementable algorithms. In particular, we examine the performance of the short-time Fourier transform (STFT), wavelet transformation (WT), Wigner–Ville distribution (WVD), synchrosqueezed transform (SST), and multi-synchrosqueezed transform (MSST) methods. This study is conducted using experimental data from the DROPBEAR (Dynamic Reproduction of Projectiles in Ballistic Environments for Advanced Research) testbed, consisting of a rapidly moving cart on a cantilever beam that acts as a moving boundary condition. The capability of each method at extracting the beam’s fundamental frequency is evaluated in terms of precision, spectral energy concentration, computation speed, and convergence speed. It is found that both the STFT and WT methods are promising methods due to their fast computation speed, with the WT showing particular promise due to its faster convergence, but at the cost of lower precision on the estimation depending on circumstances.

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Variable input observer for nonstationary high-rate dynamic systems

Cited by 19 publications

References 37 publications

Model-assisted validation of a strain-based dense sensor network

Model-assisted validation of a strain-based dense sensor network

Multi-Time Resolution Ensemble LSTMs for Enhanced Feature Extraction in High-Rate Time Series

A Comparison of Time-Frequency Methods for Real-Time Application to High-Rate Dynamic Systems

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