A Scaled Spherical Simplex Filter (S3F) with a decreased n + 2 sigma points set size and equivalent 2n + 1 Unscented Kalman Filter (UKF) accuracy

Παπακωνσταντίνου, Κωνσταντίνος; Amir, M.; Warn, Gordon P.

doi:10.1016/j.ymssp.2020.107433

Cited by 19 publications

(8 citation statements)

References 41 publications

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“…It was observed that the performance of damage detection presented in the case studies relies heavily on the accuracy of the fuzzy WNN-based system identification technique adopted. For real-world SHM applications, more robust and powerful system identification techniques such as conventional neural networks, 67 unscented Kalman filters, 68 and scaled spherical simplex filters 69 are available and would be utilized in compliance with the complexity of target structures. In addition, a scalar DSF may not be able to effectively discriminate between undamaged and damaged states of the target structure and a vectorial DSF of high dimension would be favorable.…”

Section: Discussionmentioning

confidence: 99%

A Bayesian hypothesis testing-based statistical decision philosophy for structural damage detection

Zhang

2022

Structural Health Monitoring

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In this article, a new statistical decision philosophy is developed to tackle structural damage detection problems which are defined in the context of novelty detection. In line with this philosophy, structural damage detection is achieved by deriving the posterior probability of damage presence from the Bayesian testing of two competing hypotheses, with the null and alternative hypotheses representing the undamaged and damaged states of a structure of concern, respectively. To resolve the tricky problem of prior appropriateness in Bayesian hypothesis testing, a general prior specification criterion is devised based on the notion of risk management, including the risk of false positive indication (an undamaged structure is incorrectly identified as damaged) and the risk of false negative indication (a damaged structure is incorrectly identified as undamaged). To determine an optimal risk level, two principles, namely the principle of posterior probability difference minimization (PPDM) and the principle of posterior probability product maximization (PPPM), are defined. The PPDM principle is to minimize the difference between the ability of a novelty detector to avoid a false positive and its ability to avoid a false negative, and the PPPM principle is to maximize the product of the two capabilities. Both principles essentially act as a means of achieving an optimal trade-off between the false positive and false negative risks stipulated in pursuing damage detection. To demonstrate the effectiveness of the proposed statistical decision philosophy for structural damage detection, experimental data obtained from a 5-story steel frame model and a 38-story concrete building model have been investigated.

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Section: Discussionmentioning

confidence: 99%

A Bayesian hypothesis testing-based statistical decision philosophy for structural damage detection

Zhang

2022

Structural Health Monitoring

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“…The unscented transform first approximates a d-dimensional probability distribution by choosing a set of points (sigma points) in the d-dimensional space, with the constraint that their moments are equal to those of the initial probability density. In this paper, we adopted spherical simplex sigma points defined in [55] and [56], choosing a null weight for the central point 𝑊 0 = 0, thus further reducing the set to 𝑑 + 1 points. We further set 𝛼 = √ 𝑑∕(𝑑 + 1).…”

Section: Appendix a Mapping Between Circuits And Structuresmentioning

confidence: 99%

Quantifying the impact of shape uncertainty on predicted arrhythmias

Corrado¹,

Roney²,

Razeghi³

et al. 2023

Computers in Biology and Medicine

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“…The KF has been massively derived and extended to process nonlinear systems. Among them, the Extended Kalman Filter (EKF) is based on the principle of operator linearization [14], whereas the Unscented Kalman Filter (UKF) [21] and the Scaled Spherical Simplex Filter (S3F) [22] are alternative algorithms based on statistical regularization: these techniques are based on the fact that sampling points (called σ-points) transformed by nonlinear operators allow for a better approximation of state statistics when nonlinearities are hardly linearizable. The Ensemble Kalman Filter (EnKF) [13] and the Particle Filter (PF) [6] use the same principle with much more propagated sampling-points as they aim to reconstruct the full probability density of the estimated state.…”

Section: Data Assimilation and Kalman Filteringmentioning

confidence: 99%

“…Figure 2: Sigma-points locations around the current mean state estimate (n = 3) for UKF (spread over a hypersphere -left) and S3F (corners of a simplex -right) -from [22].…”

Section: Data Assimilation and Kalman Filteringmentioning

confidence: 99%

A New Physics-Guided Data Assimilation Framework for Online Structural Monitoring: Application to Shaking-Table Tests

Diaz,

Charbonnel,

Chamoin

2023

Proceedings of the 8th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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The modified Constitutive Relation Error (mCRE) is a model updating functional whose physics-based construction avoids the explicit dependency into a priori user's expertise. Its robustness to measurement noise and remarkable convexity properties make it a credible alternative to classical model updating methods. In recent works, the authors developed an automated mCRE-based model updating framework for the offline update of finite element models of structures submitted to ground motion inputs, before deriving it to data assimilation with the development of the Modified Dual Kalman Filter (MDKF). In the latter, we addressed sequential data assimilation by integrating the mCRE as new observer within a dual Kalman filter. Contrary to classical Kalman filters, the comparison between measurements and model predictions is achieved through the mCRE functional itself, in which the data-to-model distance is enriched with a model error term with strong mechanical content (the CRE).In this contribution, we focus on MDKF numerical improvements to achieve real-time data assimilation for structural health monitoring applications where an extensive number of parameters may need to be tracked with a few amount of data, which makes the identification process ill-posed and prone to instabilities. Using (i) parallelized mCRE computation and sigma-points propagation, (ii) the Scaled Spherical Simplex Kalman filter structure and (iii) a CRE-based clustering pre-step, CPU requirements are reduced by partial state update without loss of accuracy. The MDKF methodology and the novel key ingredients for efficient (near-optimal) data assimilation are illustrated throughout (simulated) earthquake engineering examples of growing complexity. 4217COMPDYN 2023 9 th ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering M. Papadrakakis, M. Fragiadakis (eds.

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A Scaled Spherical Simplex Filter (S3F) with a decreased n + 2 sigma points set size and equivalent 2n + 1 Unscented Kalman Filter (UKF) accuracy

Cited by 19 publications

References 41 publications

A Bayesian hypothesis testing-based statistical decision philosophy for structural damage detection

A Bayesian hypothesis testing-based statistical decision philosophy for structural damage detection

Quantifying the impact of shape uncertainty on predicted arrhythmias

A New Physics-Guided Data Assimilation Framework for Online Structural Monitoring: Application to Shaking-Table Tests

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