Learning Data-Driven Stable Corrections of Dynamical Systems. Application to the Simulation of the Top-Oil Temperature Evolution of a Power Transformer

Ghnatios, Chady; Kestelyn, Xavier; Denis, Guillaume; Champaney, Victor; Chinesta, Francisco

doi:10.20944/preprints202306.1895.v1

2023

DOI: 10.20944/preprints202306.1895.v1

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Learning Data-Driven Stable Corrections of Dynamical Systems. Application to the Simulation of the Top-Oil Temperature Evolution of a Power Transformer

Chady Ghnatios¹,

Xavier Kestelyn²,

Guillaume Denis³

et al.

Abstract: Many engineering systems are described by using differential models whose solutions, generally obtained after discretization, can exhibit a noticeable deviation with respect to the response of the physical systems that those models are expected to represent. In those circumstances one possibility consists of enriching the model in order to reproduce the physical system behavior. The present paper considers a dynamical system, and proposes enriching the model solution by learning the dynamical model of the gap … Show more

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Cited by 3 publications

References 32 publications

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Data-Completion and Model Correction by Means of Evanescent Regularization

Ghnatios,

Jiang,

Tourbier

et al. 2023

Applied Sciences

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System components are often regarded as part of a whole system, especially when it comes to data-driven modeling. Thus, subsystem modeling is disregarded in general when building a data-driven response, especially since multiple subsystem outputs are never measured in real applications. However, subsystem knowledge and accurate modeling are of utmost importance when aiming to repair, tune or troubleshoot a system. This work proposes a holistic modeling of subsystems in an embedded system setting. A hybrid modeling starting from the physics-based model is proposed in this work, correcting or enhancing the model, and predicting output variables, even when a measurement is never available for some of those variables. The process relies on the variables’ history, and employs an adjoint-free neural ordinary differential equation technique, along with evanescent regularization to enhance the convergence on the unmeasurable variables. The updated model converges to the exact measurements, for both the measurable and the unmeasurable variables. Multiple examples are presented using synthetic data, to allow an easy evaluation of the hidden or unmeasurable variables. The relative error offered by the updated model is around 0.001% for the measurable quantities and 0.1% for the unmeasurable ones.

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Data-Completion and Model Correction by Means of Evanescent Regularization

Ghnatios,

Jiang,

Tourbier

et al. 2023

Applied Sciences

Self Cite

View full text Add to dashboard Cite

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Learning Transformed Dynamics for Efficient Control Purposes

Ghnatios,

Mouterde,

Tomezyk

et al. 2024

Mathematics

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Learning linear and nonlinear dynamical systems from available data is a timely topic in scientific machine learning. Learning must be performed while enforcing the numerical stability of the learned model, the existing knowledge within an informed or augmented setting, or by taking into account the multiscale dynamics—for both linear and nonlinear dynamics. However, when the final objective of such a learned dynamical system is to be used for control purposes, learning transformed dynamics can be advantageous. Therefore, many alternatives exists, and the present paper focuses on two of them: the first based on the discovery and use of the so-called flat control and the second one based on the use of the Koopman theory. The main contributions when addressing the first is the discovery of the flat output transformation by using an original neural framework. Moreover, when using the Koopman theory, this paper proposes an original procedure for learning parametric dynamics in the latent space, which is of particular interest in control-based engineering applications.

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Hybrid Twins Modeling of a High-Level Radioactive Waste Cell Demonstrator for Long-Term Temperature Monitoring and Forecasting

Muñoz,

Thomas,

Cotton

et al. 2024

Sensors

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Monitoring a deep geological repository for radioactive waste during the operational phases relies on a combination of fit-for-purpose numerical simulations and online sensor measurements, both producing complementary massive data, which can then be compared to predict reliable and integrated information (e.g., in a digital twin) reflecting the actual physical evolution of the installation over the long term (i.e., a century), the ultimate objective being to assess that the repository components/processes are effectively following the expected trajectory towards the closure phase. Data prediction involves using historical data and statistical methods to forecast future outcomes, but it faces challenges such as data quality issues, the complexity of real-world data, and the difficulty in balancing model complexity. Feature selection, overfitting, and the interpretability of complex models further contribute to the complexity. Data reconciliation involves aligning model with in situ data, but a major challenge is to create models capturing all the complexity of the real world, encompassing dynamic variables, as well as the residual and complex near-field effects on measurements (e.g., sensors coupling). This difficulty can result in residual discrepancies between simulated and real data, highlighting the challenge of accurately estimating real-world intricacies within predictive models during the reconciliation process. The paper delves into these challenges for complex and instrumented systems (multi-scale, multi-physics, and multi-media), discussing practical applications of machine and deep learning methods in the case study of thermal loading monitoring of a high-level waste (HLW) cell demonstrator (called ALC1605) implemented at Andra’s underground research laboratory.

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Learning Data-Driven Stable Corrections of Dynamical Systems. Application to the Simulation of the Top-Oil Temperature Evolution of a Power Transformer

Cited by 3 publications

References 32 publications

Data-Completion and Model Correction by Means of Evanescent Regularization

Data-Completion and Model Correction by Means of Evanescent Regularization

Learning Transformed Dynamics for Efficient Control Purposes

Hybrid Twins Modeling of a High-Level Radioactive Waste Cell Demonstrator for Long-Term Temperature Monitoring and Forecasting

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