# Machine learning based digital twin for stochastic nonlinear multi-degree of freedom dynamical system

arXiv: https://arxiv.org/abs/2103.15636 · HTML: https://mlsanity.com/paper/2103.15636/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 47 references that are in the map.
- First posted on arXiv 29 Mar 2021.

## Builds on (most cited first, 10 of 10)

- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications](https://mlsanity.com/paper/1908.10407/) (2019)
- [Transfer learning enhanced physics informed neural network for phase-field modeling of fracture](https://mlsanity.com/paper/1907.02531/) (2019)
- [Transfer learning based multi-fidelity physics informed deep neural network](https://mlsanity.com/paper/2005.10614/) (2020)
- [The role of surrogate models in the development of digital twins of dynamic systems](https://mlsanity.com/paper/2001.09292/) (2020)
- [A Gaussian process latent force model for joint input-state estimation in linear structural systems](https://mlsanity.com/paper/1904.00093/) (2019)
- [Digital twin, physics-based model, and machine learning applied to damage detection in structures](https://mlsanity.com/paper/2005.14360/) (2020)
- [Machine learning based digital twin for dynamical systems with multiple time-scales](https://mlsanity.com/paper/2005.05862/) (2020)
- [Simulation free reliability analysis: A physics-informed deep learning based approach](https://mlsanity.com/paper/2005.01302/) (2020)
- [State estimation with limited sensors -- A deep learning based approach](https://mlsanity.com/paper/2101.11513/) (2021)

## Built on by (most cited first, 4 of 4)

- [Explainable, Interpretable & Trustworthy AI for Intelligent Digital Twin: Case Study on Remaining Useful Life](https://mlsanity.com/paper/2301.06676/) (2023)
- [Improved generalization with deep neural operators for engineering systems: Path towards digital twin](https://mlsanity.com/paper/2301.06701/) (2023)
- [Physics-integrated hybrid framework for model form error identification in nonlinear dynamical systems](https://mlsanity.com/paper/2109.00538/) (2021)
- [Probabilistic machine learning based predictive and interpretable digital twin for dynamical systems](https://mlsanity.com/paper/2212.09240/) (2022)

## Abstract (arXiv)

The potential of digital twin technology is immense, specifically in the infrastructure, aerospace, and automotive sector. However, practical implementation of this technology is not at an expected speed, specifically because of lack of application-specific details. In this paper, we propose a novel digital twin framework for stochastic nonlinear multi-degree of freedom (MDOF) dynamical systems. The approach proposed in this paper strategically decouples the problem into two time-scales -- (a) a fast time-scale governing the system dynamics and (b) a slow time-scale governing the degradation in the system. The proposed digital twin has four components - (a) a physics-based nominal model (low-fidelity), (b) a Bayesian filtering algorithm a (c) a supervised machine learning algorithm and (d) a high-fidelity model for predicting future responses. The physics-based nominal model combined with Bayesian filtering is used combined parameter state estimation and the supervised machine learning algorithm is used for learning the temporal evolution of the parameters. While the proposed framework can be used with any choice of Bayesian filtering and machine learning algorithm, we propose to use unscented Kalman filter and Gaussian process. Performance of the proposed approach is illustrated using two examples. Results obtained indicate the applicability and excellent performance of the proposed digital twin framework.