Neural Extended Kalman Filters for Learning and Predicting Dynamics of Structural Systems

Accurate structural response prediction forms a main driver for structural health monitoring and control applications. This often requires the proposed model to adequately capture the underlying dynamics of complex structural systems. In this work, we utilize a learnable Extended Kalman Filter (EKF), named the Neural Extended Kalman Filter (Neural EKF) throughout this paper, for learning the latent evolution dynamics of complex physical systems. The Neural EKF is a generalized version of the conventional EKF, where the modeling of process dynamics and sensory observations can be parameterized by neural networks, therefore learned by end-to-end training. The method is implemented under the variational inference framework with the EKF conducting inference from sensing measurements. Typically, conventional variational inference models are parameterized by neural networks independent of the latent dynamics models. This characteristic makes the inference and reconstruction accuracy weakly based on the dynamics models and renders the associated training inadequate. We here show how the structure imposed by the Neural EKF is beneficial to the learning process. We demonstrate the efficacy of the framework on both simulated and real-world monitoring datasets, with the results indicating significant predictive capabilities of the proposed scheme.Comment: This manuscript has been submitted to an international journal for revie

The Modal Identification of Structure Using Distributed ERA and EFDD Methods

Conference Name:International Conference on Structures and Building Materials. Conference Address: Guangzhou, PEOPLES R CHINA. Time:JAN 07-09, 2011.Structural health monitoring (SHM) is an emerging field in civil engineering, offering the potential for continuous and periodic assessment of the safety and integrity of civil infrastructure. In this paper, a distributed computing strategy for modal identification of structure is proposed, which is suitable for the problem of solving large volume of data set in structural health monitoring. Numerical example of distribute computing the modal properties of truss illustrates the distributed out-put only modal identification algorithm based on NExT / ERA techniques and EFDD. This strategy can also be applied to other complicated structure to determine modal parameters

Full-field structural monitoring using event cameras and physics-informed sparse identification

ISSN:0888-3270ISSN:1096-121

Physics-guided Deep Markov Models for learning nonlinear dynamical systems with uncertainty

In this paper, we propose a probabilistic physics-guided framework, termed Physics-guided Deep Markov Model (PgDMM). The framework targets the inference of the characteristics and latent structure of nonlinear dynamical systems from measurement data, where exact inference of latent variables is typically intractable. A recently surfaced option pertains to leveraging variational inference to perform approximate inference. In such a scheme, transition and emission functions of the system are parameterized via feed-forward neural networks (deep generative models). However, due to the generalized and highly versatile formulation of neural network functions, the learned latent space often lacks physical interpretation and structured representation. To address this, we bridge physics-based state space models with Deep Markov Models, thus delivering a hybrid modeling framework for unsupervised learning and identification of nonlinear dynamical systems. The proposed framework takes advantage of the expressive power of deep learning, while retaining the driving physics of the dynamical system by imposing physics-driven restrictions on the side of the latent space. We demonstrate the benefits of such a fusion in terms of achieving improved performance on illustrative simulation examples and experimental case studies of nonlinear systems. Our results indicate that the physics-based models involved in the employed transition and emission functions essentially enforce a more structured and physically interpretable latent space, which is essential for enhancing and generalizing the predictive capabilities of deep learning-based models.ISSN:0888-3270ISSN:1096-121

Structural identification with physics-informed neural ordinary differential equations

This paper exploits a new direction of structural identification by means of Neural Ordinary Differential Equations (Neural ODEs), particularly constrained by domain knowledge, such as structural dynamics, thus forming Physics-informed Neural ODEs, aiming at governing equations discovery/approximation. Structural identification problems often entail complex setups featuring high-dimensionality, or stiff ODEs, which pose difficulties in the training and learning of conventional data-driven algorithms who seek to unveil the governing dynamics of a system of interest. In this work, Neural ODEs are re-casted as a two-level representation involving a physics-informed term, that stems from possible prior knowledge of a dynamical system, and a discrepancy term, captured by means of a feed-forward neural network. The re-casted format is highly adaptive and flexible to structural monitoring problems, such as linear/nonlinear structural identification, model updating, structural damage detection, driving force identification, etc. As an added step, for inferring an explainable model, we propose the adoption of sparse identification of nonlinear dynamical systems as an additional tool to distill closed-form expressions for the trained nets, that embed a more straightforward engineering interpretation. We demonstrate the framework on a series of numerical and experimental examples, with the latter pertaining to a structural system featuring highly nonlinear behavior, which is successfully learned by the proposed framework. The proposed structural identification with Physics-informed Neural ODEs comes with the benefits of direct approximation of the governing dynamics, and a versatile and flexible framework for discrepancy modeling in structural identification problems.ISSN:0022-460XISSN:1095-856

Computer Vision Aided Structural Identification: Feature Tracking Using Particle Tracking Velocimetry versus Optical Flow

Recent advances in computer vision techniques allow to obtain information on the dynamic behaviour of structures using commercial grade video recording devices. The advantage of such schemes lies in the non-invasive nature of video recording and the ability to extract information at a high spatial density utilizing structural features. This creates an advantage over conventional contact sensors since constraints such as cabling and maximum channel availability are alleviated. In this study, two such schemes are explored, namely Particle Tracking Velocimetry (PTV) and the optical flow algorithm. Both are validated against conventional sensors for a lab-scale shear frame and compared. In cases of imperceptible motion, the recently proposed Phase-based Motion Magnification (PBMM) technique is employed to obtain modal information within frequency bands of interest and further used for modal analysis. The optical flow scheme combined with (PBMM) is further tested on a large-scale post-tensioned concrete beam and validated against conventional measurements, as a transition from lab- to outdoor field applications

Symplectic encoders for physics-constrained variational dynamics inference

We propose a new variational autoencoder (VAE) with physical constraints capable of learning the dynamics of Multiple Degree of Freedom (MDOF) dynamic systems. Standard variational autoencoders place greater emphasis on compression than interpretability regarding the learned latent space. We propose a new type of encoder, based on the recently developed Hamiltonian Neural Networks, to impose symplectic constraints on the inferred a posteriori distribution. In addition to delivering robust trajectory predictions under noisy conditions, our model is capable of learning an energy-preserving latent representation of the system. This offers new perspectives for the application of physics-informed neural networks on engineering problems linked to dynamics.ISSN:2045-232

Experimental Study on Impact-Induced Damage Detection Using an Improved Extended Kalman Filter

This paper presents an experimental study on using an improved extended Kalman filter (EKF) to identify impact-induced structural damage. By introducing the optimization of estimated residual error into the classical EKF, this real-time approach demonstrates an excellent capability to identify the abrupt changes of structural parameters instantly and accurately. The optimization procedure is activated when a prescribed threshold is exceeded. A shaking table test of a three-story steel frame subjected to abrupt damage induced by impact load was conducted to validate the improved EKF approach. The results clearly reveal its improved performance and good anti-noise ability in identifying time-variant structural parameters