Sparse Bayesian learning for structural damage identification

TL;DR: The proposed PhyCNN approach is capable of accurately predicting building's seismic response in a data-driven fashion without the need of a physics-based analytical/numerical model and outperforms conventional pure data-based neural networks.

TL;DR: This work proposes an innovative physics-constrained Bayesian deep learning approach to reconstruct flow fields from sparse, noisy velocity data, where equation-based constraints are imposed through the likelihood function and uncertainty of the reconstructed flow can be estimated.

TL;DR: In this paper, a physics-constrained Bayesian deep learning approach is proposed to reconstruct flow fields from sparse, noisy velocity data, where equation-based constraints are imposed through the likelihood function and uncertainty of the reconstructed flow can be estimated.

TL;DR: Results demonstrate that the posterior probability distributions of the unknown structural parameters can be successfully identified, and reliable probabilistic model updating and damage identification can be achieved.

TL;DR: It is demonstrated that by exploiting a probabilistic Bayesian learning framework, the 'relevance vector machine' (RVM) can derive accurate prediction models which typically utilise dramatically fewer basis functions than a comparable SVM while offering a number of additional advantages.

TL;DR: The decomposition of A is called the singular value decomposition (SVD) and the diagonal elements of ∑ are the non-negative square roots of the eigenvalues of A T A; they are called singular values.

TL;DR: Inverse problems arise in a number of important practical applications, ranging from biomedical imaging to seismic prospecting as mentioned in this paper, and a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.

TL;DR: By introducing a decomposition of the spectral density function matrix, the response spectra can be separated into a set of single degree of freedom systems, each corresponding to an individual mode, and close modes can be identified with high accuracy even in the case of strong noise contamination of the signals.