Bayesian nonparametric models, especially Dirichlet process mixture models (DPMMs), have attracted increasing attention in structural health monitoring (SHM) using vibration responses such as transmissibility functions (TFs). Their nonparametric nature enables dynamically adapting model complexity to observed data, thus effectively capturing diverse patterns of structural behavior under varying ambient and environmental conditions. Their clustering property further provides an unsupervised mechanism to distinguish structural states via clusters for structural anomaly detection. The induced clusters also capture discriminative information about the underlying statistical structure of measured vibration responses, which can be integrated into a semi-supervised pipeline to facilitate training supervised models for higher-level SHM tasks, such as structural damage diagnostics. Furthermore, as fully Bayesian approaches, DPMMs offer a principled scheme to quantify uncertainty arising from model complexity, model parameters, and data noise, making them well-suited for reliable SHM and supporting more informed decision-making by operators and stakeholders. Building on these advantages, this work introduces a coherent framework that leverages DPMMs for TF-based SHM, which spans from classical statistical pattern recognition methods to deep learning-based approaches and covers tasks from unsupervised structural anomaly detection to semi-supervised damage diagnosis.
The first work introduces a streaming variational inference (VI)-empowered Dirichlet process Gaussian mixture model (DPGMM) for online structural anomaly detection, which develops a truncation-free VI (TFVI) to approximate the posterior of the DPGMM from an unbounded variational family. This characteristic allows the TFVI to dynamically add mixture components and handle streaming data by utilizing the variational posterior conditioned on the previous data as the prior when new data are observed, making it well-suited for online structural anomaly detection. It also provides a systematic framework for quantifying uncertainty in anomaly detection results based on posterior component assignment probabilities and posterior distributions of component parameters.
The second work integrates the TFVI-DPGMM with deep generative models (DGMs) to deliver an end-to-end framework, referred to as Dirichlet Process-Deep Generative Model-Integrated Incremental Learning (DPGIIL), for structural anomaly detection and condition assessment directly from raw dynamic responses (e.g., high-dimensional TF vectors). This framework places a DPGMM prior in the latent space of DGMs and derives a variational lower bound, which is tighter than the standard evidence lower bound, to jointly optimize the parameters of neural networks and the DPGMM. The nonparametric nature of the DPGMM, combined with the representation learning capability of DGMs, enables extracting informative representations directly from raw dynamic responses that are multimodally distributed, while also supporting incremental learning as new data arrive.
Since DPGMMs partition the dataset into clusters indicating different patterns of structural behavior, the third work leverages this discriminative information to train a deep classifier in a semi-supervised manner, thereby reducing the amount of labeled data required. It first modifies standard DPGMM into a constrained variant by incorporating human supervision (labels) into the model via pairwise constraints and develops a constraint-aware TFVI for posterior inference. Then the discriminative information identified by the DPGMM, which is encoded in the cluster assignments, is utilized to train a deep classifier through a knowledge transfer technique for structural damage classification. The approach achieves performance comparable to state-of-the-art models with fewer than 10% labeled training data.
These contributions demonstrate the promise and recent advances of Bayesian nonparametric models in vibration-based SHM. Owing to their nonparametric nature, Bayesian nonparametric models are well-suited for modeling dynamic responses under complex operating environments. The clusters they identify also provide discriminative information that can be used in downstream classification and regression tasks. Furthermore, they provide a systematic uncertainty quantification framework that captures both aleatoric and epistemic components. Overall, these Bayesian nonparametric approaches bridge unsupervised detection and semi-supervised diagnostics, enabling robust and scalable SHM using vibration responses such as TFs.
 

Bayesian nonparametric models,Streaming variational inference,Online structural anomaly detection,Semi-supervised structural damage diagnostics