Bayesian Selective Surrogate Gaussian Process for Structural Health Indicator Modeling

The Bayesian selective surrogate Gaussian process (BSSGP), as a novel progressive probabilistic approach, is proposed for nonparametric modeling. In Gaussian process (GP) regression, the kernel for specifying the similarity between the input data is commonly assigned through trial and error with the captured input variables. However, an improper choice of the kernel type and/or redundant input variables can significantly degrade the modeling performance. To address this problem, the proposed approach provides a generative kernel augmentation scheme to develop the optimal kernel with the appropriate input variables. The scheme starts with a candidate kernel set. By adopting more features, these candidates evolve as augmented kernels. A Bayesian indicator is formulated to assess the performance of the potential kernels. Hence, the set of kernels that strike the optimal balance between fitting capacity and robustness is chosen for further enhancement. The generation procedure is conducted iteratively until further augmentation ceases to provide considerable improvement in the kernel performance. To illustrate the efficacy of the proposed approach, a case study with three-year continuous monitoring of a 22-story reinforced concrete building is presented.

Probabilistic Settlement Prediction and System Serviceability Assessment of Immersed Tunnel

Based on the engineering background of the Hong Kong-Zhuhai-Macao Bridge (HZMB) immersed tunnel, a simple and efficient method for predicting tunnel settlement is proposed. This method employs Bayesian inference combined with field measurement data to update the model and quantify uncertainties, enabling accurate prediction of tunnel settlement. Furthermore, drawing on reliability theory and considering multiple failure modes related to differential settlement of tubes and joints, a framework is established for evaluating the system serviceability performance of the immersed tunnel.

Online Bayesian Learning for Uncertainty-Aware Anomaly Detection with Streaming Transmissibility Measurements

Transmissibility function (TF) is widely applied in structural anomaly detection due to its sensitivity to damage and robustness against external excitations, while its application in online detection is limited, primarily due to challenges in handling data streams. To address this issue, a Bayesian nonparametric clustering approach is introduced for online structural anomaly detection with TF, which integrates a truncation-free variational inference-based Dirichlet process Gaussian mixture model (VI-DPGMM) within a streaming variational inference (SVI) framework. As a Bayesian nonparametric approach, the truncation-free VI-DPGMM dynamically adapts model complexity during online learning with increasing data by setting the variational distributions of parameters for components without data to their prior distributions, which enables computing the probabilities to assign data points to these components and determining the creation of new components. As a result, the truncation-free VI-DPGMM allows dynamically adding components to the mixture model, providing the flexibility to automatically adapt the number of components for arbitrary amounts of data. This characteristic enables its intuitive integration into the SVI featured as the variational posterior conditioned on the previous data as the prior when new data are observed, facilitating continuous refinement of the mixture model without repeatedly making inference of previous data. Therefore, the proposed method is highly efficient and well-suited for online structural anomaly detection. Moreover, as a density estimator, this approach supports outlier-based anomaly detection, providing robustness to environmental effects and comprehensive uncertainty quantification.

Physical-Knowledge-Guided and Explainable CNNs for Gear Fault Severity Level Diagnosis

Despite much success that deep-learning (DL) models have achieved, their interpretability, however, remains opaque and thus often impedes their real applications in the scenarios of fault diagnosis for risk-sensitive equipment. Fortunately, Class Activation Mapping (CAM) has significantly enhanced the interpretability of convolutional neural networks (CNNs) because it can perform saliency analysis and then illuminate which areas of an input contribute more to a classification result c. Nevertheless, CAM fails to enhance diagnostic accuracy and actively leverage interpretability due to its passively explanatory property for the trained models. To address this issue, in this paper, a Physically Meaningful Regularization (PMR) term is proposed by using Grad-CAM, to guide the models in focusing on the same frequency bands of the input spectra and ignoring other parts of noisy and irrelevant signals. Based on the PMR term, a two-step back propagation training algorithm is accordingly proposed to train the diagnostic models embedded with physical knowledge. Consequently, the obtained physical-knowledge-guided and explainable CNNs can offer not only higher interpretability but also stronger anti-noise ability. Finally, the proposed method is validated in two datasets containing multiple fault severity levels. The diagnostic results and the saliency analysis demonstrate the efficacy of the proposed method.

Two Stage Nonparametric Framework for Missing Data Imputation, Uncertainty Quantification and Incorporation in System Identification

In many engineering applications, missing data during system identification can hinder the performance of the identified model. The proposed framework is a two-stage approach where the first stage is to impute the missing values in the dataset with plausible values inferred from the observed data and quantify the corresponding imputation uncertainty. The second stage proposes to incorporate imputation uncertainty in a single modeling process by mitigating the influence of samples with imputations during training and testing. The framework is applied to the structural health monitoring data of East Asian Hall. Results reveal a minimum reduction of 50% in root mean squared error values compared to those achieved by directly removing incomplete samples.