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Characterizing probability distributions of geotechnical data plays an important role in data-centric geotechnics. On the one hand, geotechnical data are Multivariate, Uncertain, and Irregular (MUI), where the irregular characteristic implies that asymmetry and/or multimodality are often observed in the histograms of geotechnical data, so the corresponding probability distribution is Multivariate, Asymmetric, and Multimodal (MAM). On the other hand, many geotechnical datasets are unavoidably subjected to the issue of modelling and prediction stages missing values (called "dual-stage missing values"), so characterising the MAM distribution of geotechnical data with dual-stage missing values becomes an essential task. There are three fundamental difficulties for this purpose. The first is on joint Probability Density Function (PDF) modelling for a MAM distribution given data with modelling stage missing values. Many traditional and advanced approaches collapse in the presence of MAM distributions and modelling stages missing values, respectively. The second is on joint PDF prediction for a MAM distribution given data with prediction stage missing values. The third is on Credible Region (CR) construction of a MAM distribution as there is no unique CR of a MAM distribution given an exceedance probability only. We propose the three-stage BAyeSIan Copula-based Highest density region/contour (BASIC-H). Stage-1 constructs the posterior distribution of data with modelling stage missing values based on Copula theory and Bayesian inference. Stage-2 derives the posterior predictive distribution of data with prediction stage missing values based on marginalisation and conditionalisation of the posterior distribution. Stage-3 constructs the CRs for the posterior and predictive distributions adopting the reasonable constraint imposed by the Highest Density Region (HDR). Examples using simulated data, CLAY/10/7490 and CLAY/5/345 are presented to illustrate the capability of the proposed BASIC-H. [ABSTRACT FROM AUTHOR]

Modal frequency is an important indicator reflecting the health status of a structure. Numerous investigations have shown that its fluctuations are related to the changing environmental factors. Thus, modelling the modal frequency–multiple environmental factors relation is essential for making reliable inference in structural health monitoring. In this study, the Bayesian network (BN)-based algorithm is developed for recognizing the pattern between modal frequency and multiple environmental factors. Different candidates of network structure of the BN are proposed to describe the possible statistical relations of different variables. In the BN-based pattern recognition, the learning phase conducts uncertainty quantification in both parameter and model levels; and the prediction phase makes inference under complete and incomplete observed information. Based on the long-term monitoring data, the most plausible network structure is selected, and its associated parameters are identified. The developed algorithm is then utilized for analyzing the long-term monitoring data (modal frequencies, temperature, humidity, wind speed and traffic volume) of the Xinguang Bridge (a 782-m three-span half-through arch bridge). It turns out that the selected network structure properly captures the pattern of modal frequency–multiple environmental factors. [ABSTRACT FROM AUTHOR]

Load effect characterization under traffic flow has received tremendous attention in bridge engineering, and uncertainty quantification (UQ) of load effect is critical in the inference process. Bayesian probabilistic approach is developed to overcome the unreliable issue caused by negligence of uncertainty of parametric and modeling aspects. Stochastic traffic load simulation is conducted by embedding the random inflow component into the Nagel–Schreckenberg (NS) model, and load effects are calculated by stochastic traffic load samples and influence lines. Two levels of UQ are performed for traffic load effect characterization: at parametric level of UQ, not only the optimal parameter values but also the associated uncertainties are identified; at model level of UQ, rather than using a single prescribed probability model for load effects, a set of probability distribution model candidates is proposed, and model probability of each candidate is evaluated for selecting the most suitable/plausible probability distribution model. Analytic work was done to give closed-form solutions for the expression involved in both parametric and model UQ. In the simulated examples, the efficiency and robustness of the proposed approach are firstly validated, and UQ are performed to different load effect data achieved by varying the structural span length under the changing total traffic volume. It turns out that the uncertainties of load effects are traffic-specific and response-specific, so it is important to conduct UQ of load effects under different traffic scenarios by using the developed approach. [ABSTRACT FROM AUTHOR]

Highlights • Modal frequency-environmental condition relation is developed. • Different functions and combinations of environmental factors are validated. • Sparse Bayesian Learning can capture data pattern without overfitting. • Temperature and relative humidity are important for modal frequency prediction. • The design prediction contour along with associated uncertainty is achieved. Abstract The goal of structural health monitoring is to infer structural health status using available measurement. It is well accepted that structural modal frequency can be utilized as an indicator revealing health status of a monitored structure, but this indicator exhibits substantial seasonal variation due to changing environmental conditions (such as temperature and humidity). There are three critical issues in modal frequency-environmental condition relation development: 1) a significant level of uncertainty in both structural dynamical responses and environmental factors; 2) huge number of possible components of input features of environmental factors; 3) capability of multivariate prediction on modal frequencies of several modes. This paper develops an updated version of the Sparse Bayesian Learning (SBL), enhancing the efficiency in the hyperparameter optimization process, with capabilities in uncertainty quantification, sparse feature selection and multivariate prediction. The approach is utilized for modal frequency-environmental condition relation development of a reinforced concrete building based on one-year measurement. It turns out that the optimal multivariate sparse model can depict the pattern between the modal frequencies of the first three modes and the environmental conditions with high fitting capacity and low error sensitivity. [ABSTRACT FROM AUTHOR]

A correction to the article "Real-Time System Identification: An Algorithm for Simultaneous Model Class Selection and Parametric Identification' that was published in a previous issue is presented.