Algorithms for Bayesian Model Class Selection of Higher-Dimensional Dynamic Systems

The presence of missing values is common in real‐world datasets, so modeling and uncertainty quantification (UQ) of incomplete datasets have gained increasing attention in various research areas, including structural health monitoring (SHM). However, modeling and UQ utilizing incomplete datasets are nontrivial tasks. On the other hand, prediction based on a set of incomplete measured input variables is also an important task, but most existing methods, which are discriminative models, do not possess this capability. Aiming to tackle these two challenges, we propose the two‐stage analytical Bayesian copula‐based uncertainty quantification (A‐BASIC‐UQ) using incomplete SHM data. In the modeling stage, the copula‐based multivariate joint probability density function (PDF) is modeled directly according to an incomplete dataset without imputation or disposal of any data points. For the univariate marginal PDF, using the measured (nonmissing) values of the corresponding random variable (RV), Bayesian model class selection is conducted to select the most suitable model class. For the Gaussian copula PDF, using the bivariate complete data points of entry‐by‐entry pairwise data, the optimal parameter vector is obtained from the estimation of the Pearson correlation coefficient. In the prediction stage, the analytical expressions of the predictive PDF, the predicted value and the credible region of the output variables are derived according to a set of incomplete measured input variables. The analytical expression of the predictive PDF is obtained based on the analytical operations on the auxiliary RVs and that of the predicted value and the credible region are obtained based on the analysis of multivariate Gaussian distribution. Therefore, the proposed method does not require numerical integration nor Monte Carlo simulation and does not suffer from computational burden even when there are many variables (say 4 or above). Examples using simulated data and real SHM data are presented to illustrate the capability of the proposed A‐BASIC‐UQ.

The opening of segment joints is vital to structural stability and leakage prevention for the underwater shield tunnels and it is governed by many environmental variables, e.g., water pressure, earth pressure, and temperature. Identifying the key variables and selecting a reliable predictive model for the joint opening are challenging but important tasks but they are usually done according to subjective judgments. To develop a reliable predictive model, the Nanjing Yangtze River tunnel was introduced as a case study for field monitoring and theoretical analysis. First, the structural health monitoring system in this shield tunnel was used to construct a database of measurements including joint opening, water pressure, earth pressure, and temperatures in the escape layer and inside the segment. Then, Bayesian model class selection was conducted for the variable selection and model construction. Consequently, the water pressure and temperature inside the segment were identified as the input variables for joint opening evaluation. This two-parameter model was validated by using the measurement data. It is useful for the evaluation of similar projects in tunneling engineering.

The Transitional Markov chain Monte Carlo (TMCMC) method is a widely used method for Bayesian updating and Bayesian model class selection. The method is based on successively sampling from a sequence of distributions that gradually approach the posterior target distribution. The samples of the intermediate distributions are used to obtain an estimate of the evidence, which is needed in the context of Bayesian model class selection. The properties of the TMCMC method are discussed and the following three modifications to the TMCMC method are proposed: (1) The sample weights should be adjusted after each MCMC step; (2) a burn-in period in the MCMC sampling step can improve the posterior approximation; and (3) the scale of the proposal distribution of the MCMC algorithm can be selected adaptively to achieve a near-optimal acceptance rate. The performance of the proposed modifications is compared with the original TMCMC method by means of three example problems. The proposed modifications reduce the b...

A Bayesian model updating method using subset simulation optimization given ambient vibration data is proposed to improve the efficiency in sampling and avoid local optimums, which is applied to a full-scale high-rise structure. In the proposed method, the Bayesian fast Fourier transform method is used to extract the most probable values (MPVs) and coefficients of variation (COVs) of modal parameters of the structure, which are considered as the weighting factors in the likelihood function. The posterior probability density function (PDF) of the updating parameters is then derived considering the prior PDF as the regularization term. The subset simulation optimization algorithm is extended to find the global optimal solution of the posterior PDF. The MPVs and COVs of the updating parameters are finally presented. The proposed method is first verified by updating the 15 story stiffness scaling factors of a shear building model. Then, the proposed method is investigated through a numerical application of a four-story frame structure, in which accurate parameter estimations are observed independent of the prior PDF. Finally, the proposed method is applied to a real-world 13-story twin-tower masonry structure which is a modern heritage building. Ambient vibrations were measured through a series of accelerometers instrumented in the structure. The updating parameters are the moduli of elasticity of selected substructures with two model classes studied: three parameters and six parameters. The model-predicted modal parameters from the updated model are in good agreement with their identified counterparts. It is also shown that the case using three parameters provides larger evidence based on the Bayesian model class selection method. The updated refined finite element model provides a basis for the long-term structural health monitoring.

This paper addresses the quantification of the value of structural health monitoring (SHM) before its implementation for structural systems on the basis of its Value of Information (VoI). The value of SHM is calculated utilizing the Bayesian pre-posterior decision analysis modelling the structural life cycle performance, the integrity management and the structural risks. The relevance and precision of SHM information for the reduction of the structural system risks and the expected cost of the structural integrity management throughout the life cycle constitutes the value of SHM and is quantified with this framework. The approach is focused on fatigue deteriorating structural steel systems for which a continuous resistance deterioration formulation is introduced. In a case study, the value of SHM for load monitoring is calculated for a Daniels system subjected to fatigue deterioration. The influence of and the value of SHM in regard to the structural system risks and the integrity management is explicated and explained. The results are pointing to the importance of the consideration of the structural system risks for the quantification of the value of SHM.

Guided wave-based identification of multiple cracks in beams using a Bayesian approach

In order to avoid the safety problems of the public building structure in the dense passenger flow environment, the structural health monitoring system is combined with the Building Information Modeling (BIM) method. This paper proposed a dynamic building information management system based on Structural Health Monitoring (SHM) information to ensure the security of its passenger flow information for a crowded exhibition hall. The continuous development of BIM (building information modeling) technology has greatly promoted the development of the construction industry. We can achieve real-time updating and visualization of sensor monitoring data and effectively manage different types of monitoring information as well as improve the controllability and safety of building structure monitoring by introducing BIM technology into structural health monitoring. A static building information model (BIM) was established to generate dynamic passenger flow information through video data learning, and provide a basis for structural health monitoring system for structural safety analysis and emergency response functions under dense passenger flow conditions. A dynamic building information management system suitable for structural health monitoring was built to display the dynamic network of traffic capacity in real time, so that the building information model is dynamic and predictable. The establishment for the combination mechanism of BIM and SHM system improved the data information circulation of BIM system. It could carry out dynamic health monitoring management and early warning control of building structures, realize information sharing in the process of health monitoring, and effectively improve the safety and operational efficiency of public building structures.

Current earthquake early warning (EEW) systems lack the ability to appropriately handle multiple concurrent earthquakes, which led to many false alarms during the 2011 Tohoku earthquake sequence in Japan. This paper uses a Bayesian probabilistic approach to handle multiple concurrent events for EEW. We implement the theory using a two-step algorithm. First, an efficient approximate Bayesian model class selection scheme is used to estimate the number of concurrent events. Then, the Rao-Blackwellized Importance Sampling method with a sequential proposal probability density function is used to estimate the earthquake parameters, that is hypocentre location, origin time, magnitude and local seismic intensity. A real data example based on 2 months data (2011 March 9–April 30) around the time of the 2011 M9 Tohoku earthquake is studied to verify the proposed algorithm. Our algorithm results in over 90 per cent reduction in the number of incorrect warnings compared to the existing EEW system operating in Japan.

Bayesian inference with Subset Simulation: Strategies and improvements

Scenario-based tsunami risk assessment provides valuable insights into the socio-economic consequences of a specific scenario. Although it is focused on a specific scenario or a range of scenarios, this type of analysis can still encompass uncertainty characterisation.  Hazard: Focusing on Coquimbo Bay, which was affected by the 2015 Ilapel tsunami, we demonstrate how the uncertainties are quantified and propagated from the tsunami source level all the way towards risk metrics such as the economic losses.  We have chosen a range of near-field tsunami scenarios with moment magnitude between 8.6 <Mw <9.3 from a subduction interface zone on the Nazca–South American plate interface running parallel to the Chilean coastline. We have worked with a large set of stochastic scenarios generated compatible with the scaling laws, with variable slip distribution according to a prescribed correlation structure. We have estimated the seismicity rate through different sources: paleo seismic data, historical catalogue, and moment balancing and have combined the resulting probability distributions through a logic tree approach. The weights of the logic tree are assigned through a Bayesian model class selection procedure as related to the log-evidence calculated for each model. This will lead to scenario-based hazard curves with confidence intervals for different points of interest in the port city of Coquimbo. Vulnerability: Based on the exposure model for Coquimbo, we have identified two different pre-dominant building categories in Coquimbo, namely the low-rise mixed (wood and masonry) building type and the high-rise residential buildings. For the first category, we have used empirical fragility curves for a similar building type in Dichato and damaged by the Chile 2010 and have characterised the epistemic uncertainty for these fragility curves. We have derived the vulnerability curves and their confidence band through convolution of the fragility curves and the consequence models.  Risk: We demonstrate how hazard and vulnerability curves and their confidence intervals can be convolved to obtain loss curves for certain locations of interest and how this information can be processed to derive scenario-based risk maps for Coquimbo for different return periods.  We conclude by demonstrating the importance of a thorough characterization of uncertainties and their propagation from the tsunami source towards the estimation of the economic losses. This provides important insights about the relative sensitivity of tsunami risk to different sources of uncertainty.  

Real‐Time System Identification: An Algorithm for Simultaneous Model Class Selection and Parametric Identification

Combining microstructural mechanical models with experimental data enhances our understanding of the mechanics of soft tissue, such as tendons. In previous work, a Bayesian framework was used to infer constitutive parameters from uniaxial stress–strain experiments on horse tendons, specifically the superficial digital flexor tendon (SDFT) and common digital extensor tendon (CDET), on a per-experiment basis. Here, we extend this analysis to investigate the natural variation of these parameters across a population of horses. Using a Bayesian mixed effects model, we infer population distributions of these parameters. Given that the chosen hyperelastic model does not account for tendon damage, careful data selection is necessary. Avoiding ad hoc methods, we introduce a hierarchical Bayesian data selection method. This two-stage approach selects data per experiment, and integrates data weightings into the Bayesian mixed effects model. Our results indicate that the CDET is stiffer than the SDFT, probably due to a higher collagen volume fraction. The modes of the parameter distributions yield estimates of the product of the collagen volume fraction and Young’s modulus as 811.5 MPa for the SDFT and 1430.2 MPa for the CDET. This suggests that positional tendons have stiffer collagen fibrils and/or higher collagen volume density than energy-storing tendons.

Structural health monitoring has arisen as an important tool for managing and maintaining civil infrastructure. A critical problem for all structural health monitoring systems is data loss or data corruption due to sensor failure or other malfunctions, which bring into question in subsequent structural health monitoring data analysis and decision-making. Probability density functions play a very important role in many applications for structural health monitoring. This article focuses on data loss compensation for probability density function estimation in structural health monitoring using imputation methods. Different from common data, continuous probability density functions belong to functional data; the conventional distribution-to-distribution regression technique has significant potential in missing probability density function imputation; however, extrapolation and directly borrowing shape information from the covariate probability density function are the main challenges. Inspired by the warping transformation of distributions in the field of functional data analysis, a new distribution regression approach for imputing missing correlated probability density functions is proposed in this article. The warping transformation for distributions is a mapping operation used to transform one probability density function to another by deforming the original probability density function with a warping function. The shape mapping between probability density functions can be characterized well by warping functions. Given a covariate probability density function, the warping function is first estimated by a kernel regression model; then, the estimated warping function is used to transform the covariate probability density function and obtain an imputation for the missing probability density function. To address issues with poor performance when the covariate probability density function is contaminated, a hybrid approach is proposed that fuses the imputations obtained by the warping transformation approach with the conventional distribution-to-distribution regression approach. Experiments based on field monitoring data are conducted to evaluate the performance of the proposed approach. The corresponding results indicate that the proposed approach can outperform the conventional method, especially in extrapolation. The proposed approach shows good potential to provide more reliable estimation of distributions of missing structural health monitoring data.

Structural health monitoring plays an increasingly significant role in detecting damages for large and complex structures to ensure their serviceability and sustainability. Optimal sensor placement is critical in the structural health monitoring system as the sensor configuration directly impacts the quality of collected data used for structural health diagnosis. Therefore, this study presents a comprehensive review of computational methodologies for optimal sensor placement in structural health monitoring. The problem formulation of optimal sensor placement is first introduced, including commonly used evaluation criteria for sensor configurations. Then, various existing optimization methodologies for sensor placement are summarized and introduced in detail, especially for the evolutionary algorithms and their improved variants. Finally, the suitability of computational methods for specific structural health monitoring applications is also discussed. The main goal of this study is to deliver a comprehensive reference of computational methodologies for optimal sensor placement in structural health monitoring studies and applications. This article is concluded by highlighting the most widely utilized evaluation criteria and optimization methodologies for sensor configuration determination.

The worldwide construction sector is moving towards digitization due to the development of Industry 4.0. However, when it comes to digitizing building techniques, structural health monitoring, or SHM, it is still one factor that needs to be considered. Artificial Intelligence (AI) is a remarkable invention in the construction sector. Artificial Intelligence can improve structural health monitoring and provide better solutions. Evaluating previous studies and current developments in AI-based structural health monitoring is essential to achieving this. Through a thorough Patentometric study using the industry-leading databases Espacenet and The Lens, the research seeks to present an analysis of AI in structural health monitoring. For analysis, patent information covering 2019 to 2023 is taken into account. The chosen data is evaluated for patents by nation and year, and the IPC and CPC codes for patents in artificial intelligence for structural health monitoring are also covered. The United States is currently at the forefront of patenting artificial intelligence AI-based structural health monitoring systems. This report presents an in-depth Patentometric analysis that enumerates state-of-the-art innovations. In addition to highlighting the previous art, it offers a route for strategic patenting with higher odds of publication and patent award.