Analytical Bayesian Copula‐Based Uncertainty Quantification (A‐BASIC‐UQ) Using Data with Missing Values in Structural Health Monitoring

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.

The dynamic performance of railway bridges under high-speed trains draws the attention of bridge engineers. The vibration issue for long-span bridges under high-speed trains is still not well understood due to lack of validations through structural health monitoring (SHM) data. This paper investigates the correlation between bridge acceleration and train speed based on structural dynamics theory and SHM system from three foci. Firstly, the calculated formula of acceleration response under a series of moving load is deduced for the situation that train length is near the length of the bridge span, the correlation between train speed and acceleration amplitude is analyzed. Secondly, the correlation scatterplots of the speed–acceleration is presented and discussed based on the transverse and vertical acceleration response data of Dashengguan Yangtze River Bridge SHM system. Thirdly, the warning indexes of the bridge performance for correlation scatterplots of speed–acceleration are established. The main conclusions are: (1) The resonance between trains and the bridge is unlikely to happen for long-span bridge, but a multimodal correlation curve between train speed and acceleration amplitude exists after the resonance speed; (2) Based on SHM data, multimodal correlation scatterplots of speed–acceleration exist and they have similar trends with the calculated formula; (3) An envelope line of polylines can be used as early warning indicators of the changes of bridge performance due to the changes of slope of envelope line and peak speed of amplitude. This work also gives several suggestions which lay a foundation for the better design, maintenance and long-term monitoring of a long-span high-speed bridge.

Structural identification (St-Id) using finite element models for optimum sensor configuration and uncertainty quantification

Copula-based JPDF of wind speed, wind direction, wind angle, and temperature with SHM data

Visualization of sensor networks, data, and metadata is becoming one of the most pivotal aspects of the structural health monitoring (SHM) process. Without the ability to communicate efficiently and effectively between disparate groups working on a project, an SHM system can be underused, misunderstood, or even abandoned. For this reason, this work seeks to evaluate visualization techniques in the field, identify flaws in current practices, and devise a new method for visualizing and accessing SHM data and metadata in 3D. More precisely, the work presented here reflects a method and digital workflow for integrating SHM sensor networks, data, and metadata into a virtual reality environment by combining spherical imaging and informational modeling. Both intuitive and interactive, this method fosters communication on a project enabling diverse practitioners of SHM to efficiently consult and use the sensor networks, data, and metadata. The method is presented through its implementation on a case study, Streicker Bridge at Princeton University campus. To illustrate the efficiency of the new method, the time and data file size were compared to other potential methods used for visualizing and accessing SHM sensor networks, data, and metadata in 3D. Additionally, feedback from civil engineering students familiar with SHM is used for validation. Recommendations on how different groups working together on an SHM project can create SHM virtual environment and convey data to proper audiences, are also included.

Reliability of a ship structure has been investigated in this study under two factors of fatigue and corrosion failure using structural health monitoring data. In order to use structural health monitoring data in assessing the reliability, Bayesian inference method has been used to update the distribution of loads applied on the structure. This study used structural health monitoring data to assess the reliability of a ship construction under two conditions: fatigue and corrosion failure. A Bayesian inference method was utilized to update the distribution of loads applied to the structure to employ structural health monitoring data in determining reliability. The load distribution obtained from the equations was used to assess the reliability of a ship structure during corrosion. The proposed mathematical model was examined using the data output of the force sensors installed on the commercial ship in the laboratory, whose model has been scale tested. According to the reliability analysis, the reliability index of the structure decreases with time as a result of corrosion and fatigue failures. The utilization of structural health monitoring data has boosted confidence in the reliability index for estimating the structure's real-life as determined by the study. The findings suggest that using the reliability criterion and health monitoring data during the design stage can provide a better knowledge of the structure's performance throughout time, according to the environmental conditions.

Complex analysis and design of structures, especially landmark structures such as long-span bridges, have been conducted by many engineers and researchers. Currently, it is possible to collect more and precise monitoring data as well as to develop complex three-dimensional (3D) FEM models. These models, which can be calibrated using structural health-monitoring (SHM) data, can be used for the estimation of component and system reliability of bridges. However, the uncertainties related to the data, analysis, and nonstationary nature of the structural behavior need to be better incorporated by using a set of models that are continuously updated with monitoring data. This set of models constitutes a family as a result of the approach by which the models are obtained and the relationships among them. The objective of this paper is to explore the impact of uncertainty in predicting the system reliability obtained by a one-time, initially calibrated FEM model as well as by a family of FEM models continu...

In recent years, Bayesian model updating techniques based on measured data have been applied in structural health monitoring. Often we are faced with the problem of how to select the ‘best’ model from a set of competing candidate model classes for the system based on data. To tackle this problem, Bayesian model class selection is used, which provides a rigorous Bayesian updating procedure to give the probability of different candidate classes for a system, based on the data from the system. There may be cases where more than one model class has significant probability and each of these will give different predictions. Bayesian model class averaging provides a coherent mechanism to incorporate all the considered model classes in the probabilistic predictions for the system. However, both Bayesian model class selection and Bayesian model class averaging require the calculation of the evidence of the model class which requires the nontrivial computation of a multi-dimensional integral. In this paper, several methods for solving this computationally challenging problem of model class selection are presented, proposed and compared. The efficiency of the proposed methods is illustrated by an example involving a structural dynamic system.

Structural health monitoring (SHM) of bridges has gained rapid development in the past few years. This paper describes application of SHM on long-span bridges in China, with the aim to illustrate its practical value. A short review of its development and practice is firstly introduced. Three case studies are subsequently presented on utilization of SHM data in engineering practice. In the first case study, a ship collision incident is analyzed using SHM data. An alarm is sent and confirmed when the collision occurred, and mode parameters are identified with GPS measurements to evaluate the bridge condition. In the second case study, damage of expansion joints in a suspension bridge is assessed with girder end displacement measurements. Malfunction of viscous damper is found to correlate with cumulative displacement. The results show that cumulative displacement can be used for condition assessment of expansion joints. In the third case study, the performance of tuned mass dampers is evaluated with wind and vibration measurements before and after tuned mass damper installation. Through explanation of these case studies, the paper illustrates how to distill useful insights from SHM data, which could be instructive for further research in this field.

In order to solve the problem of abnormal structural health monitoring data of large-span bridges, the construction of civil engineering structural health monitoring platform based on intelligent algorithm is proposed. This paper utilizes the Internet of Things RFID technology to deploy health monitoring sensor nodes and process the bridge structural health monitoring data, so as to realize the large-span bridge structural health monitoring. The experimental results show that the structural health monitoring method designed in this paper for large-span bridges is effective, and the accuracy rate between the measured data values and the real values is 90%, which is highly reliable and has certain application value. Conclusion: The designed structural health monitoring method for large-span bridges has a high degree of agreement between the main girder vertical deformation variables and the actual main girder vertical deformation variables at different monitoring points, which proves that the adopted structural health monitoring method for large-span bridges has a good accuracy and has certain application value.

One of the primary challenges in civil engineering today is the safety assessment and management of existing infrastructures. In this context, structural health monitoring (SHM) plays a fundamental role in data acquisition and assessment of the safety of a given infrastructure. SHM data are instrumental for quantifying uncertainties, informing structural models, and updating structural reliability over time. In principle, an SHM system should provide the best information possible for assessing and updating structural reliability. Since infrastructure management resources are inevitably limited, SHM information quality assessment becomes a key issue. Several metrics are available in the scientific literature to measure the SHM information quality. Most of these are based on the accuracy of SHM information or the impact of monitoring on decision-making. This article introduces novel information quality metrics that quantify how SHM affects the structural reliability assessment. First, we state a comprehensive framework based on Bayesian networks for structural reliability updating. Based on this, we define a metric based on the measurement resolution concept. Next, according to structural reliability theory, we present an importance measure of the SHM observations. Finally, we propose two explanatory case studies.

Because of the critical role that bridges play in land transport networks and broader economy, the assessment of existing bridges is gradually becoming a global concern. Structural health monitoring (SHM) systems have been installed on many bridges to provide data for the evaluation of bridge performance and safety. The challenge for bridge engineers is now to make use of the data and convert them into usable information and knowledge. Integrating SHM data with reliability analysis procedures offers a useful and practical methodology for bridge assessment since reliability is an important performance index and reliability-based procedures have the capability of accommodating uncertainties in structural models, responses, loads and monitoring data. In this paper, an approach for integrating SHM data in a reliability assessment framework is proposed. The reliability of the bridge is quantified by incorporating SHM information in the resistance, load and structural models. Advanced modeling tools and techniques, such as finite element analysis, finite model updating and Bayesian updating, are used for the reliability computations. Data from the SHM system installed on the Newmarket Viaduct, a newly constructed, 12-span, post-tensioned box girder bridge erected by the balanced cantilever method in Auckland, New Zealand, are also presented in this paper and used to explain the proposed framework.

Structural health monitoring (SHM) of civil infrastructures is becoming more feasible with the help of recent developments in sensing and computing technologies being more available and affordable. The SHM system may contain various types of measurements including, but not limited to, vibration, strain and image data. In this paper, the authors provide a general discussion of the two critical aspects of SHM: assessment of the current condition and future performance prediction from their recent studies at the University of Central Florida. First, SHM data can be used to track and evaluate the current condition of the structure with the help of statistical pattern recognition algorithms and computer vision techniques. Statistical analysis of these types of data can provide rapid extraction of information about the changes in structural behavior whereas the use of the computer vision technologies in a monitoring system offers to detect events visually. Subsequently, the available information obtained can be used for decision-making about the future performance of the structure. Prediction of the future performance is a very crucial step in better managing the life cycle safety, serviceability and costs.

This work newly proposes an uncertainty quantification (UQ) method named sparse approximation of moment-based arbitrary polynomial chaos (SAMBA PC) that offers a single solution to many current problems in turbomachinery applications. At the moment, every specific case is characterized by a variety of different input types such as histograms (from experimental data), normal probability density functions (PDFs) (design rules) or fat tailed PDFs (for rare events). Thus, the application of UQ requires the adaptation of ad hoc methods for each individual case. A second problem is that parametric PDFs have to be determined for all inputs. This is difficult if only few samples are available. In gas turbines, however, the collection of statistical information is difficult, expensive, and having scarce information is the norm. A third critical limitation is that if using nonintrusive polynomial chaos (NIPC) methods, the number of required simulations grows exponentially with increasing numbers of input uncertainties: the so-called “curse of dimensionality.” It is shown that the fitting of parametric PDFs to small data sets can lead to large bias and the direct use of the available data is more accurate. This is done by propagating uncertainty through several test functions and the computational fluid dynamics (CFD) simulation of a diffuser, highlighting the impact of different PDF fittings on the output. From the results, it is concluded that the direct propagation of the experimental data set is preferable to the fit of parametric distributions if data is scarce. Thus, the suggested method offers an alternative to the maximum entropy theorem to handle scarce data. SAMBA simplifies the mathematical procedure for many different input types by basing the polynomial expansion on moments. Its moment-based expansion automatically takes care of arbitrary combinations of different input data. It is also numerically efficient compared to other UQ implementations. The relationship between the number of random variables and number of simulation is linear (only 21 simulations for ten input random variables are required). It is shown in this paper that SAMBA's algorithm can propagate a high number of input distributions through a set of nonlinear analytic test functions. Doing this, the code needs a very small number of simulations and preserve a 5% error margin. SAMBA's flexibility to handle different forms of input distributions and a high number of input variables is shown on a low-pressure turbine (LPT) blade-based on H2 profile. The relative importance of manufacturing errors in different location of the blade is analyzed.

LQD-RKHS-based distribution-to-distribution regression methodology for restoring the probability distributions of missing SHM data