Bayesian system identification has been extensively adopted in Structural Health Monitoring as a way to probabilistically infer unobservable parameters of the physical model of a structure using measurement data. Combining the Bayesian approach with distributed optic fibre sensors can potentially improve the accuracy and reduce the uncertainty in parameter estimation problems, given the large amount of quasi-continuous data produced by this sensing technology; however, its computational cost could be prohibitively high when using conventional methods since Bayesian inference typically involves a large number of samples, each of which entails a physical model evaluation.
The focus of this work is on performing Bayesian system identification for real-world civil engineering structures within an acceptable running time, while using optic fibre measurements with a high spatial resolution. The proposed methodology employs a cheap-to-compute Gaussian process (GP) surrogate that replaces the main bottleneck of the Bayesian workflow for these type of problems: the evaluation of the log-likelihood. The GP surrogate is actively built by sequentially selecting new training points in areas that are expected to highly contribute to the accuracy of the posterior distribution. Once convergence is achieved, the surrogate is used to obtain the parameter estimates via Markov chain Monte Carlo (MCMC) sampling. Additionally, in order to accelerate the Bayesian workflow, cloud-based parallelization is used to perform multiple finite element analyses simultaneously.
A first synthetic case with an inexpensive frame model is used to test the methodology for problems with two and five probabilistic parameters. An encouraging outcome is obtained with the actively learned GP surrogate, with posterior distributions very close to the full MCMC procedure while requiring a number of physical model evaluations orders of magnitude lower. 
After that, a second case study consisting of an existing reinforced concrete bridge with real measurements and a relatively expensive finite element model is investigated. A subset of discrete strain and translation sensors are used to perform an initial parameter estimation that almost exactly resembles the results from previous research on this bridge by Rózsás, et al. (2022), successfully validating the proposed procedure. Then, another parameter estimation is computed using available high resolution optic fibre measurements, after which is shown that the optic fibre provides the best improvements in model predictive capacity among all sensor groups, confirming its potential when combined with Bayesian system identification.
The results of the case studies indicate that the approach presented in this thesis has the capacity to greatly reduce the wall-clock time of Bayesian parameter estimation for real world civil engineering structures with optic fibre measurements, while maintaining a high degree of accuracy. Nevertheless, additional research is required for cases where the statistical parameters governing the measurement and model uncertainty are inferred along with the physical parameters.

Cracks in masonry structures are a cause for concern as they signal a potential lack of functionality and/or aesthetics. It thus becomes important to identify the cause of damage in order to mitigate it and to prevent its occurrence in the future. Similarities in crack patterns may correlate to similarities in the damage cause. Currently, the assessment of similarities in crack patterns and their corresponding damage causes is done by masonry experts and structural engineers. This process is often expensive and subjective. The use of a Convolutional Neural Network (CNN) may offer an alternate robust and dependable means to automate the assessment of masonry crack patterns by processing their images.

The main research goal of this MSc thesis is to answer how accurately can the CNN -- fitted to data generated from finite element models -- estimate masonry crack pattern similarities. To develop a neural network that can perform such an automated assessment of masonry crack patterns with a high degree of accuracy, a large number of crack patterns with similarity ratings given by human experts are required. This data is collected in increasing complexity, first from a statistics-based approach by generating synthetic crack patterns from Markov walks. This is followed by a computational physics-based approach, such as the Finite Element Method (FEM), that generates crack patterns on 2D masonry façades subjected to differential settlements and out-of-plane loads. Finally, real-world data is also collected. This data is used to fit and test a convolutional neural network developed by Kleijn (Kleijn, 2022). Continuing along the previous line of research done at TNO (where 12 crack patterns were chosen and developed using the statistics-based approach), this thesis focuses on developing parametric finite element models of 8 out of these 12 Pattern IDs. Additionally, real-world images are also collected from Gouda in The Netherlands. This data is then used to form crack pattern image pairs that can be assessed for their similarities by 28 raters using three similarity label categories: crack pattern similarity label, damage severity label, and the overall similarity label. Using these labels, the raters assessed 2587 image pairs generated from the statistics-based approach, 500 image pairs from the computational physics-based approach, and 50 image pairs from the combination of images from the statistics-based approach, computational physics-based approach, and the real-world cases.

An inter-rater agreement analysis is performed on the similarity assessments using Krippendorff’s alpha measure. Additionally, the agreement of each rater with a chosen standard rater is studied using Lin’s Concordance Correlation Coefficient (CCC). Using Lin’s CCC, the intra-rater agreement is also assessed for the standard rater to see how consistent a rater is with their own annotations. These labelled image pairs are then used to fit and test the regression neural network to evaluate its accuracy in predicting the similarity labels. The neural network is also fitted to and tested with various combinations of labelled data to study its generalisability.

It is found that in all three sets of data, Krippendorff’s alpha is less than 0.80 for all the labels, which indicates an insufficient agreement among the raters. It is also seen that, in general, agreement among the raters increases with their experience level, i.e. the descending order of agreement within the rater group is: industry experts, PhD students, and MSc students. Studying the Lin’s CCC of each rater’s performance compared to that of the standard rater helps to choose the raters who can be considered as reliable as the standard rater. Additionally, the intra-rater agreement analysis of the chosen standard rater shows that the highest self-consistency (agreement) is achieved for the crack pattern similarity label, followed by the overall similarity label and finally the damage severity label, with corresponding Lin's CCC values of 0.96, 0.86 and 0.72, respectively.

The neural network is tasked to predict the similarity level in each similarity rating for each image pair in the test sample. The ground truth of this neural network is established by averaging the similarity ratings given to each image pair by multiple raters. It is found that the neural network is able to achieve a sufficiently high degree of accuracy when fitted to and tested with all the image pairs generated from the computational physics-based approach. The crack pattern similarity label, the damage severity label, and the overall similarity label achieve an accuracy of 87%, 82%, and 69%, respectively. However, the generalisability experiments on the neural network that consist of predicting the similarity of a type of crack pattern image pair that is not included in the fitting data set, show very poor performance with respect to the prediction accuracy of the similarity labels. When the neural network attempts to predict the similarity of Pattern ID or a façade geometry that it did not see in the fitting procedure, it predicts all three labels with an accuracy that varies from 40% to 50%. Additionally, the neural network is also fitted to images generated from the computational physics-based approach and then tested with a pool of image pairs generated from the statistics-based approach, computational physics-based approach, and real-world images. The average accuracy with which the three similarity labels are predicted is even lower, lying between 25% and 40%.

This MSc thesis concludes that the neural network fitted to data generated from the computational physics-based approach and assessed by all the raters is able to predict the crack pattern similarity label, the damage severity label and the overall similarity label with sufficiently high degrees of accuracy. However, the generalisability experiments on the neural network show very poor results. This indicates that in order to achieve a greater prediction accuracy, the neural network may need to be fitted to a considerably larger sample of crack patterns that covers all of the relevant situations. Furthermore, the substantial inter-rater variability in the labelling of crack pattern image pairs suggests that even an ideal neural network architecture may not be able to overcome the inconsistencies in the fitting data.

Bayesian system identification, including parameter estimation and model selection, is widely used to infer partially known, unobservable parameters of the models of physical systems when measurement data is available. A common assumption in the Bayesian system identification literature is that the discrepancy between model predictions and measurements can be described as independent, identically distributed realizations from a univariate Gaussian distribution. However, the decreasing cost of sensors and monitoring systems leads to more frequent structural measurements in close proximity to each other (e.g. fiber optics and strain gauges). In such cases, dependency in modeling uncertainty could be significant, both in space and time, and the assumption of uncorrelated Gaussian error may lead to inaccurate parameter estimation.

The aim of this thesis is to explore how Bayesian system identification can be feasibly performed using large datasets when spatial and/or temporal dependence might be present and to assess the impact of considering this dependence. A pool of models, each assuming a different correlation structure, is defined and Bayesian inference is performed. In particular, stress measurements obtained on a steel road bridge are used to update the parameters of the corresponding FE model and the parameters of the correlation structure. The results are compared to a reference model where only measurements of the response peaks are used under the assumption of independence. Nested sampling is utilized to compute the evidence under each model and Bayesian model selection is applied. The question of efficiently performing system identification for large datasets (N > 10² for temporal dependencies and N > 10³ for combined spatial and temporal dependencies) is investigated, and a novel approach for efficiently calculating the exact log-likelihood is derived. An approximation based on the Fisher information matrix is used to efficiently calculate the information content of measurements.

It is found that the choice of correlation function can significantly affect the posterior distribution of the model prediction uncertainty. Additionally, it is shown that using large datasets and considering dependence makes it possible to perform system identification for a larger number of parameters compared to the reference model. The results of the case study indicate that using measurements from multiple sensors under combined spatial and temporal dependence and additive model prediction error yields reduced uncertainty in the posterior and up to 29% reduction of the posterior predictive credible interval range compared to the reference case. Furthermore, the efficiency of the proposed likelihood evaluation method is assessed. Using this method, exact calculation of the log-likelihood can be performed for >10⁶ points in under a second in the case of correlation in one dimension. For combined spatial and temporal correlation it is shown to be approximately 900 times faster than naive evaluation for a 64 by 64 grid of observations. The results of the case study indicate that the described approach can be feasibly applied to real-world structures and can potentially improve parameter estimation and reduce prediction uncertainty. These findings suggest that further research into the approach could yield improvements over current methods.

Given its geographical location and history, water defense is of utmost importance for the Netherlands. Structural Health Monitoring (SHM) offers a promising approach for system identification of hydraulic structures in this water defense system. The aim of SHM is to set sensors on structures and use the monitored responses to identify structural parameters of interest. However, many pertaining questions are unanswered concerning realistic hydraulic structures and monitoring systems: What type of sensors (e.g. strain gauge, SAAF, etc.) can and should be used in the monitoring system? How many sensors are needed, where and when to install these sensors? What is the influence of construction stages of structures on system identification? Considering the evaluation of a structure, what is the influence of system identification as well as construction stages on reliability (failure probability) of structures? Considering practical implementation: which computational algorithm is suitable and feasible? How to construct a proper surrogate model of the mechanical model to reduce computational time?
To answer these questions, a single anchored sheet pile wall is studied using a probabilistic approach. The sheet pile wall is modeled using the finite element (FE) method, synthetic data are used and Bayesian approach is adopted to cope with measurement uncertainty and model uncertainty. The information conveyed by sensors is quantified by the Kullback–Leibler (KL) divergence between prior and posterior distributions. Moreover, the correlation in model uncertainty of various structural responses is quantified by comparing a full-scale experiment from the literature and a corresponding calibrated 3D finite element model.
The results show that:
• A combination of different sensor types (in our case they are SAAF and strain gauge) should be used in the monitoring system (e.g. the combination of four different types of sensors outperforms the strain sensors on the sheet pile wall by conveying 40% more information with respect to the former); 
• Even limited number of sensors can convey sufficient information. In our case, 3 sensors placed at proper locations can convey 90% information carried by 6, 8 and 9 sensors considering different responses. They should be installed as early as possible;
• The failure probability computed using posterior from system identification largely decreases compared with that computed using prior (the ratio of prior and posterior failure probabilities can go up to 15¹⁰ in our case); 
• Delay of the start of monitoring during the construction stages decreases the information conveyed by sensors in system identification (the conveyed information can decrease by 50% in our case) and increases the computed failure probability in reliability analysis: the ratio of prior and posterior failure probabilities can be as large as 30¹⁰ ); 
• MultiNest performs well in Bayesian inference in high dimensional problems; 
• Gaussian process regression (GPR) with anisotropic radial basis function (RBF) kernel and white kernel as well as an adaptive infilling criterion is capable of constructing an accurate surrogate model even when it goes to high dimensionality. The error of surrogate model prediction can be explicitly explained.
To my knowledge the work presented in this thesis is the first application of combined system identification and reliability assessment for hydraulic structures, and the first detailed analysis of the effect of sensor installation time on system identification and structural reliability of hydraulic structures.
The findings imply that probabilistic system identification is a promising approach to substantially reduce our uncertainty in modelling hydraulic structures and in turns to increase their calculated safety. The approach has the potential to extend the working life of aging hydraulics structures and save costly strengthening and replacement. The analysis framework can also be applied to other structures in civil engineering.

The rapid development in statistics, information technology, and computational power have en- abled numerous innovative methods to emerge in Structural Health Monitoring (SHM) for structural damage detection, both in practical application and research. The intention of such methods is to use the data obtained from the monitoring system to extract sufficient information to identify damage types that may appear in the structure. However, the following type of questions are mostly unanswered for realistic structural types and monitoring systems: Which responses of the structure should be monitored? Which sensor locations and sensor combinations carry the most information? Among the currently available computational algorithms, which one is the most suit- able one in this context? Hence, this study aims to contribute on this front and provide answers for practical applicability. A comprehensive study of a realistic, prestressed concrete bridge built by the cantilever method - the Lezíria Bridge in Portugal is undertaken to provide insight into these questions.
The engineering challenge is studied in a probabilistic framework where the uncertainty sources are model uncertainty and measurement uncertainty. The Bayesian paradigm is used to handle the uncertainty component and a validated Finite Element (FE) model is applied to capture the mechanical behavior. The influence of the potential damage scenario, severity of damage, sensor type, the combination of sensors, prior knowledge of the structure, and the extent of uncertainty of the FE model and measurements are analyzed in this thesis. The informativeness of the Damage Identification (DI) process is reflected by the information content of its resulting posterior distributions. The information content is quantified using measures based on information entropy and the area of credible regions.
It is demonstrated that selecting different responses to monitor may lead to a significant change in the informativeness of the result. It is also shown that for all analyzed cases using the most informative sensor type provides adequate information that reflects the damage state, while the rest types could only complement very limited information. In addition, the hybrid Markov Chain Monte Carlo(MCMC) seems more efficient and effective to conduct Bayesian inference. The findings provide valuable, quantitative insight into the design of new monitoring systems.