Support Vector Machines (SVMs) are widely used in various domains, with their performance heavily dependent on hyperparameter selection. However, hyperparameter tuning is computationally demanding due to the SVM training complexity, which is at best $O(n^2)$, where $n$ represents the number of training samples. To mitigate this challenge, we propose integrating a validation-based early stopping criterion into the Sequential Minimal Optimization (SMO) algorithm to enhance tuning efficiency.

We evaluate this approach within Random Search and Successive Halving frameworks, aiming to reduce tuning runtime while preserving model performance. We introduce a composite score function to facilitate a balanced assessment of accuracy and efficiency. Our empirical analysis reveals that incorporating early stopping into SMO significantly reduces hyperparameter tuning time under RS but provides limited benefits in successive halving, given its inherent efficiency. Additionally, while dataset characteristics influence the effectiveness of early stopping, we found evidence that dimensionality does not. We also observe that frequent early stopping objective assessments introduce computational overhead, which can offset runtime improvements. Reducing assessment frequency alleviates this issue, but it diminishes the effectiveness of early stopping.

Our findings highlight the potential of early stopping in SMO for optimizing SVM hyperparameter tuning, particularly within random search-based approaches. They also identify trade-offs in assessment frequency and dataset-specific factors.

Composite materials are crucial for advancing sustainable engineering practices as they offer high strength-to-weight ratios, making them ideal for applications in aerospace, automotive and civil engineering. Meeting global sustainability goals demands a shift towards efficient materials, resulting in composites becoming increasingly significant. Besides difficulties in producing highly complex composites there are also challenges in computational methods to accurately predict the behavior of structures made from composite materials within a reasonable computational time frame. In most civil engineering practices, the Finite Element Analysis (FEA) is a useful method to derive stress-strain paths. However, these methods often rely on homogenized material assumptions which fail to capture complex microstructural stresses in high-performance composites. A more suitable method to predict the behavior of these materials under complex loading conditions is available using multi-scale modeling techniques. This approach is essential but computationally expensive, especially when high accuracy at the microscale is needed. Surrogate models based on a machine learning framework have been investigated in prior research. These models typically make predictions on homogenized average stress at macroscale rather than the maximum stress at microscale, which identifies as the research gap. The maximum microscopic stress has been recently used as a failure indicator. The main objective of this research is to design a surrogate model, based on the physically recurrent neural network (PRNN) designed in previous research, that can accurately predict the local maximum stress at the microscale in heterogeneous composite materials. Additionally, this research explores how knowledge from existing models that predict average stresses can be leveraged to enhance new models that predict local quantities at the microscale through transfer learning and multi-task learning techniques. Among the three developed models, two models using an encoder-decoder architecture performed poorly because the decoder averages the results instead of being able to find the limits. The decoder was removed in the third model and this yielded promising results. This model maintains high fidelity in stress predictions with lower computational costs because the number of trainable parameters in this model is limited. Transfer learning yielded faster convergence but did overall not improve significantly in terms of error. The decrease in computational time is very limited when transfer learning is applied over direct training as the models used in this thesis are small and do not need extensive datasets or epochs to converge. The multi-task approach achieved very promising results as it enables accurate predictions for average and maximum stresses in a single model. Cross validation showed strong model robustness and flexibility across unseen loading scenarios. Finally, a triple-task model showed that the PRNN is able to act as a modular framework as also the minimum microscopic stress can be accurately predicted without increasing the model and or training set size. The developed surrogate model shows that the architecture of the PRNN developed in previous research can be effectively modified to make predictions on other tasks. It provides a viable tool for simulating composite materials behavior at microscale.

It is well-established that the effect of the soil significantly influences the overall behaviour of structures, particularly in the presence of vibrations. The majority of the developed approaches can be categorised into two groups: the direct approach and the substructure method. The first one is based on detailed modelling of the soil, foundation and structure using FEM and is not commonly used because it is computationally expensive and thus not feasible for standard engineering practice. The second method uses the dynamic stiffness matrix of the substructure to include it in the analysis of the general structure. Due to the impracticality of the first method, various methodologies have been investigated to better address SSI through the dynamic stiffness matrix, also known as impedance functions. They provide an approximate representation of the SSI that facilitates quicker analysis and sufficiently accurate results.

These approximation techniques typically involve intricate systems composed of lumped masses, dashpots, and springs. The characteristics of these elements vary based on soil and foundation types. For instance, a circular plate laying on homogeneous soil can be modelled as a mass, spring, dashpot single-degree-of-freedom system, where the coefficients of the elements represent the SSI of the disc. Similarly, a pile embedded in soil can be modelled with springs on the side that represent the effect of the friction between the structure and the soil. Some of the existing models for these two cases will be studied in this work.

Four mechanical analogues will be computed and compared for the first SSI problem: Lysmer's, Kausel's, and two of Wolf's models. These models define the mass, stiffness, and damping coefficients differently, but yield similar responses. Additionally, the results will be compared to a finite element (FE) model with the same soil and foundation characteristics to assess their applicability. For the second SSI problem, Novak's solution for piles under vertical vibrations will be studied and compared to the response of an FE model. The relevance of these SSI problems lies in the simplicity of reproducing the analogues to use as a reference. They are suitable benchmark problems to evaluate an alternative computational approach that is proposed in this work.

This work's objective is to determine the feasibility of analysing the response of these systems using a hybrid computational approach. This method involves generating responses using an FE model with a range of soil and foundation parameters as a first step. Secondly, these results are input into a Neural Network (NN). The NN is trained to reproduce the response of any system by knowing only the geometric characteristics of the foundation, and the shear modulus, Poisson's ratio, and density of the soil. The network's output is the frequency response function (FRF) of said system, which is subsequently used in an optimisation process. The output of this second process is the values for the system's mass, stiffness, and damping characteristics. Ultimately, these values can be used to construct the dynamic stiffness matrix necessary for solving the soil-structure interaction of a particular structure.

The central question addressed in this research is: What constitutes an efficient data-driven process for translating large soil-foundation datasets into simplified mechanical analogues that provide a reduced and accurate representation of the system? After assessing its applicability, it can be concluded that a hybrid two-step computational approach is an efficient and generic method for solving SSI problems.

This thesis explores the application of a Bayesian approach to hyperparameter optimization in surrogate modeling for geotechnical engineering problems. Surrogate modeling, particularly employing Gaussian Processes and Kriging, has become an essential tool for accelerating complex numerical simulations in geotechnical engineering. Traditional Maximum Likelihood Estimation (MLE) approaches to hyperparameter optimization, although straightforward, often overlook the inherent uncertainties in model hyperparameters, potentially leading to sub-optimal prediction accuracy and poor generalization.

The research presented in this thesis investigates the feasibility and benefits of applying a Bayesian inference approach to the tuning of hyperparameters in surrogate models. This approach allows for a probabilistic treatment of hyperparameters, providing a comprehensive quantification of uncertainty. The Markov Chain Monte Carlo sampling method, specifically the No-U-Turn Sampler, was employed to sample from the posterior distributions of hyperparameters, addressing the challenges posed by their non-Gaussian nature and non-linear relationship with model outputs.

Three case studies of varying complexity from geotechnical engineering practice are examined to compare the Bayesian approach against traditional MLE in terms of hyperparameter determination, prediction accuracy, uncertainty quantification, and computational efficiency. The findings suggest that the Bayesian approach, while computationally more intensive, could potentially offer more accurate predictions in terms of the mean-squared error and provide a deeper understanding of uncertainty, which is crucial for risk-informed decision-making in geotechnical engineering.

The study concludes that Bayesian hyperparameter optimization in surrogate modelling holds significant potential for improving the robustness and reliability of predictions in geotechnical engineering, particularly in applications involving complex dependencies and where a thorough understanding of uncertainty is crucial. Further research is recommended to enhance the computational efficiency of the Bayesian method and to explore its integration with multi-point enrichment strategies for practical engineering applications.

The Hyperloop concept tackles the challenges conventional transport modes face, despite the considerable research gap. This research reduces the gap by focusing on the dynamic response of the periodically supported Hyperloop tube since the Hyperloop greatly exceeds the operational speed of traditional transport modes. Complexity is incorporated to obtain a detailed dynamic response using a finite element method. Progress has been made in incorporating the moving reference frame within the model with recommendations for the numerical stability of the transient analyses. Despite the computational inefficiency of the conventional non-moving reference frame, the model is utilised to conduct a parametric study. The study examines correlations between the stiffness properties of various Hyperloop elements, including the tube, rail, and the interface between the Hyperloop tube and column. These correlations are analyzed based on the system's response at the pod's location and the intersections between the tube segments. Here, the velocity of the pod is of paramount importance. Within the operational velocity range, only one critical velocity is identified, despite the system's infinite number of natural frequencies. The only dynamic amplification, identified as the main critical velocity, can be shifted beyond the operational range by increasing the overall structural stiffness. The shift can be realised due to the positive correlation with the main critical velocity and a negative correlation with the displacement difference at the interface between two tube segments relative to the structural stiffness. Within the research, the soil and pod interactions with the Hyperloop structure are excluded, leading to potential resonance with no risk of instability. The limitation can be addressed by modelling the pod as a mass-spring system and the soil as a two-dimensional medium. The files developed for the finite element models and the parametric study are available on GitHub (https://github.com/dedenner3/MasterThesis_Hyperloop). The files support reproducibility and further exploration of the methods described.

Bridges are instrumented with joints to facilitate free thermal expansion of separate structural elements and prevent development of internal stresses due to differential settlements of the supports. In the past, mostly between the years 1960 and 1970, joints were frequently designed as half-joints, which were easy to construct and automatically maintained a level-running surface on the bridge. Additionally, half-joints can be implemented outside of the supports, which minimises the magnitude of the sagging bending moment caused by traffic loads. However, half-joints quickly started displaying signs of degradation, caused by development of a crack in one of the re-entrant corners in combination with water leakage into the joint. This crack, often buried deep inside the joint, is difficult to inspect, causing the exact state of the half-joints to often remain unknown. Another way of assessing the structural integrity of the half-joints of a bridge, is to monitor it using a structural health monitoring (SHM) system.

In this research, the measurement data of the SHM system on the Naardertrekvaart bridge is used to to evaluate its current state and serve as an early warning system for detecting damage. The SHM system, which has been collecting measurement data since 2022, includes inclinometers, displacement sensors, and temperature sensors. The research consists of an extensive data analysis procedure on two datasets of the SHM system. The first dataset contains two years of measurement data, obtained at a low measurement frequency. The second dataset contains one day of high-frequency measurement data. Next, the structural integrity of the half-joints is inferred from the measurement data using multiple custom-built FEM models in combination with manual calculations. Based on the outcome of this research, recommendations are provided on SHM systems on other half-joint bridges and improvements of the SHM system of the Naardertrekvaart bridge are proposed.

Analysis of the deformation of the bridge revealed a distinct dependence on seasonal temperature changes, presumably caused by hindered thermal contraction of the half-joints. Analysis of high-frequency measurement data showed that traffic loads significantly affect bridge deformation, with a substantial portion of rotations occurring from the support platforms' movement. Differences in rotational behaviour can be observed along the width of the bridge and a stiffness parameter is used to identify potential damage. A significant variation in stiffness can be observed at specific support locations, particularly on the east and west sides of support 6. The study highlights difficulties in using the SHM system to determine the bridge's state, suggesting improvements such as understanding traffic load magnitudes, modelling damage effects, and increasing measurement frequency. These adaptations may require cloud storage solutions. Oscillatory measurement approaches on half-joint bridges can reduce thermal influence sensitivity, mitigate the need for development of a digital twin, and enable broader monitoring with fewer sensors.

Probabilistic numerics methods are a novel approach to quantifying the approximation errors in numerical computations as probabilistic uncertainties. A recent method that was developed is the Bayesian Finite Element Method, which aims to determine the discretization errors along a coarse mesh probabilistically. This work analyzes the use of priors in this method. It is shown that the priors in the right-hand side or forcing term of the partial differential equation are superior to applying them directly in the solution. It is demonstrated that the maximum log-likelihood is not an appropriate estimator of hyperparameters, and as solutions, hyperparameters are optimized using objective functions to capture the discretization error with the posterior deviation. The advantages of non-stationary priors are studied in order to have standard deviations that show the error along the mesh. Additionally, this work examines how the optimal hyperparameters change for mesh refinements and different arrangements of elements in the same problem. Finally, the research delves into determining the approximate number of samples necessary for ensembling covariance matrices and obtaining similar results.

Delamination is a significant failure mode that has been the subject of extensive research in laminated structures. The interface in assembly structures often represents the susceptibly weak link and necessitates careful consideration to guarantee structural stability. It is of utmost significance to understand the behaviour of the delamination phenomenon and precisely evaluate the fracture toughness (resistance to delamination) in composites. Numerous test techniques have been established over time, some of which have been recognized and adopted as standards. The complexity associated with the standardized tests (crack tip monitoring, design configuration) and the limitations in the scope of testing various interface configurations have led to favoring of alternative testing methods in recent years. This thesis primarily aims at exploiting the new potentials of the Mandrel Peel Test method by incorporating the novel “Multi-Mandrel Concept” in determining the fracture toughness of the Thermoplastic Composites. Mandrel Peel test, a modified adaptation of the standard 90-degree peel test, presents as a promising technique for the delamination fracture testing of composites by determining the energy necessary for peeling off a flexible adherend (generally referred to as the peel-arm) from a rigid substrate. In this thesis, the objective was to further the understanding of the Mandrel Peel test, investigate the sensitivity of specimen configuration and testing parameters on different thermoplastic materials systems, and
evaluate the suitability of the Mandrel Peel test method for establishing a relationship between mandrel roller size and mixed mode fracture behavior. Comparative assessments were conducted between the multi-mandrel radii peel test and standardized tests, including DCB, ENF, and MMB tests. Experimental tests, fractography studies, and numerical validation were performed on UD GF/PP and UD CF/PPS composites.

The results show that the average fracture toughness values are slightly higher and more consistent for 2-ply peel arm specimens compared to 1-ply peel arm specimens. This is attributed to the microstructure (matrix and fiber distribution) at the interface and its influence on damage mechanism and fracture propagation behavior. The thickness of the ply also affects delamination propagation behavior and depends on the microstructure, with thicker plies exhibiting non-uniform fiber and matrix distribution. The experimental investigation reveals that the fracture toughness values increase as the mandrel
radius increases for UD GF/PP and UD CF/PPS composites with a 0|0 interface. The fracture toughness of CF/PPS peel specimens with a 0|90 interface shows limited variation
with respect to the mandrel radius. The relationship between mandrel radius and fracture toughness may not follow a linear trend, and it can depend on other factors such as material thickness, interface orientation, and fracture energy at pure loading modes. Comparative assessments between standardized tests and mandrel peel tests show similar trends in fracture toughness values with increasing mode mixture and mandrel roller radii.
Fractography analysis provides valuable insights into the fracture behavior of tested materials, and a correlation is identified between the failure modes observed in mixed-mode bending (MMB) tests and mandrel peel tests. The mandrel peel test enables establishing a relatively straight crack front during the delamination propagation, controlled by the mandrel’s kinematics, resulting in a more uniform distribution of strain energy across the specimen’s width, unlike standard tests.
The findings suggest that utilizing the multi-mandrel concept in assessing mixed-mode fracture toughness offers the possibility of extrapolating pure mode I and II fracture toughness values. This approach presents a viable tool for characterizing the fracture energy of composites with non-zero fiber-oriented interfaces that cannot be effectively assessed using classical tests. The results support the claim that mandrel roller size influences the degree of mode-mixity and suggests considering mandrel size when assessing mode-mixity in fracture phenomena.
Overall, this study provides valuable insights into the sensitivity of specimen configuration and testing parameters, the influence of mandrel roller size on mixed-mode fracture behavior, and the potential benefits of the mandrel peel test for delamination studies. By considering these findings, further advancements can be made in understanding and characterizing fracture properties in hybrid material systems.


Keywords: Delamination, fracture toughness, mixed-mode fracture, DCB, ENF,
MMB, Mandrel Peel test, thermoplastic composite, GF/PP, CF/PPS, Multi-
Mandrel Concept, peel arm, mandrel roller, mode mixity

The two most common Post Consumer Recycled (PCR) plastics, isotactic polypropylene (iPP) and high density polyethylene (HDPE), differ in composition and mechanical behavior when compared to their virgin counterparts. This thesis focuses on understanding and modeling the mechanical performance of these two PCR plastics separately. Within this context, the present work implements three finite strain thermoelasto-viscoplastic constitutive models developed by Johnsen et al., Mirkhalaf et al. and Anand et al. proposed in the literature to predict the behavior of PCR-iPP and PCR-HDPE. The models are compared and further developed to take into account the effects of recycling. All the models depend on the fully implicit return mapping algorithm and associated state update procedures.

Given the complexity of the models, this thesis proposes the use of Bayesian optimization to facilitate the material parameter calibration when provided with the experimental data. A two-step procedure is proposed where first the models are calibrated for yielding, and then for post yielding behavior (strain softening and orientational hardening).

The models are assessed considering different experimental tests, including standardized specimens with different radius of curvature. A simple modification is suggested to capture the strain hardening response at large deformations accurately. This work concludes that the model developed by Mikhalaf et al. is capable of accurately reproducing the experimental results obtained in the validation experiments of PCR-PP where as the modified Anand model is capable of accurately reproducing the experimental results of PCR-PE.

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.

Designing engineering structures relies on accurate numerical simulations to predict the behaviour of a structure before its realization. In the design process, many variables influence the final structure. There is an incentive for optimizing the design based on the desire for cheaper structures and less material usage. Although a wide variety of optimization techniques exist, in practice many structures are not fully optimized and could fulfill their purpose with less material usage. This partly results from optimization techniques generally requiring many simulations for problems with a high number of variables. In creating increasingly complex models, simulating its performance can take up to days or weeks to compute, incentivizing the development of optimization methods that use as little simulations as possible. The goal of this thesis is to provide a method of optimization which significantly reduces the required number of simulations to be performed, aiming to overcome the issue of required computational effort. The optimization problem used in this thesis is the geometric optimization of a fiber reinforced polymer (FRP) microstructure. Each evaluation requires a Finite Element analysis, and many parameters are required to describe the geometry. The goal is to find the maximum stress at perfect plasticity during uniaxial tension, interpreted as a measure of strength. While generally only fibers with a circular cross-section are used, here a morphing parameter is introduced that changes this shape between being circular and square. Furthermore, fibers are allowed to overlap, effectively creating a single fiber with a complex shape. This geometry optimization provides a challenging problem for which different optimization techniques can be compared. The approach taken in attempting to minimize the number of function evaluations is a combination of several machine learning methods. Based on a limited number of initial samples, Bayesian optimization (BO) is applied. In BO a prediction model in the form of a Bayesian Neural Network (BNN) is created and used to inform further sampling. This prediction model provides a mean and a standard deviation in its prediction, both of which are used to find the best point to sample next. The number of initial samples required to create an accurate prediction model increases exponentially with the number of parameters. It is therefore opted to first use a variational autoencoder (VAE) to reduce the number of parameters in which BO is performed, by encoding the parameters in a lower dimensional representation. The variational autoencoder does this without requiring any function evaluation. Results show that when encoding the original parameters using the VAE, the encoded representation is unable to recreate all possible configurations of the original parameters. Furthermore, by transforming to a lower dimensional representation, within this representation the complexity of a function increases compared to the original function, generally leading to many local optima. This complexity proves difficult for the BNN to accurately predict based on a limited number of samples. As a result, BO does optimize the result, but does not reliably find the global optimum of the reduced parameter space. No clear conclusion can be made on the overall performance of the method compared to alternative optimization methods. Recommendations are made for what additional studies could be performed. Further recommendations are given for solving issues limiting the current performance as well as possible additions to the framework. The fiber geometry optimization serves as a good case to compare different optimization methods. It is shown that the geometry has a significant influence on the mechanical performance of a FRP microstructure, and optimization is therefore beneficial. The load case considered is however too specific for the optimized result to have direct practical use. Still, it does demonstrate that the results of an optimization study can be generalized. As the optimization framework is data driven, the optimization objective could easily be extended to study more realistic problems.

This research considers the offline training stage of the Reduced Order Models (ROM), that has been getting attention recently on the endeavor to come up with efficient solutions for the highly complex numerical models. In this work, a simply supported beam problem has been considered, for which a reduced basis creation has been investigated. Reduced basis creation is in utmost importance for the accuracy and reliability of the ROM. Main focus is on the efficient parameter sampling strategies to enrich the reduced basis, which brings forth computational burden. To decrease this burden, a statistical tool Gaussian Processes Regression (GPR) based Bayesian Optimization (BO) is utilized. These tools are used to create a surrogate function of error indicator that is used to select additional training points for ROM. Results of this work show that randomness in the proposed procedure influences parameter sampling but does not have an impact on the overall accuracy. Finally, this work suggests further work on creation of a stopping criteria and finding a method of storing previous information and combining it with current information regarding training points without losing information. With the help of proposed further research topics, this work intends to be used as a foundation for efficient reduced basis construction.