TU Delft Repository

In this thesis, we study fractional differential equations with Hilfer derivative operators. Solutions are approximated using a newly developed Bernstein-splines approach and subsequently applied to the Van der Pol oscillator with fractional damping. Fractional derivatives generalize differentiation to the order α ∈ (0,∞), resulting in order α differential operators. The Hilfer-derivative of order α ∈ (0,1) and type β ∈ [0,1] is one of such operators and combines two of the most commonly used operators through parametrization: the Riemmann-Liouville-derivative (β = 0) and Caputo-derivative (β=1). The choice of β results in different kernel behavior of the operator, commonly yielding singular behavior of solutions of initial value problems (IVP's) and boundary value problems (BVP's) for β ∈ [0,1). Based on existing results for IVP's, we develop a new proof for existence and uniqueness of solutions to BVP's for Hilfer-fractional derivatives. To obtain solution approximations numerically for IVP's and BVP's, a Bernstein splines solution approach is developed and implemented, providing accurate convergence results for nonlinear IVP's and BVP's in an efficient vectorized approach. Implementation difficulties for the singular behavior of solutions for β ∈ [0,1) are successfully resolved through time-domain transformation approximation techniques. Finally, the methods are applied to numerically study the behavior of the fractionally damped Van der Pol oscillator, a nonlinear equation of interest in electrical engineering and control theory. We study the approximate limit cycle, of which behavior corresponds with existing analytical results for the Caputo-derivative (β=1). Convergence of solutions can also be obtained for Hilfer type values of β ∈ [0,1), appearing to be of little influence on the long-term limit cycle. Furthermore, when forcing is applied, we observe periodic, quasiperiodic and chaotic behavior.

Integrating hydrogen into energy systems presents challenges involving social dynamics among stakeholders beyond technical considerations. A gap exists in understanding how these dynamics influence the deployment of hydrogen technologies and infrastructure, particularly in infrastructure development and market demand for widespread adoption. In the Netherlands, despite ambitious strategies and investments, comprehensive explanations of social dynamics' impact on integration processes and market development are lacking. This study addresses this gap by analyzing the hydrogen value chain and stakeholder interactions in the Dutch hydrogen sector. A literature review highlights system integration challenges and the need for decentralized coordination and cross-sector collaboration. Using the Dutch energy grid and its hydrogen initiatives as a case study, social network analysis and semi-structured interviews are applied to analyze over 60 hydrogen initiatives involving more than 340 stakeholders. Initiatives are categorized into large-scale centralized and decentralized local types based on scale and stakeholder involvement, allowing targeted analysis of stakeholder interactions in different contexts. Findings reveal that centralized networks may limit innovation due to concentrated influence, while decentralized networks encourage innovation but require better coordination. These insights guide strategic planning and policymaking in hydrogen energy initiatives, aiming to enhance scalability and efficiency of hydrogen technologies for sustainable energy solutions.

The identification of time-varying human operator (HO) dynamics is critical for advancing adaptive support systems in manual control tasks. This study evaluates the performance of Adaptive Model Selection (AMS), a framework extending recursive ARX identification methods, for estimating time-varying HO parameters, particularly effective time delay (τ(t)). Two configurations of AMS were tested: AMS_q, employing the z-domain ARX representation, and AMS_δ, utilizing the delta-domain ARX representation.

A Monte Carlo simulation framework was used to simulate a compensatory manual control task under varying conditions, including remnant noise (P_n) and dynamic transitions in system parameters. Stability and convergence rates of delay estimates were analyzed for different window sizes (W_s). Results show that the correlation between W_s and convergence time was linear and remained unaffected by remnant noise, demonstrating that window size is the primary determinant of responsiveness. Larger Ws improved stability but introduced tracking delays, whereas smaller W_s allowed for faster adaptation to dynamic changes at the cost of increased sensitivity to noise.

The comparative analysis between the configurations revealed a strong dependence of delay estimation accuracy on the precision of the natural frequency estimate of the neuromuscular system (NMS). The natural frequency estimation directly influences HO dynamic response modeling, and inaccuracies in this parameter propagate through the recursive identification process, affecting the reliability of delay estimates.

These findings underscore the critical role of window size and natural frequency estimation in determining the accuracy and stability of effective time delay estimation through AMS. This study provides a foundation for refining AMS to better balance stability and responsiveness in estimating time-varying HO dynamics. Such advancements can facilitate more accurate modeling of time-varying HO behavior, deepen understanding of HO adaptation, and contribute to the advancement of adaptive support systems.

This report examines the long-term comfort of seating supports in Level 3 and Level 4 automated vehicles, addressing the challenges and opportunities of autonomous mobility. It evaluates how the transition from active driving to passive passenger roles necessitates a redefinition of comfort standards. The study assesses comfort and discomfort across four seating configurations at Levels 3 and 4 automations, combining subjective feedback with objective measures such as IMU sensors, skeleton tracking, thermal imaging, and physiological data. Subjective measurements capture participant feedback on comfort and discomfort during extended use of different seating configurations. Questionnaires and interviews examine factors such as fatigue, local postural discomfort, and thermal comfort. Objective findings identify key factors influencing comfort and discomfort, including passenger movement, seat pan angles, headrest adjustability, and backrest shape. Combining subjective and objective measurements, the report provides actionable recommendations to address the identified issues, emphasising design improvements aimed at enhancing user experience in automated vehicle environments.

Geotechnical engineering faces challenges in subsurface characterization due to reliance on sparse site investigations and empirical correlations, which limit the accuracy of soil property estimations. This study addresses this issue by leveraging machine learning (ML) methods to predict cone penetration test (CPT) measurements using data from driven cast in-situ (DCIS) pile installations. A comprehensive dataset, including cone resistance, sleeve friction, and friction ratio measurements, was used to train and evaluate ML models—Random Forest (RF), eXtreme Gradient Boosting (XGB), and TabNet. Among these, XGB trained at a 30 cm depth resolution demonstrated a strong balance of predictive accuracy, efficiency, and granularity, achieving R2 values exceeding 80% for cone resistance predictions even with limited data availability. By improving predictions at unseen locations, the study showcases the feasibility of integrating ML models into geotechnical workflows to enhance real-time decision-making, optimize construction practices, and support the development of digital twins for pile-supported structures.
Interpretability methods, specifically SHAP values, provided insights into feature significance and highlighted the critical roles of depth, spatial coordinates, machine-related features and representative sampling strategies in achieving reliable predictions. These findings demonstrate ML’s potential to align predictive capabilities with engineering principles, bolstering confidence in its adoption for practical applications.