Structural joints influence the design strength, material requirement of a structure. Structural joints experience damping dissipation due to friction damping or hysteresis damping. Damping is often used for reducing the vibrations in a structure. However, large amount of energy dissipation leads to deterioration of the material used for constructing the joint. Hence it is important to identify the system parameters like stiffness, viscous damping, friction force as well as the hysteretic restoring force that cause the energy dissipation in the structure.
For identifying the uncertain system parameters like stiffness, viscous damping and magnitude of friction force, the SINDy algorithm is extended by using stick and slip temporal constraints. This is done by segregating the data of external forcing and response of SDoF system, applying the existing SINDy algorithm and applying the sticking and slipping conditions in the time domain. The proposed Extended SINDy approach estimates the system parameters more accurately compared to the existing SINDy algorithm.
For studying the hysteresis in the structural joints, a pinned column base-plate was considered in an elastic region. Further, the Dahl model with different slope parameter for each branch of moment-rotation hysteresis is employed. The correct values of parameters are estimated using the Bayesian Optimization technique. This procedure yields a functional form representing a resisting hysteretic moment-rotation behaviour in a structural joint with good accuracy.

Offshore nautical radar systems are exposed to harsh environmental conditions during their service life. The structure is subjected in return to multiple random vibrations. Assessing the impact that these vibrations have on the structural integrity of the radar is necessary for creating a concrete operation and maintenance plan, that can enable the avoidance of structural damage due to fatigue. The development of a sensor network for the long term monitoring of such vibrations can provide an insight into the structural behaviour of a structure and predict possible damage scenarios.

The objective of this thesis is to determine how to instrument an offshore nautical radar in order to monitor vibrations in operating conditions. To achieve such a feat, short term vibration measurements (for non-opearating conditions) are performed on a 5.7-meter-long radar antenna that is supported by truss tower (or mast) with a height of 20 meters, located in Rijkswaterstaat’s test site in Stellendam. The aim of this approach is initially to extract the modal properties of the two structures, examine their interaction, and gather relevant information that can facilitate the determination of what a future sensor network, for the long term monitoring of the antenna, could look like.

For the realization of such measurements two main system identification techniques are used along with a small sensor suite of accelerometers. Experimental Modal Analysis (EMA) is performed on the radar antenna, by approximating a laboratory setting with minimal environmental interference. The system’s dynamic properties are extracted and analyzed critically in order to identify suitable sensor specifications and fitting sensor positioning among others. On the other hand, an Operational Modal Analysis (OMA) is executed on the truss tower in an attempt to see how its structural behaviour may affect the radar antenna’s response and any future monitoring plan.

The results obtained from the aforementioned modal analyses, are employed to propose a long term sensor network for the radar antenna, along with monitoring techniques that can be used to achieve the goal of damage detection. What becomes also evident from the current approach, is the need of a better equipped sensor suite and a cross-validating Finite Element model, in order to achieve more robust results.

To reduce the environmental impact or cost of a civil engineering structure their designs are optimized. A promising method to optimize are iterative optimization algorithms. If both the design calculations and the iterative optimization algorithm are automated, an optimized design solution can be found within a feasible timeframe. To be able to automate the design calculations they need to be fully parameterizable. In this context it becomes interesting to research whether yet unparameterizable calculation processes can be made parameterizable. One of these processes is the determination of the locations in which the fatigue resistance has to be determined in a steel orthotropic bridge deck. This location is the location where the first fatigue crack is expected. Therefore, Antea Group requested if a study could be performed with the objective to answer the following research question:
How can the determination of the location of the first fatigue crack in the deck, at a stiffener to deck plate weld toe, be parameterized?
To answer the research question, the (in the Netherlands active) regulations are studied. Based on the regulations the process of determining fatigue damage of a point in the bridge can be understood. As well as the reason why, this process is too computational demanding and complex to be able to be applied to all points in all welds.
In response to this an alternative method is proposed. This method reduces the complexity and the computational budget that is needed, by using 1D elements instead of the currently prescribed 2D elements. To determine if this method can be used it was decided to apply it on a case study. The bridge which served as the case study was the Goereese bridge. The alternative method was applied to determine the expected distribution of fatigue damages in all welds in the case study. Based on this obtained distribution a limited number of interesting locations in the deck could be identified. At these points to regulatory required method was used to obtain results which can be compared with the alternative method.
It is concluded that the predicted location of the first fatigue crack of both methods is directly next to each other. However, the distribution of the remaining points suggest by the alternative method does not agree with the obtained results of the regulatory method. Remarkable enough, both these methods predict a location which is counter intuitive to the structural engineers participating in the research.
Therefore, the following general recommendations are given:- Research if the regulatory method, to determine the location of the first fatigue crack, can be simplified. - Research the cause(s) of the differences between the regulatory method and the alternative method. - Increase the awareness of structural engineers regarding their intuition on the location of the first fatigue crack.

Given the desire to construct more structures using sustainable building materials, demand for wood and other bio-based building materials has risen dramatically over the decade. While timber itself is a carbon-neutral material and can sometimes even be carbon-negative, reusing wooden structural members made that have been in service for several years can widen the approach to structural design using wood. In the extensive network of rivers and canal systems that the Netherlands has, the banks are often covered with sheet-pile walls and a majority of these are made of timber. Tropical hardwood, especially Azobé (Lophira alata), due to its high biological resistance to decay, is used to make these sheet-piles. However, when exposed to the groundwater table for a long period of time, the wood undergoes decay due to bacteria destroying the cellulose slowly, while the lignin remains constant, and over decades the large cellulose molecules are replaced by water making the walls weaker.

In this study, the characteristic mechanical properties of Azobé sheet-piles that have been in service for 57 years have been found, so that they can be assigned with an appropriate strength class and reused. Destructive, quasi-destructive and non-destructive tests have been performed on the sheet-pile boards to understand the correlation between them and to also ascertain to what level tests on timber specimens that do not affect their usability can be reliable. Since the knowledge of how visual grading can be performed on used, decayed structural timber, especially hardwood specimens is limited, a methodology has been developed in line with NEN-EN 14081-1:2019 along with the definition of a visual decay score. The results from the RPD tests are quantified in terms of the resistographic measure value to identify whether, in tropical hardwood, is there any effect in the drilling direction and whether this value can qualitatively or quantitatively describe the actual mechanical strength of the sheet-pile boards. The stress-wave tests and the four-point bending test are used to calculate the strength and stiffness of the boards, which determine the characteristic values, that are also based on their wet density (at which the tests are conducted). The results obtained are also analyzed for occurring patterns in terms of the location of the board in the sheet-pile wall (top or bottom), testing configuration (E-side or W-side-up) and variation in thickness within the boards due to decay.

The bending test performed on the boards is modelled numerically in multiple iterations with curved-shell, layered-shell and 3D brick elements also varying the respective material models to find which one of them is best suitable to model bending of timber. The load-sharing mechanism observed when grouping multiple timber specimens has been simulated numerically to predict the characteristic load-sharing factor of the sheet-pile wall system.

Nautical radar systems are subjected to random vibrations during their service life, which may lead to the degradation of the materials and a possible fatigue failure. Assessing the impact of these vibrations to the structural integrity of the radar is crucial for drafting appropriate maintenance plans and therefore, the development of a new tool is required, which will be capable of evaluating the fatigue lifetime of the radar system.

This thesis examines a 5.7-meter-long radar antenna, supported by a lattice tower with a height of 20 meters, located in Rijkswaterstaat’s test environment in Stellendam. Although the lattice structure and the radar system are coupled, they are treated separately in this study. Firstly, a Finite Element Model of the tower is developed in ANSYS, where the radar is represented by an added mass at the top floor. The aim of the model is to identify the vibrations of the structure under the influence of the incoming wind. The stochastic description of the turbulent wind is taken into account in the evaluation of the wind loads and a random vibration analysis is performed, resulting into the response of the structure in the frequency domain.

Furthermore, a second, simplified Finite Element Model of the radar system is built in ANSYS. Time series of the fluctuating wind velocity are generated and the wind load acting on the radar is approximated by the aerodynamic force in the along-wind direction, considering also the rotation of the radar antenna. In addition, the previously obtained response of the lattice structure serves as input for the radar model, representing the vibrations induced to the radar due to the motion of the structure below. The output of the model is the occurring stress response, which is subsequently used to assess the fatigue damage of the radar antenna.

The results show that the development of stresses at the bottom surface of the antenna mainly occurs at its central area. Given the assumptions used throughout the thesis, the motion of the lattice tower is found to be the governing loading condition for the resulting stresses and the magnitude of the motion significantly influences the fatigue damage of the antenna. Finally, the fatigue lifetime appears to be very sensitive to the construction materials used for the radar system. These results should be verified by future measurements in order to improve the suggested models.

This research investigates how the current friction design standard should be improved, specifically for monopile sea fastening with polymers. Literature and results from tests performed previously to this research are investigated in order to obtain a complete overview of the factors that should be considered in the design standard. Additional tests are carried out on factors for which literature and previous test exercises are inconclusive. Friction test methods are compared to determine the best method for testing monopile sea fastening friction. The total test variability is analyzed to determine why safety measures are required. The validity of these measures is studied with a large set of test results. Finally, modelling as an alternative for testing is investigated.

In recent years, there has been a lot of focus on system identification using vibration data instead of building mathematical models based on domain knowledge. The Sparse Identification of Nonlinear Dynamical System (SINDy) is a method that has been a great tool to identify the nonlinear dynamics. Therefore, in this report, the nonlinear systems such as duffing oscillator, Single Degree of Freedom (SDoF) with friction are identified using SINDy algorithm. An impact of noise in the measurement data is studied briefly. The components used in the process of identification are smooth finite difference-based differentiator, Sequential Threshold Least Squares (STLSq) optimizer and custom candidate
library. Further, a comparison is made between the numerical models and the models obtained from PySINDy. The Root Mean Squares Errors are calculated for all the cases. It is seen that SINDy is capable of identifying these nonlinearities with good accuracy.

The dynamic behavior of structural components can largely change in the presence of damages. Understanding this behavior is of particular importance for critical engineering systems, and in particular bridges. Damage identification methods forms a key objective in structural health monitoring of bridges so many researches have been conducted in this area. In this thesis, damage identification techniques on beam bridges under moving vehicle loads will be presented in order to produce useful conclusions about the assessment of existing bridges by investigating various numerical applications of different scenarios.
The first objective of this thesis is to derive the analytical expressions needed to be able to predict the dynamic response of many different cases of bridges so that as many real scenarios as possible can be treated. This means that these expressions would be used to investigate damaged beam bridges that can be modelled as an assembly of beams with any number of different material properties, any type of interface or boundary conditions and any number of cracks. For this reason an approach to analyze the bridge as an assembly of n piecewise homogeneous damaged Euler-Bernoulli beams jointed at their edges, will be presented, using the generalized functions to obtain a single expression of the solution which depends on the 4 integration constants associated with the boundary conditions. The closed-form expressions of these 4 constants will be provided. Furthermore, in the presence of internal or externals springs, translational or rotational, additional constants representing the discontinuities have to be taken into account and are computed by considering one additional condition for each discontinuity. The feasibility of this approach and the corresponding analytical formulations is shown with two numerical applications that include all the different capabilities mentioned. Moreover, the implementation of these expressions in a deterministic approach for damage localization is presented, mainly as another example of the many possibilities of the use of analytical formulations instead of other approaches and as an introduction of the so called Inverse Problem with deterministic and probabilistic methods.
The second objective concerns the optimization of damage identification on bridges by comparing different quantities that are evaluated while measuring the response of the bridge (direct monitoring) and the response of the moving vehicle when it passes along the bridge (indirect monitoring). First, the governing equations for the dynamic response of these models are derived, considering the crack(s) as a rotational spring, the bridge as an Euler-Bernoulli beam (or multiple with different properties) and the moving vehicle as a spring-mass system. In this manner, the dynamic response of the bridge is calculated (modal characteristics and displacement) as well as the one of the moving oscillator (displacement and acceleration) and the reaction force acting on the surface of the beam from the moving vehicles. Numerical applications with different beam properties and different number of cracks are performed, using MATLAB for the analytical expressions and SAP2000 for the finite element model, to derive the optimal quantity to be used for damage identification. Lastly, the results are validated by considering and comparing an alternative way of modelling crack, namely as a zone with reduced rigidity, for the same numerical examples, leading to the same conclusions about the crack(s) identification.
Last but not least, the third objective of this thesis is to be able deal not only with the widely used time-invariant damages, namely the always-open crack model, but also with time-variant damages and in this case with the switching crack model. To achieve this, the analytical expressions for the closed-form solutions of the mode shapes derived for the always-open crack are modified to be able to tackle the switching crack model by introducing a Boolean switching crack array which identifies open cracks, modelled as rotational springs. These new expressions would still be able to be used for any number of Euler-Bernoulli beams, any type of interface or boundary conditions and any number of switching cracks. Then, the governing equations for the dynamic response of this model are derived, considering the moving vehicles as moving masses in order to validate the approach with numerical examples existing in the literature and then by introducing its new capabilities. Further, as the computational strategy has been validated, a comparison between time-variant and time-invariant damages is performed concerning crack identification, so that the reader would recognize the importance of understanding the dynamic behavior of different ways of modelling damage in complicate engineering systems like bridges.

Structural elements under compression can fail due to instability. Such type of failure may present itself as flexural buckling, which is the sudden change of configuration of one state to another at a critical compressive load. Actual structure characteristics, such as cracks, real joints, sudden changes of flexural stiffness, bracing, and actual boundary conditions, make current analytical buckling methods inefficient. For this reason, most structures are evaluated using Finite Element (FE) software based on the Finite Element Method (FEM). However, such a numerical method may have a high computational cost when parametric studies need to be performed. The motivation for this thesis was to develop an analytical alternative for the buckling analysis of columns and beam-columns.
The thesis analyses jointed Euler-Bernoulli columns and beam-columns with N discontinuities due to step-changes of flexural stiffness, and influence of open edge cracks, real joints, bracing, and actual support conditions. The approach considered utilizes the Heaviside function to obtain a single piecewise expression for the deflection, slope, moment, and shear of columns and beam-columns. The use of the Heaviside function, along with proposed closed-form expressions, reduce the number of unknown integration constants to only four.
Main findings are listed as following: (i) Linear buckling analysis of a column only depends on solving the determinant of the 4x4 matrix of unknown coefficients, obtained by imposing four boundary conditions. (ii) Solving the four unknown constants of integration results in performing a geometrical non-linear static analysis of the beam-column, which perfectly agrees with results obtained through FE software. (iii) Closed-form expressions reduce the number of unknown constants of integrations to only four, regardless of the number of sections composing a column or beam-column.
Concluding remarks and recommendations include: (i) Closed-form expressions accurately provide linear buckling loads for columns and geometrical non-linear expressions for beam-columns. (ii) Equations solved algebraically can be stored and used for future analysis, saving the computation time of rerunning the analysis for specific columns or beam-columns. Having the equations expressed algebraically allows for the ease of performing parametric analysis and exploring the performance of new designs. (iii) Computational cost (time needed for the computer to obtain the results) may depend on the mathematical software used for the calculations. Other software may result in having lower computational time for the same calculations.

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.

Damen is designing more and more slender hull forms, which leads to a small dock block contact area, and therefore a high load on the block bed. Dry docking is achieved by using multiple blocks located along the longitudinal length of the ship. Dock blocks are constituted by several layers, normally three or more. The configuration of the block bed (concrete in combination with hard­ and softwood) creates the support of the vessel with non­linear behaviour. This study focuses on a prediction of the blockload in the dry dock, taking into account non­linear material behaviour of the timber layers. Nowadays, the approach to predict the dock block load makes the assumption of linear elastic behaviour of the timber layers. The loads produced can cause a non­linear behaviour of each block, which might lead to an over­stress failure of one or more blocks. The assumption of linear elastic behaviour possibly results in wrong load distributions, which eventually leads to a redistribution of the loads on the other blocks. In turn this can force other block failures and ultimately this produces damages of the hull forms. The consequences of a poor dry docking analysis are potentially catastrophic. A docking failure can lead to extensive ship and dock damage, disruption of docking schedules, and loss of the ship to active duty until repairs can be made. Two set of models are conducted to predict the load on a dock block and evaluate the influence of the non­linear behaviour. The Timoshenko beam theory with multiple springs is used to calculate the load on every single dock block location. The load on every particular location is used in the model for a single dock block formed by elastically connected beams. A double Winkler foundation system represents the interaction of the stacked block layers and dictates the non­linear behaviour. Non­linear material properties are captured by the secant modulus of the top layer. A test campaign pointed out that for each layer of nominal identical specimens a large variability in material properties is noticed. Material properties found in the literature were different from those obtained during experiments. Moisture content has a significant influence on linear and non­linear effect, with the Young’s modulus and yield point being shifted to lower values. The variability in material behaviour and moisture content must be considered when predicting the block load. Moisture content variability lead to changing block bed load distributions. Underestimation of the moisture content can lead to large differences in the single dock block analysis. With the good matching in the validation work, this research confirms the reliability of a double Winkler system to prescribe non­linear material behaviour of a single dock block. Although the analysis of a single dock block matches results obtained from finite element models, further research is still needed. The model of a Timoshenko beam on spring supports gives reasonable results, but underestimates the load in case of local increased stiffness caused by a transverse bulkhead. Optimization on this particular section is needed to get more realistic results.