Comparability of Water Infrastructure Resilience of Different Urban Structures

Urban water distribution systems (WDS) ensure the demand-driven supply of a city at multiple ends. Well-being of the population as well as multiple economic sectors depend on its viability and thereby classify it as a critical infrastructure. Therefore, its behavior when exposed to changes is of interest to water suppliers as well as local decision-makers. It can be determined by resilience metrics, assessing the capability to meet and recover its functioning when exposed to disturbances. These disturbances can occur in form of changes in the water availability, the WDS topology, or the water demand pattern. Since networks as WDS are studied by graph theory, also different graph-theoretical resilience metrics were derived. In this work a well-established topology-based resilience metric is adapted and deployed to assess the present resilience of the urban main-line WDS of the German city of Darmstadt as well as of a suburb in the Rhine-Main region. Thereby, the intercomparability of the resilience for the different urban structures were of interest. Based on this analysis the comparability of different urban main-line WDS regarding their resilience is facilitated. Additionally, the conducted approach to allow for the comparability of absolute resilience values of urban structures of varying size can be applied to different resilience metrics as well as technical systems.

Reconstructing Stress Resultants in Wind Turbine Towers Based on Strain Measurements

Support structures of offshore wind turbines are subject to cyclic stresses generated by different time-variant random loadings such as wind, waves, and currents in combination with the excitation by the rotor. In the design phase, the cyclic demand on wind turbine support structure is calculated and forecasted with semi or fully probabilistic engineering models. In some cases, additional cyclic stresses may be induced by construction deviations, unbalanced rotor masses and structural dynamic phenomena such as, for example, the Sommerfeld effect. Both, the significant uncertainties in the design and a validation of absence of unforeseen adverse dynamic phenomena necessitate the employment of measurement systems on the support structures. The quality of the measurements of the cyclic demand on the support structures depends on (a) the precision of the measurement system consisting of sensors, amplifier and data normalization and (b) algorithms for analyzing and converting data to structural health information. This paper presents the probabilistic modelling and analysis of uncertainties in strain measurements performed for the purposes of reconstructing stress resultants in wind turbine towers. It is shown how the uncertainties in the strain measurements affect the uncertainty in the individual components of the reconstructed forces and moments. The analysis identifies the components of the vector of stress resultants that can be reconstructed with sufficient precision.

Investigation on Tool Deflection During Tapping

Tapping is a challenging process at the end of the value chain. Hence, tool failure is associated with rejected components or expensive rework. For modelling the tapping process we choose a mechanistic approach. In the present work, we focus on the tool model, which describes the deflection and inclination of the tool as a result of the radial forces during tapping. Since radial forces always occur during tapping due to the uneven load distribution on the individual teeth, the tool model represents an essential part of the entire closed-loop model. Especially in the entry phase of the tap, when the guidance within the already cut thread is not yet given, radial forces can lead to deflection of the tool. Therefore, the effects of geometric uncertainty in the thread geometry are experimentally investigated, using optical surface measurement to evaluate the position of the thread relative to the pre-drilled bore. Based on the findings, the tool deflection during tapping is mapped using a cylindrical cantilever beam model, which is calibrated using experimental data. The model is then validated and the implementation within an existing model framework is described.

Detection of Model Uncertainty in the Dynamic Linear-Elastic Model of Vibrations in a Truss

Dynamic processes have always been of profound interest for scientists and engineers alike. Often, the mathematical models used to describe and predict time-variant phenomena are uncertain in the sense that governing relations between model parameters, state variables and the time domain are incomplete. In this paper we adopt a recently proposed algorithm for the detection of model uncertainty and apply it to dynamic models. This algorithm combines parameter estimation, optimum experimental design and classical hypothesis testing within a probabilistic frequentist framework. The best setup of an experiment is defined by optimal sensor positions and optimal input configurations which both are the solution of a PDE-constrained optimization problem. The data collected by this optimized experiment then leads to variance-minimal parameter estimates. We develop efficient adjoint-based methods to solve this optimization problem with SQP-type solvers. The crucial test which a model has to pass is conducted over the claimed true values of the model parameters which are estimated from pairwise distinct data sets. For this hypothesis test, we divide the data into k equally-sized parts and follow a k-fold cross-validation procedure. We demonstrate the usefulness of our approach in simulated experiments with a vibrating linear-elastic truss.

Mastering Model Uncertainty by Transfer from Virtual to Real System

Two chassis components were developed at the Technische Universität Darmstadt that are used to isolate the body and to reduce wheel load fluctuation.The frequency responses of the components were identified with a stochastic foot point excitation in a hardware-in-the-loop (HiL) simulation environment at the hydropulser. The modelling of the transmission behaviour influence of the testing machine on the frequency response was approximately represented with a time delay of $$10\,\mathrm {ms}$$ 10 ms in the frequency range up to $$25\,\mathrm {Hz}$$ 25 Hz . This is considered by a Padé approximation. It can be seen that the dynamics of the testing machine have an influence on the wheel load fluctuation and the body acceleration, especially in the natural frequency of the unsprung mass. Therefor, the HiL stability is analysed by mapping the poles of the system in the complex plane, influenced by the time delay and virtual damping.This paper presents the transfer from virtual to real quarter car to quantify the model uncertainty of the component, since the time delay impact does not occur in the real quarter car test rig. The base point excitation directly is provided by the testing machine and not like in the case of the HiL test rig, the compression of the spring damper calculated in the real-time simulation.

Modelling of Resilient Coping Strategies within the Framework of the Resilience Design Methodology for Load-Carrying Systems in Mechanical Engineering

During the development of load-carrying systems uncertainty caused by nescience can be handled applying resilience design. With this systematic approach, in addition to robust design, resilient system properties can be achieved. The resilience design methodology comprises new and extended models and methods. The central aspect of resilient properties is an adaptivity of the system. The procedure for resilience design starts with choosing a ‘general coping strategy’ appropriate for the design task. Based on this, a more detailed ‘system coping strategy’ is developed. This concrete strategy is based on the resilience functions responding, monitoring, anticipating and learning. The coping strategies always contain the function ‘responding’ because it represents the actual adaption of the system. The central, most abstract synthesis model for developing robust and resilient systems is the functional structure model. In this model the system functions and their interconnection by signals, material and energy flows are depicted. However, the realisation of resilience properties requires additional signals and flows. Hitherto, the functional structure for robust systems is static, whereas adaptivity requires flexible control of functions and flows. Therefore, an extension of the functional structure model is proposed to be able to depict the resilient system coping strategy and adaptivity. Within the resilient system the coping strategy is depicted by adaption functions based on the four resilience functions. Via an introduced interface and an enabler-structure the adaption functions are connected to the robust functional structure. The application of the proposed extension is illustrated by the example of a by-wire car brake system.

Robust Topology Optimization of Truss-Like Space Structures

Due to the additional design freedom and manufacturing possibilities of additive manufacturing compared to traditional manufacturing, topology optimization via mathematical optimization gained importance in the initial design of complex high-strength lattice structures. We consider robust topology optimization of truss-like space structures with multiple loading scenarios. A typical dimensioning method is to identify and examine a suspected worst-case scenario using experience and component-specific information and to incorporate a factor of safety to hedge against uncertainty. We present a quantified programming model that allows us to specify expected scenarios without having explicit knowledge about worst-case scenarios, as the resulting optimal structure must withstand all specified scenarios individually. This leads to less human misconduct, higher efficiency and, thus, to cost and time savings in the design process. We present three-dimensional space trusses with minimal volume that are stable for up to 100 loading scenarios. Additionally, the effect of demanding a symmetric structure and explicitly limiting the diameter of truss members in the model is discussed.

Assessment of Model Uncertainty in the Prediction of the Vibroacoustic Behavior of a Rectangular Plate by Means of Bayesian Inference

Designing the vibroacoustic properties of thin-walled structures is of particularly high practical relevance in the design of vehicle structures. The vibroacoustic properties of thin-walled structures, e.g., vehicle bodies, are usually designed using finite element models. Additional development effort, e.g., experimental tests, arises if the quality of the model predictions are limited due to inherent model uncertainty. Model uncertainty of finite element models usually occurs in the modeling process due to simplifications of the geometry or boundary conditions. The latter highly affect the vibroacoustic properties of a thin-walled structure. The stiffness of the boundary condition is often assumed to be infinite or zero in the finite element model, which can lead to a discrepancy between the measured and the calculated vibroacoustic behavior. This paper compares two different boundary condition assumptions for the finite element (FE) model of a simply supported rectangular plate in their capability to predict the vibroacoustic behavior. The two different boundary conditions are of increasing complexity in assuming the stiffness. In a first step, a probabilistic model parameter calibration via Bayesian inference for the boundary conditions related parameters for the two FE models is performed. For this purpose, a test stand for simply supported rectangular plates is set up and the experimental data is obtained by measuring the vibrations of the test specimen by means of scanning laser Doppler vibrometry. In a second step, the model uncertainty of the two finite element models is identified. For this purpose, the prediction error of the vibroacoustic behavior is calculated. The prediction error describes the discrepancy between the experimental and the numerical data. Based on the distribution of the prediction error, which is determined from the results of the probabilistic model calibration, the model uncertainty is assessed and the model, which most adequately predicts the vibroacoustic behavior, is identified.

Surrogate Model-Based Uncertainty Quantification for a Helical Gear Pair

Competitive industrial transmission systems must perform most efficiently with reference to complex requirements and conflicting key performance indicators. This design challenge translates into a high-dimensional multi-objective optimization problem that requires complex algorithms and evaluation of computationally expensive simulations to predict physical system behavior and design robustness. Crucial for the design decision-making process is the characterization, ranking, and quantification of relevant sources of uncertainties. However, due to the strict time limits of product development loops, the overall computational burden of uncertainty quantification (UQ) may even drive state-of-the-art parallel computing resources to their limits. Efficient machine learning (ML) tools and techniques emphasizing high-fidelity simulation data-driven training will play a fundamental role in enabling UQ in the early-stage development phase.This investigation surveys UQ methods with a focus on noise, vibration, and harshness (NVH) characteristics of transmission systems. Quasi-static 3D contact dynamic simulations are performed to evaluate the static transmission error (TE) of meshing gear pairs under different loading and boundary conditions. TE indicates NVH excitation and is typically used as an objective function in the early-stage design process. The limited system size allows large-scale design of experiments (DoE) and enables numerical studies of various UQ sampling and modeling techniques where the design parameters are treated as random variables associated with tolerances from manufacturing and assembly processes. The model accuracy of generalized polynomial chaos expansion (gPC) and Gaussian process regression (GPR) is evaluated and compared. The results of the methods are discussed to conclude efficient and scalable solution procedures for robust design optimization.

Ontology-Based Calculation of Complexity Metrics for Components in CAD Systems

The high complexity of assemblies and components in Computer-Aided Design (CAD) leads to a high effort in the maintenance of the models and increases the time required for adjustments. Metrics indicating the complexity of a CAD Model can help to reduce it by showing the results of changes. This paper describes a concept to calculate metrics aiming to describe the extent of complexity of components in CAD systems based on an ontology-based representation in a first step. The representation is initially generated from CAD models using an automated process. This includes both a boundary representation and the history of the feature-based design. Thus, the design strategy also contributes to measuring the complexity of the component so that the same shape can lead to different complexity metrics. Semantic rules are applied to find patterns of the design and to identify and evaluate various strategies. Different metrics are proposed to indicate the particular influence factors of complexity and a single measure for the overall complexity. Furthermore, the influencing factors can also be used to allow the designer to see how to reduce the complexity of the component or assembly.