Browsing by Author "Sinsbeck, Michael"

Now showing 1 - 2 of 2

Open Access
Characterization of export regimes in concentration-discharge plots via an advanced time-series model and event-based sampling strategies
(2021) González-Nicolás, Ana; Schwientek, Marc; Sinsbeck, Michael; Nowak, Wolfgang
Currently, the export regime of a catchment is often characterized by the relationship between compound concentration and discharge in the catchment outlet or, more specifically, by the re-gression slope in log-concentrations versus log-discharge plots. However, the scattered points in these plots usually do not follow a plain linear regression representation because of different processes (e.g., hysteresis effects). This work proposes a simple stochastic time-series model for simulating compound concentrations in a river based on river discharge. Our model has an ex-plicit transition parameter that can morph the model between chemostatic behavior and che-modynamic behavior. As opposed to the typically used linear regression approach, our model has an additional parameter to account for hysteresis by including correlation over time. We demonstrate the advantages of our model using a high-frequency data series of nitrate concen-trations collected with in situ analyzers in a catchment in Germany. Furthermore, we identify event-based optimal scheduling rules for sampling strategies. Overall, our results show that (i) our model is much more robust for estimating the export regime than the usually used regres-sion approach, and (ii) sampling strategies based on extreme events (including both high and low discharge rates) are key to reducing the prediction uncertainty of the catchment behavior. Thus, the results of this study can help characterize the export regime of a catchment and manage water pollution in rivers at lower monitoring costs.
Open Access
Uncertainty quantification for expensive simulations : optimal surrogate modeling under time constraints
(2017) Sinsbeck, Michael; Nowak, Wolfgang (Prof. Dr.-Ing.)
Motivation and Goal Computer simulations allow us to predict the behavior of real-world systems. Any simulation, however, contains imperfectly adjusted parameters and simplifying assumptions about the processes considered. Therefore, simulation-based predictions can never be expected to be completely accurate and the exact behavior of the system under consideration remains uncertain. The goal of uncertainty quantification (UQ) is to quantify how large the deviation between the real-world behavior of a system and its predicted behavior can possibly be. Such information is valuable for decision making. Computer simulations are often computationally expensive. Each simulation run may take several hours or even days. Therefore, many UQ methods rely on surrogate models. A surrogate model is a function that behaves similarly to the simulation in terms of its input-output relation, but is much faster to evaluate. Most surrogate modeling methods are convergent: with increasing computational effort, the surrogate model converges to the original simulation. In engineering practice, however, results are often to be obtained under time constraints. In these situations, it is not an option to increase the computational effort arbitrarily and so the convergence property loses some of its appeal. For this reason, the key question of this thesis is the following: What is the best possible way of solving UQ problems if the time available is limited? This is a question of optimality rather than convergence. The main idea of this thesis is to construct UQ methods by means of mathematical optimization so that we can make the optimal use of the time available. Contributions This thesis contains four contributions to the goal of UQ under time constraints. 1. A widely used surrogate modeling method in UQ is stochastic collocation, which is based on polynomial chaos expansions and therefore leads to polynomial surrogate models. In the first contribution, I developed an optimal sampling rule specifically designed for the construction of polynomial surrogate models. This sampling rule showed to be more efficient than existing sampling rules because it is stable, flexible and versatile. Existing methods lack at least one of these properties. Stability guarantees that the response surface will not oscillate between the sample points, flexibility allows the modeler to choose the number of function evaluations freely, and versatility means that the method can handle multivariate input distributions with statistical dependence. 2. In the second contribution, I generalized the previous approach and optimized both the sampling rule and the functional form of a surrogate in order to obtain a general optimal surrogate modeling method. I compared three possible approaches to such optimization and the only one that leads to a practical surrogate modeling method requires the modeler to describe the model function by a random field. The optimal surrogate then coincides with the Kriging estimator. 3. I developed a sequential sampling strategy for solving Bayesian inverse problems. Like in the second contribution, the modeler has to describe the model function by a random field. The sequential design strategy selects sample points one at a time in order to minimize the residual error in the solution of the inverse problem. Numerical experiments showed that the sequential design is more efficient than non-sequential methods. 4. Finally, I investigated what impact available measurement data have on the model selection between a reference model and a low-fidelity model. It turned out that, under time constraints, data can favor the use of a low-fidelity model. This is in contrast to model selection without time constraint where the availability of data often favors the use of more complex models. Conclusions From the four contributions, the following overarching conclusions can be drawn. • Under time constraints, the number of possible model evaluations is restricted and the model behavior at unobserved input parameters remains uncertain. This type of uncertainty should be taken into account explicitly. For this reason, random fields as surrogates should be preferred over deterministic response surface functions when working under time constraints. • Optimization is a viable approach to surrogate modeling. Optimal methods are automatically flexible which means that they are easily adaptable to the computing time available. • Under time constraints, all available information about the model function should be used. • Model selection with and without time constraints is entirely different.