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In this paper, we introduce a Gaussian process based moving horizon estimation (MHE) framework. The scheme is based on offline collected data and offline hyperparameter optimization. In particular, compared to standard MHE schemes, we replace the mathematical model of the system by the posterior mean of the Gaussian process. To account for the uncertainty of the learned model, we exploit the posterior variance of the learned Gaussian process in the weighting matrices of the cost function of the proposed MHE scheme. We prove practical robust exponential stability of the resulting estimator using a recently proposed Lyapunov-based proof technique. Finally, the performance of the Gaussian process based MHE scheme is illustrated via a nonlinear system.

This paper introduces a data-based moving horizon estimation (MHE) scheme for linear time-invariant discretetime systems. The scheme solely relies on collected data without employing any system identification step. It is formulated for a robust case in which the online output measurements are corrupted by some non-vanishing measurement noise. Robust global exponential stability of the data-based MHE is proven under standard assumptions. A simulation example illustrates the behavior of the data-based MHE scheme.

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Objective: A mathematical model of the pituitary-thyroid feedback loop is extended to deepen the understanding of the Allan-Herndon-Dudley syndrome (AHDS). Background: The AHDS is characterized by unusual thyroid hormone concentrations and a mutation in the SLC16A2 gene encoding for the monocarboxylate transporter 8 (MCT8). This mutation leads to a loss of thyroid hormone transport activity. One hypothesis to explain the unusual hormone concentrations of AHDS patients is that due to the loss of thyroid hormone transport activity, thyroxine (T4) is partially retained in thyroid cells. Methods: This hypothesis is investigated by extending a mathematical model of the pituitary-thyroid feedback loop to include a model of the net effects of membrane transporters such that the thyroid hormone transport activity can be considered. Two modeling approaches of the membrane transporters are employed: on the one hand a nonlinear approach based on the Michaelis-Menten kinetics and on the other hand its linear approximation. The unknown parameters are identified through a constrained parameter optimization. Results: In dynamic simulations, damaged membrane transporters result in a retention of T4 in thyroid cells and ultimately in the unusual hormone concentrations of AHDS patients. The two different modeling approaches lead to similar results. Conclusion: The results support the hypothesis that a partial retention of T4 in thyroid cells represents one mechanism responsible for the unusual hormone concentrations of AHDS patients. Moreover, our results suggest that the retention of T4 in thyroid cells could be the main reason for the unusual hormone concentrations of AHDS patients.

In this paper, we address the problem of optimal thyroid hormone replacement strategy development for hypothyroid patients. This is challenging for the following reasons. First, it is difficult to determine the correct dosage leading to normalized serum thyroid hormone concentrations of a patient. Second, it remains unclear whether a levothyroxine L-T4) monotherapy or a liothyronine/levothyroxine (L-T3/L-T4) combined therapy is more suitable to treat hypothyroidism. Third, the optimal intake frequency of L-T3/L-T4 is unclear. We address these issues by extending a mathematical model of the pituitary-thyroid feedback loop to be able to consider an oral intake of L-T3/L-T4. A model predictive controller (MPC) is employed to determine optimal dosages with respect to the thyroid hormone concentrations for each type of therapy. The results indicate that the L-T3/L-T4 combined therapy is slightly better (in terms of the achieved hormone concentrations) to treat hypothyroidism than the L-T4 monotherapy. In case of a specific genetic variant, namely genotype CC in polymorphism rs2235544 of gene DIO1, the simulation results suggest that the L-T4 monotherapy is better to treat hypothyroidism. In turn, when genotype AA is considered, the L-T3/L-T4 combined therapy is better to treat hypothyroidism. Furthermore, when genotype CC of polymorphism rs225014 (also referred to as c.274A>G or p.Thr92Ala) in the DIO2 gene is considered, the outcome of the L-T3/L-T4 combined therapy is better in terms of the steady-state hormone concentrations (for a triiodothyronine setpoint at the upper limit of the reference range of healthy individuals). Finally, the results suggest that two daily intakes of L-T3 could be the best trade-off between stable hormone concentrations and inconveniences for the patient.

In this paper, a robust data-driven moving horizon estimation (MHE) scheme for linear time-invariant discrete-time systems is introduced. The scheme solely relies on offline collected data without employing any system identification step. First, robust global exponential stability is proven under standard assumptions for a nominal case where the offline collected data are noise-free but the online measured outputs are corrupted by some non-vanishing measurement noise. Second, practical robust exponential stability is shown for the case where, in addition to the measurement noise in the online phase, the offline collected data are corrupted by some non-vanishing and bounded noise. The behavior of the novel robust data-driven MHE scheme is illustrated by means of a simulation example and compared to a standard model-based MHE, where the model is identified using the same offline data as for the data-driven MHE.

Numerical methods have become the basis for the aerodynamic design of turbomachinery in order to reduce the time for development cycles and associated cost. Designing modern axial compressors requires high confidence in the quality of numerical predictions. In terms of the aerodynamics, the loading of the blades as well as the efficiency targets constantly increase. Losses have to be predicted precisely and the impact of three-dimensional secondary flows, separation, and laminar-turbulent transition must be taken into account. In the present paper, the aerodynamic prediction quality of the state-of-the-art turbomachinery design code TRACE is validated against experimental data from a 2.5-stage axial compressor. The aerodynamic prediction quality is systematically investigated to determine errors and uncertainties regarding the discretization, turbulence and transition models, and importance of considering unsteady effects. Computations are performed for several operating points and the results are validated by means of the compressors integral pressure ratio as well as by means of local pneumatic probe measurements. It is shown that using the empirical γ–ReΘ model improves the prediction quality of the boundary layers and wake flows. Time-resolved computations at the design point of the compressor show that the strength and the losses of a corner separation in both vane rows are reduced to realistic levels when the periodic-unsteady interaction with the upstream wakes is considered. The generally good aerodynamic predictions for both local and integral experimental quantities qualify TRACE for aeroelastic predictions which are planned for the future.