Low Parametric Sensitivity Realizations with relaxed L2-dynamic-range-scaling constraints

This paper presents a new dynamic-range scaling for the implementation of filters/controllers in state-space form. Relaxing the classical L2-scaling constraints by specific fixed-point considerations allows for a higher degree of freedom for the optimal L2-parametric sensitivity problem. However, overflows in the implementation are still prevented. The underlying constrained problem is converted into an unconstrained problem for which a solution can be provided. This leads to realizations which are still scaled but less sensitive

Digital Filters and Signal Processing

Digital filters, together with signal processing, are being employed in the new technologies and information systems, and are implemented in different areas and applications. Digital filters and signal processing are used with no costs and they can be adapted to different cases with great flexibility and reliability. This book presents advanced developments in digital filters and signal process methods covering different cases studies. They present the main essence of the subject, with the principal approaches to the most recent mathematical models that are being employed worldwide

Decomposition Approach to Parametric Nonconvex Regression; Nuclear Resonance Analysis

Parameterized nonconvex regression is a difficult problem for any optimization solver packages, often resulting in approximations and linearizations of the problem in order to be able to arrive a solution, if the problem is even solvable at all. These changes to the initial problem are largely dependent upon having appropriate domain knowledge and still often times result in a sizable gap between the achieved solution and the best true solution. We propose a novel method of decomposing the global problem into small, overlapping windows. Thus, the independent windows are now solvable. Subsequently, we offer a novel, sequential method of parameter cardinality and parameter value agreement in order to stitch the windows back together to arrive at the solution to the initial global problem. While this method is problem agnostic, we demonstrate the successful results of its application to the nuclear data analysis problem of properly characterizing the resonances of the capture cross section for Copper-63. By being able to solve the 100 resonance problem, this method demonstrates it can solve up to the thousands of possible resonances an isotope can have within a single spin group

High angular resolution Sunyaev-Zel'dovich observations of MACS J1423.8+2404 with NIKA: Multiwavelength analysis

The prototype of the NIKA2 camera, NIKA, is an instrument operating at the IRAM 30-m telescope, which can observe simultaneously at 150 and 260GHz. One of the main goals of NIKA2 is to measure the pressure distribution in galaxy clusters at high resolution using the thermal SZ (tSZ) effect. Such observations have already proved to be an excellent probe of cluster pressure distributions even at high redshifts. However, an important fraction of clusters host submm and/or radio point sources, which can significantly affect the reconstructed signal. Here we report on <20" resolution observations at 150 and 260GHz of the cluster MACSJ1424, which hosts both radio and submm point sources. We examine the morphology of the tSZ signal and compare it to other datasets. The NIKA data are combined with Herschel satellite data to study the SED of the submm point source contaminants. We then perform a joint reconstruction of the intracluster medium (ICM) electronic pressure and density by combining NIKA, Planck, XMM-Newton, and Chandra data, focusing on the impact of the radio and submm sources on the reconstructed pressure profile. We find that large-scale pressure distribution is unaffected by the point sources because of the resolved nature of the NIKA observations. The reconstructed pressure in the inner region is slightly higher when the contribution of point sources are removed. We show that it is not possible to set strong constraints on the central pressure distribution without accurately removing these contaminants. The comparison with X-ray only data shows good agreement for the pressure, temperature, and entropy profiles, which all indicate that MACSJ1424 is a dynamically relaxed cool core system. The present observations illustrate the possibility of measuring these quantities with a relatively small integration time, even at high redshift and without X-ray spectroscopy.Comment: 15 pages, 17 figures, submitted to A&

A Formal Approach to Empirical Dynamic Model Optimization and Validation

A framework was developed for the optimization and validation of empirical dynamic models subject to an arbitrary set of validation criteria. The validation requirements imposed upon the model, which may involve several sets of input-output data and arbitrary specifications in time and frequency domains, are used to determine if model predictions are within admissible error limits. The parameters of the empirical model are estimated by finding the parameter realization for which the smallest of the margins of requirement compliance is as large as possible. The uncertainty in the value of this estimate is characterized by studying the set of model parameters yielding predictions that comply with all the requirements. Strategies are presented for bounding this set, studying its dependence on admissible prediction error set by the analyst, and evaluating the sensitivity of the model predictions to parameter variations. This information is instrumental in characterizing uncertainty models used for evaluating the dynamic model at operating conditions differing from those used for its identification and validation. A practical example based on the short period dynamics of the F-16 is used for illustration

Sensitivitätsanalyse und robustes Prozessdesign pharmazeutischer Herstellungsprozesse

The existence of parameter uncertainties(PU) limits model-based process design techniques. It also hinders the modernization of pharmaceutical manufacturing processes, which is necessitated for intensified market competition and Quality by Design (QbD) principles. Thus, in this thesis, proper approaches are proposed for efficient and effective sensitivity analysis and robust design of pharmaceutical processes. Moreover, the point estimate method (PEM) and polynomial chaos expansion (PCE) are further implemented for uncertainty propagation and quantification (UQ) in the proposed approaches. Global sensitivity analysis (GSA) provides quantitative measures on the influence of PU on process outputs over the entire parameter domain. Two GSA techniques are presented in detail and computed with the PCE. The results from case studies show that GSA is able to quantify the heterogeneity of the information in PU and model structure and parameter dependencies affects significantly the final GSA result as well as output variation. Frameworks for robust process design are introduced to alleviate the adverse effect of PU on process performance. The first robust design framework is developed based on the PEM. The proposed approach has high computational efficiency and is able to take parameter dependencies into account. Then, a novel approach, in which the Gaussian mixture distribution (GMD) concept is combined with PEM, is proposed to handle non-Gaussian distribution. The resulting GMD-PEM concept provides a better trade-off between process efficiency and probability of constraint violations than other approaches. The second robust design framework is based on the iterative back-off strategy and PCE. It provides designs with the desired robustness, while the associated computational expense is independent from the optimization problem. The decoupling of optimization and UQ provides the possibility of implementing robust process design to more complex pharmaceutical manufacturing processes with large number of PU. In this thesis, the case studies include unit operations for (bio)chemical synthesis, separation (crystallization) and formulation (freeze-drying), which cover the complete production chain of pharmaceutical manufacturing. Results from the case studies reveal the significant impact of PU on process design. Also they show the efficiency and effectiveness of the proposed frameworks regarding process performance and robustness in the context of QbD.Die pharmazeutische Industrie muss sowohl den gestiegenen Wettbewerbsdruck standhalten als auch die von Regulierungsbehörden geforderte QbD-Initiative (Quality by Design) umsetzen. Modellgestützte Verfahren können einen signifikanten Beitrag leisten, aber Parameterunsicherheiten (PU) erschweren jedoch eine zuverlässige modellgestützte Prozessauslegung. Das Ziel dieser Arbeit ist daher die Erforschung von effizienten Approaches zur Sensitivitätsanalyse und robusten Prozessdesign der pharmazeutische Industrie. Methoden, Point Estimate Method (PEM) und Polynomial Chaos Expansion (PCE), wurde implementiert, um effizient Unsicherheitenquantifizierung (UQ) zu erlauben. Der globalen Sensitivitätsanalyse (GSA) ist eine systematische Quantifizierung von Parameterschwankungen auf die Simulationsergebnisse. Zwei GSA Techniken werden im Detail vorgestellt und an Beispielen demonstriert. Die Ergebnisse zeigen sowohl den Mehrwert der GSA im Kontext des robusten Prozessdesigns als auch die Relevanz zur korrekten Berücksichtigung von Parameterkorrelationen bei der GSA. Um den schädlichen Einfluss von PU auf die modellgestützte Prozessauslegung zusätzlich zu minimieren, wurden weitere Konzepte aus der robusten Optimierung untersucht. Zunächst wurde das erste Konzept basierend auf der PEM entwickelt. Das erste Konzept zeigt einen deutlich reduzierte Rechenaufwand und kann auch die Parameterkorrelationen entsprechend in der robusten Prozessauslegung berücksichtigen. In einem zweiten Schritt wurde ein neuer Ansatz, der die Gauß-Mischverteilung mit der PEM kombiniert, hierzu für nicht normalverteilte PU erfolgreich implementiert. Weiterhin wurde eine iterative Back-off-Strategie erforscht, die auch die PU entsprechend berücksichtigt aber leichte Rechenaufwand zeigt. Durch die Entkoppelung von UQ und Optimierung können wesentlich komplexere pharmazeutische Herstellungsprozesse mit einer hohen Anzahl an PU implementiert werden. Die in dieser Arbeit untersuchten verfahrenstechnische Grundoperationen decken somit einen Großteil der gesamten Produktionskette der pharmazeutischen Herstellung ab. Die Ergebnisse der untersuchten Beispiele zeigen deutlich den Einfluss von PU auf das modellgestützte Prozessdesign auf. Mithilfe der vorgeschlagenen Approaches können die PU effektiv und effizient bei einer optimalen Balance von Rechenaufwand und der geforderten Zuverlässigkeit ganz im QbD-Sinne berücksichtigt werden

Analysis & Synthesis of Distributed Control Systems with Sparse Interconnection Topologies

This dissertation is about control, identification, and analysis of systems with sparse interconnection topologies. We address two main research objectives relating to sparsity in control systems and networks. The first problem is optimal sparse controller synthesis, and the second one is the identification of sparse network. The first part of this dissertation starts with the chapter focusing on developing theoretical frameworks for the synthesis of optimal sparse output feedback controllers under pre-specified structural constraints. This is achieved by establishing a balance between the stability of the controller and the systems quadratic performance. Our approach is mainly based on converting the problem into rank constrained optimizations.We then propose a new approach in the syntheses of sparse controllers by em- ploying the concept of Hp approximations. Considering the trade-off between the controller sparsity and the performance deterioration due to the sparsification pro- cess, we propose solving methodologies in order to obtain robust sparse controllers when the system is subject to parametric uncertainties.Next, we pivot our attention to a less-studied notion of sparsity, namely row sparsity, in our optimal controller design. Combining the concepts from the majorization theory and our proposed rank constrained formulation, we propose an exact reformulation of the optimal state feedback controllers with strict row sparsity constraint, which can be sub-optimally solved by our proposed iterative optimization techniques. The second part of this dissertation focuses on developing a theoretical framework and algorithms to derive linear ordinary differential equation models of gene regulatory networks using literature curated data and micro-array data. We propose several algorithms to derive stable sparse network matrices. A thorough comparison of our algorithms with the existing methods are also presented by applying them to both synthetic and experimental data-sets

The Payload for Ultrahigh Energy Observations (PUEO): a white paper

The Payload for Ultrahigh Energy Observations (PUEO) long-duration balloon experiment is designed to have world-leading sensitivity to ultrahigh-energy neutrinos at energies above 1 EeV. Probing this energy region is essential for understanding the extreme-energy universe at all distance scales. PUEO leverages experience from and supersedes the successful Antarctic Impulsive Transient Antenna (ANITA) program, with an improved design that drastically improves sensitivity by more than an order of magnitude at energies below 30 EeV. PUEO will either make the first significant detection of or set the best limits on ultrahigh-energy neutrino fluxes