Probabilistic Robustness Analysis with Aerospace Applications

This thesis develops theoretical and computational methods for the robustness analysis of uncertain systems. The considered systems are linearized and depend rationally on random parameters with an associated probability distribution. The uncertainty is tackled by applying a polynomial chaos expansion (PCE), a series expansion for random variables similar to the well-known Fourier series for periodic time signals. We consider the linear perturbations around a system's operating point, i.e., reference trajectory, both from a probabilistic and worst-case point of view. A chief contribution is the polynomial chaos series expansion of uncertain linear systems in linear fractional representation (LFR). This leads to significant computational benefits when analyzing the probabilistic perturbations around a system's reference trajectory. The series expansion of uncertain interconnections in LFR further delivers important theoretical insights. For instance, it is shown that the PCE of rational parameter-dependent linear systems in LFR is equivalent to applying Gaussian quadrature for numerical integration. We further approximate the worst-case performance of uncertain linear systems with respect to quadratic performance metrics. This is achieved by approximately solving the underlying parametric Riccati differential equation after applying a polynomial chaos series expansion. The utility of the proposed probabilistic robustness analysis is demonstrated on the example of an industry-sized autolanding system for an Airbus A330 aircraft. Mean and standard deviation of the stochastic perturbations are quantified efficiently by applying a PCE to a linearization of the system along the nominal approach trajectory. Random uncertainty in the aerodynamic coefficients and mass parameters are considered, as well as atmospheric turbulence and static wind shear. The approximate worst-case analysis is compared with Monte Carlo simulations of the complete nonlinear model. The methods proposed throughout the thesis rapidly provide analysis results in good agreement with the Monte Carlo benchmark, at reduced computational cost

Energy Retrofit Strategies for Residential Building Envelopes: An Italian Case Study of an Early-50s Building

During the last few years, the issues of energy efficiency and energy saving have dominated the buildings research field. New constructions are based on efficient design and, because of this, the real challenge is to retrofit existing buildings. Italian standards impose thermal transmittance limits for opaque and transparent surfaces, according to the climatic area. In order to understand buildings' energy behavior, an accurate analysis, carried out by employing advanced calculation codes and instrumental diagnosis—provided by the use of heat flow meter, surface temperature probes and thermal imaging camera—is needed. In this paper, a structure built in the 50 s has been analyzed, by means of a measurement campaign, to investigate the building's characteristics and its vulnerability. Finally, some retrofit hypotheses have been evaluated by means of a well-known dynamic code. All investments have to be analyzed under a financial point of view, considering materials and installation costs. For this reason, the payback time has been calculated in order to understand how quickly the energy upgrading can be repaid

Characterization of ammonia-water clusters by broadband rotational spectroscopy

Neon carrier gas at 0.3 MPa of backing pressure is flowed over a room-temperature ammonia hydroxide solution before being expanded into a chirped-pulse Fourier transform microwave (CP-FTMW) spectrometer operating between 2 and 8 GHz. A dense spectrum was observed and the investigation allowed unambiguous assignment of the (NH$_{3}$)$_{2}$(H$_{2}$O)$_{n}$ with n=1,2 and NH$_{3}$(H$_{2}$O)$_{n}$ with n=2,3,4,5,6,8 with a signal to noise of at least 3:1. The structures show a cyclic arrangement for clusters with up four monomer and then move to a 3D arrangement. These clusters are of interest because of the different possibilities for hydrogen bond network related to the isolated water clusters. Calculations indicate that there are several possible low-energy isomers, with different levels of theory identifying different isomers as the global minimum. The evidence for the assignment and a discussion of the derived properties for the species are presented

Chiral analysis of isopulegol by fourier transform molecular rotational spectroscopy

Chiral analysis on molecules with multiple chiral centers can be performed using pulsed-jet Fourier transform rotational spectroscopy. This analysis includes quantitative measurement of diastereomer products and, with the three wave mixing methods developed by Patterson, Schnell, and Doyle (Nature 497, 475-477 (2013)), quantitative determination of the enantiomeric excess of each diastereomer. The high resolution features enable to perform the analysis directly on complex samples without the need for chromatographic separation. Isopulegol has been chosen to show the capabilities of Fourier transform rotational spectroscopy for chiral analysis. Broadband rotational spectroscopy produces spectra with signal-to-noise ratio exceeding 1000:1. The ability to identify low-abundance (0.1-1\%) diastereomers in the sample will be described. Methods to rapidly identify rotational spectra from isotopologues at natural abundance will be shown and the molecular structures obtained from this analysis will be compared to theory. The role that quantum chemistry calculations play in identifying structural minima and estimating their spectroscopic properties to aid spectral analysis will be described. Finally, the implementation of three wave mixing techniques to measure the enantiomeric excess of each diastereomer and determine the absolute configuration of the enantiomer in excess will be described

Large molecule structures by broadband fourier transform molecular rotational spectroscopy

Fourier transform molecular rotational resonance spectroscopy (FT-MRR) using pulsed jet molecular beam sources is a high-resolution spectroscopy technique that can be used for chiral analysis of molecules with multiple chiral centers. The sensitivity of the molecular rotational spectrum pattern to small changes in the three dimensional structure makes it possible to identify diastereomers without prior chemical separation. For larger molecules, there is the additional challenge that different conformations of each diastereomer may be present and these need to be differentiated from the diastereomers in the spectral analysis. Broadband rotational spectra of several larger molecules have been measured using a chirped-pulse FT-MRR spectrometer. Measurements of nootkatone (C$_{15}$H$_{22}$O), cedrol (C$_{15}$H$_{26}$O), ambroxide (C$_{16}$H$_{28}$O) and sclareolide (C$_{16}$H$_{26}$O$_{2}$) are presented. These spectra are measured with high sensitivity (signal-to-noise ratio near 1,000:1) and permit structure determination of the most populated isomers using isotopic analysis of the $^{13}$C and $^{18}$O isotopologues in natural abundance. The accuracy of quantum chemistry calculations to identify diastereomers and conformers and to predict the dipole moment properties needed for three wave mixing measurements is examined

ANALYSIS OF THE ROTATIONAL SPECTRUM OF LARGE DIFLUOROMETHANE CLUSTERS

In the last few years the development of chirp pulsed Fourier transform microwave (CP-FTMW) spectrometers has enables the studies of relatively large rotors and observations of molecular clusters that were difficult to detect previously. In this work we present the study of large oligomers of difluoromethane ((CH$_2$F$_2$)$_n$, with n from 5 to 7) for which experimental measurements were obtained during a collaboration between different research groups (especially at the University of Virginia – USA\footnote{Broadband Fourier transform rotational spectroscopy for structure determination: The water heptamer. C. Perez et al. Chem. Phys. Lett. 571 (2013) 1-15.} and Universidad del País Vasco – Spain\footnote{Structural Studies of Nicotinoids: Cotinine versus Nicotine. I. Uriarte et al. Chem. Eur. J. 23 (2017) 7238 -7244.}). State-of-the-art quantum chemical calculations and structural results for the molecular species will be presented. The challenging decomposition of the spectrum into the individual rotational spectra for each species presented in the jet expansion will be carried out. In particular the approach using AUTOFIT algorithm\footnote{AUTOFIT, an automated fitting tool for broadband rotational spectra, and applications to 1-hexanal. N.A. Seifert et al. J. Mol. Spectrosc. 312 (2015) 13-21.} running on Amazon Web Service (AWS) and High Performance Computing (HPC) systems and its modified version for large molecular system will be presented

PROTON IN A DOUBLE-WELL POTENTIAL AS SEEN FROM MICROWAVE AND CORE LEVEL PHOTOEMISSION SPECTROSCOPY

The extended nature of the proton wave function, the shape of the ground and final state potentials in which the proton is located has been investigated in gaseous acetylacetone and three of its derivatives, benzoylacetone, dibenzoylmethane\footnote{Vitaliy Feyer, Kevin C. Prince, Marcello Coreno, Sonia Melandri, Assimo Maris, Luca Evangelisti, Walther Caminati, Barbara M. Giuliano, Henrik G. Kjaergaard, and Vincenzo Carravetta, J. Phys. Chem. Lett. 9 (2018) 521–526. DOI: 10.1021/acs.jpclett.7b03175} and 3,5-heptanedione by quantum chemical calculations, microwave spectroscopy and core level photoemission study. These molecules show intramolecular hydrogen bonds, in which a proton is located in a double well potential, whose barrier height is different for the four compounds, allowing us to examine the effect of the shape of double well on photoemission and rotational spectra. For all of them, two distinct O 1s core hole peaks are observed, previously assigned to two chemical states of oxygen in the ground state. We provide an alternative assignment by taking full account of the finite temperature of the samples based on quantum chemical calculations and symmetry consideration

Influence of insulating materials on green building rating system results

This paper analyzes the impact of a change in the thermal insulating material on both the energy and environmental performance of a building, evaluated through two different green building assessment methods: Leadership in Energy and Environmental Design (LEED) and Istituto per l'innovazione e Trasparenza degli Appalti e la Compatibilità Ambientale (ITACA). LEED is one of the most qualified rating systems at an international level; it assesses building sustainability thanks to a point-based system where credits are divided into six different categories. One of these is fully related to building materials. The ITACA procedure derives from the international evaluation system Sustainable Building Tool (SBTool), modified according to the Italian context. In the region of Umbria, ITACA certification is composed of 20 technical sheets, which are classified into five macro-areas. The analysis was developed on a residential building located in the central Italy. It was built taking into account the principles of sustainability as far as both structural and technical solutions are concerned. In order to evaluate the influence of thermal insulating material, different configurations of the envelope were considered, replacing the original material (glass wool) with a synthetic one (expanded polystyrene, EPS) and two natural materials (wood fiber and kenaf). The study aims to highlight how the materials characteristics can affect building energy and environmental performance and to point out the different approaches of the analyzed protocols

Energy Management of an Off-Grid Hybrid Power Plant with Multiple Energy Storage Systems

In this paper, an off-grid hybrid power plant with multiple storage systems for an artificial island is designed and two possible strategies for the management of the stored energy are proposed. Renewable power sources (wind/solar technologies) are used as primary power suppliers. A lead-acid battery pack (BAT) and a reversible polymer electrolyte fuel cell are employed to fulfill the power demand and to absorb extra power. The reversible fuel cell allows reducing costs and occupied space and the fuel cell can be fed by the pure hydrogen produced by means of its reversible operation as an electrolyzer. A diesel engine is employed as backup system. While HOMER Pro ® has been employed for a full-factorial-based optimization of the sizes of the renewable sources and the BAT, Matlab/Simulink ® has been later used for simulating the plant operation and compare two possible power management control strategies. For the reversible fuel cell sizing, a sensitivity analysis has been carried out varying stack and hydrogen tank sizes. The final choice for plant configuration and power management control strategy has been made on the basis of a comparative analysis of the results, aimed at minimizing fossil fuel consumption and CO 2 emissions, battery aging rate and at maximizing the power plant overall efficiency. The obtained results demonstrate the possibility of realizing a renewable power plant, able to match the needs of electrical power in a remote area, by achieving a good integration of different energy sources and facing the intermittent nature of renewable power sources, with very low use of fossil fuels

Polynomial Chaos Approximation of the Quadratic Performance of Uncertain Time-Varying Linear Systems

This paper presents a novel approach to robustness analysis based on quadratic performance metrics of uncertain time-varying systems. The considered time-varying systems are assumed to be linear and defined over a finite time horizon. The uncertainties are described in the form of real-valued random variables with a known probability distribution. The quadratic performance problem for this class of systems can be posed as a parametric Riccati differential equation (RDE). A new approach based on polynomial chaos expansion is proposed that can approximately solve the resulting parametric RDE and, thus, provide an approximation of the quadratic performance. Moreover, it is shown that for a zeroth order expansion this approximation is in fact a lower bound to the actual quadratic performance. The effectiveness of the approach is demonstrated on the example of a worst-case performance analysis of a space launcher during its atmospheric ascent