Substructuring approache in state space models for dynamic system parameters identification

In the recent decade, the request for structural health monitoring expertise increased exponentially in the United States. The aging issues that most of the transportation structures are experiencing can put in serious jeopardy the economic system of a region as well as of a country. At the same time, the monitoring of structures is a central topic of discussion in Europe, where the preservation of historical buildings has been addressed over the last four centuries. More recently, various concerns arose about security performance of civil structures after tragic events such the 9/11 or the 2011 Japan earthquake: engineers looks for a design able to resist exceptional loadings due to earthquakes, hurricanes and terrorist attacks. After events of such a kind, the assessment of the remaining life of the structure is at least as important as the initial performance design. Consequently, it appears very clear that the introduction of reliable and accessible damage assessment techniques is crucial for the localization of issues and for a correct and immediate rehabilitation. The System Identification is a branch of the more general Control Theory. In Civil Engineering, this field addresses the techniques needed to find mechanical characteristics as the stiffness or the mass starting from the signals captured by sensors. The objective of the Dynamic Structural Identification (DSI) is to define, starting from experimental measurements, the modal fundamental parameters of a generic structure in order to characterize, via a mathematical model, the dynamic behavior. The knowledge of these parameters is helpful in the Model Updating procedure, that permits to define corrected theoretical models through experimental validation. The main aim of this technique is to minimize the differences between the theoretical model results and in situ measurements of dynamic data. Therefore, the new model becomes a very effective control practice when it comes to rehabilitation of structures or damage assessment. The instrumentation of a whole structure is an unfeasible procedure sometimes because of the high cost involved or, sometimes, because it’s not possible to physically reach each point of the structure. Therefore, numerous scholars have been trying to address this problem. In general two are the main involved methods. Since the limited number of sensors, in a first case, it’s possible to gather time histories only for some locations, then to move the instruments to another location and replay the procedure. Otherwise, if the number of sensors is enough and the structure does not present a complicate geometry, it’s usually sufficient to detect only the principal first modes. This two problems are well presented in the works of Balsamo [1] for the application to a simple system and Jun [2] for the analysis of system with a limited number of sensors. Once the system identification has been carried, it is possible to access the actual system characteristics. A frequent practice is to create an updated FEM model and assess whether the structure fulfills or not the requested functions. Once again the objective of this work is to present a general methodology to analyze big structure using a limited number of instrumentation and at the same time, obtaining the most information about an identified structure without recalling methodologies of difficult interpretation. A general framework of the state space identification procedure via OKID/ERA algorithm is developed and implemented in Matlab. Then, some simple examples are proposed to highlight the principal characteristics and advantage of this methodology. A new algebraic manipulation for a prolific use of substructuring results is developed and implemented.

A LES study of a modified Ahmed body geometry

A numerical study using Large Eddy Simulation Coherent Structure Model (LES-CSM), of the flow around a simplified Ahmed body, has been done in this work of thesis. The models used are two salient geometries from the experimental investigation performed in [1], and consist, in particular, in two notch-back body geometries. Six simulation are carried out in total, changing Reynolds number and back-light angle of the model’s rear part. The Reynolds numbers used, based on the height of the models and the free stream velocity, are Re = 10000, Re = 30000 and Re = 50000. The back-light angles of the slanted surface with respect to the horizontal roof surface, that characterizes the vehicle, are taken as B = 31.8◦ and B = 42◦ respectively. The experimental results in [1] have shown that, depending on the parameter B, asymmetric and symmetric averaged flow over the back-light and in the wake for a symmetric geometry can be observed. The aims of the present work of master thesis are principally two. The first aim is to investigate and confirm the influence of the parameter B on the presence of the asymmetry of the averaged flow, and confirm the features described in the experimental results. The second important aspect is to investigate and observe the influence of the second variable, the Reynolds number, in the developing of the asymmetric flow itself. The results have shown the presence of the mentioned asymmetry as well as an influence of the Reynolds number on it.

Geometry of BV quantization and Mathai-Quillen formalism

Il formalismo Mathai-Quillen (MQ) è un metodo per costruire la classe di Thom di un fibrato vettoriale attraverso una forma differenziale di profilo Gaussiano. Lo scopo di questa tesi è quello di formulare una nuova rappresentazione della classe di Thom usando aspetti geometrici della quantizzazione Batalin-Vilkovisky (BV). Nella prima parte del lavoro vengono riassunti i formalismi BV e MQ entrambi nel caso finito dimensionale. Infine sfrutteremo la trasformata di Fourier “odd" considerando la forma MQ come una funzione definita su un opportuno spazio graduato.

Simplicial Complexes From Graphs Toward Graph Persistence

Persistent homology is a branch of computational topology which uses geometry and topology for shape description and analysis. This dissertation is an introductory study to link persistent homology and graph theory, the connection being represented by various methods to build simplicial complexes from a graph. The methods we consider are the complex of cliques, of independent sets, of neighbours, of enclaveless sets and complexes from acyclic subgraphs, each revealing several properties of the underlying graph. Moreover, we apply the core ideas of persistence theory in the new context of graph theory, we define the persistent block number and the persistent edge-block number.

Investigation of novel methodologies for the MCNP geometry preparation: application on the Upper Launcher BSM of ITER

La tesi si divide in due macroargomenti relativi alla preparazione della geometria per modelli MCNP. Il primo è quello degli errori geometrici che vengono generati quando avviene una conversione da formato CAD a CSG e le loro relazioni con il fenomeno delle lost particles. Il passaggio a CSG tramite software è infatti inevitabile per la costruzione di modelli complessi come quelli che vengono usati per rappresentare i componenti di ITER e può generare zone della geometria che non vengono definite in modo corretto. Tali aree causano la perdita di particelle durante la simulazione Monte Carlo, andando ad intaccare l' integrità statistica della soluzione del trasporto. Per questo motivo è molto importante ridurre questo tipo di errori il più possibile, ed in quest'ottica il lavoro svolto è stato quello di trovare metodi standardizzati per identificare tali errori ed infine stimarne le dimensioni. Se la prima parte della tesi è incentrata sui problemi derivanti dalla modellazione CSG, la seconda invece suggerisce un alternativa ad essa, che è l'uso di Mesh non Strutturate (UM), un approccio che sta alla base di CFD e FEM, ma che risulta innovativo nell'ambito di codici Monte Carlo. In particolare le UM sono state applicate ad una porzione dell' Upper Launcher (un componente di ITER) in modo da validare tale metodologia su modelli nucleari di alta complessità. L'approccio CSG tradizionale e quello con UM sono state confrontati in termini di risorse computazionali richieste, velocità, precisione e accuratezza sia a livello di risultati globali che locali. Da ciò emerge che, nonostante esistano ancora alcuni limiti all'applicazione per le UM dovuti in parte anche alla sua novità, vari vantaggi possono essere attribuiti a questo tipo di approccio, tra cui un workflow più lineare, maggiore accuratezza nei risultati locali, e soprattutto la possibilità futura di usare la stessa mesh per diversi tipi di analisi (come quelle termiche o strutturali).

Advanced numerical modeling of masonry vaulted structures based on BIM parametric geometry generation

Vaults are an architectural element which during construction history have been built with a great variety of different materials, shapes, and sizes. The shape of these structural elements was often dependent by the necessity to cover complex spaces, by the needed loading capacity, or by architectural aesthetics. Within this complex scenario masonry patterns generates also different effects on loading capacity, load percolation and stiffness of the structure. These effects were been extensively investigated, both with empirical observations and with modern numerical methods. While most of them focus on analyzing the load bearing capacity or the texture effect on vaulted structures, the aim of this analysis is to investigate on the effects of the variation of a single structural characteristic on the load percolation in the vault. Moreover, an additional purpose of the work is related to the coding of a parametrical model aiming at generating different masonry vaulted structures. Nevertheless, proposed script can generate different typology of vaulted structure basing on some structural characteristics, such as the span and the length to cover and the dimensions of the blocks.

Quantum Riemannian geometry on graphs for gauge field theory

In questo lavoro estendiamo concetti classici della geometria Riemanniana al fine di risolvere le equazioni di Maxwell sul gruppo delle permutazioni $S_3$. Cominciamo dando la strutture algebriche di base e la definizione di calcolo differenziale quantico con le principali proprietà. Generalizziamo poi concetti della geometria Riemanniana, quali la metrica e l'algebra esterna, al caso quantico. Tutto ciò viene poi applicato ai grafi dando la forma esplicita del calcolo differenziale quantico su $\mathbb{K}(V)$, della metrica e Laplaciano del secondo ordine e infine dell'algebra esterna. A questo punto, riscriviamo le equazioni di Maxwell in forma geometrica compatta usando gli operatori e concetti della geometria differenziale su varietà che abbiamo generalizzato in precedenza. In questo modo, considerando l'elettromagnetismo come teoria di gauge, possiamo risolvere le equazioni di Maxwell su gruppi finiti oltre che su varietà differenziabili. In particolare, noi le risolviamo su $S_3$.