116 research outputs found
Branching Time
No full textThis is the final draft of the SEP entry "Branching time" by me and the great Alberto Zanardo. See external links for the published versio
Branching Time
No full textThis is the final draft of the SEP entry "Branching time" by me and the great Alberto Zanardo. See external links for the published versio
Structural Modification Approaches to Modal Design Optimisation of Vibrating Systems
No full textThis dissertation addresses the problem of assigning the desired dynamic behaviour to vibrating systems, with particular attention on the generality of the approaches proposed. The main focus of this work is in developing structural modification approaches ensuring the feasibility and the optimality of the computed solution. The proposed approaches are suitable for both the design of new mechanical systems, and the performance optimisation of existing ones. Three formulations are proposed: in the first, the original system is modelled by means of mass and stiffness matrices, while in the second the Frequency Response Functions of the original system are employed. The final formulation allows for discrete structural modification, by casting the structural modification problem as a mixed-integer non-linear optimisation problem.
Compared with most of the approaches appearing in literature, one of the strengths of the approaches proposed is the capability to handle different design tasks. Also, the proposed approaches allow the modification of an arbitrary number of parameters (even in the presence of linear interrelated modifications) and of assigned vibration modes (regardless of their magnitude), as well as the possibility of dealing with mass and stiffness matrices with an arbitrary topology. To this purpose, the structural modification problem is formulated as a constrained inverse eigenvalue problem. The problem is constrained in the sense that a wide family of parameter constraints can be included in the formulations adopted in order to incorporate the physical constraints to the system modifications. Moreover, a regularization term biases the solution towards preferable modifications and assures good numerical conditioning. The problem is then solved within the frame of constrained convex optimisation, which ensures that a unique, and hence global, optimal and feasible solution exists and that it can be efficiently computed by means of reliable numerical algorithms.
The effectiveness and the capabilities of the proposed approaches are demonstrated by firstly applying it to theoretical test cases and secondly through experiments on industrial and laboratory test cases. Such test cases involve lumped and distributed parameter modifications, as well as multimode and single mode assignments.In questa Tesi si affronta il problema di assegnare il comportamento dinamico desiderato a sistemi vibranti, e si dedica particolare attenzione alla generalità degli approcci proposti. Questo lavoro si concentra sullo sviluppo di approcci per il calcolo di modifiche strutturali che siano in grado di assicurare la realizzabilità fisica e l’ottimalità della soluzione calcolata. Gli approcci proposti sono adatti sia al progetto di nuovi sistemi meccanici, sia all’ottimizzazione delle performance di quelli esistenti. Vengono proposte tre formulazioni: nella prima il sistema originale é modellato per mezzo di matrici di massa e rigidezza, mentre nella seconda vengono impiegate le funzioni di risposta in frequenza (Frequency Response Functions). La terza formulazione prende in considerazione modifiche strutturali discrete, in quanto il problema delle modifiche strutturali viene formulato come un problema di ottimizzazione non-lineare mista-intera.
In confronto agli approcci presenti in letteratura, uno dei punti di forza degli approcci proposti risiede nella capacità di poter affrontare obiettivi di progetto diversificati tra loro. Degna di nota é la modifica di un numero arbitrario di parametri (anche in presenza di modifiche tra loro linearmente correlate) e di modi di vibrare (a prescindere dalla loro normalizzazione), cosi pure la possibilità di trattare matrici di massa e rigidezza con topologia arbitraria. A tale fine, il problema di modifica strutturale viene formulato come un problema agli autovalori inverso vincolato. Il problema é vincolato nel senso che una ampia famiglia di vincoli sui parametri può essere introdotta nelle formulazioni adottate, per includere nel problema i vincoli fisici sulle modifiche del sistema. Inoltre, un termine di regolarizzazione permette di dirigere la soluzione verso modifiche preferenziali, ed assicura un buon condizionamento numerico. Il problema è risolto all’interno del contesto matematico dell’ottimizzazione convessa vincolata, che assicura l’esistenza di un’unica, e quindi globale, soluzione ottima realizzabile, e che tale soluzione sia calcolabile efficacemente per mezzo di algoritmi numerici consolidati ed affidabili.
L’efficacia degli approcci proposti, e la loro capacità di fornire soluzioni realizzabili è stata dapprima dimostrata applicandoli dapprima su esempi teorici, e successivamente su test case industriali e da laboratorio. Tali test case includono sia modifiche di parametri concentrati che parametri distribuiti, così come l’assegnazione di uno o più modi di vibrare
Modalities in Temporal Logic
No full textIn logics of branching-time, ‘possibility’ can be conceived as ‘existence of a suitable set of histories’ passing through the moment under consideration. A particular limit case of this is the Ockhamist notion of possibility, which is explained as truth at some history. The tree-like representation of time offers other ways of defining possibility as, for instance, truth at any history in some equivalence class modulo undividedness. In general, we can consider representations of time in which, at any moment t, the set of histories passing through t can be decomposed into indistinguishability classes. This yields to a new general notion of possibility including, as particular cases, other notions previously considered
Branching-Time as a relative closeness relation among histories
No full textIn the traditional approaches to branching-time, histories are dened as linearly
ordered and maximal sets of moments. The `geometrical' approach considers
both moments and histories as primitive entities with no set-theoretical and ontological
dependency of the latter on the former. In the a topological approach
the original perspective is inverted: only histories are primitive entities and moments
are dened as sets of histories. Moreover, these particular sets of histories
can be dened also by means of a relative closeness relation among histories
Quantification over Sets of Possible Worlds in Branching-Time Semantics
No full textTemporal logic is one of the many areas in which a possible world semantics
is adopted. Prior's Ockhamist and Peircean semantics for branching-time, though, depart
from the genuine Kripke semantics in that they involve a quanti ̄cation over histories,
which is a second-order quanti ̄cation over sets of possible worlds. In the paper, variants
of the original Prior's semantics will be considered and it will be shown that all of them
can be viewed as ̄rst-order counterparts of the original semantics
Indistinguishability, choices, and logics of agency
No full textThis paper deals with structures in which T is a tree and I is a function assigning each moment a partition of the set of histories passing through it. The function I is called indistinguishability and generalizes the notion of undividedness. Belnap’s choices are particular indistinguishability functions. Structures provide a semantics for a language L with tense and modal operators. The first part of the paper investigates the set-theoretical properties of the set of indistinguishability classes, which has a tree structure. The significant relations between this tree and T are established within a general theory of trees. The aim of second part is testing the expressive power of the language L . The natural environment for this kind of investigations is Belnap’s seeing to it that (stit). It will be proved that the hybrid extension of L (with a simultaneity operator) is suitable for expressing stit concepts in a purely temporal language
Moment/History Duality in Prior's Logics of Branching-Time
No full textThe basic notions in Prior's Ockhamist and Peircean logics of branching-time are the notion of moment and that of history (or Course of events). In the tree semantics, histories are defined as maximal linearly ordered sets of moments. In the geometrical approach, both moments and histories are primitive entities and there is no set theoretical (and ontological) dependency of the latter on the former. In the topological approach, moments can be defined as the elements of a rank 1 base of a non-Archimedean topology on the set of histories. In this paper, it will be shown that the topological approach, and hence the other approaches, can be reconstructed in a framework in which the basic notions are those of history and of relative closeness relation among histories
Logiche Temporali
No full textViene presentata una panoramica, anche in prospettiva storica, della logica temporale
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