Probabilistic approaches in civil engineering: generation of random fields and structural identification with genetic algorithms

The inherent stochastic character of most of the physical quantities involved in engineering models has led to an always increasing interest for probabilistic analysis. Many approaches to stochastic analysis have been proposed. However, it is widely acknowledged that the only universal method available to solve accurately any kind of stochastic mechanics problem is Monte Carlo Simulation. One of the key parts in the implementation of this technique is the accurate and efficient generation of samples of the random processes and fields involved in the problem at hand. In the present thesis an original method for the simulation of homogeneous, multi-dimensional, multi-variate, non-Gaussian random fields is proposed. The algorithm has proved to be very accurate in matching both the target spectrum and the marginal probability. The computational efficiency and robustness are very good too, even when dealing with strongly non-Gaussian distributions. What is more, the resulting samples posses all the relevant, welldefined and desired properties of “translation fields”, including crossing rates and distributions of extremes. The topic of the second part of the thesis lies in the field of non-destructive parametric structural identification. Its objective is to evaluate the mechanical characteristics of constituent bars in existing truss structures, using static loads and strain measurements. In the cases of missing data and of damages that interest only a small portion of the bar, Genetic Algorithm have proved to be an effective tool to solve the problem.

Reasoning with incomplete and imprecise preferences

Preferences are present in many real life situations but it is often difficult to quantify them giving a precise value. Sometimes preference values may be missing because of privacy reasons or because they are expensive to obtain or to produce. In some other situations the user of an automated system may have a vague idea of whats he wants. In this thesis we considered the general formalism of soft constraints, where preferences play a crucial role and we extended such a framework to handle both incomplete and imprecise preferences. In particular we provided new theoretical frameworks to handle such kinds of preferences. By admitting missing or imprecise preferences, solving a soft constraint problem becomes a different task. In fact, the new goal is to find solutions which are the best ones independently of the precise value the each preference may have. With this in mind we defined two notions of optimality: the possibly optimal solutions and the necessary optimal solutions, which are optimal no matter we assign a precise value to a missing or imprecise preference. We provided several algorithms, bases on both systematic and local search approaches, to find such kind of solutions. Moreover, we also studied the impact of our techniques also in a specific class of problems (the stable marriage problems) where imprecision and incompleteness have a specific meaning and up to now have been tackled with different techniques. In the context of the classical stable marriage problem we developed a fair method to randomly generate stable marriages of a given problem instance. Furthermore, we adapted our techniques to solve stable marriage problems with ties and incomplete lists, which are known to be NP-hard, obtaining good results both in terms of size of the returned marriage and in terms of steps need to find a solution.

Probabilistic tomography of atmospheric parameters from GNSS data

The objective of the work is the evaluation of the potential capabilities of navigation satellite signals to retrieve basic atmospheric parameters. A capillary study have been performed on the assumptions more or less explicitly contained in the common processing steps of navigation signals. A probabilistic procedure has been designed for measuring vertical discretised profiles of pressure, temperature and water vapour and their associated errors. Numerical experiments on a synthetic dataset have been performed with the main objective of quantifying the information that could be gained from such approach, using entropy and relative entropy as testing parameters. A simulator of phase delay and bending of a GNSS signal travelling across the atmosphere has been developed to this aim.

Implicit computational complexity and probabilistic classes

The thesis applies the ICC tecniques to the probabilistic polinomial complexity classes in order to get an implicit characterization of them. The main contribution lays on the implicit characterization of PP (which stands for Probabilistic Polynomial Time) class, showing a syntactical characterisation of PP and a static complexity analyser able to recognise if an imperative program computes in Probabilistic Polynomial Time. The thesis is divided in two parts. The first part focuses on solving the problem by creating a prototype of functional language (a probabilistic variation of lambda calculus with bounded recursion) that is sound and complete respect to Probabilistic Prolynomial Time. The second part, instead, reverses the problem and develops a feasible way to verify if a program, written with a prototype of imperative programming language, is running in Probabilistic polynomial time or not. This thesis would characterise itself as one of the first step for Implicit Computational Complexity over probabilistic classes. There are still open hard problem to investigate and try to solve. There are a lot of theoretical aspects strongly connected with these topics and I expect that in the future there will be wide attention to ICC and probabilistic classes.

Monitoring Complex Processes to Verify System Conformance: A Declarative Rule-Based Framework

Over the last 60 years, computers and software have favoured incredible advancements in every field. Nowadays, however, these systems are so complicated that it is difficult – if not challenging – to understand whether they meet some requirement or are able to show some desired behaviour or property. This dissertation introduces a Just-In-Time (JIT) a posteriori approach to perform the conformance check to identify any deviation from the desired behaviour as soon as possible, and possibly apply some corrections. The declarative framework that implements our approach – entirely developed on the promising open source forward-chaining Production Rule System (PRS) named Drools – consists of three components: 1. a monitoring module based on a novel, efficient implementation of Event Calculus (EC), 2. a general purpose hybrid reasoning module (the first of its genre) merging temporal, semantic, fuzzy and rule-based reasoning, 3. a logic formalism based on the concept of expectations introducing Event-Condition-Expectation rules (ECE-rules) to assess the global conformance of a system. The framework is also accompanied by an optional module that provides Probabilistic Inductive Logic Programming (PILP). By shifting the conformance check from after execution to just in time, this approach combines the advantages of many a posteriori and a priori methods proposed in literature. Quite remarkably, if the corrective actions are explicitly given, the reactive nature of this methodology allows to reconcile any deviations from the desired behaviour as soon as it is detected. In conclusion, the proposed methodology brings some advancements to solve the problem of the conformance checking, helping to fill the gap between humans and the increasingly complex technology.

Probabilistic Recursion Theory and Implicit Computational Complexity

In this thesis we provide a characterization of probabilistic computation in itself, from a recursion-theoretical perspective, without reducing it to deterministic computation. More specifically, we show that probabilistic computable functions, i.e., those functions which are computed by Probabilistic Turing Machines (PTM), can be characterized by a natural generalization of Kleene's partial recursive functions which includes, among initial functions, one that returns identity or successor with probability 1/2. We then prove the equi-expressivity of the obtained algebra and the class of functions computed by PTMs. In the the second part of the thesis we investigate the relations existing between our recursion-theoretical framework and sub-recursive classes, in the spirit of Implicit Computational Complexity. More precisely, endowing predicative recurrence with a random base function is proved to lead to a characterization of polynomial-time computable probabilistic functions.