2023
Contribution to book
Open Access
Numerical modelling of historical masonry structures with the finite element code NOSA-ITACA
Girardi M, Padovani C, Pellegrini D, Porcelli M, Robol LThis chapter presents the finite element code NOSA-ITACA for static and modal analyses of masonry structures of architectural interest. NOSA-ITACA adopts the constitutive equation of masonrylike materials, which considers masonry a non-linear elastic material with zero tensile strength. The capability of modelling restoration and consolidation operations makes the code a helpful tool for maintaining historical buildings. In recent years, long-term vibration monitoring turned out to be an effective non-destructive technique to investigate the dynamic behaviour and check the health status of historical buildings. Changes in their dynamic properties, such as natural frequencies, can represent effective damage indicators. The latest NOSA-ITACA developments are oriented towards structural health monitoring. The availability of the experimental modal properties of a structure makes it possible to calibrate its finite element model via model updating procedures. In particular, the unknown structure's characteristics, such as materials' properties and boundary conditions, can be determined by solving a minimum problem whose objective function is expressed as the discrepancy between experimental frequencies and mode shapes and their numerical counterparts. Several case studies are presented to show the main features of NOSA-ITACA and its effectiveness in the conservation of architectural heritage.Source: SPRINGER INDAM SERIES (ONLINE), pp. 133-152
DOI: 10.1007/978-981-99-3679-3_9Metrics:
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2022
Journal article
Open Access
Implicit reward structures for implicit reliability models
Masetti G, Robol L, Chiaradonna S, Di Giandomenico FA new methodology for effective definition and efficient evaluation of dependability-related properties is proposed. The analysis targets the systems composed of a large number of components, each one modeled implicitly through high-level formalisms, such as stochastic Petri nets. Since the component models are implicit, the reward structure that characterizes the dependability properties has to be implicit as well. Therefore, we present a new formalism to specify those reward structures. The focus here is on component models that can be mapped to stochastic automata with one or several absorbing states so that the system model can be mapped to a stochastic automata network with one or several absorbing states. Correspondingly, the new reward structure defined on each component's model is mapped to a reward vector so that the dependability-related properties of the system are expressed through a newly introduced measure defined starting from those reward vectors. A simple, yet representative, case study is adopted to show the feasibility of the method.Source: IEEE TRANSACTIONS ON RELIABILITY
DOI: 10.1109/tr.2022.3190915Metrics:
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2022
Conference article
Open Access
Random bad state estimator to address false data injection in critical infrastructures
Masetti G, Chiaradonna S, Robol L, Di Giandomenico FGiven their crucial role for a society and economy, an essential component of critical infrastructures is the Bad State Estimator (BSE), responsible for detecting malfunctions affecting elements of the physical infrastructure. In the past, the BSE has been conceived to mainly cope with accidental faults, under assumptions characterizing their occurrence. However, evolution of the addressed systems category consisting in pervasiveness of ICT-based control towards increasing smartness, paired with the openness of the operational environment, contributed to expose critical infrastructures to intentional attacks, e.g. exploited through False Data Injection (FDI). In the flow of studies focusing on enhancements of the traditional BSE to account for FDI attacks, this paper proposes a new solution that introduces randomness elements in the diagnosis process, to improve detection abilities and mitigate potentially catastrophic common-mode errors. Differently from existing alternatives, the strength of this new technique is that it does not require any additional components or alternative source of information with respect to the classic BSE. Numerical experiments conducted on two IEEE transmission grid tests, taken as representative use cases, show the applicability and benefits of the new solution.DOI: 10.1109/prdc55274.2022.00024Metrics:
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2021
Journal article
Open Access
Structured backward errors in linearizations
Noferini V., Robol L., Vandebril R.A standard approach to calculate the roots of a univariate polynomial is to compute the eigenvalues of an associated confederate matrix instead, such as, for instance, the companion or comrade matrix. The eigenvalues of the confederate matrix can be computed by Francis's QR algorithm. Unfortunately, even though the QR algorithm is provably backward stable, mapping the errors back to the original polynomial coefficients can still lead to huge errors. However, the latter statement assumes the use of a non-structure-exploiting QR algorithm. In [J. L. Aurentz et al., Fast and backward stable computation of roots of polynomials, SIAM J. Matrix Anal. Appl., 36 (2015), pp. 942-973] it was shown that a structure-exploiting QR algorithm for companion matrices leads to a structured backward error in the companion matrix. The proof relied on decomposing the error into two parts: a part related to the recurrence coefficients of the basis (a monomial basis in that case) and a part linked to the coefficients of the original polynomial. In this article we prove that the analysis can be extended to other classes of comrade matrices. We first provide an alternative backward stability proof in the monomial basis using structured QR algorithms; our new point of view shows more explicitly how a structured, decoupled error in the confederate matrix gets mapped to the associated polynomial coefficients. This insight reveals which properties have to be preserved by a structure-exploiting QR algorithm to end up with a backward stable algorithm. We will show that the previously formulated companion analysis fits into this framework, and we analyze in more detail Jacobi polynomials (comrade matrices) and Chebyshev polynomials (colleague matrices).Source: ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS, vol. 54, pp. 420-442
DOI: 10.1553/etna_vol54s420DOI: 10.48550/arxiv.1912.04157Metrics:
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2020
Journal article
Open Access
Hm-toolbox: Matlab software for hodlr and HSS matrices
Massei S, Robol L, Kressner DMatrices with hierarchical low-rank structure, including HODLR and HSS matrices, constitute a versatile tool to develop fast algorithms for addressing large-scale problems. While existing software packages for such matrices often focus on linear systems, their scope of applications is in fact much wider and includes, for example, matrix functions and eigenvalue problems. In this work, we present a new MATLAB toolbox called hm-toolbox, which encompasses this versatility with a broad set of tools for HODLR and HSS matrices, unmatched by existing software. While mostly based on algorithms that can be found in the literature, our toolbox also contains a few new algorithms as well as novel auxiliary functions. Being entirely based on MATLAB, our implementation does not strive for optimal performance. Nevertheless, it maintains the favorable complexity of hierarchical low-rank matrices and offers, at the same time, a convenient way of prototyping and experimenting with algorithms. A number of applications illustrate the use of the hm-toolbox.Source: SIAM JOURNAL ON SCIENTIFIC COMPUTING (PRINT), vol. 42 (issue 2), pp. C43-C68
DOI: 10.1137/19m1288048DOI: 10.48550/arxiv.1909.07909Project(s): Fast algorithms from low-rank updates
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2020
Conference article
Open Access
FE model updating of masonry towers: modeling and numerical issues
Azzara Rm, Girardi M, Padovani C, Pellegrini D, Robol LThe goal of the paper is to investigate the role of soil-structure interaction in modeling the dy-namic behavior of masonry towers. The study, conducted on the bell tower of the Basilica of San Frediano in Lucca (Italy), is based on both experimental and numerical results. The former were collected during an experimental campaign carried out on the tower using seismometric stations, while the latter have been obtained via the modal analysis and model updating proce-dures implemented in the finite element code NOSA-ITACA. Combining experimental and nu-merical outcomes made it possible to assess the influence of the soil, modeled as a system of elastic springs, on the natural frequencies of the tower. Finite element models of the tower have been calibrated by taking the presence of the adjacent church into account and choosing differ-ent unknown parameters, including the soil stiffness.
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2019
Journal article
Open Access
Quasi-Toeplitz matrix arithmetic: a MATLAB toolbox
Bini Da, Massei S, Robol LQuasi Toeplitz (QT) matrix is a semi-infinite matrix of the kind $A=T(a)+E$ where $T(a)=(a_{j-i})_{i,j\in\mathbb Z^+}$, $E=(e_{i,j})_{i,j\in\mathbb Z^+}$
is compact and the norms $\lVert a\rVert_{\mathcal W} = \sum_{i\in\mathbb Z}|a_i|$ and $\lVert E \rVert_2$ are finite. These properties allow to approximate any QT-matrix, within any given precision, by means of a finite number of parameters. QT-matrices, equipped with the norm $\lVert A \rVert_{\mathcal QT}=\alpha\lVert a\rVert_{\mathcal{W}} \lVert E \rVert_2$, for $\alpha = (1+\sqrt 5)/2$, are a Banach algebra with the standard arithmetic operations. We provide an algorithmic description of these operations on the finite parametrization of QT-matrices, and we develop a MATLAB toolbox implementing them in a transparent way. The toolbox is then extended to perform arithmetic operations on matrices of finite size that have a Toeplitz plus low-rank structure. This enables the development of algorithms for Toeplitz and quasi-Toeplitz matrices whose cost does not necessarily increase with the dimension of the problem. Some examples of applications to computing matrix functions and to solving matrix equations are presented, and confirm the effectiveness of the approach.Source: NUMERICAL ALGORITHMS, vol. 81 (issue 2), pp. 741-769
DOI: 10.1007/s11075-018-0571-6DOI: 10.48550/arxiv.1801.08158Metrics:
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2019
Contribution to book
Open Access
Factoring block Fiedler Companion Matrices
Del Corso G M, Poloni F, Robol L, Vandebril RWhen Fiedler published his "A note on Companion matrices" in 2003 in Linear Algebra and its Applications, he could not have foreseen the significance of this elegant factorization of a companion matrix into essentially two-by-two Gaussian transformations, which we will name \emph{(scalar) elementary Fiedler factors}. Since then, researchers extended these results and studied the various resulting linearizations, the stability of Fiedler companion matrices, factorizations of block companion matrices, Fiedler pencils, and even looked at extensions to non-monomial bases.
In this chapter, we introduce a new way to factor block Fiedler companion matrices into the product of scalar elementary Fiedler factors. We use this theory to prove that, e.g., a block (Fiedler) companion matrix can always be written as the product of several scalar (Fiedler) companion matrices. We demonstrate that this factorization in terms of elementary Fiedler factors can be used to construct new linearizations. Some linearizations have notable properties, such as low band-width, or allow for factoring the coefficient matrices into unitary-plus-low-rank matrices. Moreover, we will provide bounds on the low-rank parts of the resulting unitary-plus-low-rank decomposition.
To present these results in an easy-to-understand manner we rely on the flow-graph representation for Fiedler matrices recently proposed by Del Corso and Poloni in Linear Algebra and its Applications, 2017.Source: SPRINGER INDAM SERIES, pp. 129-155
DOI: 10.1007/978-3-030-04088-8_7Metrics:
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2019
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2019
Journal article
Open Access
Low-rank updates and a divide-and-conquer method for linear matrix equations
Kressner D, Massei S, Robol LLinear matrix equations, such as the Sylvester and Lyapunov equations, play an important role in various applications, including the stability analysis and dimensionality reduction of linear dynamical control systems and the solution of partial differential equations. In this work, we present and analyze a new algorithm, based on tensorized Krylov subspaces, for quickly updating the solution of such a matrix equation when its coefficients undergo low-rank changes. We demonstrate how our algorithm can be utilized to accelerate the Newton method for solving continuous-time algebraic Riccati equations. Our algorithm also forms the basis of a new divide-and-conquer approach for linear matrix equations with coefficients that feature hierarchical low-rank structure, such as hierarchically off-diagonal low-rank structures, hierarchically semiseparable, and banded matrices. Numerical experiments demonstrate the advantages of divide-and-conquer over existing approaches, in terms of computational time and memory consumption.Source: SIAM JOURNAL ON SCIENTIFIC COMPUTING (PRINT), vol. 41 (issue 2)
DOI: 10.1137/17m1161038DOI: 10.48550/arxiv.1712.04349Metrics:
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2019
Journal article
Open Access
Model updating procedure to enhance structural analysis in FE Code NOSA-ITACA
Girardi M, Padovani C, Pellegrini D, Robol LThis paper describes a model updating procedure implemented in NOSA-ITACA, a finite-element (FE) code for the structural analysis of masonry constructions of historical interest. The procedure, aimed at matching experimental frequencies and mode shapes, allows for fine-tuning the calculations of the free parameters in the model. The numerical method is briefly described, and some issues related to its robustness are addressed. The procedure is then applied to a simple case study and two historical structures in Tuscany, the Clock Tower in Lucca and the Maddalena Bridge in Borgo a Mozzano.Source: JOURNAL OF PERFORMANCE OF CONSTRUCTED FACILITIES, vol. 33 (issue 4), pp. 04019041-1-04019041-16
DOI: 10.1061/(asce)cf.1943-5509.0001303Metrics:
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Journal of Performance of Constructed Facilities
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2019
Other
Open Access
ISTI Young Researcher Award "Matteo Dellepiane" - Edition 2019
Barsocchi P, Candela L, Crivello A, Esuli A, Ferrari A, Girardi M, Guidotti R, Lonetti F, Malomo L, Moroni D, Nardini Fm, Pappalardo L, Rinzivillo S, Rossetti G, Robol LThe ISTI Young Researcher Award (YRA) selects yearly the best young staff members working at Institute of Information Science and Technologies (ISTI). This award focuses on quality and quantity of the scientific production. In particular, the award is granted to the best young staff members (less than 35 years old) by assessing their scientific production in the year preceding the award. This report documents the selection procedure and the results of the 2019 YRA edition. From the 2019 edition on the award is named as "Matteo Dellepiane", being dedicated to a bright ISTI researcher who prematurely left us and who contributed a lot to the YRA initiative from its early start.
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