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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 L.
This 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: Mathematical Modeling in Cultural Heritage. MACH 2021, edited by Bretti G., Cavaterra C., Solci M., Spagnuolo M., pp. 133–152, 2023
DOI: 10.1007/978-981-99-3679-3_9
Metrics:
Girardi M., Padovani C., Pellegrini D., Porcelli M., Robol L.
This 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: Mathematical Modeling in Cultural Heritage. MACH 2021, edited by Bretti G., Cavaterra C., Solci M., Spagnuolo M., pp. 133–152, 2023
DOI: 10.1007/978-981-99-3679-3_9
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ISTI Repository 
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2022
Journal article
Open Access
Implicit reward structures for implicit reliability models
Masetti G., Robol L., Chiaradonna S., Di Giandomenico F.
A 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 (2022). doi:10.1109/TR.2022.3190915
DOI: 10.1109/tr.2022.3190915
Metrics:
Masetti G., Robol L., Chiaradonna S., Di Giandomenico F.
A 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 (2022). doi:10.1109/TR.2022.3190915
DOI: 10.1109/tr.2022.3190915
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ISTI Repository | ieeexplore.ieee.org | CNR ExploRA
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 F.
Given 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.Source: PRDC 2022 - 27th IEEE Pacific Rim International Symposium on Dependable Computing, pp. 98–108, Beijing, China, 28/11/2022 - 01/12/2022
DOI: 10.1109/prdc55274.2022.00024
Metrics:
Masetti G., Chiaradonna S., Robol L., Di Giandomenico F.
Given 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.Source: PRDC 2022 - 27th IEEE Pacific Rim International Symposium on Dependable Computing, pp. 98–108, Beijing, China, 28/11/2022 - 01/12/2022
DOI: 10.1109/prdc55274.2022.00024
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ISTI Repository | doi.org | ieeexplore.ieee.org | CNR ExploRA
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 54 (2021): 420–442. doi:10.1553/ETNA_VOL54S420
DOI: 10.1553/etna_vol54s420
DOI: 10.48550/arxiv.1912.04157
Metrics:
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 54 (2021): 420–442. doi:10.1553/ETNA_VOL54S420
DOI: 10.1553/etna_vol54s420
DOI: 10.48550/arxiv.1912.04157
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Aaltodoc Publication Archive | arXiv.org e-Print Archive | Electronic Transactions on Numerical Analysis | Electronic Transactions on Numerical Analysis | epub.oeaw.ac.at | ISTI Repository | doi.org | CNR ExploRA
2020
Journal article
Open Access
Hm-toolbox: Matlab software for hodlr and HSS matrices
Massei S., Robol L., Kressner D.
Matrices 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) 42 (2020): C43–C68. doi:10.1137/19M1288048
DOI: 10.1137/19m1288048
DOI: 10.48550/arxiv.1909.07909
Project(s): Fast algorithms from low-rank updates
Metrics:
Massei S., Robol L., Kressner D.
Matrices 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) 42 (2020): C43–C68. doi:10.1137/19M1288048
DOI: 10.1137/19m1288048
DOI: 10.48550/arxiv.1909.07909
Project(s): Fast algorithms from low-rank updates
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arXiv.org e-Print Archive | SIAM Journal on Scientific Computing | ISTI Repository | SIAM Journal on Scientific Computing | doi.org | epubs.siam.org | Infoscience - EPFL scientific publications | CNR ExploRA
2020
Journal article
Open Access
Computing performability measures in Markov chains by means of matrix functions
Masetti G., Robol L.
We discuss the efficient computation of performance, reliability, and availability measures for Markov chains; these metrics - and the ones obtained by combining them, are often called performability measures. We show that this computational problem can be recasted as the evaluation of a bilinear form induced by appropriate matrix functions, and thus solved by leveraging the fast methods available for this task.Source: Journal of computational and applied mathematics 368 (2020). doi:10.1016/j.cam.2019.112534
DOI: 10.1016/j.cam.2019.112534
DOI: 10.48550/arxiv.1803.06322
Metrics:
Masetti G., Robol L.
We discuss the efficient computation of performance, reliability, and availability measures for Markov chains; these metrics - and the ones obtained by combining them, are often called performability measures. We show that this computational problem can be recasted as the evaluation of a bilinear form induced by appropriate matrix functions, and thus solved by leveraging the fast methods available for this task.Source: Journal of computational and applied mathematics 368 (2020). doi:10.1016/j.cam.2019.112534
DOI: 10.1016/j.cam.2019.112534
DOI: 10.48550/arxiv.1803.06322
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arXiv.org e-Print Archive | Journal of Computational and Applied Mathematics | ISTI Repository | ISTI Repository | Journal of Computational and Applied Mathematics | doi.org | www.sciencedirect.com | CNR ExploRA
2020
Journal article
Open Access
Rational Krylov and ADI iteration for infinite size quasi-Toeplitz matrix equations
Robol L.
We consider a class of linear matrix equations involving semi-infinite matrices which have a quasi-Toeplitz structure. These equations arise in different settings, mostly connected with PDEs or the study of Markov chains such as random walks on bidimensional lattices. We present the theory justifying the existence of the solution in an appropriate Banach algebra which is computationally treatable, and we propose several methods for computing them. We show how to adapt the ADI iteration to this particular infinite dimensional setting, and how to construct rational Krylov methods. Convergence theory is discussed, and numerical experiments validate the proposed approaches.Source: Linear algebra and its applications 604 (2020): 210–235. doi:10.1016/j.laa.2020.06.013
DOI: 10.1016/j.laa.2020.06.013
DOI: 10.48550/arxiv.1907.02753
Metrics:
Robol L.
We consider a class of linear matrix equations involving semi-infinite matrices which have a quasi-Toeplitz structure. These equations arise in different settings, mostly connected with PDEs or the study of Markov chains such as random walks on bidimensional lattices. We present the theory justifying the existence of the solution in an appropriate Banach algebra which is computationally treatable, and we propose several methods for computing them. We show how to adapt the ADI iteration to this particular infinite dimensional setting, and how to construct rational Krylov methods. Convergence theory is discussed, and numerical experiments validate the proposed approaches.Source: Linear algebra and its applications 604 (2020): 210–235. doi:10.1016/j.laa.2020.06.013
DOI: 10.1016/j.laa.2020.06.013
DOI: 10.48550/arxiv.1907.02753
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arXiv.org e-Print Archive | Linear Algebra and its Applications | ISTI Repository | ISTI Repository | Linear Algebra and its Applications | doi.org | www.sciencedirect.com | CNR ExploRA
2020
Conference article
Open Access
FE model updating of masonry towers: modeling and numerical issues
Azzara R. M., Girardi M., Padovani C., Pellegrini D., Robol L.
The 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.Source: EURODYN 2020 XI International Conference on Structural Dynamics, pp. 2285–2298, 25/11/2020
Azzara R. M., Girardi M., Padovani C., Pellegrini D., Robol L.
The 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.Source: EURODYN 2020 XI International Conference on Structural Dynamics, pp. 2285–2298, 25/11/2020
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eurodyn2020.org | ISTI Repository | CNR ExploRA
2020
Journal article
Open Access
A finite element model updating method based on global optimization
Girardi M., Padovani C., Pellegrini D., Robol L.
Finite element model updating of a structure made of linear elastic materials is based on the solution of a minimization problem. The goal is to find some unknown parameters of the finite element model (elastic moduli, mass densities, constraints and boundary conditions) that minimize an objective function which evaluates the discrepancy between experimental and numerical dynamic properties. The objective function depends nonlinearly on the parameters and may have multiple local minimum points. This paper presents a numerical method able to find a global minimum point and assess its reliability. The numerical method has been tested on two simulated examples - a masonry tower and a domed temple - and validated via a generic genetic algorithm and a global sensitivity analysis tool. A real case study monitored under operational conditions has also been addressed, and the structure's experimental modal properties have been used in the model updating procedure to estimate the mechanical properties of its constituent materials.Source: Mechanical systems and signal processing 152 (2020). doi:10.1016/j.ymssp.2020.107372
DOI: 10.1016/j.ymssp.2020.107372
DOI: 10.48550/arxiv.2007.00278
Metrics:
Girardi M., Padovani C., Pellegrini D., Robol L.
Finite element model updating of a structure made of linear elastic materials is based on the solution of a minimization problem. The goal is to find some unknown parameters of the finite element model (elastic moduli, mass densities, constraints and boundary conditions) that minimize an objective function which evaluates the discrepancy between experimental and numerical dynamic properties. The objective function depends nonlinearly on the parameters and may have multiple local minimum points. This paper presents a numerical method able to find a global minimum point and assess its reliability. The numerical method has been tested on two simulated examples - a masonry tower and a domed temple - and validated via a generic genetic algorithm and a global sensitivity analysis tool. A real case study monitored under operational conditions has also been addressed, and the structure's experimental modal properties have been used in the model updating procedure to estimate the mechanical properties of its constituent materials.Source: Mechanical systems and signal processing 152 (2020). doi:10.1016/j.ymssp.2020.107372
DOI: 10.1016/j.ymssp.2020.107372
DOI: 10.48550/arxiv.2007.00278
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arXiv.org e-Print Archive | Mechanical Systems and Signal Processing | ISTI Repository | ISTI Repository | Mechanical Systems and Signal Processing | doi.org | www.sciencedirect.com | CNR ExploRA
2019
Journal article
Open Access
Fast and backward stable computation of the eigenvalues and eigenvectors of matrix polynomials
Aurentz J., Mach T., Robol L., Vandebril R., Watkins D. S.
In the last decade matrix polynomials have been investigated with the primary focus on adequate linearizations and good scaling techniques for computing their eigenvalues and eigenvectors. In this article we propose a new method for computing a factored Schur form of the associated companion pencil. The algorithm has a quadratic cost in the degree of the polynomial and a cubic one in the size of the coefficient matrices. Also the eigenvectors can be computed at the same cost. The algorithm is a variant of Francis's implicitly shifted QR algorithm applied on the companion pencil. A preprocessing unitary equivalence is executed on the matrix polynomial to simultaneously bring the leading matrix coefficient and the constant matrix term to triangular form before forming the companion pencil. The resulting structure allows us to stably factor each matrix of the pencil as a product of k matrices of unitary-plus-rank-one form, admitting cheap and numerically reliable storage. The problem is then solved as a product core chasing eigenvalue problem. A backward error analysis is included, implying normwise backward stability after a proper scaling. Computing the eigenvectors via reordering the Schur form is discussed as well. Numerical experiments illustrate stability and efficiency of the proposed methods.Source: Mathematics of computation (Online) 88 (2019): 313–347. doi:10.1090/mcom/3338
DOI: 10.1090/mcom/3338
DOI: 10.48550/arxiv.1611.10142
Project(s): FUNCOMP
Metrics:
Aurentz J., Mach T., Robol L., Vandebril R., Watkins D. S.
In the last decade matrix polynomials have been investigated with the primary focus on adequate linearizations and good scaling techniques for computing their eigenvalues and eigenvectors. In this article we propose a new method for computing a factored Schur form of the associated companion pencil. The algorithm has a quadratic cost in the degree of the polynomial and a cubic one in the size of the coefficient matrices. Also the eigenvectors can be computed at the same cost. The algorithm is a variant of Francis's implicitly shifted QR algorithm applied on the companion pencil. A preprocessing unitary equivalence is executed on the matrix polynomial to simultaneously bring the leading matrix coefficient and the constant matrix term to triangular form before forming the companion pencil. The resulting structure allows us to stably factor each matrix of the pencil as a product of k matrices of unitary-plus-rank-one form, admitting cheap and numerically reliable storage. The problem is then solved as a product core chasing eigenvalue problem. A backward error analysis is included, implying normwise backward stability after a proper scaling. Computing the eigenvectors via reordering the Schur form is discussed as well. Numerical experiments illustrate stability and efficiency of the proposed methods.Source: Mathematics of computation (Online) 88 (2019): 313–347. doi:10.1090/mcom/3338
DOI: 10.1090/mcom/3338
DOI: 10.48550/arxiv.1611.10142
Project(s): FUNCOMP
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arXiv.org e-Print Archive | Mathematics of Computation | Lirias | ISTI Repository | www.ams.org | doi.org | CNR ExploRA
2019
Journal article
Open Access
Quasi-Toeplitz matrix arithmetic: a MATLAB toolbox
Bini D. A., Massei S., Robol L.
Quasi 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 81 (2019): 741–769. doi:10.1007/s11075-018-0571-6
DOI: 10.1007/s11075-018-0571-6
DOI: 10.48550/arxiv.1801.08158
Metrics:
Bini D. A., Massei S., Robol L.
Quasi 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 81 (2019): 741–769. doi:10.1007/s11075-018-0571-6
DOI: 10.1007/s11075-018-0571-6
DOI: 10.48550/arxiv.1801.08158
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arXiv.org e-Print Archive | Numerical Algorithms | Numerical Algorithms | doi.org | link.springer.com | CNR ExploRA
2019
Contribution to book
Open Access
Factoring block Fiedler Companion Matrices
Del Corso G. M., Poloni F., Robol L., Vandebril R.
When 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: edited by Bini, Dario; Di Benedetto, Fabio; Tyrtyshnikov, Eugene; Van Barel, Marc, pp. 129–155. Berlin: Springer International Publishing AG, 2019
DOI: 10.1007/978-3-030-04088-8_7
Metrics:
Del Corso G. M., Poloni F., Robol L., Vandebril R.
When 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: edited by Bini, Dario; Di Benedetto, Fabio; Tyrtyshnikov, Eugene; Van Barel, Marc, pp. 129–155. Berlin: Springer International Publishing AG, 2019
DOI: 10.1007/978-3-030-04088-8_7
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ISTI Repository | doi.org | link-springer-com-443.webvpn.fjmu.edu.cn | CNR ExploRA
2019
Report
Unknown
MOSCARDO - Tecnologie ICT per il MOnitoraggio Strutturale di Costruzioni Antiche basato su Reti di sensori wireless e DrOni [MMS Lab, Rapporto tecnico n. 2]
Girardi M., Padovani C., Pellegrini D., Robol L.
MOSCARDO - ICT technologies for structural monitoring of age-old constructions based on wireless sensor networks and drones. Description of the activities conducted by the Mechanics of Materials and Structures Laboratory of ISTI-CNR. Project Report n. 2.Source: Project report, MOSCARDO, 2019
Girardi M., Padovani C., Pellegrini D., Robol L.
MOSCARDO - ICT technologies for structural monitoring of age-old constructions based on wireless sensor networks and drones. Description of the activities conducted by the Mechanics of Materials and Structures Laboratory of ISTI-CNR. Project Report n. 2.Source: Project report, MOSCARDO, 2019
See at: CNR ExploRA
2019
Report
Open Access
Tensor methods for the computation of MTTF in large systems of loosely interconnected components
Masetti G., Robol L.
We are concerned with the computation of the mean-time-to-failure(MTTF) for a large system of loosely interconnected components, mod-eled as continuous time Markov chains. In particular, we show that split-ting the local and synchronization transitions of the smaller subsystemsallows to formulate an algorithm for the computation of the MTTF whichis proven to be linearly convergent. Then, we show how to modify themethod to make it quadratically convergent, thus overcoming the difficul-ties for problems with convergent rate close to1.In addition, it is shown that this decoupling of local and synchroniza-tion transitions allows to easily represent all the matrices and vectors in-volved in the method in the tensor-train (TT) format -- and we providenumerical evidence showing that this allows to treat large problems withup to billions of states -- which would otherwise be unfeasible.Source: ISTI Technical reports, 2019
Masetti G., Robol L.
We are concerned with the computation of the mean-time-to-failure(MTTF) for a large system of loosely interconnected components, mod-eled as continuous time Markov chains. In particular, we show that split-ting the local and synchronization transitions of the smaller subsystemsallows to formulate an algorithm for the computation of the MTTF whichis proven to be linearly convergent. Then, we show how to modify themethod to make it quadratically convergent, thus overcoming the difficul-ties for problems with convergent rate close to1.In addition, it is shown that this decoupling of local and synchroniza-tion transitions allows to easily represent all the matrices and vectors in-volved in the method in the tensor-train (TT) format -- and we providenumerical evidence showing that this allows to treat large problems withup to billions of states -- which would otherwise be unfeasible.Source: ISTI Technical reports, 2019
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dcl.isti.cnr.it | ISTI Repository | CNR ExploRA
2019
Journal article
Open Access
Low-rank updates and a divide-and-conquer method for linear matrix equations
Kressner D., Massei S., Robol L.
Linear 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) 41 (2019). doi:10.1137/17M1161038
DOI: 10.1137/17m1161038
DOI: 10.48550/arxiv.1712.04349
Metrics:
Kressner D., Massei S., Robol L.
Linear 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) 41 (2019). doi:10.1137/17M1161038
DOI: 10.1137/17m1161038
DOI: 10.48550/arxiv.1712.04349
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arXiv.org e-Print Archive | SIAM Journal on Scientific Computing | ISTI Repository | SIAM Journal on Scientific Computing | doi.org | epubs.siam.org | Infoscience - EPFL scientific publications | CNR ExploRA
2019
Journal article
Open Access
Model updating procedure to enhance structural analysis in FE Code NOSA-ITACA
Girardi M., Padovani C., Pellegrini D., Robol L.
This 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 33 (2019): 04019041-1–04019041-16. doi:10.1061/(ASCE)CF.1943-5509.0001303
DOI: 10.1061/(asce)cf.1943-5509.0001303
Metrics:
Girardi M., Padovani C., Pellegrini D., Robol L.
This 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 33 (2019): 04019041-1–04019041-16. doi:10.1061/(ASCE)CF.1943-5509.0001303
DOI: 10.1061/(asce)cf.1943-5509.0001303
Metrics:
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Journal of Performance of Constructed Facilities | ISTI Repository | ascelibrary.org | Journal of Performance of Constructed Facilities | CNR ExploRA
2019
Report
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 F. M., Pappalardo L., Rinzivillo S., Rossetti G., Robol L.
The 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.Source: ISTI Technical reports, 2019
Barsocchi P., Candela L., Crivello A., Esuli A., Ferrari A., Girardi M., Guidotti R., Lonetti F., Malomo L., Moroni D., Nardini F. M., Pappalardo L., Rinzivillo S., Rossetti G., Robol L.
The 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.Source: ISTI Technical reports, 2019
See at:
ISTI Repository | CNR ExploRA
2019
Conference article
Open Access
Nonlinear FE model updating for masonry constructions via linear perturbation and modal analysis
Girardi M., Padovani C., Pellegrini D., Robol L.
This paper describes the automated nonlinear model updating procedure for ma-sonry structures implemented in the NOSA-ITACA code. The algorithm, aimed at matchingnumerical and experimental natural frequencies and mode shapes, combines nonlinear staticanalysis, linear perturbation and modal analysis and allows fine-tuning the free parametersof the model. The numerical method is applied to two simple case studies, which prove itseffectiveness.Source: COMPDYN 2019, Crete, Greece, 24-26/06/2019
Girardi M., Padovani C., Pellegrini D., Robol L.
This paper describes the automated nonlinear model updating procedure for ma-sonry structures implemented in the NOSA-ITACA code. The algorithm, aimed at matchingnumerical and experimental natural frequencies and mode shapes, combines nonlinear staticanalysis, linear perturbation and modal analysis and allows fine-tuning the free parametersof the model. The numerical method is applied to two simple case studies, which prove itseffectiveness.Source: COMPDYN 2019, Crete, Greece, 24-26/06/2019
See at:
2019.compdyn.org | ISTI Repository | CNR ExploRA
2019
Contribution to conference
Open Access
FE model updating of the Matilde donjon in Livorno
Azzara R. M., Girardi M., Padovani C., Pellegrini D., Robol L.
The paper describes a preliminary experimental campaign conducted on The Matilde donjon in Livorno (Italy) aimed to characterize its dynamic behaviour, and the corresponding numerical analysis conducted on a FE model created via the NOSA-ITACA code.Source: CIVIL-COMP 2019, Riva del Garda Italy, 16-19/09/2019
Azzara R. M., Girardi M., Padovani C., Pellegrini D., Robol L.
The paper describes a preliminary experimental campaign conducted on The Matilde donjon in Livorno (Italy) aimed to characterize its dynamic behaviour, and the corresponding numerical analysis conducted on a FE model created via the NOSA-ITACA code.Source: CIVIL-COMP 2019, Riva del Garda Italy, 16-19/09/2019
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ISTI Repository | CNR ExploRA
2019
Contribution to conference
Open Access
FE model updating: sensitivity, reliability and regularization issues
Girardi M., Padovani C., Pellegrini D., Robol L.
Combining ambient vibration monitoring and finite element (FE) modelling through suitable model updating procedures allows for obtaining an estimate of the boundary conditions and mechanical material properties of engineering structures. Application of FE model updating to historical buildings is relatively recent and involves the solution of a constrained minimum problem, whose objective function is generally expressed as the discrepancy between experimental and numerical quantities, such as natural frequencies and mode shapes. The paper presents an algorithm for FE model updating based on the construction of local parametric reduced-order models embedded in a trust-region scheme and implemented in NOSA-ITACA, a non-commercial FE code developed by the authors. The algorithm exploits the structure of the stiffness and mass matrices and the fact that only a few of the smallest eigenvalues have to be calculated. This new procedure enables to compute eigenvalues and eigenvectors cheaply and thus to solve the minimum problem very efficiently. Besides reducing the overall computation time of the numerical process and enabling the accurate analysis of large scale models with little effort, the proposed algorithm allows for getting information on both the reliability of the solution and its sensitivity to noisy experimental data. Some case studies are presented and discussed and the adoption of regularization techniques to recover meaningful solutions investigated.Source: XXIV Congresso AIMETA 2019, pp. 286–286, Roma, 15-19/10/2019
Girardi M., Padovani C., Pellegrini D., Robol L.
Combining ambient vibration monitoring and finite element (FE) modelling through suitable model updating procedures allows for obtaining an estimate of the boundary conditions and mechanical material properties of engineering structures. Application of FE model updating to historical buildings is relatively recent and involves the solution of a constrained minimum problem, whose objective function is generally expressed as the discrepancy between experimental and numerical quantities, such as natural frequencies and mode shapes. The paper presents an algorithm for FE model updating based on the construction of local parametric reduced-order models embedded in a trust-region scheme and implemented in NOSA-ITACA, a non-commercial FE code developed by the authors. The algorithm exploits the structure of the stiffness and mass matrices and the fact that only a few of the smallest eigenvalues have to be calculated. This new procedure enables to compute eigenvalues and eigenvectors cheaply and thus to solve the minimum problem very efficiently. Besides reducing the overall computation time of the numerical process and enabling the accurate analysis of large scale models with little effort, the proposed algorithm allows for getting information on both the reliability of the solution and its sensitivity to noisy experimental data. Some case studies are presented and discussed and the adoption of regularization techniques to recover meaningful solutions investigated.Source: XXIV Congresso AIMETA 2019, pp. 286–286, Roma, 15-19/10/2019
See at:
ISTI Repository | CNR ExploRA