MOX Reports
The preprint collection of the Laboratory for Modeling and Scientific Computation MOX. It mainly contains works on numerical
analysis and mathematical modeling applied to engineering problems. MOX web site is mox.polimi.it
Found 1288 products
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38/2015 - 07/16/2015
Grasso, M.; Menafoglio, A.; Colosimo, B.M.; Secchi, P.
Using Curve Registration Information for Profile Monitoring | Abstract | | The quality characteristics in manufacturing processes are often represented in terms of spatially or time ordered data, called “profiles”, which are characterized by amplitude and phase variability. In this context, curve registration plays a key role, as it allows separating the two kinds of between-profiles variability, and to reduce any undesired inflation of the natural phase variability. In the mainstream literature, registration warping functions are not generally considered in the monitoring process, even though this may cause a significant information loss. We propose a novel approach for profile monitoring, which combines the Functional Principal Component Analysis and the use of parametric warping functions. The key idea is to
jointly monitor the stability over time of the registered profiles (i.e., the information related to amplitude variability) and the registration coefficients (i.e., the information related to phase
variability). This allows improving the capability of detecting unnatural pattern modifications, thanks to a better characterization of the overall natural variability. The benefits of a proper management of functional data registration, together with the advantages over the most common approaches used in the literature, are demonstrated by means of Monte Carlo simulations. The proposed methodology is finally applied to a real industrial case study relying on a dataset acquired in waterjet cutting processes under different health conditions of
the machine tool. |
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37/2015 - 07/10/2015
Aletti, M.; Perotto, S.; Veneziani, A.
Educated bases for the HiMod reduction of advection-diffusion-reaction problems with general boundary conditions | Abstract | | Hierarchical Model (HiMod) reduction is a method introduced in cite{perotto:2008} to effectively solve
advection-diffusion-reaction (ADR) and fluid dynamics problems in pipes. The rationale of the method is to regard
the solution as a mainstream axial dynamics added by transverse components. The mainstream
component is approximated by finite elements as often done in classical 1D models (like the popular Euler equations for gasdynamics). However, the HiMod formulation includes also the transverse dynamics by a spectral expansion.
A few modes are expected to capture the transverse (somehow secondary) dynamics with a good level of approximation. This
drastically reduces the size of the discrete problem, yet preserving accuracy. The method is ``hierarchical'' since the selection of the number of transverse modes can be hierarchically and adaptively performed~cite{perotto:2013}.
We have previously considered only Dirichlet boundary conditions for the lateral walls of the pipe and the procedure was tested only in 2D domains. With an appropriate selection of the spectral basis functions,
here we extend our formulation to 3D problems with general boundary conditions, still pursuing an essential approach.
The modal basis functions fulfill by construction the (homogeneous) boundary conditions associated with the solution.
This is achieved
by solving a Sturm-Liouville eigenpair problem.
We analyze this approach and provide a convergence analysis for the numerical error in the case of a linear ADR problem in rectangles (2D) and slabs (3D). Numerical results confirm the theory. |
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36/2015 - 07/10/2015
Fedele, M.; Faggiano, E.; Barbarotta, L.; Cremonesi, F.; Formaggia, L.; Perotto, S.
Semi-Automatic Three-Dimensional Vessel Segmentation Using a Connected Component Localization of the Region-Scalable Fitting Energy | Abstract | | Segmentation of patient-specific vascular segments of interest from
medical images is an important topic for numerous applications. De-
spite the great importance of having semi-automatic segmentation meth-
ods in this field, the process of image segmentation is still based on
several operator-dependent steps which make large-scale segmentation
a non trivial and time consuming task. In this work we present a
semi-automatic segmentation method to reconstruct vascular struc-
tures from three-dimensional medical images. We start from the mini-
mization of the Region Scalable Fitting Energy using the Split-Bregman
method and we modify the resulting algorithm adding a connected
component extraction of the solution starting from a point that identi-
fies the vascular structure of interest. In this way, we add a constraint
to the algorithm focusing it only on the vascular structure we want
to reconstruct and avoiding the attachment with the nearby objects.
Finally, we describe a strategy to minimize the number of involved
parameters in order to limit the user effort. The results obtained on
two different images (a Magnetic Resonance and a Computed Tomog-
raphy) demonstrate that our method outperforms the original method
in segmenting the vascular region of interest without the inclusion of
nearby objects in the result. |
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35/2015 - 06/26/2015
Manzoni, A.; Pagani, S.
A certified reduced basis method for PDE-constrained parametric optimization problems by an adjoint-based approach | Abstract | | In this paper we present a certified reduced basis (RB) framework for the efficient solution of PDE-constrained parametric optimization problems. We consider optimization problems (such as optimal control and optimal design) governed by elliptic PDEs and involving possibly non-convex cost functionals, assuming that the control functions are described in terms of a parameters vector. At each optimization step, the high-fidelity approximation of state and adjoint problems is replaced by a certified RB approximation, thus yielding a very efficient solution through an “optimize-then-reduce” approach. We develop a posteriori error estimates for the solutions of state and adjoint problems, for the cost functional, its gradient and the optimal parameters. We confirm our theoretical results in the case of optimal control/design problems dealing with potential and thermal flows. |
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34/2015 - 06/26/2015
Bernardi, M.S.; Mazza, G.; Ramsay, J.O.; Sangalli, L.M.
A separable model for spatial functional data with application to the analysis of the production of waste in Venice province | Abstract | | We propose a method for the analysis of functional data with complex dependencies, such as spatially dependent curves or time dependent surfaces, over highly textured domains. The models are based on the idea of regression with partial di erential regularizations. We focus in particular on a separable space-time version of the model. Among the various modelling features, the proposed method is able to deal with spatial domains featuring peninsulas, islands and other complex geometries.
Space-varying covariate information is included in the model via a semi-parametric framework. The proposed method is compared via simulation
studies to other spatio-temporal techniques and it is applied to the analysis of the annual production of waste in the towns of Venice province. |
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33/2015 - 06/26/2015
Fumagalli, A; Pasquale, L; Zonca, S.; Micheletti, S.
An upscaling procedure for fractured reservoirs with non-matching grids | Abstract | | Upscaling of geological models for reservoir simulation is an active and important area of research. In particular, we are interested in reservoirs where the rock matrix exhibits an intricate network of fractures, which usually act as a preferential path to the flow. Accounting for fractures’ contribution in the simulation of a reservoir is of paramount importance. Here, we have focused on obtaining effective parameters (e.g. transmissibility) on a 3D computational grid on the reservoir scale, that account for the presence, at a finer spatial scale, of fractures, and network of fractures. We have, essentially, followed the idea illustrated in Karimi-Fard et al. [2006], yet this work has some notable aspects of innovation in the way the procedure has been implemented, and in its capability to consider rather general corner-point grids, like the ones normally used in reservoir simulations in the industry, and complex and realistic fracture networks. In particular, novel contribution is the employment of EDFM for computing fracture-fracture and matrix-fracture transmissibilities, with a remarkable gain in speed-up. The output is in form of transmissibility that can be used for reservoir simulations with software like Eclipse, Intersect, or GPRS. The results demonstrate the effectiveness and computational efficiency of the numerical procedure, and of the developed software, which is now ready for further testing and industrialization.
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32/2015 - 06/26/2015
Agasisti,T.; Ieva, F.; Masci, C.; Paganoni, A.M.
Does class matter more than school? Evidence from a multilevel statistical analysis on Italian junior secondary school students | Abstract | | This paper assesses the differences in educational attainments between
students across classes and schools they are grouped by, in the context of
Italian educational system. The purpose is to identify a relationship between pupils’ reading test scores and students’ characteristics, stratifying for classes, schools and geographical areas. The dataset contains detailed information about more than 500,000 students at the first year of junior secondary school in the year 2012/2013. By means of multilevel linear models, it is possible to estimate statistically significant school and class effects, after adjusting for pupil’s characteristics, including prior achievement.
The results show that school and class effects are very heterogeneous
across macro-areas (Northern, Central and Southern Italy), and that there are substantial discrepancies between and within schools; overall,
class effects on achievement tend to be larger than school ones. |
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31/2015 - 06/26/2015
Pini, A.; Vantini, S.; Colombo, D.; Colosimo, B. M.; Previtali, B.
Domain-selective functional ANOVA for process analysis via signal data: the remote monitoring in laser welding | Abstract | | In many application domains, process monitoring and process optimization have to deal with functional responses, also known as profile data.
In these scenarios, a relevant industrial problem consists in discovering which specific parts of the functional response is mostly affected by the process changes. As a matter of fact, knowledge of the specific locations where the curve is more sensitive to process changes can bring several advantages. It can be exploited to design specific monitoring devices directly focusing on the functional data pertaining to the selected intervals. Secondly, the dimensional reduction can eventually bring to an increase of the power to detect process changes.
This paper proposes a methodology to inferentially select the parts of the output functions that are more informative in terms of the underlying factors. The procedure is based on a non-parametric domain-selective ANOVA for functional data, which results in the selection of the intervals of the domain presenting statistically significant effects of each factor. To illustrate its potential in industrial applications, the proposed procedure is applied to a case study on remote laser welding, where the main aim is monitoring the gap between the welded plates through the observation of the emission spectra of the welded material. |
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