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This is the peer reviewed version of the following article: Diez, P. [et al.]. Nonlinear dimensionality reduction for parametric problems: a kernel proper orthogonal decomposition. "International journal for numerical methods in engineering", 30 Desembre 2021, vol. 122, núm. 24, p. 7306-7327, which has been published in final form at DOI: 10.1002/nme.6831. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving. Reduced-order models are essential tools to deal with parametric problems in the context of optimization, uncertainty quantification, or control and inverse problems. The set of parametric solutions lies in a low-dimensional manifold (with dimension equal to the number of independent parameters) embedded in a large-dimensional space (dimension equal to the number of degrees of freedom of the full-order discrete model). A posteriori model reduction is based on constructing a basis from a family of snapshots (solutions of the full-order model computed offline), and then use this new basis to solve the subsequent instances online. Proper orthogonal decomposition (POD) reduces the problem into a linear subspace of lower dimension, eliminating redundancies in the family of snapshots. The strategy proposed here is to use a nonlinear dimensionality reduction technique, namely, the kernel principal component analysis (kPCA), in order to find a nonlinear manifold, with an expected much lower dimension, and to solve the problem in this low-dimensional manifold. Guided by this paradigm, the methodology devised here introduces different novel ideas, namely, 1) characterizing the nonlinear manifold using local tangent spaces, where the reduced-order problem is linear and based on the neighboring snapshots, 2) the approximation space is enriched with the cross-products of the snapshots, introducing a quadratic description, 3) the kernel for kPCA is defined ad hoc, based on physical considerations, and 4) the iterations in the reduced-dimensional space are performed using an algorithm based on a Delaunay tessellation of the cloud of snapshots in the reduced space. The resulting computational strategy is performing outstandingly in the numerical tests, alleviating many of the problems associated with POD and improving the numerical accuracy. Generalitat de Catalunya, 2017-SGR-1278; Ministerio de Ciencia e Innovación, CEX2018-000797-S; PID2020-113463RB-C32; PID2020-113463RB-C33

© 2022 Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ Searching for achieving an ambitious reduction in greenhouse gas emissions, the EU has set as a goal a modal shift in freight transport of 30% by rail for the near future. In this context, it is vital to use modal choice models road versus rail to assess the shippers' acceptance of the actions promoting the use of rail. This paper develops a combined model for jointly evaluating modal split and railway freight ows, addressed to the case when a modal split based on a random utility model is available, and some of its coe -cients may present a non-negligible variability. To this end, after the initial deterministic formulation a robust counterpart of the model is developed. The model, formulated as a non-linear integer programming problem, is oriented to a multi-carrier environment and includes constraints to consider the interactions between the di erent types of ows on the railway network, allowing a good evaluation of the cost types of the carriers and the network capacity. An algorithmic solution based on the outer approximation method is shown to provide accurate solutions in a reasonable computational time for the robust and non-robust versions of the model. Examples centered on a section of the Trans-European Transport Network, the TEN-T Core network corridors, are reported to test the model's applicability. Results show that this model can be a helpful tool for analyzing the possible shippers' response to the di erent railway carriers' services competing with the road.

Renewable and distributed energy sources, with photovoltaic in the first place, are leading the energy transition. However, they alone will hardly find the way to success in this challenge because of their intrinsic limitations, such as their dependency on weather condition and the unpredictability of their production. Demand Response services are considered crucial for the integration of renewable sources in the grid. This study presents a methodology to evaluate potential flexibility in commercial buildings by managing air conditioning and lighting systems of the site. The study proposes two different data-driven approaches to evaluate flexibility depending on the technology considered. For lighting systems, flexibility is evaluated using the XGBoost classification algorithm combined with a piecewise function. The thermal behavior of the building is modeled with a simplified RC equivalent state-space model. For both algorithms, preprocessing showed to be a critical part of the process, which is explained stage-by-stage in the paper. Results show that the lighting flexibility algorithm is very reliable, reaching an average error of less than 1 % during the months considered. The simplified thermal modeling proposed shows promising results, having less than 0.2 o C of RMSE error for the internal temperature forecast. In addition, results show the flexibility potentiality of the building, which is potentially able to shift up to 23 % of its power consumption during certain hours of the day. This opens huge opportunities for taking advantage from dynamic tariffs, increase self-consumption from renewable sources or participate in flexibility markets to reduce buildings' electricity bill and help renewable integration.

The main objective of this study was to introduce a survival model to contemplate two simultaneous accelerating factors affecting a food product's shelf life: temperature and illumination. A second objective was to consider the case where the same consumer tests different experimental conditions and thus his/her data are not independent. Sample data comprised 108 consumers who evaluated a lemon-flavored juice stored at 24 °C, 37 °C and 45 °C; under conditions of no-illumination and with illumination; with seven different storage times for each of the six experimental conditions. Aiming to estimate the storage time at which a consumer rejects a sample a model including an Arrhenius term for the temperature, a binomial response for illumination (with and without) and the interaction of both was developed. The model also considered that the same consumer tested different experimental conditions. Fil: Garitta, Lorena Garitta. Provincia de Buenos Aires. Dirección General de Cultura y Educación. Instituto Superior Experimental de Tecnología Alimentaria; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina Fil: Langohr, Klaus. Universidad Politécnica de Catalunya; España Fil: Elizagoyen, Eliana Soledad. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas; Argentina. Provincia de Buenos Aires. Dirección General de Cultura y Educación. Instituto Superior Experimental de Tecnología Alimentaria; Argentina Fil: Gugole Ottaviano, Maria Fernanda. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Provincia de Buenos Aires. Dirección General de Cultura y Educación. Instituto Superior Experimental de Tecnología Alimentaria; Argentina Fil: Gómez, Guadalupe. Universidad Politécnica de Catalunya; España Fil: Hough, Guillermo. Provincia de Buenos Aires. Dirección General de Cultura y Educación. Instituto Superior Experimental de Tecnología Alimentaria; Argentina. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas; Argentina

Large aeronautical structural parts present important distortions after machining. This problem is caused by the presence of residual stresses, which are developed during previous manufacturing steps (quenching). Before being put into service, the nominal geometry is restored by means of mechanical methods. This operation is called reshaping and exclusively depends on the skills of a well-trained and experienced operator. Moreover, this procedure is time consuming and nowadays, it is only based on a trial and error approach. Therefore, there is a need at industrial level to solve this problem with the support of numerical simulation tools. By using a simplification hypothesis, it was found that the springback phenomenon behaves linearly and it allows developing a strategy to implement reshaping at an industrial level. © 2018 Author(s).

In this work, a coordinate change of state variables is performed for drift-less systems of dimension m+2 with 2 inputs using Goursat Normal Form. Then, we define a feedback law that will allow us to convert the original system into chained form. Later on, we find the flat outputs and define a new feedback law. Finally, numerical simulations are presented for a planar space robot, a mobile robot with a trailer and a N-trailer.

Las enfermedades cardiovasculares son la primera causa de muerte de la población Europea. Se estima que la mortalidad por enfermedades cardiovasculares es la mitad de la mortalidad total en toda Europa y provoca 4,35 millones de fallecidos cada año en los 52 estados miembros de la Región Europea. Según la Organización Mundial de la Sanidad (OMS) más de 1,9 millones de muertos en la Unión Europea, además de ser la principal causa de deshabilitad y reducción de calidad de vida. Estos tipos de enfermedades afectan sobre todo a la mayor parte de la población, y, sabiendo que el porcentaje de ancianos en la nuestra sociedad sigue subiendo, se puede fácilmente entender que las cardio-patologías puedan constituir siempre un riesgo elevado para la salud de los países occidentales. La cirugía moderna busca cada día soluciones menos invasivas, como por ejemplo a través de cirugía llamada mini-invasiva. La cirugía mini-invasiva es la técnica quirúrgica que consiente acceder a cavidades internas sin operar incisiones (cirugía en abierto). En esta definición, es trivial intuir que entran sobre todo las técnicas endoscópicas que han permitido realizar muchas operaciones de diferente grado de peligrosidad produciendo numerosos beneficios y reduciendo los índices de riesgo. En la cirugía cardiovascular no es raro encontrar problemáticas de tener que insertar aparatos como stent, válvulas cardiacas, sondas y muchas cosas más a través pequeños orificios (como vasos sanguíneos, por ejemplo, la femoral, la aorta la carótida o la subclavia). Estos aparatos van a ser posicionados o conducidos a través de guías (catéteres) que los conducen hasta el sitio destinado. El hecho de utilizar catéteres que tienen que penetrar por estas vías obliga a que estos aparatos respecten dimensiones muy pequeñas. Es interesante entonces estudiar como estas estructuras deben de soportar esfuerzos de compresión y de expansión cuando vienen insertadas en el catéter y luego se sueltan. El ejemplo en el cual enfocaremos nuestro estudio va a ser un soporte metálico intravascular para cualquier aparato necesite ser anclado en el interior de una vena o arteria.

Let (E;A1;A2;B) be a quadruple of matrices representing a two-order generalized time-invariant linear system, E¨x = A1 ˙ x + A2x + Bu. We study the controllability character under an algebraic point of view.

Let (E;A1;A2;B) be a quadruple of matrices representing a two-order generalized time-invariant linear system, E¨x = A1 ˙ x + A2x + Bu. We study the controllability character under an algebraic point of view.

A natural equivalence relation can be considered in the generalized flag manifold. First we give a complete set of invariants of it as well as a canonical matrix description of the classes. Next we consider parametric flags. We give a miniversal deformation for the above canonical form and we use it to characterize the stable flags.

Given an orbit space $M/\Gamma$ and an equivalence relation defined in it by means of the action of a group $G$, we obtain a miniversal deformation of an orbit through a miniversal deformation in $M$ with regard to a suitable group action of $G\times \Gamma$. We show some applications to the perturbations of $m$-tuples of subspaces and $(C,A)$-invariant subspaces.

V. I. Arnold constructed smooth generic families of matrices with respect to similarity transformations depending smoothly on the entries of matrices with a small number of parameters. We Solve the same problem for a family of triples of matrices (E; A;B), E;A 2 Mn(C), B 2 Mn£m(C), representing generalized linear systems in the form E ˙ x = Ax+Bu, with respect to feedback and derivative feedback equivalence.

We extend some known results about the smooth stratification of the set of conditioned invariant subspaces for a general pair $(C,A)\in\w C^n\times\w C^{n+m}$ without any assumption on the observability. More precisely we prove that the set of $(C,A)$-conditioned invariant subspaces having a fixed Brunovsky-Kronecker structure is a submanifold of the corresponding Grassman manifold, with a vector bundle structure relating the observable and nonobservable part, and we compute its dimension. We also prove that the set of all $(C,A)$-conditioned invariant subspaces having a fixed dimension is connected, provided that the nonobservable part of $(C,A)$ has at most one eigenvalue (this condition is in general necessary).

Given an orbit space of matrices $M/\Gamma$ and an equivalence relation defined in it by means of the action of a group $G$, we obtain a miniversal deformation of an orbit through a minivesal deformation in $M$ with regard to a suitable group action of $G\times \Gamma$. We show some applications to the perturbations of $m$-tuples of subspaces and $(C,A)$-invariant subspaces.

Given an observable system defined by a pair of matrices $(C,A)$ we obtain a cellular decomposition of the manifold of $(C,A)$-conditioned invariant subspaces having the restricted system fixed observability indices and we apply this decomposition to compute their homology groups.

We find explicit miniversal deformations of flags in the generalized flag manifolds, with regard a natural equivalence relation defined by the group action that keeps fixed the reference flag.

We consider the topology of the set of conditioned invariant subspaces of an observable pair $(C,A)$ of a fixed dimension. By fixing the observability indices of the restricted system, a stratification by finitely many smooth manifolds is obtained, termed Brunovsky strata. It is shown that each Brunovsky stratum is homotopy equivalent to a generalized flag manifold. From this description an effective formula for the Betti numbers of the Brunovsky strata can be derived.

Proper Generalized Decomposition (PGD) is devised as a computational method to solve high-dimensionalboundary value problems(where many dimensions are associated with the space of parameters defining the problem). The PGD philosophy consists in providing a separated representation of the multidimensional solution using agreedy approachcombined with an alternated directions scheme to obtain the successive rank-one terms. This paper presents an algorithmic approach to high-dimensional tensorseparation based on solving theLeast Squares approximationin a separable format of multidimensional tensor using PGD. This strategy is usually embedded in a standard PGD code in order to compress the solution (reduce the number of terms and optimize the available storage capacity), but it stands also as an alternative and highly competitive method for tensor separation.

Probe-based technologies are proliferating as a means of inferring traffic states. Technological companies are interested in traffic data for computing the best routes in a traffic-aware manner and they also provide real-time traffic information with certain temporal accuracy. This paper analyses and evaluates how data provided by a fleet of probe cars can be used to develop a navigation service and how the penetration rate of this service affects a set of city-scale KPIs (Key Performance Indicators) and driver KPIs. The case study adopts a model-driven approach in which microscopic simulation emulates real-size fleets of probe vehicles that provide positions and speed data. What is noteworthy about the modelling behaviour is that drivers are segmented according to their knowledge of network conditions for selected trips: experts, regular drivers, and tourists. The paper presents and discusses the modelling approach and the results obtained from an experimental Barcelona CBD model designed to evaluate the penetration rates of probe vehicles and route guidance. An analysis of the simulation experiments reveals remarkable links among city-scale KPIs, which—from a multivariate point of view—is a novelty. A simulation-based framework for results analysis and visualization is also introduced in order to simplify the simulation results analysis and easily visualize OD paths for driver segments. Throughout this work, the authors have benefited from the support of inLab FIB team at UPC and the suggestions of Jaume Barceló (Emeritus Professor at UPC). This research was funded by Spanish R+D Programs, TRA2016-76914-C3-1-P, and by Secretaria d’Universitats-i-Recerca-Generalitat de Catalunya, 2017-SGR-1749.

New sustainable mobility concepts and smart resilient ideas are arising every day. However, there is not an easy way to bring these ideas into reality, or to test how good they are as mobility solutions. Virtual Mobility Lab offers the opportunity to evaluate the impact of new mobility concepts before taking them to the real world. In this work, a multimodal macroscopic traffic simulation model of the Barcelona Metropolitan Area is developed, including both public and private transport network. This paper explains the remarkable features developed for this model, such as the network hierarchy and the multimodal public network interchangers, allowing demand to exchange between public transportation modes along their origin-destination paths.

Given an observable system (C,A)€ K^(mxn)X K^(nxn)with K=R or C, the set of (C,A)-invariant subspaces having the restricted system fixed observability indices is a smooth manifold embedded on the corresponding Grassmannian. We obtain an explicit parametrization of it by means of an atlas of corresponding charts. As an application we obtain the set of maximal dimensional outputs making solvable a generic Disturbance Decoupling Problem.