Regularized regressions for parametric models based on separated representations

Regressions created from experimental or simulated data enable the construction of metamodels, widely used in a variety of engineering applications. Many engineering problems involve multi-parametric physics whose corresponding multi-parametric solutions can be viewed as a sort of computational vademecum that, once computed offline, can be then used in a variety of real-time engineering applications including optimization, inverse analysis, uncertainty propagation or simulation based control. Sometimes, these multi-parametric problems can be solved by using advanced model order reduction—MOR-techniques. However, solving these multi-parametric problems can be very costly. In that case, one possibility consists in solving the problem for a sample of the parametric values and creating a regression from all the computed solutions. The solution for any choice of the parameters is then inferred from the prediction of the regression model. However, addressing high-dimensionality at the low data limit, ensuring accuracy and avoiding overfitting constitutes a difficult challenge. The present paper aims at proposing and discussing different advanced regressions based on the proper generalized decomposition (PGD) enabling the just referred features. In particular, new PGD strategies are developed adding different regularizations to the s-PGD method. In addition, the ANOVA-based PGD is proposed to ally them

Hybrid Twin in Complex System Settings

Los beneficios de un conocimiento profundo de los procesos tecnológicos e industriales de nuestro mundo son incuestionables. La optimización, el análisis inverso o el control basado en la simulación son algunos de los procedimientos que pueden llevarse a cabo una vez que los conocimientos anteriores se transforman en valor para las empresas. Con ello se consiguen mejores tecnologías que acaban beneficiando enormemente a la sociedad. Pensemos en una actividad rutinaria para muchas personas hoy en día, como coger un avión. Todos los procedimientos anteriores se llevan a cabo en el diseño del avión, en el control a bordo y en el mantenimiento, lo que culmina en un producto tecnológicamente eficiente en cuanto a recursos. Este alto valor añadido es lo que está impulsando a la Ciencia de la Ingeniería Basada en la Simulación (Simulation Based Engineering Science, SBES) a introducir importantes mejoras en estos procedimientos, lo que ha supuesto avances importantes en una gran variedad de sectores como la sanidad, las telecomunicaciones o la ingeniería.Sin embargo, la SBES se enfrenta actualmente a varias dificultades para proporcionar resultados precisos en escenarios industriales complejos. Una de ellas es el elevado coste computacional asociado a muchos problemas industriales, que limita seriamente o incluso inhabilita los procesos clave descritos anteriormente. Otro problema es que, en otras aplicaciones, los modelos más precisos (que a su vez son los más caros computacionalmente) no son capaces de tener en cuenta todos los detalles que rigen el sistema físico estudiado, con desviaciones observadas que parecen escapar de nuestro conocimiento.Por lo tanto, en este contexto, a lo largo de este manuscrito se proponen novedosas estrategias y técnicas numéricas para hacer frente a los retos a los que se enfrenta la SBES. Para ello, se analizan diferentes aplicaciones industriales.El panorama anterior junto con el exhaustivo desarrollo producido en la Ciencia de Datos, brinda además una oportunidad perfecta para los denominados Dynamic Data Driven Application Systems (DDDAS), cuyo objetivo principal es fusionar los algoritmos clásicos de simulación con los datos procedentes de medidas experimentales. En este escenario, los datos y las simulaciones ya no estarían desacoplados, sino que formarían una relación simbiótica que alcanzaría hitos inconcebibles hasta estos días. Más en detalle, los datos ya no se entenderán como una calibración estática de un determinado modelo constitutivo, sino que el modelo se corregirá dinámicamente tan pronto como los datos experimentales y las simulaciones tiendan a diverger.Por esta razón, la presente tesis ha hecho especial énfasis en las técnicas de reducción de modelos, ya que no sólo son una herramienta para reducir la complejidad computacional, sino también un elemento clave para cumplir con las restricciones de tiempo real que surgen del marco de los DDDAS.Además, esta tesis presenta nuevas metodologías basadas en datos para enriquecer el denominado paradigma Hybrid Twin. Un paradigma cuya motivación radica en su habilidad de posibilitar los DDDAS. ¿Cómo? combinando soluciones paramétricas y técnicas de reducción de modelos con correcciones dinámicas generadas “al vuelo'' basadas en los datos experimentales recogidos en cada instante.<br /

Towards a data-driven debt collection strategy based on an advanced machine learning framework

The European debt purchase market as measured by the total book value of purchased debt approached 25bn euros in 2020 and it was growing at double-digit rates. This is an example of how big the debt collection and debt purchase industry has grown and the important impact it has in the financial sector. However, in order to ensure an adequate return during the debt collection process, a good estimation of the propensity to pay and/or the expected cashflow is crucial. These estimations can be employed, for instance, to create different strategies during the amicable collection to maximize quality standards and revenues. And not only that, but also to prioritize the cases in which a legal process is necessary when debtors are unreachable for an amicable negotiation. This work offers a solution for these estimations. Specifically, a new machine learning modelling pipeline is presented showing how outperforms current strategies employed in the sector. The solution contains a pre-processing pipeline and a model selector based on the best model calibration. Performance is validated with real historical data of the debt industry

From ROM of Electrochemistry to AI-Based Battery Digital and Hybrid Twin

Lithium-ion batteries are widely used in the automobile industry (electric vehicles and hybrid electric vehicles) due to their high energy and power density. However, this raises new safety and reliability challenges which require development of novel sophisticated Battery Management Systems (BMS). A BMS ensures the safe and reliable operation of a battery pack and to realize it a model must be solved. However, current BMSs are not adapted to the specifications of the automotive industry, as they are unable to give accurate results at real-time rates and during a wide operation range. For this reason, the main focus of this work is to develop a Hybrid Twin, as introduced in Chinesta et al. (Arch Comput Methods Eng (in press), 2018. https://doi.org/10.1007/s11831-018-9301-4), so as to meet the requirements of the new generation of BMS. To achieve this, three reduced order model techniques are applied to the most commonly used physics-based models, each one for a different range of application. First, a POD model is used to greatly reduce the simulation time and the computational effort for the pseudo-2D model, while maintaining its accuracy. In this way, cell design, optimization of parameters, and simulation of battery packs can be done while saving time and computational resources. In addition, its real-time performance has been studied. Next, a regression model is constructed from data by using the sparse-Proper Generalized Decomposition (s-PGD). It is shown that it achieves real-time performance for the whole electric vehicle (EV) system with a battery pack. In addition, this regression model can be used in a BMS without issues because of the simple algebraic expression obtained. A simulation of the EV with the proposed approach is demonstrated using the system simulation tool SimulationX (ESI ITI GmbH. Dresden, Germany). Furthermore, the Digital Twin created using the s-PGD does not only allow for real-time simulations, but it can also adapt its predictions taking into consideration the real driving conditions and the real driving cycle to change the planning in real-time. Finally, a data-driven model base

A novel sparse reduced order formulation for modeling electromagnetic forces in electric motors

A novel model order reduction (MOR) technique is presented to achieve fast and real-time predictions as well as high-dimensional parametric solutions for the electromagnetic force which will help the design, analysis of performance and implementation of electric machines concerning industrial applications such as the noise, vibration, and harshness in electric motors. The approach allows to avoid the long-time simulations needed to analyze the electric machine at different operation points. In addition, it facilitates the computation and coupling of the motor model in other physical subsystems. Specifically, we propose a novel formulation of the sparse proper generalized decomposition procedure, combining it with a reduced basis approach, which is used to fit correctly the reduced order model with the numerical simulations as well as to obtain a further data compression. This technique can be applied to construct a regression model from high-dimensional data. These data can come, for example, from finite element simulations. As will be shown, an excellent agreement between the results of the proposed approach and the finite element method models are observed.We thank Professor Jose Roger-Folch (Univer-sitat Politècnica de València) for useful discussion, comments and feedback about the present work

Learning stable reduced-order models for hybrid twins

The concept of “hybrid twin” (HT) has recently received a growing interest thanks to the availability of powerful machine learning techniques. This twin concept combines physics-based models within a model order reduction framework—to obtain real-time feedback rates—and data science. Thus, the main idea of the HT is to develop on-the-fly data-driven models to correct possible deviations between measurements and physics-based model predictions. This paper is focused on the computation of stable, fast, and accurate corrections in the HT framework. Furthermore, regarding the delicate and important problem of stability, a new approach is proposed, introducing several subvariants and guaranteeing a low computational cost as well as the achievement of a stable time-integration

Learning stable reduced-order models for hybrid twins

The concept of Hybrid Twin (HT) has recently received a growing interest thanks to the availability of powerful machine learning techniques. This twin concept combines physics-based models within a model-order reduction framework-to obtain real-time feedback rates-and data science. Thus, the main idea of the HT is to develop on-the-fly data-driven models to correct possible deviations between measurements and physics-based model predictions. This paper is focused on the computation of stable, fast and accurate corrections in the Hybrid Twin framework. Furthermore, regarding the delicate and important problem of stability, a new approach is proposed, introducing several sub-variants and guaranteeing a low computational cost as well as the achievement of a stable time-integration

Fast Computation of Multi-Parametric Electromagnetic Fields in Synchronous Machines by Using PGD-Based Fully Separated Representations

A novel Model Order Reduction (MOR) technique is developed to compute high-dimensional parametric solutions for electromagnetic fields in synchronous machines. Specifically, the intrusive version of the Proper Generalized Decomposition (PGD) is employed to simulate a Permanent-Magnet Synchronous Motor (PMSM). The result is a virtual chart allowing real-time evaluation of the magnetic vector potential as a function of the operation point of the motor, or even as a function of constructive parameters, such as the remanent flux in permanent magnets. Currently, these solutions are highly demanded by the industry, especially with the recent developments in the Electric Vehicle (EV). In this framework, standard discretization techniques require highly time-consuming simulations when analyzing, for instance, the noise and vibration in electric motors. The proposed approach is able to construct a virtual chart within a few minutes of off-line simulation, thanks to the use of a fully separated representation in which the solution is written from a series of functions of the space and parameters coordinates, with full space separation made possible by the use of an adapted geometrical mapping. Finally, excellent performances are reported when comparing the reduced-order model with the more standard and computationally costly Finite Element solutions

Parametric Electromagnetic Analysis of Radar-Based Advanced Driver Assistant Systems

Efficient and optimal design of radar-based Advanced Driver Assistant Systems (ADAS) needs the evaluation of many different electromagnetic solutions for evaluating the impact of the radome on the electromagnetic wave propagation. Because of the very high frequency at which these devices operate, with the associated extremely small wavelength, very fine meshes are needed to accurately discretize the electromagnetic equations. Thus, the computational cost of each numerical solution for a given choice of the design or operation parameters, is high (CPU time consuming and needing significant computational resources) compromising the efficiency of standard optimization algorithms. In order to alleviate the just referred difficulties the present paper proposes an approach based on the use of reduced order modeling, in particular the construction of a parametric solution by employing a non-intrusive formulation of the Proper Generalized Decomposition, combined with a powerful phase-angle unwrapping strategy for accurately addressing the electric and magnetic fields interpolation, contributing to improve the design, the calibration and the operational use of those systems

Jumeau Hybride dans le cadre de systèmes complexes

The benefits of a deep understanding of the technological and industrial processes of our world are unquestionable. Optimization, inverse analysis or simulation-based control are some of the procedures that can be carried out once the above knowledge is transformed into value for companies. This brings better technologies that end up greatly benefiting society. Think of a routine activity for many people today, such as taking a plane. All the above procedures are carried out in the plane design, on-board control and maintenance, culminating in a technologically resource-efficient product. This strong added value is what is driving Simulation Based Engineering Science (SBES) to make major improvements in these procedures, leading to noticeable breakthroughs in a wide variety of sectors (e.g. Healthcare, Telecommunications or Engineering, to cite only a few).However, SBES is currently confronting several difficulties to provide accurate results in complex industrial scenarios. One is the high computational cost associated with many industrial problems which severely limits or even disables the key processes described above. Another problem is that in other applications, the more accurate (and also more highly-time consuming) models are not able to take into account all the details that govern the physical system under study, with observed deviations that seem to escape our understanding.Therefore, in this context, novel numerical strategies and techniques are proposed throughout this manuscript to deal with the challenges that SBES is facing. To do that, different industrial scenarios are analyzedThe above panorama also brings a perfect opportunity to the so-called DynamicData Driven Application Systems (DDDAS), whose main objective is to merge classical simulation algorithms with data coming from experimental measures. This concept is envisaged thanks to the exhaustive development in Data Science.Within this scenario, data and simulations would no longer be uncoupled but rather they would form a symbiotic relationship which would achieve milestones inconceivable until these days. Indeed, data will no longer be understood as a static calibration of a given constitutive model but rather the model will be corrected dynamically as soon as experimental data and simulations tend to diverge.For this reason, the present dissertation placed a particular emphasis on Model Order Reduction (MOR) techniques, as they are not only a tool to reduce computational complexity, but also a key element in meeting the real time constraints arising from the DDDAS framework.Furthermore, this thesis presents new data-driven methodologies to enrich the so-called Hybrid Twin paradigm. A paradigm which is motivated because it makes DDDAS possible. How? by combining parametric solutions and the MOR framework with “on-the-fly” data-driven (i.e. machine learning) correction models.Les avantages d'une compréhension approfondie des processus technologiques et industriels de notre monde sont indiscutables. L'optimisation, l'analyse inverse ou le contrôle par simulation sont quelques-unes des procédures qui peuvent être mises en œuvre lorsque les connaissances susmentionnées sont transformées en valeur pour les entreprises. Il en résulte de meilleures technologies qui finissent par profiter grandement à la société. Pensez à une activité quotidienne pour de nombreuses personnes aujourd'hui, comme prendre l'avion. Toutes les procédures évoquées ci-dessus sont mises en œuvre dans la conception de l'avion, tel que le contrôle à bord et la maintenance, pour aboutir à un produit technologiquement efficace en termes de ressources. Cette forte valeur ajoutée est ce qui pousse les sciences de l'ingénieur basées sur la simulation (Simulation Based Engineering Science, SBES) à apporter des améliorations majeures à ces procédures, conduisant à des percées notables dans une grande variété de secteurs (comme par exemple la santé, les télécommunications ou l'ingénierie).Cependant, les SBES sont actuellement confrontées à plusieurs difficultés pour fournir des résultats précis dans des scénarios industriels complexes. L'une d'elles est le coût de calcul élevé associé à de nombreux problèmes industriels, qui limite fortement, voire rend impossible, les processus clés décrits ci-dessus. Un autre problème apparaît dans d'autres applications, où les modèles plus précis (et aussi plus gourmands en temps) ne sont pas capables de prendre en compte tous les détails qui régissent le système physique étudié, avec des déviations observées qui semblent échapper à notre compréhension.C'est pourquoi, dans ce contexte, de nouvelles stratégies et techniques numériques sont proposées tout au long de ce manuscrit pour relever les défis auxquels les SBES sont confrontées avec l'étude de différentes applications.Le panorama ci-dessus offre également une opportunité parfaite pour les Dynamic Data Driven Application Systems (DDDAS), dont l'objectif principal est de fusionner les algorithmes de simulation classiques avec les données provenant de mesures expérimentales. Ce concept est envisagé grâce au développement exhaustif de la science des données. Dans ce scénario, les données et les simulations ne seraient plus découplées, mais formeraient une relation symbiotique qui permettrait d'atteindre des étapes inconcevables jusqu'à aujourd'hui. En effet, les données ne seront plus prises en compte pour un étalonnage statique d'un modèle constitutif donné, mais plutôt comme une correction dynamique dès que les données expérimentales et les simulations auront tendance à diverger.C'est dans ce but que cette thèse met un accent particulier sur les techniques de réduction de modèles, car elles ne sont pas seulement un outil pour réduire la complexité de calcul, mais aussi un élément clé pour répondre aux contraintes de temps réel découlant du cadre des DDDAS.En outre, cette thèse présente de nouvelles méthodologies axées sur les données pour enrichir le paradigme dit des jumeaux hybrides. Un paradigme qui est motivé parce qu'il rend les DDDAS possible. Comment ? En combinant des solutions paramétriques et des techniques de réduction de modèles avec des corrections à la volée basés sur les données experimentale