José M. Vega

Universidad Politécnica de Madrid | UPM · ETSI Aeronautica y del Espacio

A very fast reduced order model is developed to monitor aeroengines condition (defining their degradation from a baseline state) in real time, by using synthetic data collected in specific sensors. This reduced model is constructed by applying higher-order singular value decomposition plus interpolation to appropriate data, organized in tensor form...

A reduced order model is developed to monitor aeroengines condition (defining their degradation from a baseline state) in real-time, by using data collected in specific sensors. This reduced model is constructed by applying higher order singular value decomposition plus interpolation to appropriate data, organized in tensor form. Such data are obta...

A reduced order model is developed to monitor aeroengines condition (defining their degradation from a baseline state) in real-time, by using data collected in specific sensors. This reduced model is constructed by applying higher order singular value decomposition plus interpolation to appropriate data, organized in tensor form. Such data are obta...

A new gradient-like methodology has been developed for aeroengine diagnosis, determining the engine health condition, which is defined by the engine degradation from an undegraded state and uses measurements at various sensors distributed along the engine. The developed tools are able to accurately compute, not only the engine degradation, but also...

A new data-driven reduced order model is developed to efficiently simulate transient dynamics, with the aim at computing the final attractor. The method combines a standard numerical solver and time extrapolation based on a recent data processing tool, called higher order dynamic mode decomposition. Such combination is made using interspersed time...

A method is presented to perform the three-dimensional reconstruction of the velocity field in laminar flows using planar PIV data. The developed method relies on a convenient, repeated application of two data processing tools developed by two of the authors and called the higher order dynamic mode decomposition and the spatio-temporal Koopman deco...

Time periodic patterns in a semiconductor superlattice, relevant to microwave generation, are obtained upon numerical integration of a known set of drift-diffusion equations. The associated spatio-temporal transport mechanisms are uncovered by applying (to the computed data) two recent data processing tools, known as the higher order dynamic mode d...

Time periodic patterns in a semiconductor superlattice, relevant to microwave generation, are obtained upon numerical integration of a known set of drift-diffusion equations. The associated spatiotemporal transport mechanisms are uncovered by applying (to the computed data) two recent data processing tools, known as the higher order dynamic mode de...

A new sampling technique for the application of proper orthogonal decomposition to a set of snapshots has been recently developed by the authors to facilitate a variety of data processing tasks (J. Comput. Phys. 335, 2017). According to it, robust modal expansions result from performing the decomposition on a limited number of relevant snapshots an...

This paper deals with the data-driven reduced order modeling of high dimensional systems, using a tensor decomposition plus one-dimensional interpolation. The (many) involved dimensions are usually associated with space, and/or time, and/or various parameters the system may depend on. Three tensor decomposition methods are considered, namely recurs...

Available online xxxx Communicated by T. Sauer Keywords: Spatio-temporal Koopman decomposition Nonlinear dynamical systems Hydrodynamic instabilities Thermal convection in a two-dimensional circular annulus Spatio-temporal dynamics Symmetries Periodic and quasi-periodic dynamics Invariant tori a b s t r a c t This paper deals with the analysis of n...

This article presents a new data processing method, based on higher order dynamic mode decomposition, to analyze actual flight test experimental data. The new methodology (i) is fast and effcient, (ii) is automatic, (iii) provides a clean spectrum in terms of the frequencies and damping rates of the flutter modes, and (iv) reconstructs the spatial...

A review of available results on non-destructive testing of physical systems, using the concept of topological sensitivity, is presented. This mathematical tool estimates the sensitivity of a set of measurements in some given sensors, distributed along the system, to defects/flaws that produce a degradation of the system. Such degradation manifests...

This work studies in detail the energy amplification produced by inflow excitation of a steady flow over a backward-facing step. The disturbances introduced in the inflow are composed of a convergent series of sine functions with different wavenumbers, but the same temporal frequency. The evolution of the perturbations in time is solved using a lin...

This chapter addresses some preliminary data processing tools that are needed in the remainder of the book. These tools include singular value decomposition in its various versions (economy, compact, and truncated singular value decomposition), proper orthogonal decomposition, and higher order singular value decomposition in its various versions (e...

Even though magnetic resonance and aircraft flight tests are associated with two different phenomena from the physical point of view, they are mathematically similar. This is because they both intend to calculate the natural frequencies and associated damping rates of a system from its experimentally measured response to impulsive excitation. In ai...

This chapter is devoted to the development of the spatio-temporal Koopman decomposition method, which is able to provide a semi-analytic description of spatio-temporal dynamics as a spatio-temporal expansion showing oscillations and exponential growth or decay along time and one or more distinguished spatial coordinates (called the longitudinal coo...

This chapter deals with the application of the HODMD and STKD methods to several pattern forming systems. These include the one-dimensional complex Ginzburg–Landau equation, with both Neumann and periodic boundary conditions, and two thermal convection problems, namely the extremely simple Lorenz system and that associated with thermal convection i...

This chapter is devoted to the description of the higher order dynamic mode decomposition, which is an improvement of the standard dynamic mode decomposition method. The new method uses, not only each given snapshot, but also a set of d−1 time-lagged snapshots. After establishing the necessity of improving the standard dynamic mode decomposition me...

The aim of this chapter is to use the semi-analytical expressions for the temporal or spatio-temporal dynamics underlying a given database, provided by the higher order dynamic mode decomposition or spatio-temporal Koopman decomposition methods, to construct data-driven reduced order models for these dynamics. The accuracy of these two methods allo...

This chapter shows the potential of the HODMD and STKD methods to detect coherent structures in fluid dynamics. Using these algorithms provides information about the main global instabilities driving the flow dynamics, which are leading the bifurcation process responsible for the transition from laminar to turbulent flow. In particular, two applica...

This chapter applies the HODMD and STKD methods to detect the spatio-temporal patterns driving the flow in the wake of wind turbines, considering two types of applications. In the first application, HODMD and STKD will identify the main flow instabilities that permit studying the bifurcation process that occurs in the wake of the wind turbine, cons...

Higher Order Dynamic Mode Decomposition and Its Applications provides detailed background theory, as well as several fully explained applications from a range of industrial contexts to help readers understand and use this innovative algorithm. Data-driven modelling of complex systems is a rapidly evolving field, which has applications in domains in...

Nowadays, there is an ever growing interest for gas turbine and aeroengines prognostics. The capability to assess not only the current state of an asset, but also to be able to predict its remaining useful life (RUL), and hence to perform condition-based maintenance (CBM) —if, and only when, it is needed— can represent a huge deal in the manufactur...

Numerical simulations have been performed to study the near and far fields of an axisymmetric zero-net-mass flux (ZNMF) jet in the laminar-transitional regime, before the three-dimensional vortex breakdown that promotes transition to turbulence. The main frequencies driving the flow and their associated spatial modes have been calculated using the...

The topological derivative tool is applied here in structural health monitoring (SHM) problems to locate small defects in a material plate with complex geometry that is subject to permanent multifrequency guided waves excitation. Compared to more standard SHM methods, based in measuring the time-lag between emitted and received propagative pulses p...

The objective of this work is to develop a procedure that allows for reconstructing three-dimensional flow fields from two-dimensional information contained in some representative planes, conveniently distributed throughout the domain. The reconstructing tool is based on two recent methods developed by two of the authors, namely the higher order dy...

A preliminary version of a data driven reduced order model (ROM) for dynamical systems is presented in this Chapter. This ROM synergically and adaptively combines a black-box full model (FM) of the system and extrapolate conveniently using a recent extension of standard dynamic mode decomposition called higher order dynamic mode decomposition (HODM...

The main goal of this work is to provide a new tool to reconstruct three-dimensional data from a few two-dimensional planes. To this purpose, spatio-temporal higher order dynamic mode decomposition (HODMD) is applied to a group of vertical and horizontal planes, located at different positions in space. Firstly, the method extracts the relevant freq...

This paper deals with the use of steady active thermographic inspection as a structural health monitoring method to detect defects and inclusions in a heat conductive medium. The proposed postprocessing method has the advantage of taking into account the whole physics of the problem instead of a reduced set of physical information, as most of the t...

This paper deals with the analysis of numerically obtained spatio-temporal data for thermal convection in a two-dimensional circular annulus. These data are post-processed using a recent method called the spatio-temporal Koopman decomposition, which applies to the frequent case in which the underlying dynamics exhibit oscillatory (possibly growing...

This article deals with the low-Reynolds-number wake interaction in two- and three-body configurations, at various angles of attack and various bodies location, cross-section (circular and square cylinders), and diameter. The flow physics is studied using higher order dynamic mode decomposition, which determines the driving frequencies and associat...

We present a method based on higher order dynamic mode decomposition (HODMD) to predict aeroelas-tic modes in signals representing fluid-structure interactions. For such aim, some data are generated using an open source solver called NeoCASS (Next generation Conceptual Aero-Structural Sizing Suite), which reproduces real flight test conditions. Sym...

The cover image is based on the Research Article New method to capture traveling waves in flow passing a wind turbine, by Soledad Le Clainche et al., https://doi.org/10.1002/we.2331. Cover image © Soledad Le Clainche, Xuerui Mao, José M. Vega.

Reduced Order Models (ROMs) have recently found great application within the field of aerothermodynamics, for the study of highly complex physical systems, such as the analysis of aeroelastic effects in transonic flight of modern jet fighters, heat transfer effects in separated flows, etc. Given the great computational time reduction that can be ac...

Flow structures in the wake of a wind turbine are analysed by performing spatio‐temporal Koopman decomposition (STKD). STKD is a new method to decompose the flow field as a combination of travelling waves and to extract the frequency and wavenumbers (characterizing a specific spatial direction) of the dominant waves. The results indicate that the c...

This Chapter presents a review on two methods for the analysis of flow structures in wind turbines. These methods are higher order dynamic mode decomposition and spatio-temporal Koopman decomposition, which are highly efficient tools suitable for the detection of spatio-temporal patterns in complex flows. These two techniques have been applied to d...

This article presents a review on two methods based on dynamic mode decomposition and its multiple applications, focusing on higher order dynamic mode decomposition (which provides a purely temporal Fourier-like decomposition) and spatiotemporal Koopman decomposition (which gives a spatiotemporal Fourier-like decomposition). These methods are purel...

This paper focuses on the low-dimensional representation of multivariate functions. We study a recursive POD representation, based upon the use of the power iterate algorithm to recursively expand the modes retained in the previous step. We obtain general error estimates for the truncated expansion, and prove that the recursive POD representation...

This paper presents the application of a new method, called higher-order dynamic mode decomposition (HODMD), to extract aircraft frequencies and damping in experimental data obtained from a flight flutter test. The method is an extension of standard dynamic mode decomposition, which is a method typically used to extract flow patterns and frequencie...

This paper deals with a new purely data-driven method, called the spatio-temporal Koopman decomposition, to approximate spatio-temporal data as a linear combination of (possibly growing or decaying exponentially) standing or traveling waves. The method combines (i) either standard singular value decomposition (SVD) or higher-order SVD and (ii) eith...

This paper deals with the use of the topological derivative as an analysis tool for structural health monitoring, to locate the presence of flaws in a homogeneous material plate that is subject to guided elastic waves excitation. Using a numerical solver to compute the response of the system and defining a scalar objective function that measures th...

This article presents a new method to predict the wind velocity upstream a horizontal axis wind turbine from a set of light detection and ranging (LiDAR) measurements. The method uses higher order dynamic mode decomposition (HODMD) to construct a reduced order model (ROM) that can be extrapolated in space. LiDAR measurements have been carried out u...

DOI:https://doi.org/10.1103/PhysRevLett.120.099901

A new method to analyze spatio-temporal flow structures is presented. It consists on applying a higher order dynamic mode decomposition sequentially, in time and space. The method is successfully applied to analyze the three-dimensional wake of a circular cylinder. The results obtained are in good agreement with their counterparts predicted by the...

Download the code in the following link: https://github.com/LeClaincheVega/HODMD

This article presents the spatio-temporal analysis of the ow structures in the wake of an off-shore wind turbine using spatio-temporal Koopman decomposition (STKD). STKD is a new method that obtains and combines the main frequencies and wavenumbers (characterizing a specific spatial direction) contained in a ow, with the aim at representing the mai...

As is well known, confined fluid systems subject to forced vibrations produce mean flows, called in this context streaming flows. These mean flows promote an overall mass transport in the fluid that has consequences in the transport of passive scalars and surfactants, when these are present in a fluid interface. Such transport causes surfactant con...

This article shows the capability of using a higher order dynamic mode decomposition (HODMD) algorithm both to identify flow patterns and to extrapolate a transient solution to the attractor region. Numerical simulations are carried out for the three-dimensional flow around a circular cylinder, and both standard dynamic mode decomposition (DMD) and...

A method is presented to treat complex experimental flow data resulting from PIV. The method is based on an appropriate combination of higher order singular value decomposition (which cleans the data along the temporal dimension and the various space dimensions) and higher order dynamic mode decomposition (HODMD), a recent extension of standard dyn...

A method is presented to filter out errors in multidimensional databases. The method does not require any a priori information about the nature of the errors, which need not be small, neither random, nor exhibit zero mean. Instead, they are only required to be relatively uncorrelated to the clean information contained in the database. The method pr...

A collocation method is developed for the (truncated) POD of a set of snapshots. In other words, POD computations are performed using only a set of collocation points, whose number is comparable to the number of retained modes, in a similar fashion as in collocation spectral methods. Intending to rely on simple ideas which, moreover, are consistent...

We examine both theoretically and experimentally the breakup of a pendant drop loaded with an insoluble surfactant. The experiments show that a significant amount of surfactant is trapped in the resulting satellite droplet. This result contradicts previous theoretical predictions, where the effects of surface tension variation were limited to solut...

This paper deals with an extension of dynamic mode decomposition (DMD), which is appropriate to treat general periodic and quasi-periodic dynamics, and transients decaying to periodic and quasi-periodic attractors, including cases (not accessible to standard DMD) that show limited spatial complexity but a very large number of involved frequencies....

Modern industrial aircraft design requires a large amount of sufficiently accurate aerodynamic and aeroelastic simulations. Current computational fluid dynamics (CFD) solvers with aeroelastic capabilities, such as the NASA URANS unstructured solver FUN3D, require very large computational resources. Since a very large amount of simulation is necessa...

This paper deals with the linear and nonlinear dynamics of an axisymmetric liquid bridge whose free surface is covered with an insoluble surfactant. In particular, we focus on the effect of the Marangoni elasticity and surface viscosities, both shear and dilatational. For linear oscillations, both the frequencies and damping rates are calculated an...

A reduced order model (ROM) is presented for the long-term calculation of sub-surface oil/water flows. As in several previous ROMs in the field, the Newton iterations in the full model (FM) equations, which are implicit in time, are projected onto a set of modes obtained by applying proper orthogonal decomposition (POD) to a set of snapshots comput...

A typical experiment to measure monolayer surface rheological properties consists of two parallel, slightly immersed, moving solid barriers that compress and expand a shallow liquid layer that contains the surfactant monolayer in its free surface. The area between the barriers controls the surfactant concentration, which is frequently assumed as...

In this work we investigate the reconstruction of sound-hard obstacles buried in a bounded material medium by a non-iterative method based on the computation of topological derivatives. The main purpose is to suitably combine multi-frequency data in a fairly demanding measurement configuration: a very reduced number of aligned emitters and receiver...

A method based on an iterative application of high order singular value decomposition is derived for the reconstruction of missing data in multidimensional databases. The method is inspired by a seminal gappy reconstruction method for two-dimensional databases invented by Everson and Sirovich (1995) [20] and improved by Beckers and Rixen (2003) [21...

A flexible Galerkin method based on proper orthogonal decomposition (POD) is described to construct the bifurcation diagram, as the Rayleigh number R is varied, in the Rayleigh–Bénard convection in a rectangular box for large Prandtl number. The bifurcation diagram is approximated using the POD modes resulting from unconverged snapshots for just on...

An adaptive low dimensional model is considered to simulate time dependent dynamics in nonlinear dissipative systems governed by partial differential equations. The method combines an inexpensive POD-based Galerkin system with short runs of a standard numerical solver that provides the snapshots necessary to first construct and then update the POD...

A theory is provided for a common experimental set up that is used to measure surface properties in surfactant monolayers. The set up consists of a surfactant monolayer (over a shallow liquid layer) that is compressed/expanded in a periodic fashion by moving in counter-phase two parallel, slightly immersed solid barriers, which vary the free surfac...

The excitation of subharmonic waves on the free surface of a horizontally vibrated, rectangular container of liquid is considered and the properties of threshold patterns are obtained and discussed. These waves are generally quasiperiodic and oblique (not aligned with the container walls). The parametric forcing mechanism generated by the harmonic...

Various ideas concerning model reduction based on proper orthogonal decomposition are discussed, exploited, and suited to the approximation of complex bifurcations in some dissipative systems. The observation that the most energetic modes involved in these low dimensional descriptions depend only weakly on the actual values of the problem parameter...

A computer-aided method suitable for assisting in the design of an aircraft by providing relevant dimensioning values corresponding to an aircraft component in transonic conditions inside a predefined parameter space by means of a reconstruction of the CFD computations for an initial group of points in the parameter space using a POD reduced-order...

An adaptive method is presented for the construction of bifurcation diagrams providing the large time dynamics of dissipative systems as a bifurcation parameter is varied. The method combines a standard numerical solver and a Galerkin system resulting from Galerkin projecting the governing equations onto a set of proper orthogonal decomposition (PO...

This paper deals with nearly inviscid, capillary gravity, modulated waves parametrically excited by monochromatic horizontal vibrations in liquid containers whose width and depth are both large compared with the wavelength of the excited waves. A general linear amplitude equation is derived with appropriate boundary conditions that provides the thr...

A surrogate model is presented to predict viscous drag in the context of conceptual design activities in aeronautics, where the norm is the use of low fidelity methods. The surrogate is developed with the requirement that its computational cost has to be comparable to that of its lower fidelity counterparts. The specific problem that has been chose...

A review is presented of the dynamic behavior of confined fluid systems with interfaces under monochromatic mechanical forcing, emphasizing the associated spatio-temporal structure of the fluid response. At low viscosity, vibrations significantly affect dynamics and always produce viscous mean flows, which are coupled to the primary oscillating flo...

A computer-aided method suitable for assisting in the design of an aircraft by providing a variable distribution V over an aircraft surface inside a predefined parameter space by means of a reconstruction of the results obtained through computations for an initial group of points in the parameter space using a CFD model comprising in each of said c...

A review is made of the calculation (and comparison with experiments) of the damping of surface waves, with special emphasis in some recent results and their quantitative and qualitative consequences on the surface waves dynamics. A method is proposed to experimentally measure the main surfactant properties associated with surface wave damping usin...