arXiv subjects

Miguel A. Mendez

Publications and source records attributed to Miguel A. Mendez.

36 records · Page 2Linked to original sources

arXiv2023

Multi-objective analysis of the Sand Hypoplasticity model calibration

The Sand Hypoplastic (SH) constitutive law by von Wolffersdorff (1996) is a interesting hypoplastic model for soil mechanics. This model includes eight parameters, usually calibrated using the oedometric (OE) and the drained isotropically consolidated triaxial tests (CD). However, previous studies show that the SH model calibration in the CD test has conflicting requirements in predicting the evolution of stresses and strains. In this work, we study the SH model calibration over a wide range of testing conditions using 12 OE and 25 CD tests by Wichtmann and Triantafyllidis (2016) on the Karlsruhe sands. The parameter space is extensively explored via Genetic Algorithm Optimization (GA) using the recently developed open-source software GA-cal (available at \url{https://github.com/FraJoMen/GA-cal}). This exploration allowed us to study the SH model's predictive limits and to identify, using a multi-objective analysis, the main parameters governing the compromise between the accurate prediction of stresses versus strain in the CD tests.

cond-mat.soft↗

arXiv2023

Evolution of waves in liquid films on moving substrates

Accurate and computationally accessible models of liquid film flows allow for optimizing coating processes such as hot-dip galvanization and vertical slot-die coating. This paper extends the classic three-dimensional integral boundary layer (IBL) model for falling liquid films (FF) to account for a moving substrate (MS). We analyze the stability of the liquid films on vertically moving substrates in a linear and a nonlinear setting. In the linear analysis, we derive the dispersion relation and the temporal growth rates of an infinitesimal disturbance using normal modes and linearized governing equations. In the nonlinear analysis, we consider disturbances of finite size and numerically compute their evolution using the set of nonlinear equations in which surface tension has been removed. We present the region of (linear) stability of both FF and MS configurations, and we place the operating conditions of an industrial galvanizing line in these maps. A wide range of flow conditions was analyzed and shown to be stable according to linear and nonlinear stability analyses. Moreover, the nonlinear analysis, carried out in the absence of surface tension, reveals a nonlinear stabilizing mechanism for the interface dynamics of a liquid film dragged by an upward-moving substrate.

physics.flu-dyn↗

arXiv2022

A Robust Data-Driven Model for Flapping Aerodynamics under different hovering kinematics

Flapping Wing Micro Air Vehicles (FWMAV) are highly manoeuvrable, bio-inspired drones that can assist in surveys and rescue missions. Flapping wings generate various unsteady lift enhancement mechanisms challenging the derivation of reduced models to predict instantaneous aerodynamic performance. In this work, we propose a robust CFD data-driven, quasi-steady (QS) Reduced Order Model (ROM) to predict the lift and drag coefficients within a flapping cycle. The model is derived for a rigid ellipsoid wing with different parameterized kinematics in hovering conditions. The proposed ROM is built via a two-stage regression. The first stage, defined as `in-cycle' (IC), computes the parameters of a regression linking the aerodynamic coefficients to the instantaneous wing state. The second stage, `out-of-cycle' (OOC), links the IC weights to the flapping features that define the flapping motion. The training and test dataset were generated via high-fidelity simulations using the overset method, spanning a wide range of Reynolds numbers and flapping kinematics. The two-stage regressor combines Ridge regression and Gaussian Process (GP) regression to provide estimates of the model uncertainties. The proposed ROM shows accurate aerodynamic predictions for widely varying kinematics. The model performs best for smooth kinematics that generate a stable Leading Edge Vortex (LEV). Remarkably accurate predictions are also observed in dynamic scenarios where the LEV is partially shed, the non-circulatory forces are considerable, and the wing encounters its own wake.

physics.flu-dyn↗

arXiv2022

Linear and Nonlinear Dimensionality Reduction from Fluid Mechanics to Machine Learning

Dimensionality reduction is the essence of many data processing problems, including filtering, data compression, reduced-order modeling and pattern analysis. While traditionally tackled using linear tools in the fluid dynamics community, nonlinear tools from machine learning are becoming increasingly popular. This article, halfway between a review and a tutorial, introduces a general framework for linear and nonlinear dimensionality reduction techniques. Differences and links between autoencoders and manifold learning methods are highlighted, and popular nonlinear techniques such as kernel Principal Component Analysis (kPCA), isometric feature learning (ISOMAPs) and Locally Linear Embedding (LLE) are placed in this framework. These algorithms are benchmarked in three classic problems: 1) filtering, 2) identification of oscillatory patterns, and 3) data compression. Their performances are compared against the traditional Proper Orthogonal Decomposition (POD) to provide a perspective on their diffusion in fluid dynamics.

physics.flu-dyn↗

arXiv2022

The GA-cal software for the automatic calibration of soil constitutive laws: a tutorial and a user manual

The calibration of an advanced constitutive law for soil is a challenging task. This work describes GA-cal, a Fortran software for automatically calibrating constitutive laws using Genetic Algorithms (GA) optimization. The proposed approach sets the calibration problem as a regression, and the GA optimization is used to adjust the model parameters so that a numerical model matches experimental data. This document provides a user guide and a simple tutorial. We showcase GA-cal on the calibration of the Sand Hypoplastic law proposed by von Wolffersdorff, with the oedometer and triaxial drained test data. The implemented subroutines can be easily extended to solve other regression or optimization problems, including different tests and constitutive models. The source code and the presented tutorial are freely available at \url{https://github.com/FraJoMen/GA-cal}.

cs.NE↗

arXiv2022

Comparative analysis of machine learning methods for active flow control

Machine learning frameworks such as Genetic Programming (GP) and Reinforcement Learning (RL) are gaining popularity in flow control. This work presents a comparative analysis of the two, bench-marking some of their most representative algorithms against global optimization techniques such as Bayesian Optimization (BO) and Lipschitz global optimization (LIPO). First, we review the general framework of the model-free control problem, bringing together all methods as black-box optimization problems. Then, we test the control algorithms on three test cases. These are (1) the stabilization of a nonlinear dynamical system featuring frequency cross-talk, (2) the wave cancellation from a Burgers' flow and (3) the drag reduction in a cylinder wake flow. We present a comprehensive comparison to illustrate their differences in exploration versus exploitation and their balance between `model capacity' in the control law definition versus `required complexity'. We believe that such a comparison paves the way toward the hybridization of the various methods, and we offer some perspective on their future development in the literature on flow control problems.

physics.flu-dyn↗

arXiv2022

Generalized and Multiscale Modal Analysis

This chapter describes modal decompositions in the framework of matrix factorizations. We highlight the differences between classic space-time decompositions and 2D discrete transforms and discuss the general architecture underpinning \emph{any} decomposition. This setting is then used to derive simple algorithms that complete \emph{any} linear decomposition from its spatial or temporal structures (bases). Discrete Fourier Transform, Proper Orthogonal Decomposition (POD), Dynamic Mode Decomposition (DMD), and Eigenfunction Expansions (EF) are formulated in this framework and compared on a simple exercise. Finally, this generalization is used to analyze the impact of spectral constraints on the classical POD, and to derive the Multiscale Proper Orthogonal Decomposition (mPOD). This decomposition combines Multiresolution Analysis (MRA) and POD. This chapter contains four exercises and two tutorial test cases. The \textsc{Python} scripts associated to these are provided on the book's website.

math.NA↗

arXiv2022

Continuous and Discrete LTI Systems

This chapter reviews the fundamentals of continuous and discrete Linear Time-Invariant (LTI) systems with Single Input-Single Output (SISO). We start from the general notions of signals and systems, the signal representation problem and the related orthogonal bases in discrete and continuous forms. We then move to the key properties of LTI systems and discuss their eigenfunctions, the input-output relations in the time and frequency domains, the conformal mapping linking the continuous and the discrete formulations, and the modeling via differential and difference equations. Finally, we close with two important applications: (linear) models for time series analysis and forecasting and (linear) digital filters for multi-resolution analysis. This chapter contains seven exercises, the solution of which is provided in the book's webpage.

math.OC↗

arXiv2022

A 1D Model for the Unsteady Gas Dynamics of Ejectors

We propose a 1D unsteady model for supersonic single-phase ejectors. The model treats an ejector as a pipe network with two inputs and one output and combines a 1D gas dynamics formulation in each `pipe' with a junction model for entrainment and mixing. The model is calibrated and validated on experimental data in steady-state conditions and used to analyze the choking mechanism for the mixed flow. The model was then benchmarked against 2D URANS simulations to predict the ejector response to a sudden change in operating conditions, producing traveling waves. The results show that the model can correctly predict the ejector performance and the stream-wise evolution of relevant integral quantities (e.g. mass flow rates and momentum) in both steady and transient conditions.

physics.flu-dyn↗

arXiv2022

A RANS approach to the Meshless Computation of Pressure Fields From Image Velocimetry

We propose a 3D meshless method to compute mean pressure fields in turbulent flows from image velocimetry. The method is an extension of the constrained Radial Basis Function (RBF) formulation by \citet{Sperotto2022} to a Reynolds Averaged Navier Stokes (RANS) framework. This is designed to handle both scattered data as in Particle Tracking Velocimetry (PTV) and data in uniform grids as in correlation-based Particle Image Velocimetry (PIV). The RANS extension includes the Reynolds stresses into the constrained least square problem. We test the approach on a numerical database featuring a Backward Facing Step (BFS) with a Reynolds number of 6400 (defined with respect to the inlet velocity and step height), obtained via Direct Numerical Simulation (DNS).

physics.flu-dyn↗

arXiv2022

Analysis of an unsteady quasi-capillary channel flow with Time Resolved PIV and RBF-based super resolution

We investigate the behaviour of accelerating contact lines in an unsteady quasi-capillary channel flow. The configuration consists of a liquid column that moves along a vertical 2D channel, open to the atmosphere and driven by a controlled pressure head. Both advancing and receding contact lines were analyzed to test the validity of classic models for dynamic wetting and to study the flow field near the interface. The operating conditions are characterized by a large acceleration, thus dominated by inertia. The shape of the moving meniscus was retrieved using Laser-Induced Fluorescence (LIF)-based image processing while the flow field near was analyzed via Time-Resolved Particle Image Velocimetry (TR-PIV). The TR-PIV measurements were enhanced in the post-processing, using a combination of Proper Orthogonal Decomposition (POD) and Radial Basis Functions (RBF) to achieve super-resolution of the velocity field. Large counter-rotating vortices were observed, and their evolution was monitored in terms of the maximum intensity of the Q-field. The results show that classic contact angle laws based on interface velocity cannot describe the evolution of the contact angle at a macroscopic scale. Moreover, the impact of the interface dynamics on the flow field is considerable and extends several capillary lengths below the interface.

physics.flu-dyn↗

arXiv2022

A Meshless Method to Compute Pressure Fields from Image Velocimetry

We propose a meshless method to compute pressure fields from image velocimetry data, regardless of whether this is available on a regular grid as in cross-correlation based velocimetry or on scattered points as in tracking velocimetry. The proposed approach is based on Radial Basis Functions (RBFs) regression and relies on the solution of two constrained least square problems. The first one is the regression of the measurements to create an analytic representation of the velocity field. This regression can be constrained to impose boundary conditions (e.g. no-slip velocity on a wall or inlet conditions) or differential constraints (e.g. the solenoidal condition for an incompressible flow). The second one is the meshless integration of the pressure Poisson equation, achieved by seeking a solution in the form of a RBF expansion and using constraints to impose boundary conditions. We first illustrate the derivation of the two least square problems and the numerical techniques implemented for their solution. Then, we showcase the method with three numerical test cases of growing complexity. These are a 2D Gaussian Vortex, a 2D flow past a cylinder from CFD and a 3D Stokes flow past a sphere. For each case, we consider randomly sampled vector fields simulating particle tracking measurements and analyze the sensitivity to noise and seeding density.

physics.flu-dyn↗

arXiv2021

On the Dynamics of the Jet Wiping Process: Numerical Simulations and Modal Analysis

We analyze the flow of a planar gas jet impinging on a thin film, dragged by a vertical moving wall. In the coating industry, this configuration is known as jet wiping, a process in which impinging jets control the thickness of liquid coatings on flat plates withdrawn vertically from a coating bath. We present three-dimensional (3D) two-phase flow simulations combining Large Eddy Simulation (LES) and Volume of Fluid (VOF). Three wiping configurations are simulated and the results are validated with experimental data from previous works. Multiscale modal analysis is used to analyze the dynamic interaction between the gas flow and the liquid film. In particular, we present a combination of Multiscale Proper Orthogonal decomposition (mPOD) and correlation analysis. The mPOD is used to identify the dominant travelling wave pattern in the liquid film flow, and the temporal structures are used to determine the most correlated flow features in the gas jet. This allows for revealing a two-dimensional (2D) mechanism for wave formation in the liquid coat. Finally, we use the numerical results to analyze the validity of some of the critical assumptions underpinning the derivation of integral film models of jet wiping.

physics.flu-dyn↗

arXiv2020

MODULO: A software for Multiscale Proper Orthogonal Decomposition of data

In the era of the Big Data revolution, methods for the automatic discovery of regularities in large datasets are becoming essential tools in applied sciences. This article presents an open software package, named MODULO (MODal mULtiscale pOd), to perform the Multiscale Proper Orthogonal Decomposition (mPOD) of numerical and experimental data. This novel decomposition combines Multi-resolution Analysis (MRA) and standard Proper Orthogonal Decomposition (POD) to allow for the optimal compromise between decomposition convergence and spectral purity of its modes. The software is equipped with a Graphical User Interface (GUI) and enriched by numerous examples and video tutorials (see Youtube channel MODULO mPOD). The MATLAB source codes and an executable for Windows users can be downloaded at \url{https://github.com/mendezVKI/MODULO/releases}; a collection of exercises in Matlab and Python are provided in \url{https://github.com/mendezVKI/MODULO}

physics.data-an↗

arXiv2020

Calibration of the von Wolffersdorff model using Genetic Algorithms

This article proposes an optimization framework, based on Genetic Algorithms (GA), to calibrate the constitutive law of von Wolffersdorff. This constitutive law is known as Sand Hypoplasticity (SH), and allows for robust and accurate modeling of the soil behavior but requires a complex calibration involving eight parameters. The proposed optimization can automatically fit these parameters from the results of an oedometric and a triaxial drained compression test, by combining the GA with a numerical solver that integrates the SH in the test conditions. By repeating the same calibration several times, the stochastic nature of the optimizer enables the uncertainty quantification of the calibration parameters and allows studying their relative importance on the model prediction. After validating the numerical solver on the ExCaliber-Laboratory software from the SoilModels' website, the GA calibration is tested on a synthetic dataset to analyze the convergence and the statistics of the results. In particular, a correlation analysis reveals that two couples of the eight model parameters are strongly correlated. Finally, the calibration procedure is tested on the results from von Wolffersdorff, 1996, and Herle & Gudehus, 1999, on the Hochstetten sand. The model parameters identified by the Genetic Algorithm optimization improves the matching with the experimental data and hence lead to a better calibration.

cs.CE↗

arXiv2020

Shift-Plethystic Trees and Rogers-Ramanujan Identitites

By studying non-commutative series in an infinite alphabet we introduce shift-plethystic trees and a class of integer compositions as new combinatorial models for the Rogers-Ramanujan identities. We prove that the language associated to shift-plethystic trees can be expressed as a non-commutative generalization of the Rogers-Ramanujan continued fraction. By specializing the noncommutative series to $q$-series we obtain new combinatorial interpretations to the Rogers-Ramanujan identities in terms of signed integer compositions. We introduce the operation of shift-plethysm on non-commutative series and use this to obtain interesting enumerative identities involving compositions and partitions related to Rogers-Ramanujan identities.

math.CO↗

arXiv2016

Combinatorial differential operators in: Faà di Bruno formula, enumeration of ballot paths, enriched rooted trees and increasing rooted trees

We obtain a differential equation for the enumeration of the path length of general increasing trees. By using differential operators and their combinatorial interpretation we give a bijective proof of a version of Faà di Bruno formula, and model the generation of ballot and Dyck paths. We get formulas for its enumeration according with the height of their lattice points. Recursive formulas for the enumeration of enriched increasing trees and forests with respect to the height of their internal and external vertices are also obtained. Finally we present a generalized form of all those results using one-parameter groups in the general context of formal power series in an arbitrary number of variables.

math.CO↗

arXiv2008

Koszul duality for monoids and the operad of enriched rooted trees

We introduce here the notion of Koszul duality for monoids in the monoidal category of species with respect to the ordinary product. To each Koszul monoid we associate a class of Koszul algebras in the sense of Priddy, by taking the corresponding analytic functor. The operad $\mathscr{A}_M$ of rooted trees enriched with a monoid $M$ was introduced by the author many years ago. One special case of that is the operad of ordinary rooted trees, called in the recent literature the permutative non associative operad. We prove here that $\mathscr{A}_M$ is Koszul if and only if the corresponding monoid $M$ is Koszul. In this way we obtain a wide family of Koszul operads, extending a recent result of Chapoton and Livernet, and providing an interesting link between Koszul duality for associative algebras and Koszul duality for operads.

math.CO↗