FlexWing-ROM: A matlab framework for data-driven reduced-order modeling of flexible wings

Flexible wings pose a considerable modeling challenge, as they involve highly coupled and nonlinear interactions between the aerodynamic and structural dynamics. In this work, we provide an open source code framework, unifying recent data-driven modeling methods that extend the dynamic mode decomposition with control (DMDc) to model the nonlinear aeroelasticity of flexible wings. Our framework consists of (1) a fully parametrized flexible wing model; (2) a fluid-structure interaction (FSI) solver that couples a detailed finite element model of the wing structure with a 3D unsteady aerodynamic panel method; and (3) three different data-driven reduced-order aeroelastic modeling methods. We demonstrate our framework on two flexible wings and provide tutorials to compare the different data-driven methods. The code is widely applicable and useful for generating accurate and efficient data-driven reduced-order models, and it provides a benchmark for future developments of aeroelastic reduced-order modeling methods

Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control

Sparse model identification enables the discovery of nonlinear dynamical systems purely from data; however, this approach is sensitive to noise, especially in the low-data limit. In this work, we leverage the statistical approach of bootstrap aggregating (bagging) to robustify the sparse identification of the nonlinear dynamics (SINDy) algorithm. First, an ensemble of SINDy models is identified from subsets of limited and noisy data. The aggregate model statistics are then used to produce inclusion probabilities of the candidate functions, which enables uncertainty quantification and probabilistic forecasts. We apply this ensemble-SINDy (E-SINDy) algorithm to several synthetic and real-world datasets and demonstrate substantial improvements to the accuracy and robustness of model discovery from extremely noisy and limited data. For example, E-SINDy uncovers partial differential equations models from data with more than twice as much measurement noise as has been previously reported. Similarly, E-SINDy learns the Lotka Volterra dynamics from remarkably limited data of yearly lynx and hare pelts collected from 1900 to 1920. E-SINDy is computationally efficient, with similar scaling as standard SINDy. Finally, we show that ensemble statistics from E-SINDy can be exploited for active learning and improved model predictive control

An empirical mean-field model of symmetry-breaking in a turbulent wake

Improved turbulence modeling remains a major open problem in mathematical physics. Turbulence is notoriously challenging, in part due to its multiscale nature and the fact that large-scale coherent structures cannot be disentangled from small-scale fluctuations. This closure problem is emblematic of a greater challenge in complex systems, where coarse-graining and statistical mechanics descriptions break down. This work demonstrates an alternative data-driven modeling approach to learn nonlinear models of the coherent structures, approximating turbulent fluctuations as state-dependent stochastic forcing. We demonstrate this approach on a high-Reynolds number turbulent wake experiment, showing that our model reproduces empirical power spectra and probability distributions. The model is interpretable, providing insights into the physical mechanisms underlying the symmetry-breaking behavior in the wake. This work suggests a path toward low-dimensional models of globally unstable turbulent flows from experimental measurements, with broad implications for other multiscale systems

Data-driven nonlinear aeroelastic models of morphing wings for control

Accurate and efficient aeroelastic models are critically important for enabling the optimization and control of highly flexible aerospace structures, which are expected to become pervasive in future transportation and energy systems. Advanced materials and morphing wing technologies are resulting in next-generation aeroelastic systems that are characterized by highly coupled and nonlinear interactions between the aerodynamic and structural dynamics. In this work, we leverage emerging data-driven modelling techniques to develop highly accurate and tractable reduced-order aeroelastic models that are valid over a wide range of operating conditions and are suitable for control. In particular, we develop two extensions to the recent dynamic mode decomposition with control (DMDc) algorithm to make it suitable for flexible aeroelastic systems: (1) we introduce a formulation to handle algebraic equations, and (2) we develop an interpolation scheme to smoothly connect several linear DMDc models developed in different operating regimes. Thus, the innovation lies in accurately modelling the nonlinearities of the coupled aerostructural dynamics over multiple operating regimes, not restricting the validity of the model to a narrow region around a linearization point. We demonstrate this approach on a high-fidelity, three-dimensional numerical model of an airborne wind energy system, although the methods are generally applicable to any highly coupled aeroelastic system or dynamical system operating over multiple operating regimes. Our proposed modelling framework results in real-time prediction of nonlinear unsteady aeroelastic responses of flexible aerospace structures, and we demonstrate the enhanced model performance for model predictive control. Thus, the proposed architecture may help enable the widespread adoption of next-generation morphing wing technologies

Nonlinear stochastic modelling with Langevin regression

Many physical systems characterized by nonlinear multiscale interactions can be modelled by treating unresolved degrees of freedom as random fluctuations. However, even when the microscopic governing equations and qualitative macroscopic behaviour are known, it is often difficult to derive a stochastic model that is consistent with observations. This is especially true for systems such as turbulence where the perturbations do not behave like Gaussian white noise, introducing non-Markovian behaviour to the dynamics. We address these challenges with a framework for identifying interpretable stochastic nonlinear dynamics from experimental data, using forward and adjoint Fokker–Planck equations to enforce statistical consistency. If the form of the Langevin equation is unknown, a simple sparsifying procedure can provide an appropriate functional form. We demonstrate that this method can learn stochastic models in two artificial examples: recovering a nonlinear Langevin equation forced by coloured noise and approximating the second-order dynamics of a particle in a double-well potential with the corresponding first-order bifurcation normal form. Finally, we apply Langevin regression to experimental measurements of a turbulent bluff body wake and show that the statistical behaviour of the centre of pressure can be described by the dynamics of the corresponding laminar flow driven by nonlinear state-dependent noise

Modal Analysis of Fluid Flows: An Overview

Simple aerodynamic configurations under even modest conditions can exhibit complex flows with a wide range of temporal and spatial features. It has become common practice in the analysis of these flows to look for and extract physically important features, or modes, as a first step in the analysis. This step typically starts with a modal decomposition of an experimental or numerical dataset of the flow field, or of an operator relevant to the system. We describe herein some of the dominant techniques for accomplishing these modal decompositions and analyses that have seen a surge of activity in recent decades. For a non-expert, keeping track of recent developments can be daunting, and the intent of this document is to provide an introduction to modal analysis in a presentation that is accessible to the larger fluid dynamics community. In particular, we present a brief overview of several of the well-established techniques and clearly lay the framework of these methods using familiar linear algebra. The modal analysis techniques covered in this paper include the proper orthogonal decomposition (POD), balanced proper orthogonal decomposition (Balanced POD), dynamic mode decomposition (DMD), Koopman analysis, global linear stability analysis, and resolvent analysis

Improved vision based pose estimation for industrial robots via sparse regression

In this work amonocular machine vision based pose estimation system is developed for industrial robots and the accuracy of the estimated pose is im-proved via sparse regression. The proposed sparse regressionbased methodis usedimprove the accuracy obtained from the Levenberg-Marquardt (LM) based pose estimation algorithmduring the trajectory tracking of an industrial robot’s end effector. The proposed method utilizes a set of basis functions to sparsely identify the nonlinear relationship between the estimated pose and the true pose provided by a laser tracker.Moreover,a camera target was designed and fitted with fiducial markers,andto prevent ambiguities in pose estimation, the markers are placed in such a way to guarantee the detection of at least two distinct nonparallel markers from a single camera within ± 90° in all directions of the cam-era’s view. The effectiveness of the proposed method is validated by an experi-mental study performed using a KUKA KR240 R2900 ultra robot while follow-ing sixteen distinct trajectories based on ISO 9238. The obtained results show that the proposed method provides parsimonious models which improve the pose estimation accuracy and precision of the vision based system during trajectory tracking of industrial robots' end effector

Closed-loop separation control over a sharp edge ramp using Genetic Programming

We experimentally perform open and closed-loop control of a separating turbulent boundary layer downstream from a sharp edge ramp. The turbulent boundary layer just above the separation point has a Reynolds number $Re_{\theta}\approx 3\,500$ based on momentum thickness. The goal of the control is to mitigate separation and early re-attachment. The forcing employs a spanwise array of active vortex generators. The flow state is monitored with skin-friction sensors downstream of the actuators. The feedback control law is obtained using model-free genetic programming control (GPC) (Gautier et al. 2015). The resulting flow is assessed using the momentum coefficient, pressure distribution and skin friction over the ramp and stereo PIV. The PIV yields vector field statistics, e.g. shear layer growth, the backflow area and vortex region. GPC is benchmarked against the best periodic forcing. While open-loop control achieves separation reduction by locking-on the shedding mode, GPC gives rise to similar benefits by accelerating the shear layer growth. Moreover, GPC uses less actuation energy.Comment: 24 pages, 24 figures, submitted to Experiments in Fluid

Threat-sensitive anti-predator defence in precocial wader, the northern lapwing Vanellus vanellus

Birds exhibit various forms of anti-predator behaviours to avoid reproductive failure, with mobbing—observation, approach and usually harassment of a predator—being one of the most commonly observed. Here, we investigate patterns of temporal variation in the mobbing response exhibited by a precocial species, the northern lapwing (Vanellus vanellus). We test whether brood age and self-reliance, or the perceived risk posed by various predators, affect mobbing response of lapwings. We quantified aggressive interactions between lapwings and their natural avian predators and used generalized additive models to test how timing and predator species identity are related to the mobbing response of lapwings. Lapwings diversified mobbing response within the breeding season and depending on predator species. Raven Corvus corax, hooded crow Corvus cornix and harriers evoked the strongest response, while common buzzard Buteo buteo, white stork Ciconia ciconia, black-headed gull Chroicocephalus ridibundus and rook Corvus frugilegus were less frequently attacked. Lapwings increased their mobbing response against raven, common buzzard, white stork and rook throughout the breeding season, while defence against hooded crow, harriers and black-headed gull did not exhibit clear temporal patterns. Mobbing behaviour of lapwings apparently constitutes a flexible anti-predator strategy. The anti-predator response depends on predator species, which may suggest that lapwings distinguish between predator types and match mobbing response to the perceived hazard at different stages of the breeding cycle. We conclude that a single species may exhibit various patterns of temporal variation in anti-predator defence, which may correspond with various hypotheses derived from parental investment theory

Diversity of Matriptase Expression Level and Function in Breast Cancer

Overexpression of matriptase has been reported in a variety of human cancers and is sufficient to trigger tumor formation in mice, but the importance of matriptase in breast cancer remains unclear. We analysed matriptase expression in 16 human breast cancer cell lines and in 107 primary breast tumors. The data revealed considerable diversity in the expression level of this protein indicating that the significance of matriptase may vary from case to case. Matriptase protein expression was correlated with HER2 expression and highest expression was seen in HER2-positive cell lines, indicating a potential role in this subgroup. Stable overexpression of matriptase in two breast cancer cell lines had different consequences. In MDA-MB-231 human breast carcinoma cells the only noted consequence of matriptase overexpression was modestly impaired growth in vivo. In contrast, overexpression of matriptase in 4T1 mouse breast carcinoma cells resulted in visible changes in morphology, actin staining and cell to cell contacts. This correlated with downregulation of the cell-cell adhesion molecule E-cadherin. These results suggest that the functions of matriptase in breast cancer are likely to be variable and cell context dependent