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.

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Automated data-driven modeling, the process of directly discovering the governing equations of a system from data, is increasingly being used across the scientific community. PySINDy is a Python package that provides tools for applying the sparse identification of nonlinear dynamics (SINDy) approach to data-driven model discovery. In this major update to PySINDy, we implement several advanced features that enable the discovery of more general differential equations from noisy and limited data. The library of candidate terms is extended for the identification of actuated systems, partial differential equations (PDEs), and implicit differential equations. Robust formulations, including the integral form of SINDy and ensembling techniques, are also implemented to improve performance for real-world data. Finally, we provide a range of new optimization algorithms, including several sparse regression techniques and algorithms to enforce and promote inequality constraints and stability. Together, these updates enable entirely new SINDy model discovery capabilities that have not been reported in the literature, such as constrained PDE identification and ensembling with different sparse regression optimizers.

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.

In this paper, we present the design and computational model of a representative multi-megawatt airborne wind energy (AWE) system, together with a simulation framework that accounts for the flight dynamics of the fixed-wing aircraft and the sagging of the tether, combining this with flight control and optimisation strategies to derive the power curve of the system. The computational model is based on a point mass approximation of the aircraft, a discretisation of the tether by five elastic segments and a rotational degree of freedom of the winch. The aircraft has a wing surface area of 150 m2 and is operated in pumping cycles, alternating between crosswind flight manoeuvres during reel out of the tether, and rapid decent towards the ground station during reel in. To maximise the net cycle power, we keep the design parameters of the aircraft constant, while tuning the operational and controller parameters for different wind speeds and given contraints. We find that the presented design can generate a net cycle power of up to 3.8 megawatts.