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This paper presents a physics-based data-driven method to learn predictive reduced-order models (ROMs) from high-fidelity simulations, and illustrates it in the challenging context of a single-injector combustion process. The method combines the perspectives of model reduction and machine learning. Model reduction brings in the physics of the problem, constraining the ROM predictions to lie on a subspace defined by the governing equations. This is achieved by defining the ROM in proper orthogonal decomposition (POD) coordinates, which embed the rich physics information contained in solution snapshots of a high-fidelity computational fluid dynamics (CFD) model. The machine learning perspective brings the flexibility to use transformed physical variables to define the POD basis. This is in contrast to traditional model reduction approaches that are constrained to use the physical variables of the high-fidelity code. Combining the two perspectives, the approach identifies a set of transformed physical variables that expose quadratic structure in the combustion governing equations and learns a quadratic ROM from transformed snapshot data. This learning does not require access to the high-fidelity model implementation. Numerical experiments show that the ROM accurately predicts temperature, pressure, velocity, species concentrations, and the limit-cycle amplitude, with speedups of more than five orders of magnitude over high-fidelity models. Moreover, ROM-predicted pressure traces accurately match the phase of the pressure signal and yield good approximations of the limit-cycle amplitude.

Sensors are crucial to modern mechanical systems. The location of these sensors can often make them vulnerable to outside interferences and failures, and the use of sensors over a lifetime can cause degradation and lead to failure. If a system has access to redundant sensor output, it can be trained to autonomously recognize errors in faulty sensors and learn to correct them. In this work, we develop a novel data-driven approach to detect sensor failures and predict the corrected sensor data using machine learning methods in an offline/online paradigm. Autocorrelation is shown to provide a global feature of failure data capable of accurately classifying the state of a sensor to determine if a failure is occurring. Feature selection of the redundant sensor data in combination with k-nearest neighbors regression is used to predict the corrected sensor data rapidly, while the system is operational. We demonstrate our methodology on flight data from a four-engine commercial jet that contains failures in the pitot static system resulting in inaccurate airspeed measurements.

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