Monitoring the dynamics processes in combustors is crucial for safe and efficient operations. However, in practice, only limited data can be obtained due to limitations in the measurable quantities, visualization window, and temporal resolution. Therefore, computational tools aiming at the inference of unknown information based on available measurements have been developed and are often termed as inverse models. Conventional inverse models, such as the surrogate approach, suffer the curse of dimensionality since the computational cost increases significantly as the number of unknown quantities increases. In the present work, we aimed at utilizing neural networks to approximate the unknown quantities and training the neural networks efficiently with available measurements by differential programming. Different from the conventional regression methods to train neural networks, physical constraints are imposed during the training by the governing differential equations. Therefore, the training can be viewed as unsupervised learning to avoid the need for obtaining labeled training data, in this case, the unmeasurable, which are intrinsic obstacles for modeling industrial combustors with data-driven approaches.We demonstrated the inverse modeling approach in a model combustor system by simulating the oscillation of an industrial combustor with a perfect stirred reactor. Given the sparse measurements of the temperature inside the combustor, upstream fluctuations in compositions and/or temperature can be inferred. To achieve this goal, an open-source differentiable combustion simulation package of Arrhenius.jl was developed, where the differential programing language of Julia was utilized to encode and solve the governing equations of a perfect stirred reactor, conduct auto-differentiation, and train the neural network models. Various types of fluctuations in the upstream, as well as the responses in the combustor, were synthesized to train and validate the algorithm. The results demonstrated that the approach can efficiently and accurately infer the dynamics of the compositions and temperature upstream, even without assuming the types of fluctuations.While in this work a combustor was modeled as a zero-dimensional reactor, the approach can be generalized to three-dimensional modeling with flow-chemistry interactions. We, therefore, discussed the challenges in differential programming for combustion modeling and proposed potential solutions. For instance, since the modeling of combustion usually involves stiff chemistry that makes the differential programming of combustion systems challenging due to high computational cost, we discussed the current and future computational techniques that can handle stiffness, such as parallel auto-differentiation. Comparing to a non-reacting flow system, the kinetic models in combustion that incorporated in the governing equations usually contain substantial uncertainties, we thus proposed to simultaneously optimize the unknown quantities and the kinetic models to mitigate the effect of the chemical model uncertainties. Finally, we also discussed the opportunities and challenges of employing the current approach for the dynamic control of industrial power systems.

Neural Differential Equations for Inverse Modeling in Model Combustors

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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