Global Nonlinear Modeling Using Automated Local Model Networks in Real Time

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Global nonlinear modeling is a challenging task that spans multiple disciplines. When it is necessary to develop a model across the global input space, and a single linear model is insufficient, nonlinear modeling methods are required. If the model is constrained to be developed autonomously in real time, the modeling problem is more difficult, and there are fewer available resources, tools, and techniques for efficient and effective model development. This scenario specifically arises in the context of the NASA Learn-to-Fly concept, which aims to develop tools for real-time aerodynamic modeling and control for new or modified flight vehicles, and which serves as the motivation for this research. This work aims to develop a modeling method that enables the model to be developed automatically in real time, with limited prior knowledge required, and that provides a model that is easily interpretable, allows physical insight into the system, and offers good global and local prediction capabilities. A novel method is developed and presented in this work for automated real-time global nonlinear modeling using local model networks, known as Smoothed Partitioning with LocalIzed Trees in Real time (SPLITR). The global nonlinear system behavior is partitioned into several local regions known as cells, with the dimension, location, and timing of each partition automatically selected based on a new residual characterization procedure, under the constraints of real-time operation. Regression trees represent the successive partitioning of the global input space and describe the evolution of the cell structure. Recursive equation-error least-squares parameter estimation in the time domain is used to estimate a model that represents the local system behavior in each region so that the model can be updated independently with data in the explanatory variable ranges of each cell, even if the data are not contiguous in time. A weighted superposition of these piecewise local models across the input space forms a global nonlinear model that also accurately captures the local behavior. The SPLITR approach was tested and validated using both simplified simulated test data, as well as experimental flight test data, and the results were analyzed in terms of model predictive capabilities and interpretability. The results show that SPLITR can be used to automatically partition complex nonlinear behavior in real time, produce an accurate model, and provide valuable physical insight into the local and global system behavior.