We are developing the methods and algorithms that enable creation of a Predictive Digital Twin. We combine scientific machine learning with predictive physics-based models. Component-based reduced-order modeling makes the approach computationally efficient and scalable. Our physical asset is a custom-built 12ft wingspan unmanned aerial vehicle. We build a structural Digital Twin that we use to monitor vehicle structural health and to drive dynamic flight planning decisions.
Digital Twin component-based library
At the heart of our digital twin is a library of physics-based models, each representing a different structural state. We use a component-based reduced-order modeling approach, so that these physics-based models are accurate and fast to evaluate, even at the scale of the full UAV structure. We model different damage states by creating multiple versions of each component in the model. Each version has a different damage state. In this example we create five copies of two components in the right wing of the UAV. Each copy has a reduction in stiffness of between 0% (pristine case) and 80% (worst damage case). In flight, we use onboard structural sensor data to estimate which model best matches the current state of the UAV, and use this model in the digital twin. This ensures that the digital twin is constantly updated to reflect the current state of the UAV.
Interpretable machine learning
We use interpretable machine learning to train an optimal classification tree that predicts which model from the library best matches a set of structural measurements. These trees partition the space of sensor measurements so that each resulting region corresponds to a particular damage state. When a new sensor measurement is acquired, we use the classification tree to decide which damage state best matches the data. The classification tree is interpretable because explicitly characterizes decision boundaries and it naturally enables sparse sensing.
Although the methods we develop can be applied to a wide range of physical assets, our testbed for this research is a custom-built 12ft wingspan fixed-wing UAV, developed in collaboration with Aurora Flight Sciences. This UAV is outfitted with a suite of structural sensors such as strain gauges, accelerometers, and high frequency vibration sensors.
Dynamic decision making
We demonstrate the benefits of our approach on an illustrative UAV scenario. In this scenario, the UAV must fly safely through a set of obstacles to a goal location. The UAV undergoes a damage event and then continues to accumulate structural degradation. The UAV must choose either an aggressive flight path or a more conservative path around each obstacle. The aggressive path is faster, but requires the UAV to make sharp turns that subject the UAV to high structural loads. The more conservative route is slower, but subjects the UAV to lower structural loads. In pristine condition, the aircraft structure can safely withstand the higher loading, but as the aircraft wing structure accumulates damage, the high load may lead to structural failure. As shown in the movie above, our self-aware UAV uses the rapidly updating digital twin to monitor its evolving structural state and dynamically estimate its flight capability. Based on these capability estimates the UAV is able to dynamically replan the mission in order to maximize speed while avoiding structural failure.
Kapteyn, M., Knezevic, D. and Willcox, K. In proceedings of 2020 AIAA Scitech Forum & Exhibition, Orlando, FL, January 2020.
This work develops a methodology for creating and updating data-driven physics-based digital twins, and demonstrates the approach through the development of a structural digital twin for a 12ft wingspan unmanned aerial vehicle. The digital twin is built from a library of component-based reduced-order models that are derived from high-fidelity finite element simulations of the vehicle in a range of pristine and damaged states. In contrast with traditional monolithic techniques for model reduction, the component-based approach scales efficiently to large complex systems, and provides a flexible and expressive framework for rapid model adaptation—both critical features in the digital twin context. The digital twin is deployed and updated using interpretable machine learning. Specifically, we use optimal trees—a recently developed scalable machine learning method—to train an interpretable data-driven classifier. In operation, the classifier takes as input vehicle sensor data, and then infers which physics-based reduced models in the model library are the best candidates to compose an updated digital twin. In our example use case, the data-driven digital twin enables the aircraft to dynamically replan a safe mission in response to structural damage or degradation.
Singh, V. and Willcox, K., AIAA Journal, Vol. 55, No. 8, pp. 2727-2738, 2017.
This paper presents methodology to enable path planning for an unmanned aerial vehicle that uses dynamic data-driven flight capability estimation. The main contribution of the work is a general mathematical approach that leverages offline high-fidelity physics-based modeling together with onboard sensor measurements to achieve dynamic path planning. The mathematical framework, expressed as a constrained partially observable Markov decision process, accounts for vehicle capability constraints and is robust to modeling error and disturbances in both the vehicle process and measurement models. Vehicle capability constraints are incorporated using probabilistic support vector machine surrogates of high-fidelity physics-based models that adequately capture the richness of the vehicle dynamics. Sensor measurements are treated in a general manner and can include combinations of multiple modalities such as that through global positioning system signals, inertial mass unit outputs, and structural strain data of the airframe. Results are presented for a simulated three-dimensional environment and point-mass airplane model. The vehicle can dynamically adjust its trajectory according to the observations it receives about its current state of health, thereby retaining a high probability of survival and mission success.
Lecerf, M., Allaire, D. and Willcox, K. AIAA Journal , Vol. 53, No. 10, pp. 3073-3087, October 2015. (An earlier version of this work appeared in AIAA Paper 2014-1175, January 2014.)
This paper presents a data-driven approach for the online updating of the flight envelope of an unmanned aerial vehicle subjected to structural degradation. The main contribution of the work is a general methodology that leverages both physics-based modeling and data to decompose tasks into two phases: expensive offline simulations to build an efficient characterization of the problem and rapid data-driven classification to support online decision making. In the approach, physics-based models at the wing and vehicle level run offline to generate libraries of information covering a range of damage scenarios. These libraries are queried online to estimate vehicle capability states. The state estimation and associated quantification of uncertainty are achieved by Bayesian classification using sensed strain data. The methodology is demonstrated on a conceptual unmanned aerial vehicle executing a pullup maneuver, in which the vehicle flight envelope is updated dynamically with onboard sensor information. During vehicle operation, the maximum maneuvering load factor is estimated using structural strain sensor measurements combined with physics-based information from precomputed damage scenarios that consider structural weakness. Compared to a baseline case that uses a static as-designed flight envelope, the self-aware vehicle achieves both an increase in probability of executing a successful maneuver and an increase in overall usage of the vehicle capability.