Sensor placement for optimal aerodynamic data fusion

Aircraft design is recently evolving towards a digital twin representation that involves many heterogeneous data sources. The aerodynamic development of aircraft usually incorporates data from computational fluid dynamics simulations, wind tunnel testing, and flight tests. All of these data sources have their advantages and disadvantages, which can optimally be combined using data fusion methods. However, the quality of the data fusion result strongly depends on the experimental design, i.e. the placement of discrete sensors. Therefore, an optimized sensor placement is essential for data fusion applications, as the number of sensors is limited. This work presents a sensor placement strategy for the widely used Gappy proper orthogonal decomposition data fusion methodology. The sensor placement relies on a Bayesian formulation of the data fusion, allowing accurate error estimates. Based on the Bayesian posterior, a utility function characterizes the quality of the fused result by quantifying the expected information gain for the proper orthogonal decomposition coefficients. As the optimization of the sensor locations involves a complex combinatorial problem, we introduce an efficient genetic algorithm for this task. The method is demonstrated on a two-dimensional airfoil and the NASA Common Research Model with synthetic measurement errors. For both test cases, an optimal sensor placement results in smaller reconstruction errors than a conventional layout. The Bayesian approach leads, in most cases, to more accurate reconstructions and is more versatile than other well-established sensor placement methods. The proposed genetic algorithm finds better optima with significantly fewer function evaluations than the widely used greedy algorithms.