Data-Driven Sensor Selection for Signal Estimation of Vertical Wheel Forces in Vehicles

Sensor selection is one of the key factors that dictate the performance of estimating vertical wheel forces in vehicle durability design. To select K most relevant sensors among S candidate ones that best fit the response of one vertical wheel force, it has $(SK)$ possible choices to evaluate, which is not practical unless K or S is small. In order to tackle this issue, this paper proposes a data-driven method based on maximizing the marginal likelihood of the data of the vertical wheel force without knowing the dynamics of vehicle systems. Although the resulting optimization problem is a mixed-integer programming problem, it is relaxed to a convex problem with continuous variables and linear constraints. The proposed sensor selection method is flexible and easy to implement, and the hyper-parameters do not need to be tuned using additional validation data sets. The feasibility and effectiveness of the proposed method are verified using numerical examples and experimental data. In the results of different data sizes and model orders, the proposed method has better fitting performance than that of the group lasso method in the sense of the 2-norm based metric. Also, the computational time of the proposed method is much less than that of the enumeration-based method.