Data-driven sensor placement optimization for accurate and early prediction of stochastic complex systems

In the current work, we develop a data-driven method for sensor placement optimization (SPO) for complex dynamical systems under stochastic forcings in both form and location. The method is purely data-driven and does not require a full prior description of the system but a distribution of probable forcing locations. The objective function of the optimization process considers two essential aspects for real-world engineering systems: accuracy of response prediction at a selected set of locations of interest (LoIs) and early prediction capabilities. A Bayesian framework is introduced for the reconstruction of the stochastic forcing applied at an unknown location and the prediction of the corresponding response at the LoIs based on the data collected from the sensors. In contrast to filter-based approaches, the current method does not require reconstruction of the full state vector and is applicable for unknown forcing locations. Hence, it obtains more accurate and faster results and is suitable for real-world engineering systems. Response prediction can also be obtained for inaccessible locations. A hybrid optimization approach is suggested as a trade-off between accuracy and convergence speed. The method is demonstrated on a 2D discrete lattice and a 3D continuum finite element model and outperforms the existing methods in both efficiency and accuracy for an identical number of sensors.