Damage diagnosis based on global structural vibrations critically depends on the sensor layout, in particular when a small number of sensors is used for large structures under unknown excitation. This paper proposes a sensor placement strategy that yields an optimized sensor layout with maximum damage detectability in selected structural components. The optimization criterion is based on the Fisher information, which quantifies the information that the damage-sensitive feature carries on the design parameters of structural components, such as material constants or cross-sectional values. It is evaluated using a finite element model, and considers the statistical uncertainties of the damage-sensitive feature. The methodology is shown for the stochastic subspace-based damage detection method, but can be applied to any damage-sensitive feature whose distribution can be approximated as Gaussian. It is suitable to find the optimal layout for a fixed number of sensors and to choose an appropriate number of sensors. Since the Fisher information is defined component-wise, the sensor layout can be tuned to become more sensitive to damage in local structural components, such as damage hotspots, non-inspectable components, or components that are critical for the safety and serviceability of the structure. For proof of concept, the sensor layout on a laboratory beam is optimized based on numerical simulations, and it is showcased that the optimal sensor layout leads to the highest damage detectability for experimental data.