Identification and monitoring of structural damage have a growing importance in the maintenance of aging structures. Specifically, an optimal sensor configuration capable of fully identifying structural damage is desired. One innovative approach is casting the optimal sensor placement problem as a decision-centric, utility-maximization framework. By choosing mutual information (or relative entropy) as the utility criteria, sensor placements are chosen to maximize information about structural damage parameters. To accelerate this optimal experimental design (OED) problem, we propose the parameterization of damage using binary variables and the corresponding integration of the Bernoulli prior into this Bayesian OED framework. By limiting the damage parameter design space, we can direct the computational effort toward optimizing over informative and practical structural damage scenarios. Additionally, we convert the OED problem into a convex optimization problem, ensuring that sensor placement solutions contain the maximum information. We evaluate our proposed modified OED framework using a deterministic damage estimator also informed by the Bernoulli prior. We quantify the performance of sensor placements using a mean-squared error (MSE) metric, and we show that optimally selected sensors outperform randomly selected sensors, in general. We also provide a potential heuristic in selecting a sensor budget through the consideration of utility.