This study investigates sensor placement for condition monitoring in complex systems, focusing on capturing dominant dynamic responses that indicate abnormal conditions. Traditional sensor placement methods often rely on costly distributed sensors and heuristic strategies, which are not efficient in capturing the most informative response characteristics. To address these challenges, a data-driven Design of Experiment (DoE) approach is proposed, leveraging system science principles to optimize sensor allocation systematically. The implementation of this framework is formulated as a sparse regression problem, enabling an efficient selection of sensor locations that maximize information gain while minimizing redundancy. To solve this problem, a newly developed Compressed Orthogonalized Least Squares (Comp-OLS) algorithm is introduced. In order to validate the proposed approach, a case study on the DoE of a Duffing system is conducted. Compared with the commonly used Pivoting QR Factorization (PQRF) method, the results demonstrate that the Comp-OLS-based framework significantly enhances sensor placement efficiency, ensuring comprehensive coverage of system dynamics while anchoring the locations of required sensors. This study demonstrates the potential of data-driven DoE for improving condition monitoring in various engineering applications, offering a scalable and effective solution for sensor placement challenges.