In the present study, the objective is to detect the structural damages using the responses obtained from the sensors at the optimal location under uncertainty conditions. Reducing the error rate in damage detection process due to responses' noise is an important goal in this study. In the proposed algorithm for optimal sensor placement, the noise of responses recorded from the sensors is initially reduced using the principal component analysis. Afterward, the optimal sensor placement is obtained by the damage detection equation based sensitivity analysis. The sensors are placed on degrees of freedom corresponding to the minimum error rate in structural damage detection through this procedure. The efficiency of the proposed method is studied on a truss bridge, a space dome, a double-layer grid as well as a three-story experimental frame structure and the results are compared. Moreover, the performance of the suggested method is compared with three other algorithms of Average Driving Point Residue (ADPR), Effective Independence (EI) method, and a mass weighting version of EI. In the examples, young's modulus, density, and cross-sectional areas of the elements are considered as uncertainty parameters. Ultimately, the results have demonstrated that the presented algorithm under uncertainty conditions represents a high accuracy to obtain the optimal sensor placement in the structures.