Nondestructive methods are low-cost and economical methods for detecting faults in structures based on the information obtained from sensors. Finding optimal position of sensors in structures is the solution to an optimization problem. In this research, the effects of uncertainty parameters on the sensor position optimization method (effective independence method) have been investigated. The modulus of elasticity, density, and cross-sectional dimension are considered as uncertainty parameters. The Latin hypercube method has been used to evaluate the optimal position of the sensor with respect to uncertainty. Noise and measurement error are applied to the modes and their effects on the optimal position of the sensor are investigated. Also, the effectiveness of the effective independence method in the presence of noise in the sensor has been investigated. In order to demonstrate the efficiency and accuracy of this method, a two-dimensional frame has been investigated and compared to the results of reference 10.