Damage detection is a challenging, complex, and at the same time very important research topic in civil engineering. Identifying the location and severity of damage in a structure, as well as the global effects of local damage on the performance of the structure are fundamental elements of damage detection algorithms. Local damage detection is essential for structural health monitoring since local damages can propagate and become detrimental to the functionality of the entire structure. Existing studies present several methods which utilize sensor data, and track global changes in the structure. The challenging issue for these methods is to be sensitive enough in identifYing local damage. Autoregressive models with exogenous terms (ARX) are a popular class of modeling approaches which are the basis for a large group of local damage detection algorithms. This study presents an algorithm, called Influence-based Damage Detection Algorithm (IDDA), which is developed for identification of local damage based on regression of the vibration responses. The formulation of the algorithm and the post-processing statistical framework is presented and its performance is validated through implementation on an experimental beam-column connection which is instrumented by dense-clustered wired and wireless sensor networks. While implementing the algorithm, two different sensor networks with different sensing qualities are utilized and the results are compared. Based on the comparison of the results, the effect of sensor noise on the performance of the proposed algorithm is observed and discussed in this paper.