Acoustic emission (AE) technology faces challenges in concrete structures due to anisotropy and heterogeneity, causing wave velocity variations, reflection, refraction, and localization inaccuracies. To overcome these limitations, this study introduces a novel damage source localization approach that integrates AE technology with machine learning (ML) models. The proposed method utilizes a sensor array to capture AE signals, accurately determining their arrival times using the Akaike information criterion (AIC). Subsequently, the time difference of arrival (TDOA) between sensors is computed as input features for the model. For linear localization, a linear regression (LR) model establishes a direct relationship between TDOA and damage locations. For planar localization, lightweight models based on deep neural networks (DNNs), 1-D convolutional neural networks (1D-CNNs), and long short-term memory (LSTM) networks are developed to balance computational efficiency and localization accuracy. Additionally, a fine-tuning strategy is implemented to adjust the models with a minimal amount of new data, enhancing their adaptability to the diverse characteristics of different concrete slabs. Compared to conventional localization techniques and recent deep learning-based methods, the proposed approach demonstrates significant advancements in adaptability, computational efficiency, and localization accuracy. These improvements highlight its superior generalization capabilities and potential for practical applications.