Real-world data stream classification remains a fundamental challenge in machine learning due to the simultaneous occurrence of concept drift, class imbalance, and the limited availability of labeled data. Existing semi-supervised learning methods typically address only one of these challenges. In this study, a semi-supervised active learning framework based on a Radial Basis Function Neural Network (RBFNN) is proposed for data stream classification under simultaneous concept drift and class imbalance. In the proposed framework, a sliding window mechanism is employed to retain newly arrived samples while gradually discarding outdated data, enabling the model to remain consistent with the current data distribution. Subsequently, an active learning strategy based on the combination of uncertainty and density criteria selects the most informative samples for labeling, thereby reducing labeling costs while improving training quality. Furthermore, a smooth pseudo-labeling mechanism based on feature-space similarity is adopted to effectively exploit unlabeled data. In the modeling stage, the RBFNN architecture is enhanced with an adaptive center adjustment mechanism and dynamic updating to cope with concept drift. The initial RBF centers are initialized using an improved K-means++ algorithm and are subsequently updated online according to incoming data. In addition, to address class imbalance, a synthetic sample generation method based on weighted combinations of minority-class samples and the Logistic Map chaotic sequence is proposed, increasing the diversity of generated samples. Moreover, a weighted Focal Loss function is employed to improve the model's sensitivity to difficult samples while dynamically adjusting class weights. The network parameters are optimized using the Adam algorithm. Experimental results demonstrate that the integration of active learning, adaptive RBF center adjustment, semi-supervised pseudo-labeling, and mechanisms for handling concept drift and class imbalance significantly improves the performance of data stream classification. Compared with state-of-the-art methods, including SSALD, SSALE-EIS, AACE-DI, LEPID, and CBAL, the proposed method achieves superior performance, with average improvements of 4% in F1-score, 3% in G-Mean, and 2.5% in Specificity. These results confirm the effectiveness and robustness of the proposed framework for real-world data stream classification under concept drift and class imbalance.