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Human activity recognition using streaming data from the accelerometer sensor of smartphone is still an interesting issue for researchers. Most researches develop the recognition model based on personal model type which require the training data obtained from only user who will utilize the model. To prepare the training data, the user must perform various activities and annotate them within the specified time. This is a major inconvenience for the users. In this paper, we propose a new smartphone-based dynamic framework for physical activity recognition named "ISAR+". The new framework is an impersonal (universal) model which can be built once and used on new users without requiring labeled training data from those users. Because the proposed model is adaptability with evolving data streams of each new user by using the incremental learning for real-time recognition. This work was validated the proposed model in terms of prediction accuracy and usage times on two public activity recognition datasets. The experimental results show that ISAR+ can achieve the best performance compared with the state-of-the-art models for streaming activity recognition, especially across different users and without inquiry from users. The ISAR+ has demonstrated the average accuracy more than 85% in both datasets. [ABSTRACT FROM AUTHOR]