Adversarial training is an effective method to improve the machine learning (ML) model robustness. Most existing studies typically consider the Rectified linear unit (ReLU) activation function and centralized training environments. In this paper, we study the ML model robustness using ten different activation functions through adversarial training in centralized environments and explore the ML model robustness in federal learning environments. In the centralized environment, we first propose an advanced adversarial training approach to improving the ML model robustness by incorporating model architecture change, soft labeling, simplified data augmentation, and varying learning rates. Then, we conduct extensive experiments on ten well-known activation functions in addition to ReLU to better understand how they impact the ML model robustness. Furthermore, we extend the proposed adversarial training approach to the federal learning environment, where both independent and identically distributed (IID) and non-IID data settings are considered. Our proposed centralized adversarial training approach achieves a natural and robust accuracy of 77.08% and 67.96%, respectively on CIFAR-10 against the fast gradient sign attacks. Experiments on ten activation functions reveal ReLU usually performs best. In the federated learning environment, however, the robust accuracy decreases significantly, especially on non-IID data. To address the significant performance drop in the non-IID data case, we introduce data sharing and achieve the natural and robust accuracy of 70.09% and 54.79%, respectively, surpassing the CalFAT algorithm, when 40% data sharing is used. That is, a proper percentage of data sharing can significantly improve the ML model robustness, which is useful to some real-world applications.