This paper proposes innovative anomaly detection technologies for manufacturing systems. We combine the event ordering relationship based structuring technique and the deep neural networks to develop the structured neural networks for anomaly detection. The event ordering relationship based neural network structuring process is performed before neural network training process and determines important neuron connections and weight initialization. It reduces the complexity of the neural networks and can improve anomaly detection accuracy. The structured time delay neural network (TDNN) is introduced for anomaly detection via supervised learning. To detect anomaly through unsupervised learning, we propose the structured autoencoder. The proposed structured neural networks outperform the unstructured neural networks in terms of anomaly detection accuracy and can reduce test error by 20%. Compared with popular methods such as one-class SVM, decision trees, and distance-based algorithms, our structured neural networks can reduce anomaly detection misclassification error by as much as 64%.