There are two main approaches for fault diagnostics of dynamical systems: data-driven based and model-based approach. In data-driven approach, features are extracted from the collected data and then mapped to predefined classes of fault scenarios. Data-driven methods are based on the priori knowledge of the relationship between signal symptoms and faults and are therefore, heavily dependent on data. Because there is no physics of the system involved, this approach cannot accommodate the changes easily. For instance, this method has a poor performance in diagnosing defects with different geometry, size and location if they are not already included in the training data. In addition, newer phenomena can appear in the behavior of the system which is difficult to predict using these methods. Model-based methods on the other hand, use physics-based model of the system to identify any defect or abnormality in the performance of the system. Since the understanding of the physics of the system is involved in this approach, the diagnostics algorithm can still be effective in different domains of the system response with even unknown phenomena and faults. The main drawback of this approach however, is the difficulty of derivation of accurate models for complex systems.

Our main thesis is that the diagnostics process can be better performed with techniques that combine both model-based techniques and data-based approaches. This is an interesting trend of research on developing new algorithms that combine information from physics-based models and data-based models (time series). Since the mathematical model derived from the physics-based model is in general an approximation or incomplete (due to the presence of many unknowns), data-based techniques can be used to extract information in order to update the mathematical model and thus train a learning system for diagnostics. The overview of the diagnostics process is illustrated in the diagram below showing what we will call here a hybrid approach for diagnostics. According to this diagram, the main objective of the proposed work is to develop a model-based framework for diagnostics of nonlinear system in which the mathematical model is updated and perfected using the measured data.