Deep learning (DL) has become an essential tool in prognosis and health management (PHM), commonly used as a regression algorithm for prognosis tasks. A metric of interest is the remaining useful life (RUL) estimated using monitoring sensor data. Frequently, these DL applications are treated as black-box functions, giving little to no control of the data interpretation. Here, two essential challenges are yet to be addressed: the use of time as an explicit variable, and the relationship between the physics of degradation governing the system and the model’s inputs. Embedding the physics of degradation to a DL framework is a challenging task, mostly due to the lack of mathematical models that can represent these processes in complex systems. Latest advances in DL algorithms have shown that it is possible to embed partial differential equations (PDEs) to DL models with the use of physics-informed deep learning frameworks. This can be implemented by setting a penalty function that resembles a PDE behavior, allowing to create a dynamic relationship between the input variables and prognostics metrics. In this paper, we present an open-box approach using a deep neural network (NN) framework to explore the physics of degradation dynamics through a PDE.

The proposed framework consists of three stages represented by three different NNs to perform RUL predictions. The first stage maps the operational conditions (OCs) and the time *t* to a latent variable *x*. A second NN then takes both *t* and *x* to output the RUL of the system. A third NN is used to represent the right-hand side of a PDE, which models the time derivative of the RUL through a NN. This is the so-called dynamics of the PDE. The penalization function creates a dynamic relationship between the RUL and the latent variable *x*, which in turn is related to the initial OCs and the time at which the RUL is evaluated. The use of a latent variable provides multiple advantages for both the training of the model, and the later interpretation of its results: dimensionality reduction, PDE input variable reduction, and denoising, among others.

In this study, the FD001 sub-dataset from the benchmark C-MAPSS dataset was considered. The model presents good generalization capabilities with the training and validation loss functions showing an identical behavior during the training process and converging to the same loss value. This can be attributed to the PDE penalization function added to the model, which links the dynamics of the latent variable with the RUL. The most important result of our proposed framework comes from the latent variable graphical representation. The predicted RUL is mapped to the corresponding estimated latent variable and its time derivative *dx/dt*. Results show that the proposed framework smooths the latent variable space, creating a continuous relationship between the operational conditions and the RUL. This can be used to relate the health state of the system to the latent variable. In turn, the model gives useful information as a condition-based maintenance assessment tool. Taking time as an input variable allows the model to trace, compare, and analyze the temporal evolution of *x* and its RUL estimation based on the current OCs. These results open many doors to the application of these algorithms to real complex systems, especially on maintenance and preventive assessments.


Uncovering the Underlying Physics of Degrading System Behavior Through a Deep Neural Network Framework: The Case of Rul Prognosis

Division / Sponsors: 
Aerospace, Bioengineering, Applied Mechanics, Design Engineering Division, Advanced Energy Systems, Manufacturing Engineering Division, Noise Control and Acoustics, Nondestructive Evaluation, Diagnosis, and Prognosis (NDPD), Nuclear Engineering Division, Process Industries Division, Fluids Engineering, Heat Transfer, Materials, Microelectromechanical Systems, Safety Engineering and Risk Analysis, Computers & Information in Engineering


Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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