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Algorithms

At the Prognostics Center of Excellence we have developed a portfolio of diagnostic and prognostic algorithms for a variety of systems. While some focus on physical principles of the system operation and fault propagation, others take a data-driven approach where modeling becomes a rather difficult task. For EMA diagnostics and prognostics we employ a hybrid scheme which leverages the advantages of both a model based scheme and a data-driven approach. The choice of such combination is guided by our goal of developing a real-time integrated diagnostic and prognostic algorithm that can works in flight environments. Various key components of this system are briefly described here.

Diagnostic System

A hybrid model-based and feature-driven diagnosis approach has been developed for diagnosing faults in EMAs. The model-based approaches work well when we are able to derive analytical models for the system and its measurements, and how these faults affect the observed measurements. However it may not be possible to do so for all faults and measurements, for example, accelerometers. On the flip side the feature-driven approach do not require the derivation of models, but require a lot of data under varying experimental conditions for training the classifier. Additionally when the classifier has to consider all faults and other experimental conditions, the size and complexity of the classifier becomes intractable. Our hybrid method addresses the drawbacks of either approach to provide a comprehensive diagnostic solution for EMAs.

Hybrid Diagnosis Approach

Our diagnostic system takes a hybrid approach and consists of an offline and an online stage, as shown below:

Hybrid Diagnosis Architecture
Hybrid Diagnosis Architecture

1. Offline Stage The offline stage involves deriving a model of the target EMA system followed by a qualitative diagnosability-analysis on this model. Adapting the Transcend Diagnosis Approach , the model is used to generate qualitative signatures for all faults and identify the ambiguity groups (groups of faults that have the same fault signatures). These groups represent faults that need to be referred to feature-driven approach. The Transcend diagnosis architecture is shown below.

Transcend Diagnosis Architecture
Transcend Diagnosis Architecture

For each ambiguity group, a set of features are are identified through lab experimentation and analysis. This results in a fault feature table that indicates how specific features are influenced by faults through a qualitative signature that represents how that fault affects that feature. The selected features are integrated into a classifier, such as an Artificial Neural Network (ANN), that can isolate the fault. The offline steps for the feature-driven diagnosis approach is shown in the figure below:


Feature-driven Diagnosis Architecture
Feature-Driven Diagnosis Architecture

2. Online Stage The online stage involves two phases. In the first phase the model-based diagnosis approach described earlier is used to observe the system, detect and qualitatively isolate fault ambiguity groups. In the second phase the isolated ambiguity group triggers the selection of rows from the fault feature table. These rows correspond to the faults in the ambiguity group. The selected sub-table can then be converted to a diagnoser tree . Once the diagnoser tree has been identified, fault isolation is performed by walking down this tree from the root node. Features associated with edges from the current node are computed and depending on their values the ambiguity group is refined at each successive step until we reach a leaf node of the tree. At this point we are done with the fault isolation and the final ambiguity group can be reported as the diagnosis.

Prognostic System

After the underlying fault has been identified, the next step is to track fault propagation and predict the Remaining-Useful Life (RUL) of the EMA based on fault growth rate. A data-driven algorithm based on Gaussian Process Regression (GPR) was chosen for the initial implementation of the prognostic system. To our advantage GPR does not require explicit fault propagation model and can be implemented in a computationally inexpensive way for real-time environment.

1. Training Fault identification is followed by high frequency data analysis to compute relevant prognostic features for GPR and fed to the algorithm for a certain period to train the algorithm parameters. The longer is the training period, the better are the chances for the algorithm to learn the true fault growth characteristics. However, a balance must be struck between the length of the training period and the risk of missing out on a sufficient prediction horizon.

2. Prediction Training is followed by predicting trajectories of fault growth. Based on pre-specified failure threshold levels, predicted End of Life (EoL) is determined depending on where these trajectories cross the thresholds. Estimated EoL values can then be specified in relative terms by computing the RUL values, if needed. As time passes by, more data is collected. The GPR model is updated with new observations and, subsequently, the predictions are updated. It must be noted that GPR runs into scalability issues if a long data history is utilized. therefore, a clever subsampling scheme was implemented to upper bound the size of covariance matrix for a realtime implementation. Using these subsampled data the algorithms carries out a maximum-likelihood optimization to determine the best fitting hyperparameters for the chosen covariance function. For more details, please refer to the book - Gaussian Process for Machine Learning.

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