We propose a model-based diagnosis framework in which Modelica models of faulted behavior are used in combination with a Bayesian approach. The fault augmented models are automatically generated through a process developed as part of our Fault Augmented Model Extension (FAME) work. Fault diagnosis using a Bayesian approach is based on computing a set of probability density functions, a process that is usually intractable for any reasonably complex system. We use Approximate Bayesian Computation (ABC) to bound the numerical and computational complexity. The basic idea is to use fault augmented Modelica models to create probability distributions of possible outcomes and then compare those distributions against actual observations to perform parameter estimation. The detection of faults is treated as a model selection problem and the inference of their severity levels is treated as parameter estimation. The diagnostic precision of this approach is evaluated on a Modelica vehicle drive line model.

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We describe how to apply Hidden Markov Model (HMM) to automate the loan service monitoring process. To predict the probability of defaulting in the near future, we build a statistical model of HMM from borrowers' historical payment data. The predicted probability is dynamic in a sense that the probability keeps changing as new realized data is added to the current historical data. The time series sequence data is obtained from the composite information of the loan status and days delinquent on each month. In the training stage, various HMMs are trained: one is paid HMM and the others are defaulted HMMs. We show that more accurate monitoring can be achieved by segmenting the defaulted data and training them separately (i.e., segmented HMM method) than by training a single defaulted HMM (i.e., simple HMM method). In the prediction stage, for each active loan, we apply the following two steps: 1) classification of the loan and 2) calculation of the default probability over a prospective time period. Finally, the monitoring system sends a signal if the probability is greater than a pre-specified threshold. We also explore how to select the optimal threshold level using precision and recall analysis.

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