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State prediction is not straightforward, particularly for complex systems that cannot provide sufficient amounts of training data. In particular, it is usually difficult to analyze some signal patterns for state prediction if they were observed in both normal and fault-states with a similar frequency or if they were rarely observed in any system state. In order to estimate the system status with imbalanced state data characterized insufficient fault occurrences, this paper proposes a state prediction method that employs discrete state vectors (DSVs) for pattern extraction and then applies a naïve Bayes classifier and Brier scores to interpolate untrained pattern information by using the trained ones probabilistically. Each Brier score is transformed into a more intuitive one, termed state prediction power (SPP). The SPP values represent the reliability of the system state prediction. A state prediction power map, which visualizes the DSVs and corresponding SPP values, is provided a more intuitive way of state prediction analysis. A case study using a car engine fault simulator was conducted to generate artificial engine knocking. The proposed method was evaluated using holdout cross-validation, defining specificity and sensitivity as indicators to represent state prediction success rates for no-fault and fault states, respectively. The results show that specificity and sensitivity are very high (equal to 1) for high limit values of SPP, but drop off dramatically for lower limit values.

Estimating System State through Similarity Analysis of Signal Patterns