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The TUBE algorithm: Discovering trends in time series for the early detection of fuel leaks from underground storage tanks

The paper uses United States Environmental Protection Agency's (EPA) Statistical Inventory Reconciliation (SIR) software-based underground gasoline tank leak detection method as a baseline for acceptable true positive (not less than 95%) and false positive rates (not more than 5%). The TUBE algorithm, apart from using aforementioned SIR method, uses two-step data filtering mechanism, trend detection over time series using tubes , and detected trends’ assessment for generating a final resultSIR methodTheoretical fuel volume at the end of time frame is $V_{book}$
$V_{book} = V_{open} - V_{sales} + V_{delivery}$
Difference between actual ($V_{close}$) and theoretical ($V_{book}$) fuel volume is variance.
$Var = V_{close} - V_{book}$

Here: $V_{book}$ - fuel volume for a single time frame$V_{open}$ - starting fuel volume in the tank$V_{sales}$ - sold fuel volume$V_{delivery}$ - fuel volu…