Hierarchical Bayesian detection of impulses in Tainter valve machinery systems under uncertainty

Reliable lock operation is crucial for uninterrupted waterway traffic, but failures in fill/empty Tainter valves can hinder lock management. To address this, an in-service lock was instrumented with an array of sensors spanning the motor to the final gear shaft. Unexpected impulses were observed in the jack shaft and sector gear bearing block accelerometer signals during certain valve opening events, coinciding with anomalies in sector gear angular displacement signals. To detect these impulses, a single-channel hierarchical Bayesian framework was employed, utilizing sector gear bearing block acceleration signals. A binary hierarchical Bayesian hypothesis testing approach was developed, assuming Gaussian noise versus Gaussian-distributed signals conditioned on the mean and standard deviation (STD) of the impulses. Unlike traditional Bayesian detection methods that pool all datasets/events together or analyze single events/datasets in isolation, this approach captures aleatory and epistemic uncertainties by modeling the impulse signal mean and dispersion as random variables (RVs). The relationships among different detection models (Neyman–Pearson detection, matched filter, Bayesian detection, and hierarchical Bayesian detection) are mathematically demonstrated, showing how they are interconnected. To address signal non-stationarity within events and signal magnitude across multiple events, optimal windowing and signal normalization were applied to ensure statistical reliability and computational efficiency. A local sensitivity analysis was performed to determine the effect of the decision threshold in this binary hypothesis testing to the hyperparameters. The results provide critical insights into the operational health of the Tainter valve system, enabling more reliable diagnostics and predictive maintenance for lock machinery, although the approach could be applied to detecting impulsive signals in any time series application.