LaplaceDiag uses changing actuator effects to narrow equipment fault searches

Industrial faults do not necessarily reveal themselves where they begin. A malfunctioning pump can change measurements elsewhere in a plant, while different problems can produce similar sensor readings. Detecting abnormal behavior is therefore a different task from identifying the component responsible.

LaplaceDiag targets an intermediate goal: narrowing the equipment worth investigating. In the preprint, Oliver Niggemann proposes learning how actuator values relate to subsequent sensor measurements during healthy operation, then checking whether those relationships change. The resulting candidates are clues for inspection, not verified explanations of a fault.

Separating history from actuator effects

The method builds on LaplaceNet, a neural network that operates in Laplace space, a mathematical representation used to describe dynamic responses. Its prediction separates two contributions: a nonlinear forecast based on preceding measurements and an explicit matrix describing how actuator values contribute to later sensor values.

That separation makes the diagnostic update relatively simple. After training on healthy recordings, LaplaceDiag keeps the history predictor fixed. It subtracts that predictor’s contribution from observed sensor values and uses linear least squares to estimate the current actuator-effect matrix. The neural network itself does not need retraining during diagnosis.

A separate fit on healthy reference recordings supplies the comparison matrix. This is not necessarily identical to the matrix learned during neural-network training: the purpose is to compare healthy and current effects obtained using the same estimation procedure.

The approach does not learn a complete physical explanation of the plant. A changed pump-related effect might implicate the pump or its connected mechanism, but distinguishing pump damage from increased hydraulic resistance still requires additional evidence.

Allowing uncertainty and inconclusive answers

A large estimated change is less persuasive when its estimate is imprecise. LaplaceDiag therefore scales coefficient changes by estimated uncertainty and compares the resulting scores with healthy calibration recordings.

Calibration uses the largest score across all actuators and planned checks within each healthy recording. This addresses the repeated opportunities for false alarms when a system is checked many times. Its interpretation depends on healthy calibration and test recordings being statistically comparable, with the model, reference and checking schedule fixed.

The method can also return “not determined.” Commands that barely vary, or move together, may not provide enough information to distinguish separate actuator effects. Insufficient calibration data can likewise prevent a decision. Conversely, “no detected change” does not establish that equipment is healthy. The uncertainty estimates are approximate, and the scores are not probabilities of physical failure.

Better localization in the reported tests

The first evaluation used simulated recordings from two pumps and three tank-level sensors. Independently varied pump commands helped distinguish the pumps’ effects. The primary fault cases imposed sustained reductions in either pump’s effectiveness.

In the original-model comparison, LaplaceDiag selected only the faulty pump in 113 of 120 fault recordings at the final check, 20 minutes after fault onset. Joint projection using LaplaceNet selected it uniquely in 89 cases; joint projection using an independent LSTM did so in 57. Projection methods assess how well healthy actuator-effect directions explain sensor-prediction discrepancies, rather than estimating a changed effect matrix.

The LSTM produced more accurate healthy sensor forecasts, yet its diagnostic projection remained ambiguous in many pump cases. The reported advantage is therefore more precise actuator attribution, not uniformly superior prediction or anomaly detection.

A second evaluation used feedback-controlled Tennessee Eastman Process simulation data. LaplaceDiag identified the affected actuator in 248 of 249 feed-pressure-loss evaluations and 249 of 249 cooling-valve-fault evaluations. Those totals represent 83 base runs evaluated with three model seeds, not 249 independent replications per condition.

For feed-pressure loss, the identified actuator pointed to an affected feed path rather than the root cause, and two baselines achieved slightly higher correct counts. LaplaceDiag performed best on cooling-valve localization. It also raised alarms in nine of 249 healthy evaluations, compared with five for LSTM projection.

What remains unproven

The chemical-process estimates used 19.2 hours of predictions and were assessed at recording end. These results do not establish early-warning performance. Feedback can bias effect estimates, while sensor errors and history-prediction errors can imitate actuator-effect changes. The chemical-process implementation also restricted estimated changes to a plane defined by two healthy actuator-effect vectors.

Both evaluations concern simulated systems. The preprint leaves validation on previously unseen real-plant measurements and independent confirmation of faulty components for future work. Its supported contribution is narrower: under the tested conditions, changed actuator effects offered useful, sometimes less ambiguous directions for fault investigation.