LaplaceDiag: Fault Diagnosis through Changes in Learned Actuator Effects

Oliver Niggemann

cs.AINov 2, 2026

LaplaceDiag: Fault Diagnosis through Changes in Learned Actuator Effects

Authors: Oliver Niggemann

Organizations: Helmut Schmidt University, Hamburg, Germany

Abstract

Identifying faulty components from sensor anomalies is difficult because fault effects can propagate through a plant and different faults can produce similar observations. Detailed component models and labeled fault examples may also be unavailable. We introduce LaplaceDiag, a data-driven method that uses changes in actuator effects to narrow the search for faulty equipment. Actuators act on specific devices and mechanisms, so their changed effects can provide clues to root causes. LaplaceDiag learns a healthy plant model with LaplaceNet, a neural network that operates in Laplace space. It separates nonlinear prediction based on measured history from an explicit matrix that describes how actuator values affect sensor values. Keeping the history predictor fixed allows current actuator effects to be estimated by linear regression without retraining the neural network. Comparison with a healthy reference accounts for estimation uncertainty and normal variation to detect changes and generate actuator-related diagnostic hypotheses. The method supports online and offline diagnosis, providing an intermediate step between anomaly detection and identifying faulty components. We successfully evaluate LaplaceDiag on two datasets.

Figures & tables

Panel of Figure 1 — Fig. 1: The four steps of LaplaceDiag. LaplaceNet predicts sensor values $\widehat{Y}$ from actuator values $U$ and preceding history $h$ , using the history function $b$ and neural effect matrix $G_{\mathrm{NN}}$ . Separate fits provide the healthy diagnostic matrix $G^{0}$ and current matrix $\widehat{G}_{t}$ for the block ending at timestep $t$ . Comparing these matrices while accounting for uncertainty detects actuator-effect anomalies and supplies equipment-related hypotheses. Dashed arrows reuse the fixed healthy reference and calibration.

History-refitted models, separate scoring
Method	Correct	Multiple	None
LaplaceDiag	113	1	6
Separate projection	70	49	1
Original models, joint projections
LaplaceDiag	113	2	5
Joint LaplaceNet	89	28	3

Table 1: RQ3: pump diagnosis at the last check, 20 minutes after fault onset, over 120 recordings. Correct: only the faulty pump selected. Multiple: several candidates. None: no significant candidate. No method gives a wrong single-pump diagnosis or a not-determined result. Best correct counts per model condition are bold.

	History-refitted			Original models
Condition	LD	SP	VARX	LD	LN	LSTM
First pump, 40%	30	30	30	30	30	30
First pump, 60%	30	30	30	30	30	30
Second pump, 40%	27	30	30	28	30	30
Second pump, 60%	30	30	30	30	30	30
Healthy	1	2	5	1	2	1

Table 2: RQ1: anomaly detection, out of 30 recordings per condition. An alarm at any of 14 checks counts, regardless of which pump is identified. Bold marks most pump-fault detections and fewest healthy false alarms per model condition. LD: LaplaceDiag, SP: separate projection, LN: joint LaplaceNet projection. LSTM projection is joint.

Method	IDV7	IDV14	Healthy alarms
LaplaceDiag	248	249	9
LSTM projection	157	93	5
VARX assignment	249	204	21
LaplaceNet projection	249	60	8

Table 3: TEP: correct actuator diagnoses at the final check (RQ3) and healthy recordings with any alarm (RQ1). Each count is out of 249 evaluations from 83 base runs and three seeds, with fixed healthy means. Best counts are bold.

Fault Diagnosis

Fault diagnosis identifies, localizes, and explains failures in engineered and computational systems using sensor data, logs, models, and domain knowledge.

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Reconstruction-Based Diagnosis through Gödel-Regularized Virtual Observability

Oliver Niggemann, Jonas Ehrhardt, Alexander Diedrich

Chair of Computer Science in Mechanical Engineering, Helmut Schmidt University, Hamburg, Germany

Industrial Fault Diagnosis Fault Localization Virtual Sensing Reconstruction-Based Anomaly Detection

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Not every component in a technical system can be equipped with sensors. Hence, when a fault occurs, available sensors often detect it only after its effects have propagated. This makes the isolation of faults difficult. We approach this problem by introducing virtual sensors. For each combination of component and fault type, we let external knowledge describe the fault-sensitive variables. We introduce a novel neural observer that is only trained on normal data. For fault isolation, it uses available sensor measurements where it is possible and reconstructs missing variables as virtual sensors to predict normal behavior. It detects deviations between current values and nominal predictions and computes local symptoms, which are then compared by onset time. The result is a set of root causes describing the faulty behavior. We use Gödel logic to encode physical knowledge and guide training. We evaluate our approach on synthetic networks, the Tennessee Eastman Process, and datasets of two modular production plants.

Abstract

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