LaplaceDiag: Fault Diagnosis through Changes in Learned Actuator Effects

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.

We present a safe, real-time algorithm for active fault diagnosis and model discrimination for uncertain continuous-time nonlinear systems with process and measurement disturbances. Given a finite set of candidate models representing nominal and faulty modes, including actuator and sensor faults, we formulate an output-feedback, time-varying policy optimization problem that (i) robustly enforces state-input safety constraints over a finite horizon and (ii) drives the system to produce sampled measurements consistent with at most one model, enabling deterministic diagnosis. To solve this problem in real time, we develop a tractable approximation using interval over-approximations of reachable state and output sets, and encode diagnosability via a differentiable objective that penalizes overlap between the reachable output sets of possible models. The resulting optimization is solved efficiently online with gradient-based methods using JAX and differentiable reachability primitives. We evaluate our method on sensor and actuator fault diagnosis (up to 11 fault modes) in several high-dimensional nonlinear robotic systems, including a simulated quadrotor and fighter-jet model, a hardware differential-drive robot, and quadrupedal navigation. Across these case studies, our approach achieves reliable model discrimination in under 50 ms, outperforming baselines in discrimination success rate and speed while providing formal safety guarantees.

Integrating multi-level information, from physical models through data-driven diagnostics to natural language reasoning, into verifiable decision chains is a growing need in intelligent manufacturing. In bearing fault diagnosis, taken here as a representative testbed, the standard output is a class label and a confidence score derived from the classifier's own distribution, offering limited means of comparison against independent physical knowledge. Meanwhile, language models increasingly used for maintenance communication may introduce unsupported content. This work addresses both limitations from the output side. The proposed Diagnostic Evidence Network (DENet) is an encoder-agnostic multi-task framework that extends the output to a structured evidence record: the classification, a predicted characteristic frequency comparable against the theoretical value determined by bearing geometry and shaft speed, and a temporal localization of transient impulses inspectable on the raw waveform. Across four encoders and three public datasets, this evidence incurs no statistically significant accuracy cost, with a frequency error of about 6 Hz on 1,024-point segments. The deviation between predicted and theoretical frequency constitutes a label-free, inference-time validation signal. It detects misclassifications with AUROC of 0.970 and 0.871, and retains separation within the high-confidence subset. Finally, a QLoRA-adapted language model renders DENet's evidence into traceable maintenance reports without contributing diagnostic decisions, reducing unsupported-claim rates from 10-12% to 2% with no fabricated quantities observed.