Virtual Sensors Seek the Source of Industrial Faults

Reconstructing what sensors cannot see

Industrial fault diagnosis faces a timing problem: the first measured disturbance is not necessarily where a failure started. Effects can travel through material flows, energy connections and control systems before reaching an instrument.

In a preprint published on November 3, 2026, researchers at Helmut Schmidt University describe Reconstruction-Based Diagnosis through Virtual Observability, or ReDiVO. Its aim is to reconstruct fault-sensitive variables at otherwise unmonitored locations, then compare when local symptoms appear.

The approach requires prior knowledge. Experts or plant documentation must identify the component–fault combinations under consideration, the variables sensitive to each fault, and the measurements suitable for reconstructing missing quantities. It is not an unrestricted search for any possible failure.

Two views of the same process

ReDiVO builds two trajectories. The current trajectory uses real measurements wherever available and learned estimates elsewhere. A virtual pump sensor, for example, could estimate effective pump speed from related process measurements rather than reading a speed sensor online.

The nominal trajectory represents expected normal behavior. A long short-term memory neural network starts from an earlier estimated state and repeatedly feeds its predictions back into itself, without receiving fresh process measurements. Permitted commands or setpoints may enter if they do not reveal the fault.

Training uses fault-free recordings. Offline reference measurements can supervise virtual sensors even when those measurements will be unavailable during deployment. However, the nominal forecast is not guaranteed to be fault-free: its starting state may already contain effects of a developing fault.

Both trajectories receive uncertainty ranges calibrated using normal data. A symptom requires a sufficiently large separation between the ranges for several consecutive evaluations. This persistence requirement filters isolated exceedances, but can also miss weak or intermittent faults.

The system compares uncertainty intervals around symptom-onset times. It returns a unique candidate only when that candidate is unambiguously earlier than its competitors. Otherwise, it returns a group of possible causes, or no diagnosis if no symptoms qualify. These empirical uncertainty bounds are not guarantees under faulty conditions.

Physical knowledge as training guidance

Normal recordings may support several reconstructions that fit measured behavior but imply different hidden quantities. To discourage implausible solutions, the authors encode physical and system knowledge using Gödel fuzzy logic.

Here, relations receive truth degrees between zero and one. Violations of selected rules add penalties during training. Rules can describe flow balances, directional relationships, response delays, operating modes or sensor physics.

Crucially, these rules guide learning; they are not additional online evidence. Nor should they force every reconstructed variable to remain normal, which could erase the fault signal being sought.

Useful results, different meanings of success

The evaluation covers artificial networks, the Extended Tennessee Eastman Process and two simulated production-system datasets. These are not demonstrations of continuous operation in deployed industrial plants.

In HAI-CPPS pump experiments, recursive training—learning across several prediction steps—uniquely identified the faulty pump in 29 of 30 faulty recordings. One-step training identified the correct pump in 25. Both versions raised alarms in two of six healthy recordings. Both also used Gödel regularization, so their comparison does not establish whether the rules themselves helped.

TwinFlow illustrates why identifying a component is different from identifying its exact failure. ReDiVO selected the correct conveyor in 12 of 15 speed-calibration fault events, but uniquely identified both component and fault type in only four. Different faults could produce overlapping symptoms.

The Tennessee Eastman results require another distinction. Without rules or additional masking, the true cause appeared in the earliest symptom group in 64.74% of the reported cases. That metric allows ties; it does not mean unique isolation. The table also excluded 32 cases after testing because their sensors never activated persistently, for unresolved reasons. Including them reduced this result to 59.71%. Healthy-recording alarm rates were not evaluated, and testing used known fault windows rather than continuous monitoring.

Better estimates do not guarantee better diagnosis

The benefit of physical rules was inconsistent. In stressed linear networks, value rules improved isolation, but the reported gain was not statistically significant after correction across the comparison campaign. In hybrid systems, combined rules improved current-state reconstruction under stronger masking while worsening nominal forecasts, without a reliable diagnosis gain. Tennessee Eastman showed no consistent additional diagnosis benefit.

The central limitation is therefore not simply missing sensors. Successful isolation also needs accurate normal forecasts, detectable local symptoms and enough temporal separation to distinguish competing causes. The preprint supports virtual sensing under its tested conditions, not a general guarantee that the earliest reconstructed anomaly reveals the root cause.