Digital Twin in Metrology: Virtual Representation of Physical Measurement Processes

The static digital twin and the dynamic digital twin differ in update frequency, data basis, storage volume and application — both use the same data triple (timestamp + part ID + measurement dataset), but with different synchronization frequency.

Static Digital Twin — created once from measurement data; no live update after creation. Application: quality documentation, traceability archive, compliant inspection record (ISO 9001, IATF 16949). Storage volume per component: 1–600 MB (point cloud + Z-map + thermal heatmap + metadata).

Dynamic Digital Twin — continuously updated from live sensor data. Synchronization frequency: up to 100 Hz (IRSX infrared camera, thermal time series) or 10,000 profiles/s (C6 laser triangulation sensor, geometric time series).

Application: real-time process control, predictive maintenance, closed-loop quality control.

Real-time process control and PLC signal processing are covered in the article Process Monitoring / Process Control.

A digital twin based on AT Sensors measurement data stores five data formats, which differ in data content, file type, file size, and application within the twin model.

Each format contains the data triple — timestamp + part ID + sensor ID — as mandatory metadata.

Deviation Map

The deviation map is the central evaluation result of the Product Twin.

It is generated by pixel-wise subtraction of the actual point cloud from the CAD reference model, assigning each measurement point (x, y) a deviation in µm.

\[\Delta d(x,y) = d_{actual} – d_{nominal}\]

A C6 laser triangulation sensor resolves this deviation starting from 0.1 µm.

The deviation map visualizes each measurement point as a color value — from −tolerance (blue) through 0 (green) to +tolerance (red).

Deviations outside the GD&T tolerance band are classified as NIO pixels.

Storage efficiency:

The storage efficiency of the twin model increases through selective archiving:

• IO components without deviation → only metadata + IO/NIO signal (< 1 KB)
• NIO components → full point cloud + deviation map + thermal heatmap (up to 600 MB)

Internal links: Point Clouds, Mesh Models (STL/OBJ)

The static digital twin documents the complete actual state of each component at the time of inspection — without manual effort, compliant with ISO 9001 and IATF 16949. The twin dataset consists of: point cloud + Z-map + thermal heatmap + IO/NIO decision, linked with timestamp and part ID.

Nominal–actual comparison:

The twin model overlays the actual point cloud with the CAD reference model and calculates the deviation for each measurement point — represented as a deviation map.

A C6 laser triangulation sensor detects:

• depth deviations from 0.1 µm
• lateral resolution from 5 µm

Each measurement point is classified as:

• IO — within GD&T tolerance band
• NIO — outside tolerance band

Series evaluation:

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The digital twin aggregates deviation maps over n consecutive components and calculates the mean deviation vector per measurement point:

\[\bar{d}(x,y) = \frac{1}{n} \sum_{i=1}^{n} \Delta d_i(x,y)\]

Definitions:

• \(\bar{d}(x,y)\) — mean deviation at measurement point (x,y) across n components, in µm
• \(\Delta d_i(x,y)\) — deviation of the i-th component at (x,y), in µm
• \(n\) — number of evaluated components

If \(\bar{d}(x,y)\) increases monotonically over three consecutive components in the same direction, the twin model classifies this as process drift — a systematic manufacturing error caused by tool wear, thermal expansion, or fixture wear. Detection occurs before tolerance limits are exceeded, as the trend is already visible within the tolerance band.

Remaining lifetime:

The remaining lifetime until the tolerance limit is reached is calculated as: \[\frac{T_{limit} – \bar{d}_{current}}{a}\]

Definitions:

• \(T_{limit}\) — tolerance limit, in µm
• \(\bar{d}_{current}\) — current mean deviation, in µm
• \(a\) — drift rate in µm per component

The dynamic digital twin closes the control loop between sensor, evaluation, and production process — in two application directions:

closed-loop process optimization (geometric time series, C6 Series) and predictive maintenance (thermal time series, IRSX Series).

Closed-loop process optimization

The deviation map is fed back as a control variable to PLC / MES.

The twin model calculates the correction value proportional to the mean deviation at the critical measurement point — with a negative sign, since the correction counteracts the deviation direction.

Concrete example:

A C6 sensor detects a profile drift of +8 µm on a milled surface → the twin calculates a correction value → the PLC reduces tool feed → the next batch is within the GD&T tolerance band.

Total control loop:

sensor → twin evaluation → PLC correction: < 10 ms

The IRSX infrared camera provides a temperature time series at 100 Hz.
The twin model calculates the deviation \Delta T(t) from the baseline temperature profile T_{base} — the reference profile under normal operating conditions.

If \Delta T(t) \geq 0.5\,K and increases monotonically over three consecutive measurement intervals, the twin model classifies the anomaly as a maintenance event.

Typical lead time: 48–72 hours before failure.

The geometric counterpart:

The C6 sensor detects tool wear from the profile time series as soon as the drift rate a \geq 0.5\,\mu m/\text{component}.

Tool replacement can therefore be planned before tolerance violation occurs.

IATF 16949 Section 8.6.2 requires traceability of all inspection results for special product characteristics.

The digital twin dataset — point cloud + Z-map + thermal heatmap with timestamp and part ID — fulfills this requirement as a compliant digital inspection record, without additional manual documentation.

Digital twin and traceability use the same data basis, but differ in perspective and purpose:

• The digital twin represents the actual state of a component at a specific time
• Traceability links all digital twin snapshots across the entire product lifecycle

The shared key structure is:

timestamp + part ID + sensor ID

Each twin snapshot contains this triple as mandatory metadata.

The traceability database indexes all snapshots via the part ID and reconstructs the complete inspection history.

AT Sensors develops two product groups that supply the digital twin with geometric and thermal measurement data:

• 3D sensors (C6 Series, XCS Series, CA Series)
• IRSX infrared cameras

Both product groups are GigE Vision compliant and provide each dataset with timestamp and part ID.