From raw value to engineering unit

In brief

• Do not store only the final result; keep the input and the calculation context.
• The unit of every term and coefficient must be explicit.
• The reference, calibration coefficient and unit conversion serve different roles.
• A new formula should have a version, validity range and test set.
• Correct syntax does not guarantee engineering correctness.

Why the result "12.4 mm" may not be proof

A year after the monitoring system starts, the team sees a displacement chart in millimetres. A question follows: where exactly did 12.4 come from? The answers are often unsettling:

• the coefficient was in the spreadsheet of a person who no longer works on the project,
• the formula was copied from the manual for a different sensor variant,
• the intermediate result had inches as its unit, but it was described as millimetres,
• the reference was changed without a date,
• the negative sign came from an orientation that was never recorded anywhere,
• the formula in the platform differs from the one used in the handover report,
• historical data were recalculated with a new version without stating the change point.

The problem is not the absence of a number. The problem is the absence of provenance, meaning documented origin of the result: which data, relations, coefficients and decisions led from the reading to the value used by the engineer.

The JCGM International Vocabulary of Metrology defines a measurement model as a mathematical relation between the quantities involved in the measurement. That is more than a line of code. The model should describe the output quantity and all relevant input quantities, including corrections.

Seven elements of a reproducible result

A calculation card is a versioned description that links input data, the model and the result in a way that lets another competent person repeat the calculation.

1. Input

Record the original value delivered by the device and the time it was taken, not only the time when the server received it. You also need the unit or a clear statement that the value is dimensionless, the quality status and the source.

If the device already sends an engineering unit, do not assume there is no conversion. It may be performed in the logger. In that case, the card should identify the device configuration version and the method used to obtain the coefficients.

2. Formula

The formula must be readable outside the application. A note such as "result = function_7(value)" is not enough if the function exists only in one vendor's code. State the order of operations, variable definitions, signs and assumptions.

Simple subtraction of a reference is also a model. If the current and zero readings are in different units or were taken with a different configuration, the operation is syntactically correct but physically meaningless.

3. Coefficients

For each coefficient, record:

• value and unit,
• source: certificate, device card, manual or design decision,
• identifier of the specific sensor or channel,
• date and validity range,
• conditions under which the coefficient applies,
• uncertainty, if available and relevant.

The GEOKON GK-405 guide shows that the sensor configuration needed to present engineering units may include, among other things, the coefficient, zero and selected unit. This is an example for one specific device family, not a universal field list for all sensors.

4. Reference

The reference answers the question "relative to what are we calculating the change?" It is not a calibration coefficient and should not be changed just to make the chart look nicer. Record the source record, exact time, work stage and reason for selection. The procedure is described in more detail in the article how to choose a zero measurement.

5. Units and conversions

Every operation has a dimension. Quantities can be subtracted only in compatible units. Multiplication by a coefficient should lead to the declared output unit. Conversion from degrees to radians, metres to millimetres or microstrain to strain must be explicit.

The most dangerous unit errors are logically correct for a computer. The number 0.015 can be metres, millimetres or a dimensionless value. The parser sees a number; the engineer sees a thousandfold difference.

6. Version and validity period

Formulas change after calibration updates, orientation corrections or model refinement. Do not delete the old version. The new one should receive an identifier, effective date, author, reason and test result.

You also need to decide whether the change applies only to future data, or whether a separate, controlled history recalculation process is launched. Old and new results must not be mixed without marking.

7. Result

The final value should remain linked to the model version and the input. The user does not need to see the full card on every chart, but should be able to move from the point to the information about the unit, source and active configuration.

Illustrative example: from reading digits to millimetres

Illustrative example. A displacement sensor delivers a raw value in arbitrary reading digits. The document for a specific unit gives a coefficient of 0.00145 mm/digit. The approved reference has a value of 8620 digits, and the current reading is 8750 digits.

The calculation card looks like this:

The dimensional check is simple: digits × mm/digit = mm. An independent calculation for the sample gives 0.1885 mm. When the current reading equals the reference, the result is 0 mm. When the sign of the difference changes, the sign of the result changes.

The numbers do not come from an implementation and do not describe a specific product. The scheme is similar to the example relations published in vibrating wire sensor manuals, such as the GEOKON convergence meter manual, but coefficients must always come from the documentation for the specific unit and method. In a vibrating wire channel, you must first decide whether the input is Hz, period or digits; the three-point calibration test for a vibrating wire sensor serves that purpose.

Now consider the error: an integrator enters the coefficient 0.00145 without a unit, and later someone assumes the result is in metres. The syntax remains correct. The dependencies do not form a cycle. The result is calculated without exception. Even so, the interpretation is wrong by three orders of magnitude. That is why the technical test and engineer approval must be separate gates.

Tests that should precede formula publication

Test 1. Syntax

Does the parser recognise variables, operators, parentheses and functions? This is the lowest level of control. It detects a typo or a missing parenthesis, but it does not know the intended physics.

Test 2. Dependency existence

Check on samples with the complete set and with one missing input whether the required data are available at the right time. Inclify allows an unknown identifier as an external measurement variable, and its absence during calculation returns null, not zero. That is why the existence of inputs is an acceptance test, not a formula validator guarantee.

Test 3. Cycles

If quantity A depends on B, B on C, and C again on A, the calculation has no start. The system should reject such a dependency graph.

Test 4. Units

Perform a dimensional analysis of each term. Determine whether trigonometric functions receive radians or whether the conversion is explicit, whether lengths share a consistent unit and whether the coefficient carries the input to the expected result.

Test 5. Characteristic points

Prepare at least:

• a zero case,
• a positive and negative change,
• a value near the range limit,
• a missing input,
• a record with an incorrect status,
• a known example calculated independently.

Test 6. Sign and orientation

The mathematical sign must match the agreed axis and physical direction. Reversing the sensor or swapping ends can produce a stable but opposite trend.

Test 7. Version continuity

Calculate a sample just before and just after the change moment. The expected jump should have an explanation. If the new version was meant only to improve the description, but the result changes sharply, a diagnosis is needed.

Test 8. Independent verification

A second person should reproduce the result from the card without access to the formula author. For critical quantities, it is worth comparing the result with a control tool or a manual calculation on a fixed sample set.

Responsibility matrix: who approves what

A clear division of roles protects against two extremes. The integrator should not interpret a coefficient whose meaning they do not know. The engineer should not approve a formula from a screen without the ability to reproduce the data and version.

Syntax validation does not guarantee engineering correctness

This distinction is worth stating directly in acceptance requirements:

Software can enforce discipline, but it does not automatically know the installation, calibration certificate, structural axis or measurement purpose. A green validator status means "it can be calculated according to the system rules", not "the result is true".

How this looks in Inclify

Inclify accepts automatic measurements with UTC time and stores the input data. In a project, calculation channels can be defined with explicit equations, including references to stored references. This makes it possible to show the raw value next to the engineering result instead of replacing one with the other.

The editor controls syntax, result type and cycles between project equations. An unknown identifier can represent an external measurement variable, so the validator does not confirm its existence. When that value is missing during calculation, the dependent result is null. These safeguards reduce technical errors, but they do not confirm units, coefficients or the physical meaning of the formula. We do not declare a dedicated field for every possible manufacturer coefficient; the model must be described explicitly in the equation and project documentation.

Project configuration changes leave a trace of values before and after. The administrator can therefore determine when the model changed. If the change is meant to cover history, it should be treated as a separate, controlled process, not as a side effect of editing. Before publishing any critical result, the team should keep the calculation card, a reference sample and signed approval of the physical meaning. The input format requirements should be stated explicitly from the outset in the monitoring data specification.

An audit trail alone does not replace independent calculation review by the person responsible for engineering interpretation.

Calculation card checklist

• [ ] The source reading and execution time have been preserved.
• [ ] The input quantity and its unit have been defined.
• [ ] The full formula has been recorded without hidden steps.
• [ ] Every coefficient has a value, unit and source.
• [ ] The coefficient is assigned to the correct unit.
• [ ] The reference points to an existing record and a reason for selection.
• [ ] Unit conversions are explicit.
• [ ] The sign and orientation have a physical description.
• [ ] The formula has a version and validity time.
• [ ] The validator confirmed syntax and dependencies.
• [ ] There is no cycle between calculation channels.
• [ ] Dimensional analysis has been done manually.
• [ ] There is an independently calculated reference sample.
• [ ] Missing data and incorrect status were tested.
• [ ] An engineer approved the model correctness.
• [ ] The change procedure and any history recalculation have been defined.

Limitations and risks

A complete calculation card does not guarantee that the sensor is healthy or that its measurement represents the intended structural quantity. Documentation improves reproducibility: it helps locate where the error arose. It does not replace calibration, installation control, an independent method or engineering judgement.

VIM defines metrological traceability as a documented, unbroken chain of calibrations that relates a result to the proper reference. Recording a coefficient in an application does not establish such a chain. A credible source and information about its application are required.

NIST describes uncertainty propagation for a model in which the result depends on input quantities. In practice, this means the accuracy of the final number cannot be better just because the platform shows many decimal places. The uncertainty of the inputs, coefficients and reference still affects the result.

ISO 18674-1 covers the general rules of geotechnical monitoring and its role in assessing structures and ground. The calculation platform is part of the process, not its owner. If a calibration change is to be applied to earlier data, plan a separate workflow for safe history recalculation.

Sources and further reading

1. VIM 2.48 - Measurement model, Joint Committee for Guides in Metrology / BIPM.
2. VIM 2.41 - Metrological traceability, JCGM / BIPM.
3. NIST Technical Note 1297 - Law of Propagation of Uncertainty, NIST.
4. NIST TN 1297 - Reporting Uncertainty, NIST.
5. GK-405 Vibrating Wire Readout - Quick Start Guide, GEOKON.
6. Model 4425 Convergence Meter - Instruction Manual, GEOKON.
7. ISO 18674-1:2015 - General rules, ISO.

Next step: build one reference calculation card

Choose a critical channel, collect the raw record, the coefficient document and the current formula. We will help map the result, tests and change trail in the platform before the process is replicated across the project. Book a data and calculation workshop.