Temperature compensation or a real structural change?

In brief

• Keep the raw value, temperature, compensation result and model residual in parallel.
• Distinguish the sensor manufacturer’s correction from empirical compensation of structural behaviour.
• Validate the model on another period and under different operating conditions.
• An alarm must not be “smoothed out” by a model that has also learned the real event.
• Base the decision on the trend, lag, data quality and knowledge of the asset, not on a single coefficient.

What temperature compensation really means

Temperature compensation is an explicit recalculation of a measurement result using temperature and a defined model, in order to limit a recognised, repeatable thermal effect on the result.

This definition is intentionally narrower than the popular idea of “subtracting temperature”. In structural monitoring, temperature can act in at least three ways:

1. It changes the characteristics of the sensor itself, the cables or the readout system.
2. It causes physical deformation of the structure, which the sensor measures correctly.
3. It co-occurs with another phenomenon, for example solar radiation, live load, water level or a stage of works.

Only the first case is a classic instrument correction. The second is a real response of the asset. Automatically removing it can strip the project of important information about how the structure is working. The third requires broader diagnosis, because temperature may only be a marker of a common daily or seasonal rhythm. For vibrating wire channels, also follow the procedure for temperature compensation of vibrating wire sensors, which separates the thermistor, the wire and the structural material.

FHWA describes thermal monitoring of bridge foundations, where strains responded to the daily temperature cycle with visible delay. That is a good example of why a simple “same hour, same coefficient” relationship can be too weak. The structure has thermal inertia, and air temperature does not always match the material temperature at the measurement point.

Three questions before the first regression

1. Are you correcting the instrument or interpreting the structure?

The manual for a specific sensor may include temperature coefficients, zero and sensitivity characteristics, or a full calibration equation. In the GEOKON high-temperature piezometer manual, the pressure result uses temperature-dependent parameters determined during instrument calibration. This does not prove that the same formula fits any strain gauge, inclinometer or crack meter. It proves that instrument correction should come from the documentation and calibration of the given channel.

If you measure the thermal expansion of a beam, the change is part of the asset behaviour. You can build a reference model to detect deviations from the typical response, but you should not call a physical deformation a “sensor error”.

2. Is the temperature measured where the effect is created?

Temperature from a nearby weather station may describe sun-heated steel, shaded concrete or a sensor in the ground poorly. Different locations have different amplitudes and delays. Before modelling, define:

• the location and thermal contact of the temperature sensor,
• resolution and time synchronisation,
• solar exposure, wind, precipitation and installation operating cycles,
• the possibility of delayed response of the element under study,
• changes in geometry, loading and construction stage during the analysed period.

3. Was the training period really stable?

A model trained during cracking, support movement or a load change may treat the event as a “normal temperature effect”. The more flexible the model, the greater the risk that it will also fit the signal it was meant to detect.

Stability does not mean a flat series. It means a period for which the team has a justified reason to believe that the measurement configuration and the structural state did not change in a way that is material to the model. This decision should be recorded with dates and work context.

Procedure: raw data + temperature -> model -> residual -> validation

The safest process has five explicit layers. None replaces the previous one.

Step 1. Secure the raw data

Do not overwrite the input value with the compensated result. Keep the original UTC time, raw value, unit, quality status, temperature and configuration identifier. This allows the result to be reproduced after the model changes.

First detect gaps, duplicates, transmission restart spikes, frequency changes and implausible temperature values. A statistical model will not automatically distinguish a failure from a rare physical state.

Step 2. Synchronise the series and examine lag

Compare the measurement against several temperature candidates: at the same moment and shifted by a justified delay. Do not choose the shift only because it maximises correlation. It must be consistent with the physics of the asset, the sensor location and the data resolution.

Inspect the traces on a common time axis, the scatter plot, day and night separately, and several temperature ranges. A loop in the scatter plot may indicate hysteresis or lag: for the same temperature, the result is different during heating and cooling.

Step 3. Write down the model and its scope

The simplest linear model can be written as:

predicted result = intercept + slope × temperature

It is not always enough. Delays, separate seasonal characteristics, non-linearity, temperature-gradient effects or interaction with load are possible. Each additional variable, however, increases the demands on data and validation.

The model card should include:

Step 4. Calculate the model residual

The model residual is the difference between the measurement and the value predicted by the model. It is not the “true displacement after cleaning”, but the part of the result not explained by the adopted model.

The model residual may contain:

• a real structural change,
• the effect of a omitted variable,
• model mismatch,
• measurement or synchronisation error,
• the effect of operating outside the range on which the model was built.

This language caution matters in business terms. If a report calls the model residual “structural movement”, the recipient may make a decision that the data do not support.

Step 5. Validate outside the fitting period

Split the data in time, not at random. A model fitted to fragments from across the year may “see” future conditions and deliver an overly optimistic result. Validation should cover another period, as much of the temperature range as possible, and at least one known operating stage.

Compare before and after:

• the slope of the result-to-temperature relationship,
• the correlation coefficient, with time lag stated,
• model error and residual distribution,
• parameter stability in consecutive windows,
• behaviour during known events,
• the number and meaning of alarms.

A reduction in correlation after compensation is useful, but not sufficient. The model may remove both the thermal effect and part of the real trend. Engineer judgement and comparison with other measurements are still needed.

How to read the results without confusing correlation with cause

Correlation does not determine the direction of dependence or the presence of a common cause. Two series may co-vary because both respond to solar exposure, a work schedule or water level. They may also correlate only because of a seasonal trend. Statistics should therefore organise hypotheses, not close the diagnosis.

Illustrative example: a model that helps, but has no right to switch off vigilance

Illustrative example. A displacement sensor on a facade shows a regular daily cycle. The team selects 30 days of a stable construction stage, excludes two confirmed transmission outages and compares the result with the temperature of the element. The best physically credible fit occurs with a lag of 90 minutes.

During the fitting period, the slope is 0.42 mm/°C, the correlation is 0.86, and the root mean square error is 0.74 mm. On a separate 14-day validation period after applying the model, the slope of the residual versus temperature falls to 0.05 mm/°C, and the error to 0.36 mm. The result supports the usefulness of the model in this range, but it does not prove that all movement was caused by temperature.

After three weeks, the model residual shifts by 2.3 mm and remains offset for the next days, despite the normal temperature cycle. The team does not update the model automatically. It compares adjacent sensors, the work log, geodetic control and the fixing condition. The persistent residual becomes a diagnostic signal.

All numbers are illustrative. They are not an alarm threshold or the expected accuracy for another asset.

How to set alarms with compensation

One “cleaned” series is too little. A good setup keeps visibility of at least four elements: the raw measurement, temperature, predicted value and residual.

Thresholds can be separated by purpose:

• data integrity alarm for a gap, spike or loss of temperature,
• physical limit for the raw value, if required independently of the model,
• residual threshold for deviation from the typical response,
• alarm for operating outside the model scope, for example a temperature not seen in validation.

The model should not be retrained automatically on the newest data if those same data may contain a developing defect. Updating requires versioning, justification and re-validation. It is also worth keeping a parallel period in which the old and new model calculate the result without switching the alarm procedure.

Warning signs: when to suspend compensation

• the model coefficient has no sensible unit or sign,
• the temperature comes from a place with different exposure than the element under study,
• the model was built on too narrow a temperature range,
• the data include a change in load, support, sensor or geometry,
• the result requires more and more exceptions and separate periods,
• the model residual still has a thermal rhythm or a persistent trend,
• the effect disappears after a small change in the time window,
• different sensors on the same element give contradictory conclusions,
• the model reduces a known control event,
• loss of temperature prevents assessment of the main measurement,
• the equation version and coefficients cannot be reproduced,
• the proposed correction is intended only to reduce the number of alarms.

The last point is especially important. The purpose of compensation is not to “calm the dashboard”, but to separate the typical response from a phenomenon that requires action.

What this looks like in Inclify

Inclify makes it possible to place series on one chart with two axes, so measurements and temperature with different units remain readable. Compensation is defined as an explicit project equation. The input value is not replaced: you can keep the raw channel, temperature and calculated result, and describe the relationship in the project documentation.

The compensation report for recognised pairs compares the relationship before and after recalculation: correlation, slope and error. It is a tool for assessing the quality of the adopted model, not an automatic proof of causality and not a structural diagnosis. The engineer still remains responsible for data selection, the equation, the scope of use and the interpretation of the residual.

Equations pass syntax, dependency and cycle checks, but such validation does not confirm the physical correctness of the coefficients. Project configuration changes are audited. Before using the result for alarming, it is worth reproducing at least one sample manually and approving the model scope, the way it responds to missing temperature and the responsibility for periodic review. If you need a reproducible process from raw value to unit and model, see the guide from raw value to engineering unit.

Implementation checklist for temperature compensation

• [ ] Determine whether you are correcting the instrument or modelling the structural response.
• [ ] Collect the sensor documentation and calibration coefficients.
• [ ] Preserve unchanged raw data and original timestamps.
• [ ] Confirm the location, unit and quality of the temperature measurement.
• [ ] Document the structural state and works during the fitting period.
• [ ] Examine lag and differences between heating and cooling.
• [ ] Record the equation, parameters, version and scope of validity.
• [ ] Calculate the model residual and show it alongside the raw series.
• [ ] Validate on a later, unused period.
• [ ] Compare the model with adjacent sensors and an independent measurement.
• [ ] Define the response to missing temperature and to moving outside the model scope.
• [ ] Keep thresholds that protect against missing a large raw value.
• [ ] Version the model change instead of overwriting the interpretation history.
• [ ] Require engineer approval before using the model in alarming.

Limitations: what this procedure does not decide

A statistical model does not automatically identify the physical mechanism. Even stable correlation, good fit and small error do not prove that temperature is the cause of the whole change. The conclusion requires knowledge of the structure, measurement chain, boundary conditions and other loads.

A simple linear model may be wrong in the presence of temperature gradients, hysteresis, non-linearity, support changes or different seasonal behaviour. A model that is too complex, in turn, may overfit noise or an event. A result outside the temperature and state range used in validation is extrapolation.

ISO 18674-1 places monitoring in the wider process of assessing structures and ground before, during and after construction. Recalculating data does not replace the monitoring design, response procedure or the competence of the person interpreting it. The NIST uncertainty guidance also reminds us that a model result depends on the input quantities and the significant sources of uncertainty; omitting them does not make the result certain.

Before compensation, it is worth also following the tree of causes of a faulty reading and separating the thermal phenomenon from calibration drift. For vibrating wire sensors, a separate explanation of operating principle and temperature is useful.

Sources and further reading

1. Thermal Monitoring - Chapter 4, FHWA-HRT-09-040, Federal Highway Administration.
2. Model 4500HT High Temperature Piezometer - Instruction Manual, GEOKON.
3. ISO 18674-1:2015 - General rules, International Organization for Standardization.
4. NIST Technical Note 1297 - Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results, National Institute of Standards and Technology.
5. Law of Propagation of Uncertainty, NIST.

What next: validate the model on your own asset

Prepare the raw series, temperature, sensor descriptions and dates of site changes. We will help build a before-and-after comparison, identify assumptions and determine what the model does not decide. Talk to us about a pilot on data from your asset.