Mathematical Mapping
Analytical methods used to describe the relationship between multiple variables rely on creating a continuous function from discrete data points. In sensor characterization, surface fitting generates a mathematical map that accounts for the primary signal and environmental influences. The resulting surface provides a way to estimate values between known calibration points.
High density grids improve the accuracy of the fit but require more measurement time during production.
Compensation Logic
Error reduction is achieved by subtracting the modeled deviation from the raw sensor output. Through the use of surface fitting, a device can compensate for non-linearities that depend on both the measurand and the ambient temperature. This approach is more effective than simple linear interpolation because it accounts for the interaction between the two variables.
The resulting output is more stable across the entire operating range of the instrument.
Data Density
Grid density during the calibration phase determines the resolution of the final model. When performing surface fitting, the technician must ensure that the test points are distributed evenly across the expected operating envelope. Areas with high curvature in the sensor response require more data points to avoid approximation errors.
The trade-off between the time spent in the calibration chamber and the final precision of the fit is a primary design consideration.
Verification Standard
Model validation involves testing the fitted surface against a set of reference values not used in the regression. If the surface fitting was successful, the difference between the modeled and actual values will be within the specified tolerance. Residual analysis helps identify regions where the model may be less accurate.
This verification step is required before the calibration parameters are finalized and loaded into the device memory.
