Calibration — Introduction and Learning Goals

Short summary Calibration methods and error analysis for sensors: linear & nonlinear regression, hysteresis, sensitivity, and full calibration workflow.

Learning objectives

• Perform linear regression for sensor calibration and compute confidence intervals.

• Analyze hysteresis and nonlinearity errors.

• Design calibration experiments and propagate calibration uncertainty into measurements.

Key concepts (brief)

• Regression residuals, standard error, and calibration curve interpretation.

• Hysteresis and repeatability characterization.

• Sensitivity analysis and combining calibration with measurement uncertainty.

Recommended notebooks to run

• micrometer_calibration.ipynb

• regression_analysis.ipynb

• full_calibration_analysis_example.ipynb

• hysteresis_error_analysis.ipynb

• calibration_non_linear_relations.ipynb

Suggested exercises

• Calibrate a sample dataset, report calibration equation and uncertainty.

• Compare linear vs nonlinear fits and discuss choice and impact on measurements.

Prerequisites Basic regression, statistics, and familiarity with plotting in Python.

Pages in this chapter

• Linearity error example

• Calibration of non-linear (logarithmic) function

• [Hysteresis example](calibration_error_analysis 2.ipynb)

• Hysteresis and regression analysis example

• Calibration of non-linear relations

• Calibration and uncertainty analysis - virtual experiment

• ## Hysteresis and log-log calibration example

• ## Introduction to linear regression

• ## LVDT example

• Micrometer calibration using gage block

• Calibration and uncertainty analysis - virtual experiment

• Lecture 6

• Sensitivity estimate example