An Improved Quadratic Spline Model Using Curvature Tip Compression—Particle Swarm Optimization to Forecast Accurately the Nonlinear Fluid Calibration Curve

Calibration costs of fluid quantity are not only expensive but also take time, particularly if calibrator facilities are limited. Sometimes, calibrated measuring points do not match the needs of measuring instruments in the field, so forecasts require to be made. Further, the quadratic spline is the simplest non-linear spline model, which vows better accuracy than other linear spline and non-linear regression. For those reasons, we propose a method that minimizes the curvature tip of the quadratic spline model with the popular particle swarm optimization (PSO) technique. This research aims to enhance the accuracy of the quadratic spline prediction model on the calibration curve with a PSO-based curvature tip compression strategy. We want to reduce the effect of oscillations on forming the quadratic spline model. Experimental validation results and comparison of proposed and common methods of quadratic spline interpolation showed that our novel approach, curvature tip compression-PSO, was superior and increased accuracy of 12.18 times from the ordinary quadratic spline and 3.14 times from the linear spline. The proposed method had more minor errors and measurement uncertainties than other ordinary prediction models, thus proving its excellence in predicting unkown values. Calibration curve of turbine flowmeters and salinometers were implemented to this application of the predictive model.