What Ten Industrial Surveys Identify in a Cone-Crusher Population Balance Model: Bayesian Calibration with Structural Discrepancy

A cone-crusher model that predicts throughput, power and product size rests on a handful of fitted scalars, and a point fit to a few industrial surveys does not say which of them the surveys determine. We calibrate the eight fitted scalars of a Whiten classification-breakage population balance engine of a Metso HP500 cone crusher (capacity, Bond work index, power form, classification and breakage constants) as a Bayesian posterior against the ten surveys of Rocha et al., with a linear structural discrepancy on the closed-side setting and the feed size in the form of Kennedy and O'Hagan. The posterior is sampled with the differential-evolution moves of ter Braak, after the affine-invariant stretch move failed an autocorrelation-time criterion on the same posterior. Strict leave-one-survey-out validation refits every quantity without the held-out survey. Held out, the posterior predictive mean has a mean absolute percentage error of 12.00 % on throughput and 14.31 % on power, which is within the noise of a setting-only line (13.67 % and 12.78 %) and no gain over it on power. The 80 % bands cover 0.8 and 0.9 of the surveys, and on power the band is 43.9 % narrower than the residual band of the refit backbone at the same coverage; against the setting-only line (width 119.60 kW, coverage 0.8) and the free-form fit (129.82 kW, 0.8) its width of 117.74 kW is about the same, with a higher coverage, so the band gain is against the backbone and not against the simple line. Of the 16 parameters, 7 are identified by the surveys; the classification and breakage scalars of the population balance stay at their prior. With ten surveys and no measured product size, the data calibrate how the two outputs depend on the setting, and they cannot calibrate the population balance. Source code, data and the computational records: https://github.com/fsantibanezleal/CAOS_ChancaDEM. The application: https://chancadem.fasl-work.com.