Error-based state resolution for reduced-order prediction of particle-temperature distributions in a gas–solid fluidized bed

Abstract

Particle-temperature monitoring in gas–solid fluidized beds poses an output-resolution problem: a mean removes thermal heterogeneity, whereas retaining all measured temperature detail can make compact prediction unnecessarily complex. This study reanalyzes retained infrared histograms and synchronized thermal-probe histories from 27 calcium-carbonate heating runs. The source publication analyzed the mean temperature of identified particle pixels; here the retained histograms are used as distribution-valued outputs. First, valid 1 s histograms are aggregated into a 60 s visible-particle time–pixel temperature distribution. Second, each distribution is represented by K ordered equal-weight thermal supports, where K is the number of retained supports and therefore defines output-state resolution. Third, the supports are propagated causally from synchronized gas and external-wall histories. Two errors are then compared: representation error, which quantifies information lost by the K -support approximation, and dynamic-prediction error, which additionally includes the error of causal propagation. The divergence between them identifies where added static detail no longer yields comparable predictive benefit; the resulting resolution is then checked on later-time data and across operating conditions. Within-second heterogeneity contributes a median 94.9% of minute-scale variance. Joint gas and wall histories reduce median mean-temperature normalized root-mean-square error (NRMSE) from 4.79% to 2.90%. Static representation continues to improve with K , whereas dynamic distribution error changes little beyond K = 5 through the tested maximum of 12 supports. At the available 1 Hz boundary sampling, probe quantiles provide no statistically detectable improvement over probe means. The resulting error-based audit links distribution-resolved thermal measurement to a compact and testable monitoring model.