Blockwise Joint Conformal Prediction for Simultaneous Multi-Component Condition Monitoring of Hydraulic Systems.

Abstract

Automated condition-monitoring systems often assess several components at every operating cycle. A separate 95% prediction set for each component does not, however, provide 95% reliability for the complete system state or for a sequence of cycles. This study formulates the operating-condition block as the unit of conformal calibration. For every calibration block, the proposed score takes the maximum nonconformity over four hydraulic components and ten cycles. A finite-sample order statistic then yields Cartesian component-wise prediction sets with simultaneous block-level coverage under exchangeable blocks. The method was evaluated on 1,440 stable cycles from the UCI hydraulic test-rig data, arranged as 144 complete factorial condition blocks. Thirty block-disjoint 72/43/29 training/calibration/test partitions were run with logistic-regression and random-forest backbones. At nominal 95% coverage, conventional marginal sets covered the complete four-component state in only 0.817 and 0.818 of cycles and covered whole blocks in 0.499 and 0.546, respectively. Blockwise calibration increased mean cycle coverage to 0.994 and 0.985 and mean block coverage to 0.971 and 0.946. The price was strongly backbone-dependent: mean Cartesian set sizes were 103.9 and 13.7 out of 144 possible system states. A post-hoc unstable-cycle stress test reduced random-forest block coverage to 0.830, demonstrating that the guarantee should not be extrapolated across regime shifts. The results show that reliability claims in multi-component diagnosis must match the operational decision unit, while set efficiency and exchangeability require explicit auditing.