Multidimensional Gap Decomposition for Diagnostic Prioritization in Biomass-Based Bioenergy Plants

Biomass-based bioenergy plants are commonly compared using aggregate indices that locate a system on a utilization scale but conceal the dimensional structure of its remaining deficit. This study extends the Biopolygeneration Diagnostic Index (BDI) by defining the biopolygeneration gap as a weighted multidimensional distance between each plant profile and a synthetic componentwise best-demonstrated reference constructed exclusively from real operating plants. Each reference coordinate has been demonstrated independently; simultaneous feasibility of the complete vector is not assumed. The squared Euclidean metric is decomposed into criterion-level contributions to identify the dominant diagnostic leverage, without interpreting that leverage as a cost-optimal retrofit. The framework is evaluated using 34 literature-derived cases (21 real plants and 13 models) covering 11 conversion technologies and 16 countries. Relative gaps range from 0.198 to 0.827, and energy efficiency and exergetic output quality provide the dominant leverage in 31 of 34 baseline cases. Incremental information beyond the aggregate BDI is demonstrated by three real plants with nearly identical BDI values (0.606–0.629) but distinct dominant deficits: energy efficiency, exergetic quality, and coproduct valorization. Rank ordering remains stable under 90th-percentile and top-three-median references (ρ=0.984–0.992), alternative distance norms, local weight perturbations, and correction for the shared C1/C2 source. A bounded input-uncertainty scenario yields a mean rank correlation of 0.893 and shows that leverage stability is case-specific. The framework therefore supports transparent dimension-level diagnostic prioritization while preserving a clear boundary with techno-economic, environmental, and implementation decisions.