Stochastic Sensitivity and Consistency Analysis of Hybrid Wave–Current Energy Concept Selection

Hybrid marine energy systems that integrate wave and current technologies can improve resource complementarity and spatial utilization. However, the ranking stability of selected hybrid concepts under changes in criterion weights, score assumptions, and multi-criteria decision analysis (MCDA) methods requires further examination. This study extends an existing two-stage concept-selection procedure by evaluating four shortlisted wave energy converter–hydrokinetic turbine configurations using stochastic weight-space sampling, criterion-wise weight sensitivity, cross-method consistency, and bounded score-perturbation analyses. A fixed normalized decision matrix is first evaluated using the Simple Additive Weighting (SAW) method across three sets of 10,000 criterion-weight scenarios generated using normalized-uniform, Dirichlet α = 1, and Dirichlet α = 0.5 distributions. The same scenarios are then evaluated using the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), with ranking consistency quantified using Spearman’s rank correlation and complete-ranking agreement. Score sensitivity is subsequently examined through bounded one-point perturbations of the Stage 2 criterion scores, with SAW and TOPSIS recalculated under equal criterion weights to identify dominance-breaking and rank-reversal conditions. The oscillating water column–Savonius configuration, W1H3, remains first-ranked under all three sampled weight distributions because its normalized criterion scores are equal to or higher than those of every competing configuration across all five criteria. Criterion-wise sensitivity analysis shows that W1H3 is not outranked over the investigated weight range, although it ties with the point absorber–Savonius configuration, W2H3, when the full weight is assigned to mooring synergy or control compatibility. A crossover between W2H3 and the oscillating water column–hybrid Savonius–Darrieus configuration, W1H4, occurs at a co-location-feasibility weight of 0.384615. Across the three weight-sampling distributions, SAW and TOPSIS achieve complete-ranking agreement of 65.91–87.08%, with mean Spearman rank correlations of 0.9318–0.9742; the remaining differences are confined to the ordering of W2H3 and W1H4. Bounded score perturbations show that single one-point score change is sufficient to break the dominance of W1H3 over W2H3, whereas four changes are required for W2H3 to attain a unique first rank under both methods. The results demonstrate that W1H3 is rank-stable under the investigated weight and method variations for the adopted decision matrix, while the score-perturbation analysis identifies the bounded score changes under which the preferred ranking may change.

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Publication Details

Journal
Applied Sciences
Published
2026-08-25
DOI
https://doi.org/10.3390/app16178460
Primary Topic
Wave and Wind Energy Systems
Type
article
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article

Stochastic Sensitivity and Consistency Analysis of Hybrid Wave–Current Energy Concept Selection

Muk Chen Ong, Cheng Yee Ng
Applied Sciences
Wave and Wind Energy Systems
article

Stochastic Sensitivity and Consistency Analysis of Hybrid Wave–Current Energy Concept Selection

Muk Chen Ong, Cheng Yee Ng
article en

Abstract

Hybrid marine energy systems that integrate wave and current technologies can improve resource complementarity and spatial utilization. However, the ranking stability of selected hybrid concepts under changes in criterion weights, score assumptions, and multi-criteria decision analysis (MCDA) methods requires further examination. This study extends an existing two-stage concept-selection procedure by evaluating four shortlisted wave energy converter–hydrokinetic turbine configurations using stochastic weight-space sampling, criterion-wise weight sensitivity, cross-method consistency, and bounded score-perturbation analyses. A fixed normalized decision matrix is first evaluated using the Simple Additive Weighting (SAW) method across three sets of 10,000 criterion-weight scenarios generated using normalized-uniform, Dirichlet α = 1, and Dirichlet α = 0.5 distributions. The same scenarios are then evaluated using the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), with ranking consistency quantified using Spearman’s rank correlation and complete-ranking agreement. Score sensitivity is subsequently examined through bounded one-point perturbations of the Stage 2 criterion scores, with SAW and TOPSIS recalculated under equal criterion weights to identify dominance-breaking and rank-reversal conditions. The oscillating water column–Savonius configuration, W1H3, remains first-ranked under all three sampled weight distributions because its normalized criterion scores are equal to or higher than those of every competing configuration across all five criteria. Criterion-wise sensitivity analysis shows that W1H3 is not outranked over the investigated weight range, although it ties with the point absorber–Savonius configuration, W2H3, when the full weight is assigned to mooring synergy or control compatibility. A crossover between W2H3 and the oscillating water column–hybrid Savonius–Darrieus configuration, W1H4, occurs at a co-location-feasibility weight of 0.384615. Across the three weight-sampling distributions, SAW and TOPSIS achieve complete-ranking agreement of 65.91–87.08%, with mean Spearman rank correlations of 0.9318–0.9742; the remaining differences are confined to the ordering of W2H3 and W1H4. Bounded score perturbations show that single one-point score change is sufficient to break the dominance of W1H3 over W2H3, whereas four changes are required for W2H3 to attain a unique first rank under both methods. The results demonstrate that W1H3 is rank-stable under the investigated weight and method variations for the adopted decision matrix, while the score-perturbation analysis identifies the bounded score changes under which the preferred ranking may change.

Applied SciencesVol. 16(17)
Universiti Teknologi Petronas (MY), University of Stavanger (NO)
Life below water
Openalex Percentile: Top 13%
Wave and Wind Energy Systems
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