# Robust Grey Relational Analysis-Based Accuracy Evaluation Method
###### Abstract  
The conventional grey relational analysis (GRA) demonstrates limitations in dynamic simulation data evaluation due to its failure to simultaneously account for geometric similarity among dynamic indicators and the proximity of data curve distances. This deficiency manifests as a compromised robustness in noise resistance and interference suppression, consequently leading to discrepancies between model accuracy and practical scenarios. To address these shortcomings, this paper proposes a robust grey relational analysis-based accuracy evaluation method (RGRA-AEM). The methodology incorporates the expected penetration rate to facilitate interpolation computation and employs deviation acceptability as a distance threshold indicator. By integrating the grey relational degree, mean squared deviation distance, and accuracy modeling, this approach achieves enhanced stability in accuracy assessment. It effectively mitigates the inherent weakness of traditional GRA that overemphasizes sequential curve similarity while significantly improving the anti-noise performance and interference resistance of grey relational coefficients. Experimental validation through the internal ballistic test-simulation dynamic data of a hybrid rocket motor conclusively demonstrates the superior robustness of the proposed methodology. acuracy evaluation; grey relational analysis (GRA); anti-noise ability; tolerance index  
8 April 2025  
25 April 2025  
27 April 2025  
**Citation:** [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Robust Grey Relational Analysis-Based Accuracy Evaluation Method. _Appl. Sci._**2025**, 15, 4926. [[https://doi.org/10.3390/appl5094926](https://doi.org/10.3390/appl5094926)]([https://doi.org/10.3390/appl5094926](https://doi.org/10.3390/appl5094926))  
**Copyright:** 62 2025 by the authors. Liconsec MDPT, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ([[https://creativecommons.org/licenses/by/4.0/](https://creativecommons.org/licenses/by/4.0/)]([https://creativecommons.org/licenses/by/4.0/](https://creativecommons.org/licenses/by/4.0/))). [[https://doi.org/10.3390/appl5094926](https://doi.org/10.3390/appl5094926)]([https://doi.org/10.3390/appl5094926](https://doi.org/10.3390/appl5094926))method quantifies the spatial consistency of geometric patterns between data sequences through grey relational degree computation, thereby analyzing inter-sequence correlations. Serving as a robust tool for simulation accuracy verification, GRA facilitates the quantification of geometric congruence among dynamic data trajectories, enabling the systematic evaluation of model fidelity in time-dependent simulation scenarios [6; 7; 8]. Grey relational analysis demonstrates significant advantages in synthesizing multi-dimensional indicator information to deliver comprehensive evaluation outcomes. By virtue of its capability to holistically integrate heterogeneous data attributes, this methodology effectively addresses the limitations of single-weighting approaches in indicator prioritization. Within the context of dynamic modulus prediction models, GRA is recognized as a methodologically robust framework, exhibiting enhanced reliability and practical applicability. Its inherent capacity to reconcile geometric pattern consistency with quantitative correlation analysis ensures a rigorous validation of model outputs, thereby overcoming limitations inherent in conventional unidimensional evaluation paradigms [9]. In the study of grey relational analysis, it has been found that grey relational degrees have limitations in ordinal preservation [10; 11; 12; 13].