# Robust Grey Relational Analysis-Based Accuracy Evaluation Method
## 3 Robust Grey Relational Analysis-Based Accuracy Evaluation Method
### Expected Valve Crossing Rate
The reference sequence and the corresponding data point difference of sequence one are used as the benchmark, using a random \(\pm\) 1 times the gain to construct sequence two, to satisfy sequences one and two in the corresponding data point, and the difference between the reference sequence is equal or opposite. Grey correlation is calculated for the two sets of sequence data. The results are shown in Table 1, and it is found that, under the traditional grey correlation analysis method, the grey correlation of the two sets of sequence data is equal, which is 87.3134%, and the accuracy after model mapping is 97.1851%, which is not in accordance with the actuality; by judging the expected rate of penetration of the valve of the sequences I and II, respectively, it is obtained that the \(v_{a\,\rm I}<v_{a\,\rm II}\). Sequence merging is carried out after calculating the sequence of wearing valve points, respectively, and the merged sequence index is taken to carry out the unilinear difference on the original data sequences I and II, and calculate the grey correlation corresponding to interpolated sequences I and II. The grey correlation of the interpolated sequences I and II is 87.1090% and 89.7850%, respectively, and the accuracy of the sequences after the model mapping is 97.1377% and 97.7010%, respectively. Calculated and verified using the TIC unequal coefficients method, we get \(\text{TIC}_{\text{I}}=0.12544>\text{TIC}_{\text{II}}=0.11904\). That is, the fitting accuracy of sequence II for the reference sequence is greater than that of sequence I, which is consistent with the evaluation results of the improved method in this paper. The near-identical MAPE-accuracy scores for sequence I and sequence II (75.2848% vs. 75.2869%) reveal critical metric instability that contradicts both the a priori superiority of sequence II and TIC evaluation conclusions. This paradoxical prioritization stems from MAPE's inherent flaws, exacerbated by the following sequence perturbations: (1) Denominator-induced instability from near-zero actual values amplifies computational sensitivity; (2) Asymmetric error weighting systematically distorts positive/negative deviation impacts; (3) Percentage normalization artificially inflates minor absolute errors into exaggerated deviations in low-magnitude regions. Furthermore, the metric's sign dependence invalidates mathematical rigor when prediction-actual polarity mismatches occur, while its scale invariance obscures absolute error magnitude--a dual limitation particularly detrimental in zero-rich or volatile datasets. These compounded deficiencies depress accuracy scores below true performance thresholds, ultimately inducing distorted assessments that misrepresent sequence quality under perturbation conditions. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Statistical Indicators**} & \multicolumn{2}{c}{**Traditional Method**} & \multicolumn{2}{c}{**RGRA-AEM**} \\ \cline{2-5}  & **Sequence I** & **Sequence II** & **Sequence I** & **Sequence II** \\ \hline Grey Correlation/(\%) & 87.3134 & 87.3134 & 87.1090 & 89.7850 \\ Accuracy/(\%) & 97.1851 & 97.1851 & 97.1377 & 97.7010 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of evaluation results between two grey relational analysis methods under equidistant difference conditions. Figure 3: Gramacy and Lee function and random data series comparison.