# Robust Grey Relational Analysis-Based Accuracy Evaluation Method
## 4 Instance Validation  
In order to verify the improvement effect and practical application of the proposed method in Section 3, we carried out an example verification on a hybrid rocket motor. The hybrid rocket motor uses a solid fuel of hydroterminated polybutadiene (HTPB) and a liquid oxidizer of hydrogen peroxide (H\({}_{2}\)O\({}_{2}\)), with the return and specific impulse of the fuel improved by the addition of metal particles. An accuracy assessment method based on strong robust grey correlation analysis is applied for the internal ballistic test-simulation model validation of a certain type of hybrid rocket motor to analyze the consistency between the output timing data of the model thrust characteristics and that of the actual test [31; 32; 33]. The timing curves, composed of the experimental sequence and the simulation sequence, are shown in Figure 9, and the two sets of sequence curves have the same trend of change and the same perturbation, which belong to the simulation model with higher accuracy and more reasonable data in engineering applications. The test is carried out through the TIC inequality coefficient, and TIC = 0.03170 is obtained. Figure 8: Methodology flowchart. Figure 9: Internal ballistic experimental-simulation thrust time series data of a hybrid rocket engine. From Figure 10, it can be concluded that there is a positive correlation between grey correlation and model accuracy; grey correlation and accuracy change curves are similar. As a measure of the similarity between the model output and the actual data, an increase in the grey correlation usually predicts an increase in the model accuracy, i.e., when the correlation between the output of the simulation model and the actual observed data is enhanced, the prediction accuracy of the model tends to improve, which is in line with the nature of the linear mapping of the grey correlation-mean squared deviation distance-accuracy model. As the bias acceptability increases, there is a tendency for the grey correlation and accuracy to first decrease and then increase within a certain tolerance. The perturbation tolerance allows the grey correlation to correct the accuracy bias due to geometric similarity and distance proximity when quantifying the data series curves. In addition, the increase in bias acceptability reflects a greater tolerance for model prediction errors by the user or decision-maker, which may result in higher ratings of model accuracy during the evaluation process, thus increasing the acceptance of the model's accuracy overall. The selection criterion of bias acceptability for this example is based on the global average deviation of 5%. The relative position of the data series curve with the 5% bias acceptability added after interpolation using the through-valve is shown in Figure 11 in relation to the error tolerance boundary. Figure 12a shows the distribution of grey correlation coefficient using the traditional grey correlation analysis method, corresponding to the grey correlation degree of 80.4016% and accuracy of 95.0768% in Table 3; Figure 12b shows the distribution of grey correlation coefficient by using only valve interpolation, corresponding to the grey correlation degree of 81.8313% and accuracy of 95.6098%; comparing Figure 12a with Figure 12b, it is found that the essence of valve interpolation lies in increasing the number of data points within the proximity range of the sequence curve without changing the shape of the original sequence curve in order to indirectly increase the proportion of distance proximity in the calculation of the grey correlation coefficient. Moreover, due to the increase in the fitting accuracy caused by the increase in the number of data points, the corresponding TIC coefficients will also change accordingly: \(\text{TIC}_{\text{a}}=0.03170>\text{TIC}_{\text{b}}=0.03107\). Figure 10: Grey correlation-accuracy deviation acceptability variation curve. Figure 11: Illustration of data at 5% deviation acceptability.