## 3 Analysis of Results
### Comprehensive Assessment of the Extent of Structural Degradation of Red Sandstone
#### 3.3.3 Correlation Analysis of the Degree of Red Sandstone Degradation with CT Grayscale Images  
The work in Section 3.2 above shows that there is a correlation between the ultrasonic wave velocity values of the red sandstone specimens and their CT grayscale images, and this verifies the specificity of the degree of erosion in different directions when the red sandstone is in the same layer, and also defines the degradation degree of the overall plane of the red sandstone based on this. In order to further investigate the correlation between the CT grayscale images of the red sandstone specimens and the degradation degree, the correlation between the degradation degree and the characteristic parameters of the CT grayscale images is investigated. The method adopted is gray relation analysis (GRA), which can measure the degree of correlation between the factors of two systems based on the similarity or dissimilarity of the development trend between the factors. In the process of system development, if the trend of two factors changes with consistency, i.e., the degree of synchronous change is higher, it can be said that the degree of correlation between the two is higher; on the contrary, it is lower. Since the degradation degree has been defined as the relative degradation degree in this paper, the degradation degree of the first layer is considered to be 0, so the calculation of the gray relative correlation degree cannot be carried out, and the gray absolute correlation degree is instead chosen to measure the correlation between the degradation degree of the red sandstone specimen and the CT grayscale image. The specific calculation method is shown in Section 2.3.2. Figure 11: Comparison of predicted and true values of degradation degree. However, due to the different types of data in this paper and the large magnitude deviation of the data, the data are first processed dimensionless using normalization before performing the gray absolute correlation calculation. In order to effectively verify the relationship between the CT grayscale distribution map of red sandstone and the overall planar degradation degree defined by ultrasound, all parameters in Table 3 are selected below. The real data of degradation degree obtained in Section 3.3.2 are used, and the data predicted using the EDGM model are calculated separately for absolute correlation, so as to find out the possible correlation between the CT grayscale image of red sandstone and the degradation degree, and also to verify the accuracy of the prediction model. The results obtained from the calculations are shown in Table 5.  
It is calculated that there is a strong correlation between all the feature parameters of CT grayscale images and the defined degradation degree, in which the correlation between the third-order central moments of the feature parameters and the probability of a gray level greater than 200 and the true degradation degree reach 0.7935 and 0.8551, respectively, which show a strong correlation degree. The data also show that the correlation between the degradation degree values obtained from the simulation prediction and the feature parameters of the CT grayscale images is the same as for the true values, so it can be considered that the prediction model is highly accurate and its correlation with each feature parameter is greater than the correlation between the true values and the feature parameters, probably because the data obtained from the prediction simulation are more regular, while the true values have a little bit of randomness, so the correlation between the prediction simulation values and the feature parameters is higher.