## 3 Experimental Results and Analysis
### Experiments on Maximum Adhesion Coefficient Estimation
#### 3.4.3 Simulation of Maximum Adhesion Coefficient Estimation  
Four rail surface conditions, dry, wet, snowy, and oily rails, were selected as the simulated rails. The maximum adhesion coefficients of the four rail conditions match  
Figure 16: Plot of the \(\mu_{1}\) and \(\mu_{4}\) affiliation function.  
Figure 17: Plot of the rail surface condition correction coefficient affiliation function.  
Figure 15: Plot of the rail surface condition affiliation function.  
the experimental range of the UIC ORE B44 committee, and the maximum adhesion coefficients (ideal values) are 0.286, 0.197, 0.147, and 0.117. To emphasize the effectiveness of the proposed method, the traction level was set to a lower value for each rail condition, resulting in a certain gap between the actual adhesion coefficient and the ideal maximum adhesion coefficient. This setup allows for comparison of the estimated maximum adhesion coefficient with the ideal value, thus testing the precision of the estimation process. During the experiment, the time of rail surface image identification is considered negligible to focus on the performance of the adhesion coefficient estimation. The main discussion is about several common cases. Combinations of simulated rail and the recognized rail surface conditions include \"dry + dry\", \"wet + wet\", \"snowy + wet\", and \"oily + oil\". The experimental results are shown in Figures 18-21, where the following comparisons are made: ideal maximum adhesion coefficient, estimated maximum adhesion coefficient for unfused rail surface conditions, and estimated maximum adhesion coefficient for fused rail surface conditions.  
Where Mumax is the ideal maximum adhesion coefficient, FullMuEst is the real-time adhesion coefficient estimated by the full-dimensional state observer, MumaxEst is the maximum adhesion coefficient estimated using the fuzzy control strategy, and MumaxEst_Revise is the corrected maximum adhesion coefficient, incorporating rail surface condition information. Under the simulation conditions designed in this study, the estimation error of the dry simulation rail is reduced from 12.6% to 10.1%, the estimation error of the wet simulation rail is reduced from 6.7% to 4.1%, the estimation error of the rainy and snowy simulation rail is reduced from 4.1% to 2.7%, and the estimation error of the oiled simulation rail is reduced from 23.1% to 12.0%. These results indicate that incorporating rail surface conditions improves the accuracy of the maximum adhesion coefficient estimation, effectively reducing estimation errors across different rail conditions and their various combinations. This is particularly crucial under complex operating conditions. In comparison with the maximum adhesion coefficient estimation method presented in the literature [24] under identical experimental conditions, the approach in the literature [24] does not incorporate rail surface conditions, relying solely on the adhesion coefficient and creep and slide speed (i.e., the MumaxEst values shown in Figures 18-21). In contrast, the method proposed in this paper, by integrating critical environmental information, can better adapt to changes in the environment, thereby improving estimation accuracy. Furthermore,  
Figure 21: Oily + oil.  
Figure 20: Snowy + wet.  
this approach provides reliable operational condition awareness, which can enhance the effectiveness of adhesion control strategies and improve the safety of train operations.