## 5 Conclusions  
Addressing the issue of varying working conditions and the lack of corresponding data labels in actual cutting operations, this paper proposes a method using optimized SDP for recognizing milling cutter wear states under variable conditions. This method can use data from source conditions to build a generalized milling cutter wear state recognition model, solving the problem of traditional data-driven training models being unable to recognize conditions under variable working conditions. Experimental and comparative analyses lead to the following conclusions. 1. The vibration signals in milling operations can be transformed from one-dimensional time series to two-dimensional images using SDP transformation, merging vibration signals from the X, Y, and Z axes based on their time series in a designated area to form \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Milling Cutter Wear States** & **Precision/\%** & **Recall/\%** & **F1 Score** \\ \hline initial wear & 94.62 & 96.75 & 0.9567 \\ normal wear & 96.99 & 96.75 & 0.9687 \\ severe wear & 96.97 & 95.14 & 0.9605 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Indicators of the model’s generalization ability test. Figure 21: The confusion matrix of the test results. a unified feature representation. Using a desymmetrization dot pattern effectively avoids overlapping adjacent spiral arms from different mirrors due to parameter selection, aiding in finding optimal parameters. 2. Using cluster analysis to extract template images for each wear state, with Euclidean distance maximization as an indicator, adaptively optimizes the selection of SDP parameters \(l\) and \(\xi\) using the differential evolution algorithm. This effectively solves the problem of SDP transformation effects being limited by preset parameter selection, narrows the intra-class distance, and expands the inter-class difference, thus facilitating the construction of a generalized decision boundary and reducing the impact of working condition changes on the milling cutter wear state mapping relationship. 3. The use of the CBAM-ResNet-50 network for feature learning of images under source conditions constructs a generalized milling cutter wear state recognition model. The results show that the recognition accuracy for test samples under variable conditions can reach over 95%. This method can effectively use labeled data from source conditions to classify unlabeled data from target conditions, achieving the recognition of milling cutter wear states in variable condition scenarios with good recognition accuracy and generalization ability. Experimental analysis results indicate that this method can serve as an effective solution for milling cutter wear monitoring under variable conditions, aligning more closely with real-world cutting operation scenarios. However, recognizing only three different wear states of milling cutters is insufficient, necessitating further research and improvement to identify more precise wear states of milling cutters. Conceptualization, H.C.; methodology, H.C.; software, H.C.; validation, H.C.; formal analysis, H.C.; investigation, H.C. and L.C. ; resources, F.G. and Y.L. ; data curation, all authors; writing--original draft preparation, H.C.; writing--review and editing, H.C.; visualization, H.C. and L.C. ; supervision, F.G. and Y.L. ; project administration, F.G. and Y.L. ; funding acquisition, F.G. and L.C. All authors have read and agreed to the published version of the manuscript. This research was funded by the Key Industrial Innovation Chain Project of Shaanxi Province under grant number 2021 ZDLGY-10-07, The Project of Cultivation for young top-notch Talents of Beijing Municipal Institutions under grant number BPHR20203103, and Prosperous Social Science Action Plan Project of Beijing University of Agriculture under grant number FRSK-2024-010. Not applicable. The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy and ethical restrictions.