## 4 Conclusions  
This orthogonal experiment was designed using the Taguchi method and the effect of process parameters on the micro-hardness of the coating was analyzed via the S/N ratio and ANOVA. Moreover, the optimal combination of process parameters was obtained. Based on the back-propagation neural network (BPNN) and quantum-behaved particle swarm optimization (QPSO) algorithm, a BPNN-QPSO neural network prediction model for laser cladding Ti(C, N) ceramic coating was established, and the effects of the process parameters and their interactions on the micro-hardness of the coating were analyzed. Then, the process parameters were optimized aiming to the maximum micro-hardness of Ti(C, N) the ceramic coating. The main conclusions are summarized as follows:  
1. Through S/N ratio, ANOVA analysis and main effect plot, the combination of the optimal process parameters were determined as L2D1S1V2, namely laser power 450 W, spot diameter 1 mm, overlapping ratio 20%, and scanning velocity 7 mm/s. The micro-hardness of the coating was 1134.6 HV0.2. The BPNN-QPSO neural network model had strong training and prediction ability. The models of BPNN and BPNN-QPSO were trained for 19 epochs and 93 epochs, respectively, to reach the training goal. The maximum relative errors of BPNN and BPNN-QPSO prediction were 14.47%  
Figure 15: Interaction between process parameters: (**a,b**) \(L\times S\); (**c,b**) \(D\times S\); (**e,f**) \(S\times V\).  
and 9.12%, respectively, and the correlation coefficients of the prediction results were 0.8179 and 0.9575, respectively.
3. The BPNN-QPSO neural network model optimized the process parameters of Ti(C, N) ceramic coating prepared by laser cladding and the optimized process parameters were laser power 445.65 W, spot diameter 1 mm, overlapping ratio 20%, and scanning velocity 6.33 mm/s. The optimization results were similar to those obtained by ANOVA.
4. The BPNN-QPSO neural network model predicted the optimal micro-hardness of Ti(C, N) ceramic coating prepared by laser cladding and the optimal micro-hardness was 1118.2 HV0.2. The interaction between laser power and overlapping ratio, the interaction between the spot diameter, and the overlapping ratio, as well as the interaction between overlapping ratio and scanning velocity had significant effect on the micro-hardness of Ti(C, N) the ceramic coatings.  
[PERSON] and [PERSON] conceived and designed the experiments; [PERSON] and [PERSON] performed the experiments; [PERSON], [PERSON] and [PERSON] analyzed the data and discussed the experiment; [PERSON] and [PERSON] wrote the paper. The manuscript was reviewed by all authors. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China grant number 517/5559, the Fund of the State Key Laboratory of High-Performance Complex Manufacturing grant number ZZYJKT2019-06, and the Natural Science Foundation of Hunan province of China grant number 2020)J4716.  
The authors declared that they have no conflicts of interest in this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.