## 1 Introduction  
Laser cladding is an important surface modification technique that uses a high power density laser beam to melt powder material and form a coating bonded metallurgically to the substrate surface. It can significantly improve the wear-resistance [1, 2], corrosion resistance [3, 4], and oxidation resistance [5, 6] of a material surface. In our previous research [7], Ti(C, N) ceramic coating was prepared on a Ti6 Al4V titanium alloy surface using a laser cladding process, which significantly improved the hardness and wear resistance of the titanium alloy surface. However, the formation process of surface coatings fabricated with laser cladding is very complicated and there are many process parameters that affect coating quality, such as laser power, spot diameter, scanning velocity, preplaced powder thickness,and overlapping ratio [8; 9; 10]. At the same time, the interactions of process parameters also have a great impact on coating quality [11]. Therefore, it is necessary to establish a mapping relationship between process parameters and coating quality to analyze the mapping rule for laser cladding process parameters to coating quality. As a computational intelligence technology, a neural network provides a simple and effective tool for mapping the relationship between process parameters and quality characteristics [12]. At present, some researchers have applied a back-propagation neural network (BPNN) to the parameter prediction of laser cutting [13; 14], laser welding [15; 16], and other laser processing fields, and have achieved abundant research results. For example, [PERSON] et al. [17] combined the BPNN and particle swarm optimization (PSO) algorithm to predict the quality of laser micromachining. [PERSON] et al. [18] applied BPNN to optimize the process parameters of laser cladding cobalt-base alloy. [PERSON] et al. [19] combined BPNN and genetic algorithm (GA) to predict the quality of laser welding. The results showed that BPNN could predict processing quality according to laser processing parameters. However, the initial weights and thresholds of BPNN were randomly selected, which was easy to fall into the local optimal solution, resulting in poor prediction performance of BPNN [20]. Therefore, it is necessary to optimize the initial weights and thresholds of BPNN. In recent years, researchers have studied the effects of laser cladding process parameters on coating quality and found that the optimization of process parameters was also a difficult problem [21; 22]. The optimization of process parameters was usually based on a large number of process experiments that gradually accumulated processing experience, which had a heavy workload and high cost. [PERSON] et al. [23], [PERSON] et al. [24], and [PERSON] et al. [25] designed orthogonal experiments using the Taguchi method, and optimized laser cladding process parameters using response surface methodology (RSM), the technique for order preference by similarity to an ideal solution (TOPSIS), and analysis of variance (ANOVA), respectively, to improve cladding coating quality. However, when there are many factors involved in orthogonal experiments, it is difficult to determine the change rule of experimental data and the optimal result is usually a combination of experimental parameters that can neither predict the coating quality nor obtain the best process parameters. In order to solve these problems, some researchers used optimization algorithms to optimize process parameters on the basis of design of the orthogonal experiment using the Taguchi method. [PERSON] et al. [26] used the PSO algorithm to predict the geometry of the molten pool and optimize the process parameters. [PERSON] [27; 28] improved PSO algorithm and proposed the quantum-behaved particle swarm optimization (QPSO) algorithm, which quickly replaced the PSO algorithm for single-objective optimization problems due to its strong global search capability, easy implementation, and fewer parameters [29; 30].