Laser cladding process parameter acquisition method based on grey wolf particle swarm hybrid algorithm

Abstract

The invention relates to the field of laser cladding processes, in particular to a method for acquiring optimal process parameters of laser cladding based on a grey wolf particle swarm hybrid algorithm. The method comprises the following steps: constructing a regression prediction model for describing a relationship between each key performance index and a laser cladding process parameter; determining an optimization objective of each key performance index, and constructing a comprehensive objective function F by adopting a comprehensive weighting method based on the optimization objective; and taking the comprehensive objective function F as a fitness function, and performing optimization through a grey wolf particle swarm hybrid algorithm to obtain optimal process parameters. According to the method, the optimal laser cladding process parameter combination can be well obtained, so that the performance optimization of the cladding layer is realized.

Description

Technical Field

[0001] The present invention relates to the field of laser cladding technology, and particularly relates to a method for obtaining the optimal process parameters of laser cladding based on a grey wolf particle swarm hybrid algorithm. Background Technique

[0002] Laser cladding technology is a cutting-edge surface strengthening means. It uses a high-energy laser beam to accurately heat the cladding material and the surface of the substrate to the melting state, thereby achieving the firm welding of the required high-performance materials.

[0003] The laser cladding process includes multiple parameters. During the laser cladding process, important parameters such as the laser power, laser spot diameter, scanning speed, and powder feeding rate have a significant impact on multiple performance indicators of the cladding layer. These performance indicators are specifically reflected in aspects such as the geometric dimension accuracy of the cladding layer, the microhardness level, the dilution rate, and the depth of the heat-affected zone. And the overall performance of the cladding layer is directly related to the quality of the laser cladding formed workpiece. Since the workpiece quality is jointly determined by multiple performance indicators, it is crucial to optimize the process parameters reasonably to achieve the optimization of multiple objectives for improving the quality of the cladding layer.

[0004] However, there are numerous parameters involved in the laser cladding process, and the interaction relationships between the parameters are complex. In addition, in practical applications, in order to obtain an ideal laser cladding effect, multiple objective functions need to be comprehensively considered. Adjusting any one target parameter alone often causes changes in other target parameters, and there are often conflicting situations between these objectives.

[0005] In summary, the laser cladding effect is affected by multiple process parameters and involves the problem of multi-objective optimization. Therefore, it is difficult to determine the best combination of laser cladding parameters. Traditional trial-and-error methods, orthogonal test methods, etc. also have problems such as high cost and localized optimization results.

[0006] Therefore, it is urgent to solve the above technical problems. Summary of the Invention

[0007] The technical problem to be solved by the present invention is to overcome the defects of the prior art and provide a method for obtaining the optimal process parameters of laser cladding based on a grey wolf particle swarm hybrid algorithm, which can well obtain the best combination of laser cladding process parameters, thereby realizing the optimization of the performance of the cladding layer.

[0008] To solve the above technical problem, the technical solution of the present invention is: A method for obtaining the optimal process parameters of laser cladding based on a grey wolf particle swarm hybrid algorithm, the method includes:

[0009] Construct a regression prediction model for describing the relationship between each key performance indicator and the laser cladding process parameters;

[0010] Determine the optimization objectives of each key performance indicator, and based on this, use the comprehensive weighting method to construct the comprehensive objective function F;

[0011] Take the comprehensive objective function F as the fitness function and optimize it through the grey wolf particle swarm hybrid algorithm to obtain the optimal process parameters.

[0012] Furthermore, each key performance indicator is respectively the aspect ratio f1 of the cladding layer, the dilution rate f2, and the powder collection rate f3;

[0013] The laser cladding process parameters include the laser power A, the powder feeding rate B, the scanning speed C, and the spot diameter D.

[0014] Furthermore, the regression prediction model is expressed as:

[0015] f1 = 89.968 - 25.999A - 0.939B - 4.464C - 13.253D + 0.035AB - 0.060AC + 0.073BC + 3.435A 2 + 0.003B 2 + 0.138C 2 + 1.245D 2 ;

[0016] f2 = 55.208 - 57.408A - 0.966B - 48.976C - 7.634D + 0.109AB - 3.805AC + 0.124BC + 3.402A 2 + 0.007B 2 + 5.24C 2 + 0.927D 2 ;

[0017] f3 = -4.799 + 2.015A + 0.008B - 0.022C - 13.253D + 0.004AB - 0.018AC - 0.005BC - 0.262A 2 - 0.001B 2 + 0.039C 2 + 0.139D 2 .

[0018] Furthermore, the optimization objectives of each key performance indicator are expressed as:

[0019]

[0020] Wherein, f1(A, B, C, D) represents the regression prediction model of the aspect ratio of the cladding layer; f2(A, B, C, D) represents the regression prediction model of the dilution rate; f3(A, B, C, D) represents the regression prediction model of the powder collection rate; max f1(A, B, C, D) indicates that the optimization objective of the aspect ratio is the larger the better, min f2(A, B, C, D) indicates that the optimization objective of the dilution rate is the smaller the better; max f3(A, B, C, D) indicates that the optimization objective of the powder collection rate is the larger the better.

[0021] Furthermore, the comprehensive objective function F is expressed as:

[0022]

[0023] Wherein, W1, W2, and W3 respectively represent the weight ratio coefficients, which are obtained through the analytic hierarchy process, and W1 + W2 + W3 = 1.

[0024] Furthermore, in order to improve the applicability, during the optimization process by the grey wolf particle swarm hybrid algorithm, there are also constraint conditions, and the constraint conditions are:

[0025]

[0026] Furthermore, a grey wolf particle swarm hybrid algorithm for improving the convergence speed and solution accuracy of the algorithm is provided. The specific steps of the grey wolf particle swarm hybrid algorithm are as follows:

[0027] Step A, grey wolf algorithm stage:

[0028] Step A1, initialize the grey wolf population:

[0029] Randomly generate N grey wolves, and the position X of each wolf i =[A i , B i , C i , D i represents a set of parameter combinations, and set the maximum number of iterations T GWO ;

[0030] Step A2, calculate the fitness and sort:

[0031] Calculate the fitness value F(X i ) of each wolf, sort according to the fitness, and select the three best wolves: Alpha(X α ), Beta(X β ), Delta(X δ );

[0032] Step A3, update the grey wolf position:

[0033] D α =|E1·Xα -X i |

[0034] D β = |E2·X β -X i |

[0035] D δ = |E3·X δ -X i |

[0036] X1 = X α -P1·D α

[0037] X2 = X β -P2·D β

[0038] X3 = X δ -P3·D δ

[0039]

[0040] where D i is the distance between the grey wolf and the prey; X i is the position of the grey wolf; E1, E2, E3, P1, P1, and P3 are all coefficient vectors; X1, X2, and X3 respectively represent the positions of the ω wolf updated under the guidance of the α wolf, β wolf, and δ wolf;

[0041] Step A4, Iteration and Termination:

[0042] Repeat Steps A2 - A3 until T GWO is reached, and output the optimal solution X α the sub - optimal solution X β X δ ;

[0043] Step B, Particle Swarm Optimization (PSO) Phase:

[0044] Step B1, Initialize the particle swarm:

[0045] Set the optimal solution X α of GWO as the initial global optimum g bext ;

[0046] Generate M particles, each particle with position x i = [A i , B i , C i , D i and velocity V i , and the initial position can add random perturbations around X α : xi = X α + ∈;

[0047] Step B2, update the particle velocity and position:

[0048]

[0049] w is the inertia weight; c1, c2 are learning factors; r1, r2 are random numbers in [0, 1];

[0050] Step B3, update the individual and global optima:

[0051] Calculate the fitness F(X i ), update the individual optimum p of each particle bext,i and the global optimum g bext .

[0052] Step B4, iteration and termination:

[0053] Repeat steps B2 - B3 until the maximum number of iterations T of the PSO is reached pso , output the final g bext .

[0054] After adopting the above technical solution, for each key performance index, the present invention constructs a regression prediction model, which can quickly predict the performance indexes of the cladding layer under different combinations of process parameters, reduces the number of experiments, lowers the cost, and speeds up the optimization process; for the multi-objective optimization problem involved in the laser cladding process, a weighted method is used to construct a comprehensive objective function F, thereby transforming the multi-objective optimization into an optimization problem of a single objective, thus greatly simplifying the complexity of the optimization process; the present invention uses the comprehensive objective function F as the fitness function of the grey wolf particle swarm hybrid algorithm, and the smaller its value, the better the performance of the cladding layer. Through the optimization of the grey wolf particle swarm hybrid algorithm, the optimal combination of process parameters can be quickly obtained, thereby realizing the optimization of the cladding layer performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 is a flowchart of the method for obtaining the optimal process parameters of laser cladding based on the grey wolf particle swarm hybrid algorithm of the present invention;

[0056] Figure 2 is a schematic cross-sectional view of the cladding layer;

[0057] Figure 3 is a fitness curve diagram of the objective function during the optimization process using the grey wolf particle swarm hybrid algorithm;

[0058] Figure 4 is a residual plot of the regression prediction model of the cladding layer fitted by the present invention;

[0059] Figure 5The residual plot of the regression prediction model for the dilution rate of the clad layer fitted by the present invention;

[0060] Figure 6 The residual plot of the regression prediction model for the powder collection rate of the clad layer fitted by the present invention;

[0061] Figure 7 The macroscopic comparison diagram of the process clad layers of the optimal process parameters obtained by using the optimal process parameters of the laser cladding based on the grey wolf particle swarm hybrid algorithm in the present invention and the traditional process parameters. Detailed implementation manners

[0062] In order to make the content of the present invention easier to be clearly understood, the present invention will be further described in detail below according to specific embodiments in conjunction with the accompanying drawings.

[0063] As Figure 1 shown, a method for obtaining the optimal process parameters of laser cladding based on the grey wolf particle swarm hybrid algorithm includes:

[0064] Step S1, constructing a regression prediction model for describing the relationship between each key performance index and the laser cladding process parameters;

[0065] Among them, the quality of the clad layer is visually displayed to a great extent through its appearance morphology, and the appearance morphology is closely related to the geometric characteristics of the cross-section of the clad layer. Specifically, the forming accuracy of the clad layer is directly affected by its cross-sectional width (denoted as W) and height (denoted as H); at the same time, the depth of the clad layer (denoted as h) plays a decisive role in the dilution rate, and this index of the dilution rate can reflect the tightness of the combination between the clad layer and the substrate. To illustrate this more intuitively, Figure 2 shows the cross-sectional schematic diagram of the clad layer, in which the width W, height H and depth h of the clad layer are clearly marked.

[0066] The aspect ratio of the clad layer is a key geometric parameter for describing the shape characteristics of the cross-section of the clad layer. It is defined as the ratio of the width of the cross-section of the clad layer (denoted as W) to its height (denoted as H). This ratio not only reflects the appearance morphology of the clad layer, but also is closely related to the quality, performance of the clad layer and its bonding strength with the substrate. In surface modification technologies such as laser cladding, the aspect ratio of the clad layer is an important optimization target. By adjusting the process parameters (such as laser power, scanning speed, powder feeding rate, etc.), the aspect ratio of the clad layer can be controlled, thereby improving the forming quality of the clad layer, enhancing its bonding strength with the substrate, and optimizing the overall performance of the clad layer. Its formula is:

[0067]

[0068] Therefore, the aspect ratio is set as the first optimization objective, denoted as f1, which is equal to the ratio of the width W to the height H of the clad layer. To enhance the metallurgical bonding degree between the clad layer and the substrate, it is necessary to reduce the dilution rate, which is selected as another optimization objective. The calculation formula for the dilution rate is as follows:

[0069]

[0070] Meanwhile, define f2 as the dilution rate, which is a parameter jointly determined by the height H and the depth h of the clad layer, reflecting the mixing degree between the clad layer and the substrate material.

[0071] In addition to the dilution rate, we also focus on the powder collection rate as the last optimization objective because the effective collection of powder not only concerns the cost control of laser cladding but also directly affects the quality of the clad layer. In the cladding operation, improving the powder utilization rate and reducing waste are important links to ensure the process economy and the stability of the clad layer quality. Therefore, the optimization of the powder collection rate is crucial for achieving the high efficiency and environmental friendliness of the overall process.

[0072]

[0073] Under this optimization framework, f3 represents the powder collection rate, which measures the utilization efficiency of powder during the cladding process. M represents the total mass of powder input into the cladding operation, while m represents the mass of powder that is not utilized, i.e., not clad onto the workpiece, during the cladding process. The level of the powder collection rate f3 directly reflects the saving degree of the powder material and the potential cost - benefit of the cladding process, and is also an important indicator for evaluating the efficiency and environmental friendliness of the cladding process.

[0074] Based on the above analysis, in this step, the selected key performance indicators are the aspect ratio f1 of the clad layer, the dilution rate f2, and the powder collection rate f3.

[0075] The laser cladding process parameters selected in this embodiment include the laser power A, the powder feeding rate B, the scanning speed C, and the spot diameter D. The regression prediction model aims to describe the relationship between the process parameters and these key performance indicators mathematically. Therefore, the analysis of variance method is used to analyze the accuracy and reliability of the regression model, and the regression prediction models for the aspect ratio f1 of the clad layer, the dilution rate f2, and the powder collection rate f3 are obtained, that is,

[0076] f1 = 89.968 - 25.999A - 0.939B - 4.464C - 13.253D + 0.035AB - 0.060AC + 0.073BC + 3.435A 2 + 0.003B 2 + 0.138C 2 + 1.245D 2 ;

[0077] f2 = 55.208 - 57.408A - 0.966B - 48.976C - 7.634D + 0.109AB - 3.805AC + 0.124BC + 3.402A 2 + 0.007B 2 + 5.24C 2 + 0.927D 2 ;

[0078] f3 = -4.799 + 2.015A + 0.008B - 0.022C - 13.253D + 0.004AB - 0.018AC - 0.005BC - 0.262A 2 - 0.001B 2 + 0.039C 2 + 0.139D 2 。

[0079] The above three regression prediction models are obtained by modeling and analyzing experimental data based on Design-expert software.

[0080] The specific process and statistical judgment criteria are as follows:

[0081] Use a quadratic polynomial regression equation for modeling, and screen significant terms through the stepwise regression method shown in the graph software. This method realizes model optimization by gradually introducing / eliminating variables, ensuring that the equation only retains parameters with statistical significance.

[0082] Regarding model verification:

[0083] Under the framework of analysis of variance (ANOVA), evaluate the reliability of the model through multi-dimensional indicators;

[0084] Significance test: Use p-value < 0.05 as the factor significance determination criterion;

[0085] Analysis of influence strength: Quantify the factor effect through the mean square (MS), and the larger the MS value, the more significant the influence of the factor on the response value;

[0086] Model fitness: The lack of fit test needs to satisfy p > 0.05 to exclude systematic model bias;

[0087] Correlation measure: R 2 value reflects the explanatory ability of the model for the variation of the response value;

[0088] Signal-to-noise ratio verification: The AdeqPrecision index requires > 4 to ensure that the model has sufficient prediction resolution.

[0089] The residual plots of the regression prediction models for the width-to-height ratio f1, dilution rate, and powder collection rate f3 of the cladding layer are shown in Figure 3 , Figure 4 and Figure 5 respectively, which proves the accuracy and reliability of the above three models.

[0090] Through the regression model, the performance indicators of the cladding layer under different combinations of process parameters can be quickly predicted, reducing the number of experiments, lowering the cost, and accelerating the optimization process. The analysis of variance method provides a significance evaluation of the influence of process parameters on performance indicators. By analyzing the interaction effects between process parameters, the relationship between process parameters and target variables can be better understood, enhancing the adaptability of the algorithm.

[0091] Step S2: Determine the optimization objectives for each key performance indicator, and based on this, construct a comprehensive objective function F using the comprehensive weighting method;

[0092] Specifically, in order to pursue the best comprehensive performance, our goal is to increase the width-to-height ratio f1 to the highest possible level, while reducing the dilution rate f2 to the lowest possible degree, and ensuring that the powder collection rate f3 remains at a high level. Based on these goals, we constructed the following optimization mathematical model:

[0093]

[0094] In the formula, f1(A,B,C,D) represents the regression prediction model of the width-to-height ratio of the cladding layer; f2(A,B,C,D) represents the regression prediction model of the dilution rate; f3(A,B,C,D) represents the regression prediction model of the powder collection rate; max f1(A,B,C,D) indicates that the optimization objective of the width-to-height ratio is the larger the better, min f2(A,B,C,D) indicates that the optimization objective of the dilution rate is the smaller the better; max f3(A,B,C,D) indicates that the optimization objective of the powder collection rate is the larger the better.

[0095] Different from the optimization focusing on a single objective, multi-objective optimization involves simultaneously considering the optimization of two or more objectives during the parameter adjustment process. In engineering practice, such multi-objective optimization problems are both common and crucial, but their analysis and processing are relatively complex. In the face of a situation where multiple objectives coexist, adjusting any one objective parameter alone often causes changes in other objective parameters, and there are often conflicting situations among these objectives. Therefore, the core of multi-objective optimization is to strive for each objective to reach the optimal state under the premise of meeting all constraint conditions, so as to find the global optimal solution.

[0096] When faced with the emerging challenges of multi-objective optimization in practical applications, it becomes particularly urgent to explore efficient solutions. For this reason, in this embodiment, for the multi-objective optimization problems involved in the laser cladding process, including key indicators such as aspect ratio, dilution rate, and powder collection rate, the strategy of the comprehensive weighting method is adopted, which transforms the originally complex multi-objective optimization problem into a relatively intuitive single-objective problem. A comprehensive objective function F is designed to integrate the sub-objectives into a comprehensive objective function F, thereby transforming the original problem into an optimization problem of the parameters of F (i.e., laser power A, powder feeding rate B, scanning speed C, and spot diameter D). The specific form of the comprehensive objective function F will reflect the relative importance between sub-objectives. The purpose of this function is to find a balance among multiple conflicting objectives, thereby generating a series of balanced process parameter combinations. These parameter combinations provide a rich selection space for decision-makers, enabling them to flexibly select the most suitable optimal solution according to specific production requirements and performance indicators.

[0097] The comprehensive objective function F is expressed as:

[0098]

[0099] When determining the comprehensive objective function F, we introduce the weight ratio coefficients W1, W2, W3, which represent the key parameters of each sub-objective respectively and satisfy the condition that their sum is 1, i.e., W1 + W2 + W3 = 1. The construction of the comprehensive objective function F is based on the weighted sum of these weight coefficients and sub-objective values, and the optimal solution is obtained by minimizing F. The smaller the value of the comprehensive objective function F, the higher the quality of the cladding layer. Therefore, our ultimate goal is to minimize the value of F by optimizing the four parameters of laser power A, powder feeding rate B, scanning speed C, and spot diameter D. This formula describes the relationship between the comprehensive objective function F and each parameter, and how to optimize the quality of the cladding layer by minimizing F.

[0100] It should be noted that in order to improve the rationality of weight allocation, the scientific method of the analytic hierarchy process can be used to accurately determine the weight ratio between sub-objectives. We can hierarchize the problem and classify each influencing factor in detail, thereby constructing a clear analytic hierarchy model.

[0101] Scale of judgment matrix for relative importance of each objective

[0102] F <![CDATA[f1]]> <![CDATA[f2]]> <![CDATA[f3]]> <![CDATA[f1]]> 1 1 / 5 3 <![CDATA[f2]]> 5 1 7 <![CDATA[f3]]> 1 / 3 1 / 7 1

[0103] According to the provided table information, we can construct a judgment matrix K, which reflects the relative importance among various influencing factors during the laser cladding process. To quantify the weights of these influencing factors, we adopted the geometric mean method for calculation. Specifically, the geometric mean method is a method to determine the weights by calculating the nth root (n is the number of elements) of the product of each element. In the judgment matrix K, we multiply the elements of each row and then take the nth root (n is the order of the judgment matrix, that is, the number of influencing factors) to obtain the corresponding weight value for each row. Finally, to ensure that the sum of all weights is 1, we need to normalize the obtained weight values.

[0104] matrix

[0105] We obtain its eigenvector W = [0.188 0.731 0.081]. Therefore, the target weights of the aspect ratio f1, dilution rate f2, and powder collection rate f3 are 0.188, 0.731, and 0.081 respectively.

[0106] Therefore, the comprehensive objective function F is expressed as:

[0107]

[0108] Step S3: Taking the comprehensive objective function F as the fitness function, optimize through the hybrid grey wolf particle swarm algorithm to obtain the optimal process parameters.

[0109] Among them, during the optimization process, to ensure that each sub-objective (i.e., the aspect ratio f1, dilution rate f2, and powder collection rate f3) can be optimized within a reasonable parameter range, we set a series of constraint conditions. At the same time, for the cladding process parameters themselves, we also set corresponding constraint conditions to ensure that the entire optimization process is carried out within a feasible and effective range. The setting of these constraint conditions aims to balance the relationships among various sub-objectives, thereby achieving the optimization of the overall performance. The constraint conditions are:

[0110]

[0111] It should be noted that when determining the constraint conditions, it is necessary to comprehensively consider the constraint ranges of each sub-objective and the selection range of process parameters. Among them, the selection range of process parameters is not set arbitrarily, but is determined based on the optimized level obtained from the previous in-depth study of various single factors such as A, B, C, D, etc. This means that when setting the constraint conditions, we not only need to consider the requirements and limitations of each sub-objective itself, but also fully refer to the results of the previous single-factor research to ensure that the selected process parameters not only meet the theoretical optimized level but also can meet the constraint conditions of each sub-objective in actual operation, thus providing a solid foundation for achieving the overall optimal goal.

[0112] Introduce the coupling relationship between process parameters (such as the matching of laser power and scanning speed, etc.) as a constraint condition to improve the practicality of optimization.

[0113] In this step, a hybrid grey wolf - particle swarm optimization algorithm is adopted to optimize the laser cladding process parameters, aiming to achieve the optimization of the cladding layer performance. In this process, we define the comprehensive objective function F as the fitness function of the algorithm. The smaller its value is, the better the performance of the cladding layer. To achieve the optimization task, a series of parameters are set for the hybrid grey wolf - particle swarm optimization algorithm. These parameters include but are not limited to the population size, the number of iterations, the number of leadership levels in the grey wolf algorithm, the inertia weight in the particle swarm algorithm, etc. They jointly affect the exploration ability and convergence speed of the algorithm.

[0114] In addition, we also implement the hybrid grey wolf - particle swarm optimization algorithm using the MATLAB programming environment and draw the fitness curve to visually display the optimization process of the algorithm. As Figure 3 shown, the MATLAB program demonstrates how the algorithm gradually approaches the optimal solution through iterations, while the fitness curve clearly reflects the trend that the fitness function value continuously decreases as the iteration process progresses.

[0115] Through the optimization of the hybrid grey wolf - particle swarm optimization algorithm, we can obtain a set of optimal laser cladding process parameter combinations, thus achieving the optimization of the cladding layer performance. The MATLAB program and the fitness curve provide us with effective tools to monitor the running state of the algorithm and evaluate the optimization effect.

[0116] In this embodiment, combining the regression prediction model and the variance analysis method with the hybrid grey wolf - particle swarm optimization algorithm can further improve the optimization performance of the algorithm.

[0117] Among them, the algorithm parameter settings, the range of laser cladding process parameters, the optimized process parameters, and the cladding layer performance indicators are as follows:

[0118] Parameter input layer

[0119]

[0120] Parameter input layer

[0121]

[0122] Laser cladding optimization index

[0123]

[0124] Laser cladding optimization index feedback layer

[0125]

[0126]

[0127] It should be noted that, first of all, the switching between global search (GWO) and local development (PSO) in the traditional Grey Wolf Particle Swarm Hybrid Algorithm may not be flexible enough, resulting in slow convergence speed or falling into local optimum. This may cause the population diversity to decline with the increase of the number of iterations, leading to weakened search ability (insufficient convergence and search ability). Secondly, a major challenge faced by the traditional Grey Wolf Particle Swarm Hybrid Algorithm in multi-objective optimization tasks is the difficulty in effectively maintaining the diversity and uniform distribution of the Pareto front. This limitation significantly weakens its optimization ability in dealing with complex multi-objective problems (poor multi-objective optimization ability). Finally, the traditional Grey Wolf Particle Swarm Hybrid Algorithm relies on high-cost experiments or numerical simulations for fitness evaluation, which limits the optimization efficiency. A single model may not be able to balance computational efficiency and accuracy. The objective function is usually based on empirical formulas or simple models and may not accurately reflect the relationship between process parameters and target variables. Moreover, in terms of performance, there is a significant defect in the traditional Grey Wolf Particle Swarm Hybrid Algorithm, that is, the lack of in-depth analysis of the sensitivity of algorithm parameters, which makes it quite difficult to set algorithm parameters scientifically and reasonably (poor constraint handling ability, low fitness evaluation efficiency, unreasonable parameter setting).

[0128] The Grey Wolf Particle Swarm Hybrid Algorithm adopted in this embodiment cleverly integrates the essence of the Grey Wolf Optimization Algorithm (GWO) and the Particle Swarm Optimization Algorithm (PSO), aiming to improve the overall optimization efficiency through the combination of their advantages. The Grey Wolf Particle Swarm Hybrid Algorithm mainly adds the idea of particles to the Grey Wolf Optimization Algorithm. To improve the optimization ability and convergence speed of the Grey Wolf Algorithm, the method of memorizing the best position information of particle self-movement in the Particle Swarm Optimization Algorithm is introduced, and the particle position update is used to replace the Grey Wolf individual position update, enabling it to memorize the best position information in its own evolution process. By changing the inertia constant w, the ability of the hybrid algorithm to balance global search and local development is coordinated. The following are the detailed steps of the algorithm flow design:

[0129] Problem definition and parameter initialization:

[0130] Optimization parameters: Laser power A, powder feeding rate B, scanning speed C, spot diameter D.

[0131] Parameter range: The upper and lower limits need to be defined for each parameter, as shown in the above table

[0132] Fitness function: Design a comprehensive objective function F according to the process objectives (aspect ratio, dilution rate, powder collection rate), and the goal is to minimize this function.

[0133] The specific steps of the Grey Wolf Particle Swarm Hybrid Algorithm are as follows:

[0134] Step A, Grey Wolf Algorithm (GWO) stage:

[0135] Step A1, initialize the grey wolf population:

[0136] Randomly generate N grey wolves, and the position X of each wolf i =[[A i ,[[B i ,[[C i ,[[D i represents a set of parameter combinations, and set the maximum number of iterations T GWO .

[0137] Step A2, calculate the fitness and sort:

[0138] Calculate the fitness value F(X i ), sort by fitness, and select the top three wolves: Alpha(X α ), Beta(X β ), Delta(X δ ).

[0139] These three wolves respectively represent the optimal solution, sub-optimal solution and third-optimal solution in the current iteration.

[0140] X α : Alpha wolf is the individual with the highest fitness (optimal) in the current population, directly corresponding to the current optimal solution of the optimization problem;

[0141] X β : is the individual with the second-best fitness in the population, serving as an auxiliary decision maker for Alpha;

[0142] X δ : is the individual with the third-best fitness in the population, responsible for performing specific search tasks.

[0143] Step A3, update the grey wolf position:

[0144] D α =|E1·X α -X i |

[0145] D β =|E2·X β -X i |

[0146] D δ =|E3·X δ -X i |

[0147] X1 = X α - P1·D α

[0148] X2 = X β-P2·D β

[0149] X3 = X δ -P3·D δ

[0150]

[0151] where D i is the distance between the gray wolf and the prey, and X i is the position of the gray wolf; E1, E2, E3, P1, P1, and P3 are all coefficient vectors; X1, X2, and X3 respectively represent the positions of the ω wolf updated under the guidance of the α wolf, β wolf, and δ wolf;

[0152] E1: Controls the random perturbation of the Alpha wolf (optimal solution), balancing the exploration and exploitation of the current optimal solution;

[0153] E2: Controls the random perturbation of the Beta wolf (sub-optimal solution), expanding the search range to cover potential optimal regions;

[0154] E3: Controls the random perturbation of the Delta wolf (third-optimal solution), enhancing the adaptability of the algorithm to complex solution spaces.

[0155] Step A4, Iteration and Termination:

[0156] Repeat Steps A2 - A3 until reaching T GWO and output the optimal solution X α and the sub-optimal solution X β , X δ

[0157] Step B, Particle Swarm Optimization (PSO) Phase:

[0158] Step B1, Initialize the particle swarm:

[0159] Set the optimal solution X α of GWO as the initial global optimum g bext ;

[0160] Generate M particles, and the position of each particle x i = [A i , B i , C i , D i and velocity V i , and the initial position can add a random perturbation around X α : x i = X α + ∈;

[0161] Step B2, Update the particle velocity and position:

[0162]

[0163] w is the inertia weight (which can be linearly decreased), so that the inertia weight in PSO can be dynamically decreased to balance exploration and exploitation; c1 and c2 are learning factors; c1: the individual learning factor, which controls the weight of the particle moving towards its own historical optimal position (pbest); c2: the swarm learning factor, which controls the weight of the particle moving towards the swarm historical optimal position (gbest); r1 and r2 are random numbers in the range [0, 1], random numbers that follow the uniform distribution U(0, 1), and in practical applications, it is necessary to ensure that they are independently generated in each iteration to avoid pattern solidification, w max is the maximum value of the inertia weight, w min is the minimum value of the inertia weight.

[0164] Step B3, update the individual and global optima:

[0165] Calculate the fitness F(X i ) of each particle, and update the individual optimum p bext,i of each particle and the global optimum g bext .

[0166] Step B4, iteration and termination:

[0167] Repeat steps B2 - B3 until the maximum number of iterations T pso of PSO is reached, and output the final g bext .

[0168] Summary:

[0169] GWO global search: Use the swarm cooperation of the grey wolf algorithm to find the approximate optimal solution X α .

[0170] PSO local optimization: Fine search near the GWO result and accelerate convergence through the particle swarm algorithm.

[0171] Therefore, GWO avoids premature convergence and PSO improves the local search effect.

[0172] The following is a detailed comparison between the grey wolf particle swarm hybrid algorithm in this embodiment and the traditional GWO - PSO hybrid algorithm.

[0173] Deficiencies of the traditional hybrid algorithm:

[0174] 1. The traditional GWO - PSO hybrid algorithm adopts an alternating iteration or parallel update method (for example, in each iteration, some individuals are updated by GWO and some by PSO), which may cause interference between the search mechanisms of the two algorithms and reduce the efficiency.

[0175] 2. Most hybrid algorithms initialize PSO randomly or simply share population information, without fully utilizing the global search results of GWO.

[0176] 3. Some GWO-PSO hybrid algorithms only use the leading wolves (Alpha, Beta, Delta) of GWO as individuals in PSO, without fully exploring their guiding value.

[0177] 4. The parameters of traditional hybrid algorithms (such as the inertia weight w of PSO) are usually fixed or simply adjusted linearly, making it difficult to adapt to complex optimization processes.

[0178] Improvements to the Grey Wolf Particle Swarm hybrid algorithm in this embodiment:

[0179] 1. By fully traversing the parameter space through the Grey Wolf algorithm, PSO is prevented from falling into local optima prematurely. Initialize the particle swarm centered around the optimal solution X α of GWO, narrow the search range, and improve local accuracy.

[0180] Therefore, conflicts in the search logics of the two algorithms are avoided, the division of labor is clearly defined in stages, the global and local are decoupled, and ineffective calculations are reduced. For example, PSO does not need to repeatedly search in areas far from the optimal solution.

[0181] 2. Use the optimal solution X α output by GWO as the global optimal initial value (g bext ) of PSO, and generate an initial particle swarm around X α : x i = X α +∈. By adjusting the perturbation amplitude, ensure that the particle swarm conducts a fine search near high-quality solutions, significantly improve the starting quality of PSO, and avoid the risk of local convergence caused by random initialization.

[0182] 3. Directly assign the optimal individual X α of GWO to g bext of PSO, rather than just as an ordinary particle. In the PSO stage, the sub-optimal solutions (Beta, Delta) of GWO can be retained as the initial p bext,i of the particle swarm to accelerate convergence. Through multi-level information transmission (Alpha → global optimal, Beta / Delta → individual optimal), improve the robustness of the algorithm.

[0183] 4. Dynamically adjust w according to the iteration progress. At the beginning, w is larger (mainly for exploration), and at the end, w is smaller (mainly for exploitation). The dynamic parameter strategy better suits the phased requirements of the actual optimization process, and further improves the adaptability of the algorithm to multi-modal and non-linear problems.

[0184] 5. The grey wolf particle swarm hybrid algorithm in this embodiment has a convergence speed 40% faster than that of the traditional hybrid algorithm (the number of iterations is reduced from 150 to 90); the quality of the solution is improved, the dilution rate is reduced by 12%, and the powder collection rate is increased by 18%.

[0185] Comparison table

[0186]

[0187]

[0188] Figure 7 The figure shows the comparison of the clad layer morphologies after component remanufacturing by two different cladding processes: the left side is the result of the traditional manually controlled cladding process, while the right side is the result of the cladding process optimized by the grey wolf particle swarm hybrid algorithm. Through comparison, we can clearly see the significant advantages of the right clad layer in multiple key indicators. The right clad layer has a stronger bond with the substrate, and the metallurgical bond strength has been significantly improved; the application of the grey wolf particle swarm hybrid algorithm has brought the forming accuracy of the clad layer to a new height, ensuring the precise manufacturing of components; in addition, the new algorithm has also significantly increased the powder collection rate, effectively reducing the production cost.

[0189] Taking the above ideal embodiment of the present invention as an inspiration, through the above description, relevant staff can completely make various changes and modifications within the scope of not deviating from the technical idea of this invention. The technical scope of this invention is not limited to the content in the specification, and its technical scope must be determined according to the scope of the claims.

Claims

1. A method for obtaining optimal process parameters for laser cladding based on a gray wolf particle swarm hybrid algorithm, characterized in that: Methods include: A regression prediction model was constructed to describe the relationship between each key performance indicator and laser cladding process parameters; Determine the optimization target of each key performance indicator, and based on this, use the comprehensive weighting method to construct the comprehensive objective function F; Taking the comprehensive objective function F as the fitness function, the optimal process parameters are obtained through the Grey Wolf Particle Swarm Hybrid Algorithm optimization.

2. The method for acquiring laser cladding process parameters based on the grey wolf particle swarm hybrid algorithm according to claim 1 is characterized in that: The key performance indicators are the aspect ratio f1, dilution rate f2 and powder collection rate f3 of the cladding layer; The laser cladding process parameters include laser power A, powder feeding amount B, scanning speed C and spot diameter D.

3. The method for acquiring laser cladding process parameters based on the grey wolf particle swarm hybrid algorithm according to claim 2 is characterized in that: The regression prediction model is expressed as: f1=89.968-25.999A-0.939B-4.464C-13.253D+0.035AB- 0.060AC+0.073BC+3.435A 2 +0.003B 2 +0.138C 2 +1.245D 2 ; <h2 style=";text-align:left;direction:ltr">f2 = 55.208 - 57.408A - 0.966B - 48.976C - 7.634D + 0.109AB - 3.805AC + 0.124BC + 3.402A<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +0.007B<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +5.24C<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +0.927D<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> ; f3=-4.799+2.015A+0.008B-0.022C-13.253D+0.004AB- 0.018AC-0.005BC-0.262A 2 -0.001B 2 +0.039C 2 +0.139D 2 。 4. The method for acquiring laser cladding process parameters based on the grey wolf particle swarm hybrid algorithm according to claim 2 or 3, characterized in that: The optimization objectives of each key performance indicator are expressed as: Wherein, f1(A,B,C,D) represents the regression prediction model of the aspect ratio of the cladding layer; f2(A,B,C,D) represents the regression prediction model of the dilution rate; f3(A,B,C,D) represents the regression prediction model of the powder collection rate; maxf1(A,B,C,D) represents the optimization target of the aspect ratio as large as possible, minf2(A,B,C,D) represents the optimization target of the dilution rate as small as possible; maxf3(A,B,C,D) represents the optimization target of the powder collection rate as large as possible.

5. The method for acquiring laser cladding process parameters based on the grey wolf particle swarm hybrid algorithm according to claim 4 is characterized in that: The comprehensive objective function F is expressed as: Where W1, W2, and W3 represent weight proportional coefficients, respectively, which are obtained through the hierarchical analysis method, and W1+W2+W3=1.

6. The method for acquiring laser cladding process parameters based on the grey wolf particle swarm hybrid algorithm according to claim 2 is characterized in that: In the process of optimization through the gray wolf particle swarm hybrid algorithm, there are also constraints, which are:

7. The method for acquiring laser cladding process parameters based on the grey wolf particle swarm hybrid algorithm according to claim 2 is characterized in that: The specific steps of the gray wolf particle swarm hybrid algorithm are: Step A, Grey Wolf Algorithm Phase: Step A1, initialize the gray wolf population: Randomly generate N gray wolves, each wolf's position X i =[A i ,B i ,C i ,D i ] represents a set of parameter combinations, setting the maximum number of iterations T GWO ; Step A2, calculate fitness and sort: Calculate the fitness value F(X i ), sort by fitness and select the best three wolves: Alpha(X α )、Beta(X β )、Delta(X δ ); Step A3, update the gray wolf position: D α =|E1·X α -X i | D β =|E2·X β -X i | D δ =|E3·X δ -X i | X1=X α -P1·D α X2=X β -P1·D β X3=X δ -P3·D δ Where D i is the distance between the gray wolf and its prey; X i is the position of the gray wolf; E1, E2, E3, P1, P1 and P3 are all coefficient vectors; X1, X2 and X3 represent the updated position of the ω wolf under the guidance of the α wolf, β wolf and δ wolf respectively; Step A4, iteration and termination: Repeat steps A2-A3 until T is reached. GWO , output the optimal solution X α , suboptimal solution X β , X δ ; Step B, Particle Swarm Optimization (PSO) phase: Step B1, initialize the particle swarm: The optimal solution of GWO is X α Set as the initial global optimal g of PSO bext ; Generate M particles, each particle position x i =[A i ,B i ,C i ,D i ] and speed V i , the initial position can be around X α Add random perturbation: x i =X α +∈; Step B2, update particle velocity and position: w is the inertia weight; c1, c2 are learning factors; r1, r2 are random numbers [0,1]; Step B3, update individual and global optimal: Calculate the fitness of each particle F(X i ), update the optimal p for each particle bext,i and the global optimal g bext . Step B4, iteration and termination: Repeat steps B2-B3 until the maximum number of iterations T of PSO is reached. pso , output the final g bext .

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