Method for aero-engine blade cladding repair path planning

Abstract

The application discloses an aero-engine blade cladding repair path planning method, and is specifically implemented according to the following steps: step 1, a multi-objective optimization mathematical model of aero-engine blade cladding path planning is constructed; step 2, a chaos mapping and process experience mixed initialization population is constructed; step 3, an adaptive crossover and mutation operation is performed; step 4, a reference point dynamic adjustment and improved non-dominated sorting selection are performed; step 5, an adaptive penalty function constraint processing is performed; step 6, an iteration termination judgment is performed; and step 7, an optimal compromise solution is selected based on a fuzzy analytic hierarchy process. The application can effectively improve the aero-engine blade cladding repair quality, and provides core technical support for intelligentization and high-precision optimization of the aero-engine blade cladding path.

Description

Technical Field

[0001] This invention belongs to the technical field of path planning methods, specifically relating to a method for path planning in the cladding repair of aero-engine blades. Background Technology

[0002] As the most numerous and harshest core load-bearing components in an engine, aero-engine blades operate under extreme environments of high temperature, high pressure, high-speed airflow erosion, and alternating loads for extended periods. This makes them prone to in-service damage such as tip wear, leading-edge erosion, and microcrack propagation, severely impacting engine operational safety and service life, and resulting in extremely high blade replacement costs. The blade surface is a typical complex three-dimensional freeform surface. When using robotic arms with traditional algorithms for cladding path planning, core defects such as slow convergence speed, susceptibility to local optima, insufficient ability to handle high-dimensional variables, and decoupling between path and process parameters often exist, making it difficult to meet the high precision and high reliability requirements of aerospace-grade repair. Summary of the Invention

[0003] The purpose of this invention is to provide a method for planning the cladding repair path of aero-engine blades, which can effectively improve the quality of cladding repair of aero-engine blades.

[0004] The technical solution adopted in this invention is a method for planning the repair path of cladding on aero-engine blades, which is implemented according to the following steps: Step 1: Construct a multi-objective optimization mathematical model for the cladding path planning of aero-engine blades; Step 2: Initialize the population by combining chaotic mapping with process experience; Step 3: Adaptive crossover mutation operation; Step 4: Dynamically adjust reference points and improve non-dominated sorting selection; Step 5: Adaptive penalty function constraint processing; Step 6: Iteration termination check; Step 7: Select the optimal compromise solution based on fuzzy hierarchical analysis.

[0005] The invention is further characterized in that, Step 1 is implemented in the following steps: Step 1.1: Define decision variables The path parameters and process parameters are jointly encoded, comprising a total of 8 core decision variables, expressed as follows: (1) Where x1 is the center-to-center spacing between adjacent melt channels, with a value range of [1.2, 1.8]; x2 is the layer thickness, with a value range of [0.1, 0.3]; x3 is the tool path angle, with a value range of [0, 90]; x4 is the scanning strategy code, where 0 represents unidirectional scanning, 1 represents reciprocating scanning, and 2 represents alternating scanning in zones; x5 is the laser power, with a value range of [800, 1600]; x6 is the scanning speed, with a value range of [3, 9]; x7 is the powder feed rate, with a value range of [4, 12]; and x8 is the protective gas flow rate, with a value range of [10, 20]. Step 1.2: Establishing the objective function Five conflicting minimization objective functions are established to comprehensively cover the requirements of cladding repair: Processing time objective function The goal is to minimize the total time of the entire cladding process. The total time includes the cladding processing time and the equipment idle time. The expression is: (2) In the formula, This represents the total length of the cladding path. For scanning speed, This is the time spent idling. Objective function for profile error With the goal of minimizing the profile error of the repaired blade, the expression is calculated based on the equal residual height model: (3) In the formula, Let be the residual height of the cladding layer at the i-th position. The target residual height; Objective function for warpage deformation With the objective of minimizing the maximum warping deformation of the blade after repair, a thermo-mechanical coupled finite element model is used for prediction, and the expression is as follows: (4) In the formula, Let be the warping deformation of the j-th node; Objective function of cladding layer defect rate With the goal of minimizing the defect rate of the cladding layer, the expression calculated based on the metallurgical quality prediction model is as follows: (5) In the formula, This represents the area of ​​the defective region. This represents the total area of ​​the cladding layer; Laser head loss objective function With the goal of minimizing laser head loss, the expression is calculated based on laser power and working time: (6) In the formula, For laser power, Total processing time. This refers to the laser head loss coefficient. Step 1.3, Define Constraints Based on aviation process specifications and equipment rated capacity, four types of constraints are set: Geometric accuracy constraints: The overlap rate of the cladding layer is controlled between 25% and 35% to ensure uniform and pore-free cladding layer formation. The expression is: (7) In the formula, w(X) is the weld width of a single cladding layer, which is obtained by coupling process parameters; Physical metallurgical constraints: The molten pool temperature is controlled between the material's melting point and 1.2 times the melting point, and the dilution rate is controlled between 5% and 15% to ensure the quality of metallurgical bonding. The expression is: (0.05≤α(X)≤0.15) (8) In the formula, The melting point of TC4 titanium alloy is taken as 1600℃-1700℃; α(X) represents the molten pool temperature; α(X) represents the dilution rate. Equipment capacity constraints: All decision variables are strictly controlled within the rated parameters of the processing equipment, expressed as follows: (9) No interference constraints: The minimum distance between the cladding head and the blade, tooling fixture, etc., shall not be less than the safety distance to avoid collision interference. The expression is: (10) In the formula, This is the minimum distance between the cladding head and the obstacle. For a safe distance, choose 3-5mm.

[0006] Step 2 is implemented in the following steps: Step 2.1: Generation of Empirical Solution for the Process From the historical process database of aero-engine blade cladding repair, 10 sets of optimal process-path parameter combinations that have been verified by engineering were selected as empirical solutions to ensure that the initial population contains high-quality feasible solutions. Step 2.2, Generation of Chaotic Mapping Solutions: The remaining individuals in the population are generated using a Logistic chaotic mapping. The randomness and ergodicity of the chaotic variables ensure population diversity. The Logistic mapping expression is as follows: (11) In the formula, the control parameters =4, the system is in a completely chaotic state; the chaotic variable (z_n∈(0,1)) is transformed into the range of values ​​of each decision variable through linear mapping: (12) Step 2.3, Population Merging and Screening The empirical solution and the chaotic solution are combined, and the top N individuals are selected as the initial population through non-dominated sorting, where N is the preset population size.

[0007] In step 3, an adaptive crossover and mutation operator is designed. Based on the convergence of the population and the fitness of the individuals, the crossover probability Pc and the mutation probability Pm are dynamically adjusted to optimize the algorithm performance. Based on the evolutionary state of the population, the crossover probability Pc and the mutation probability Pm are dynamically adjusted to balance the global exploration and local development capabilities. Dynamically adjust the crossover probability: This is done by dynamically adjusting the fitness of the two individuals crossing over and the average fitness of the population. The expression is: (13) In the formula, , (f') represents the larger fitness value among the two crossover individuals; The average fitness of the population; The maximum fitness of the population; Minimum fitness of the population; Mutation probability: dynamically adjusted based on the fitness of the mutated individual and the average fitness of the population, expressed as: (14) In the formula, , f represents the fitness value of the mutated individual; By using dynamically adjusted crossover and mutation probabilities, simulated binary crossover and polynomial mutation operations are performed on the parent population to generate the offspring population.

[0008] Step 4 is implemented in the following steps: Step 4.1: Generation of the starting reference point Initial reference points are generated using a uniform design method. The number of reference points H is determined by the number of targets M and the number of segments p, and the calculation formula is as follows: (15) With target number M=5 and segmentation number p=4, the initial number of reference points is calculated to be 126. Step 4.2, Dynamic Adjustment of Reference Points After each generation of evolution is completed, the number of individuals associated with each reference point is counted; for reference points with 0 associated individuals, they are moved towards the nearest non-dominated solution to fill the missing solution region in the target space; for reference points with too many associated individuals, new reference points are generated nearby to avoid excessive concentration of solutions. Step 4.3: Improve non-dominated sorting We introduce a weighted sum of crowding distance and reference point distance as the basis for individual selection, and combine it with non-dominated ranking to screen the merged population of parents and offspring, retaining N individuals to form a new generation of parents.

[0009] Step 5 is implemented in the following steps: Step 5.1, Constraint Violation Calculation: Calculate the constraint violation degree for each individual in the population, quantifying the extent to which an individual violates the constraints. The expression is: (16) In the formula, For inequality constraints, Equality constraint; ( When CV(X) = 0, the individual is a feasible solution; when CV(X) > 0, the individual is an infeasible solution. The larger the value, the more severe the violation of the constraint. Step 5.2, Dynamic Penalty Coefficient: The penalty coefficient is dynamically adjusted based on the proportion of feasible solutions in the population. The expression is: (17) In the formula, the initial penalty coefficient =10; The number of feasible solutions in the population; This represents the total population size. Step 5.3: Fitness Correction for Infeasible Solutions For infeasible solutions, the modified fitness value is used in population selection, expressed as: (18).

[0010] In step 6, a dual termination condition is set: the maximum number of iterations and the convergence threshold. When the number of iterations reaches the preset maximum value, or the change in the hypervolume index of the population is less than the convergence threshold for several consecutive generations, the iteration is terminated and the current Pareto optimal solution set is output; otherwise, the process returns to step 3 to continue evolution.

[0011] Step 7 is implemented in the following steps: Step 7.1: Construct the fuzzy judgment matrix Based on the engineering requirements of cladding repair for aero-engine blades, the importance of five optimization objectives is compared pairwise to construct a fuzzy judgment matrix; Step 7.2, Weight Calculation The consistency of the fuzzy judgment matrix is ​​checked using the fuzzy hierarchical analysis method, and the weight vector of each objective is calculated. ; Step 7.3: Optimal Solution Selection The objective value of each Pareto optimal solution is normalized to eliminate the influence of dimensions. The weighted objective sum is then calculated, and the solution with the smallest weighted sum is selected as the optimal compromise solution. The corresponding cladding path parameters and process parameters are then output.

[0012] The beneficial effects of this invention are: 1. Hybrid Initialization Strategy: Empirical solutions provide a high-quality starting point close to the optimal solution, avoiding the blindness of random initialization; chaotic mapping ensures the ergodicity of the population, preventing premature convergence. The fusion of these two approaches accelerates convergence while preserving population diversity, improving algorithm performance from the evolutionary starting point.

[0013] 2. Adaptive crossover mutation operator: Following the evolutionary logic of inferior individuals having strong exploration and superior individuals having strong development, when the overall fitness of the population is low in the early stage of evolution, a high crossover mutation rate enhances the global search capability; when the proportion of superior individuals increases in the later stage of evolution, a low crossover mutation rate protects superior genes and strengthens local optimization, dynamically balancing the global exploration and local development capabilities.

[0014] 3. Dynamic reference point mechanism: Breaking the limitation of fixed reference points, the distribution of reference points matches the actual shape of the Pareto front, filling the selection pressure in sparse regions of the solution and alleviating the selection pressure in dense regions of the solution, thereby improving the uniformity and diversity of the solution set distribution from the perspective of selection mechanism.

[0015] 4. Adaptive penalty function: The penalty intensity is dynamically adjusted according to the proportion of feasible solutions. In the early stage of evolution, the weak penalty preserves the good genes in the infeasible solutions and avoids the algorithm getting trapped in the local feasible region too early. In the later stage of evolution, the strong penalty guides the population to converge toward the feasible region, which takes into account both population diversity and feasibility and solves the dilemma of fixed penalty coefficient. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating the present invention; Figure 2 This is a schematic diagram illustrating the principle of the improved multi-objective evolutionary algorithm in this invention; Figure 3 This is a diagram showing the iterative results of the improved multi-objective evolutionary algorithm in this invention. Detailed Implementation

[0017] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0018] The present invention provides a method for planning the repair path of cladding on aero-engine blades, such as... Figure 1As shown, please follow these steps: Step 1: Construct a multi-objective optimization mathematical model for the cladding path planning of aero-engine blades; Step 2: Initialize the population by combining chaotic mapping with process experience; Step 3: Adaptive crossover mutation operation; Step 4: Dynamically adjust reference points and improve non-dominated sorting selection; Step 5: Adaptive penalty function constraint processing; Step 6: Iteration termination check; Step 7: Select the optimal compromise solution based on fuzzy hierarchical analysis.

[0019] Example 1 The method for planning the repair path of cladding on aero-engine blades, wherein step 1 is implemented in the following steps: Step 1.1: Define decision variables The path parameters and process parameters are jointly encoded, comprising a total of 8 core decision variables, expressed as follows: (1) Where x1 is the center-to-center spacing of adjacent melt channels, in mm, with a value range of [1.2, 1.8]; x2 is the layer thickness, in mm, with a value range of [0.1, 0.3]; x3 is the tool path angle, in °, with a value range of [0, 90]; x4 is the scanning strategy code, where 0 represents unidirectional scanning, 1 represents reciprocating scanning, and 2 represents alternating scanning in zones; x5 is the laser power, in W, with a value range of [800, 1600]; x6 is the scanning speed, in mm / s, with a value range of [3, 9]; x7 is the powder feed rate, in g / min, with a value range of [4, 12]; and x8 is the protective gas flow rate, in L / min, with a value range of [10, 20]. Step 1.2: Establishing the objective function Five conflicting minimization objective functions are established to comprehensively cover the requirements of cladding repair: Processing time objective function The goal is to minimize the total time of the entire cladding process. The total time includes the cladding processing time and the equipment idle time. The expression is: (2) In the formula, This represents the total length of the cladding path. For scanning speed, This is the time spent idling. Objective function for profile error With the goal of minimizing the profile error of the repaired blade, the expression is calculated based on the equal residual height model: (3) In the formula, Let be the residual height of the cladding layer at the i-th position. The target residual height; Objective function for warpage deformation With the objective of minimizing the maximum warping deformation of the blade after repair, a thermo-mechanical coupled finite element model is used for prediction, and the expression is as follows: (4) In the formula, Let be the warping deformation of the j-th node; Objective function of cladding layer defect rate With the goal of minimizing the defect rate of the cladding layer, the expression calculated based on the metallurgical quality prediction model is as follows: (5) In the formula, This represents the area of ​​the defective region. This represents the total area of ​​the cladding layer; Laser head loss objective function With the goal of minimizing laser head loss, the expression is calculated based on laser power and working time: (6) In the formula, For laser power, Total processing time. This is the laser head loss factor, with an empirical value of 0.001. Step 1.3, Define Constraints Based on aviation process specifications and equipment rated capacity, four types of constraints are set: Geometric accuracy constraints: The overlap rate of the cladding layer is controlled between 25% and 35% to ensure uniform and pore-free cladding layer formation. The expression is: (7) In the formula, w(X) is the weld width of a single cladding layer, which is obtained by coupling process parameters; Physical metallurgical constraints: The molten pool temperature is controlled between the material's melting point and 1.2 times the melting point, and the dilution rate is controlled between 5% and 15% to ensure the quality of metallurgical bonding. The expression is: (0.05≤α(X)≤0.15) (8) In the formula, The melting point of TC4 titanium alloy is taken as 1600℃-1700℃; α(X) represents the molten pool temperature; α(X) represents the dilution rate. Equipment capacity constraints: All decision variables are strictly controlled within the rated parameters of the processing equipment, expressed as follows: (9) No interference constraints: The minimum distance between the cladding head and the blade, tooling fixture, etc., shall not be less than the safety distance to avoid collision interference. The expression is: (10) In the formula, This is the minimum distance between the cladding head and the obstacle. For a safe distance, choose 3-5mm.

[0020] Example 2 Traditional methods for path planning in aero-engine blade cladding repair suffer from uneven population distribution due to random initialization strategies and a lack of utilization of historical process experience, resulting in slow convergence and susceptibility to local optima. To address this issue, a hybrid initialization strategy combining chaotic mapping and process experience is proposed, balancing high-quality population with diversity.

[0021] Step 2 is implemented in the following steps: Step 2.1: Generation of Empirical Solution for the Process From the historical process database of aero-engine blade cladding repair, 10 sets of optimal process-path parameter combinations that have been verified by engineering were selected as empirical solutions to ensure that the initial population contains high-quality feasible solutions. Step 2.2, Generation of Chaotic Mapping Solutions: The remaining individuals in the population are generated using a Logistic chaotic mapping. The randomness and ergodicity of the chaotic variables ensure population diversity. The Logistic mapping expression is as follows: (11) In the formula, the control parameters =4, the system is in a completely chaotic state; the chaotic variable (z_n∈(0,1)) is transformed into the range of values ​​of each decision variable through linear mapping: (12) Step 2.3, Population Merging and Screening The empirical solution and the chaotic solution are combined, and the top N individuals are selected as the initial population through non-dominated sorting, where N is the preset population size.

[0022] Example 3 The traditional NSGA-III algorithm for path planning in aero-engine blade cladding repair uses fixed crossover and mutation probabilities, which cannot be dynamically adjusted according to the evolutionary state of the population, leading to an imbalance between the algorithm's global exploration and local exploitation capabilities. To address this issue, an adaptive crossover and mutation operator is designed. This operator dynamically adjusts the crossover probability Pc and mutation probability Pm based on the population's convergence and the individual's fitness, thereby optimizing algorithm performance and balancing global exploration and local exploitation capabilities. Dynamically adjust the crossover probability: This is done by dynamically adjusting the fitness of the two individuals crossing over and the average fitness of the population. The expression is: (13) In the formula, , (f') represents the larger fitness value among the two crossover individuals; The average fitness of the population; The maximum fitness of the population; Minimum fitness of the population; Mutation probability: dynamically adjusted based on the fitness of the mutated individual and the average fitness of the population, expressed as: (14) In the formula, , f represents the fitness value of the mutated individual; By using dynamically adjusted crossover and mutation probabilities, simulated binary crossover and polynomial mutation operations are performed on the parent population to generate the offspring population.

[0023] Example 4 Traditional methods for path planning in aero-engine blade cladding repair employ a fixed reference point mechanism, which cannot dynamically adjust according to the actual distribution characteristics of the target space. This results in uneven distribution of Pareto optimal solutions and missing solutions in some areas. To address this issue, a dynamic reference point adjustment mechanism is proposed, combined with an improved non-dominated sorting strategy, to enhance the uniformity and quality of Pareto optimal solution distribution. Step 4 is implemented as follows: Step 4.1: Generation of the starting reference point Initial reference points are generated using a uniform design method. The number of reference points H is determined by the number of targets M and the number of segments p, and the calculation formula is as follows: (15) With target number M=5 and segmentation number p=4, the initial number of reference points is calculated to be 126. Step 4.2, Dynamic Adjustment of Reference Points After each generation of evolution is completed, the number of individuals associated with each reference point is counted; for reference points with 0 associated individuals, they are moved towards the nearest non-dominated solution to fill the missing solution region in the target space; for reference points with too many associated individuals, new reference points are generated nearby to avoid excessive concentration of solutions. Step 4.3: Improve non-dominated sorting We introduce a weighted sum of crowding distance and reference point distance as the basis for individual selection, and combine it with non-dominated ranking to screen the merged population of parents and offspring, retaining N individuals to form a new generation of parents.

[0024] Example 5 The method for planning the repair path of cladding on aero-engine blades, specifically step 5, is implemented according to the following steps: Step 5.1, Constraint Violation Calculation: Calculate the constraint violation degree for each individual in the population, quantifying the extent to which an individual violates the constraints. The expression is: (16) In the formula, For inequality constraints, Equality constraint; ( When CV(X) = 0, the individual is a feasible solution; when CV(X) > 0, the individual is an infeasible solution. The larger the value, the more severe the violation of the constraint. Step 5.2, Dynamic Penalty Coefficient: The penalty coefficient is dynamically adjusted based on the proportion of feasible solutions in the population. The expression is: (17) In the formula, the initial penalty coefficient =10; The number of feasible solutions in the population; This represents the total population size. Step 5.3: Fitness Correction for Infeasible Solutions For infeasible solutions, the modified fitness value is used in population selection, expressed as: (18).

[0025] The advantage of this mechanism lies in the early stage of evolution, when there are fewer feasible solutions in the population and the penalty coefficient is smaller. It retains some infeasible solutions to increase population diversity and prevent the algorithm from converging too early. In the later stage of evolution, the number of feasible solutions in the population increases and the penalty coefficient increases, guiding the population to converge toward the feasible region. This effectively solves the defects of traditional constraint handling methods and improves the stability and optimization effect of the algorithm.

[0026] Example 6 The method for path planning of cladding repair of aero-engine blades includes a step 6 in which a dual termination condition is set: the maximum number of iterations and the convergence threshold are set. When the number of iterations reaches the preset maximum value, or the change in the hypervolume index of the population is less than the convergence threshold for multiple consecutive generations, the iteration is terminated and the current Pareto optimal solution set is output; otherwise, the process returns to step 3 to continue evolution.

[0027] Example 7 Methods for planning repair paths for cladding on aero-engine blades, such as Figure 2-3 As shown, the multi-objective evolutionary algorithm ultimately yields a set of Pareto optimal solutions. The optimal compromise solution must be scientifically selected from these solutions based on the actual engineering requirements of aero-engine blade cladding repair. The fuzzy hierarchical analysis (FAHP) method is used to determine the weight coefficients of each objective, and a weighted summation method is combined to select the optimal compromise solution. Step 7 is specifically implemented according to the following steps: Step 7.1: Construct the fuzzy judgment matrix Based on the engineering requirements of cladding repair for aero-engine blades, the importance of five optimization objectives is compared pairwise to construct a fuzzy judgment matrix; Step 7.2, Weight Calculation The consistency of the fuzzy judgment matrix is ​​checked using the fuzzy hierarchical analysis method, and the weight vector of each objective is calculated. ; Step 7.3: Optimal Solution Selection The objective value of each Pareto optimal solution is normalized to eliminate the influence of dimensions. The weighted objective sum is then calculated, and the solution with the smallest weighted sum is selected as the optimal compromise solution. The corresponding cladding path parameters and process parameters are then output.

[0028] Example 8 This invention uses the compressor blade of a TC4 titanium alloy aero-engine as the verification object to conduct algorithm performance simulation comparison, and the results are as follows: Algorithm performance simulation comparison The hypervolume index (HV), spacing index (SP), and convergence algebra were selected as three common evaluation metrics. The I-NSGA-III algorithm of this invention was compared with the traditional NSGA-III algorithm. The results are shown in Table 1. Table 1

[0029] The experimental subject in the following examples is a TC4 titanium alloy compressor blade, and the damage mode is uniform wear at the blade tip with a wear depth of 0.5 mm.

[0030] Example 9 Decision variable values ​​(combinations of lower limits of parameter range): Center-to-center spacing between adjacent melt channels: 1.2mm Layer thickness: 0.1mm Tool path angle: 0° Scanning strategy: Unidirectional scanning Laser power: 800W Scanning speed: 3mm / s Powder delivery rate: 4g / min Protective gas flow rate: 10L / min Results: The total cladding process took 12.5 minutes, the maximum blade warping deformation was 0.022 mm, the profile error was 0.031 mm, and the cladding layer density was 99.92%. All indicators met the aviation repair quality standards.

[0031] Example 10 Decision variable values ​​(combinations of intermediate values ​​within the parameter range): Center-to-center spacing between adjacent melt channels: 1.5mm Layer thickness: 0.2mm Tool path angle: 45° Scanning strategy: Reciprocating scan Laser power: 1200W Scanning speed: 6mm / s Powder delivery rate: 8g / min Protective gas flow rate: 15L / min Results: The total cladding process took 8.3 minutes, the maximum blade warping deformation was 0.026 mm, the profile error was 0.033 mm, and the cladding layer density was 99.91%, balancing processing efficiency and repair quality.

[0032] Example 11 Decision variable values ​​(combinations of upper limits of parameter range): Center-to-center spacing between adjacent melt channels: 1.8mm Layer thickness: 0.3mm Tool path angle: 90° Scanning strategy: Alternating scan of partitions Laser power: 1600W Scanning speed: 9mm / s Powder delivery rate: 12g / min Protective gas flow rate: 20L / min Results: The total cladding process took 6.2 minutes, the maximum blade warping deformation was 0.034 mm, the profile error was 0.035 mm, and the cladding layer density was 99.91%. The process was highly efficient and met aerospace-grade requirements.

[0033] This invention presents a method for planning the cladding repair path of aero-engine blades. The optimized algorithm exhibits a more uniform and diverse distribution of non-dominated solutions within the target space, providing multi-dimensional and differentiated compromise decision-making schemes for blade laser cladding path planning. This effectively improves the quality of aero-engine blade cladding repair and provides core technical support for the intelligent and high-precision optimization of aero-engine blade cladding paths, possessing significant engineering application value.

Claims

1. A method for planning the repair path of cladding on aero-engine blades, characterized in that, The specific steps are as follows: Step 1: Construct a multi-objective optimization mathematical model for the cladding path planning of aero-engine blades; Step 2: Initialize the population by combining chaotic mapping with process experience; Step 3: Adaptive crossover mutation operation; Step 4: Dynamically adjust reference points and improve non-dominated sorting selection; Step 5: Adaptive penalty function constraint processing; Step 6: Iteration termination check; Step 7: Select the optimal compromise solution based on fuzzy hierarchical analysis.

2. The method for planning the repair path of aero-engine blade cladding according to claim 1, characterized in that, Step 1 is implemented in the following steps: Step 1.1: Define decision variables The path parameters and process parameters are jointly encoded, comprising a total of 8 core decision variables, expressed as follows: （1） Where x1 is the center-to-center spacing between adjacent melt channels, with a value range of [1.2, 1.8]; x2 is the layer thickness, with a value range of [0.1, 0.3]; x3 is the tool path angle, with a value range of [0, 90]; x4 is the scanning strategy code, where 0 represents unidirectional scanning, 1 represents reciprocating scanning, and 2 represents alternating scanning in zones; x5 is the laser power, with a value range of [800, 1600]; x6 is the scanning speed, with a value range of [3, 9]; x7 is the powder feed rate, with a value range of [4, 12]; and x8 is the protective gas flow rate, with a value range of [10, 20]. Step 1.2: Establishing the objective function Five conflicting minimization objective functions are established to comprehensively cover the requirements of cladding repair: Processing time objective function The goal is to minimize the total time of the entire cladding process. The total time includes the cladding processing time and the equipment idle time. The expression is: （2） In the formula, This represents the total length of the cladding path. For scanning speed, This is the time spent idling. Objective function for profile error With the goal of minimizing the profile error of the repaired blade, the expression is calculated based on the equal residual height model: （3） In the formula, Let be the residual height of the cladding layer at the i-th position. The target residual height; Objective function for warpage deformation With the objective of minimizing the maximum warping deformation of the blade after repair, a thermo-mechanical coupled finite element model is used for prediction, and the expression is as follows: （4） In the formula, Let be the warping deformation of the j-th node; Objective function of cladding layer defect rate With the goal of minimizing the defect rate of the cladding layer, the expression calculated based on the metallurgical quality prediction model is as follows: （5） In the formula, This represents the area of ​​the defective region. This represents the total area of ​​the cladding layer; Laser head loss objective function With the goal of minimizing laser head loss, the expression is calculated based on laser power and working time: （6） In the formula, For laser power, Total processing time. This refers to the laser head loss coefficient. Step 1.3, Define Constraints Based on aviation process specifications and equipment rated capacity, four types of constraints are set: Geometric accuracy constraints: The overlap rate of the cladding layer is controlled between 25% and 35% to ensure uniform and pore-free cladding layer formation. The expression is: （7） In the formula, w(X) is the weld width of a single cladding layer, which is obtained by coupling process parameters; Physical metallurgical constraints: The molten pool temperature is controlled between the material's melting point and 1.2 times the melting point, and the dilution rate is controlled between 5% and 15% to ensure the quality of metallurgical bonding. The expression is: (0.05≤α(X)≤0.15) （8） In the formula, The melting point of TC4 titanium alloy is taken as 1600℃-1700℃; α(X) represents the molten pool temperature; α(X) represents the dilution rate. Equipment capacity constraints: All decision variables are strictly controlled within the rated parameters of the processing equipment, expressed as follows: （9） No interference constraints: The minimum distance between the cladding head and the blade, tooling fixture, etc., shall not be less than the safety distance to avoid collision interference. The expression is: （10） In the formula, This is the minimum distance between the cladding head and the obstacle. For a safe distance, choose 3-5mm.

3. The method for planning the repair path of aero-engine blade cladding according to claim 1, characterized in that, Step 2 is implemented in the following steps: Step 2.1: Generation of Empirical Solution for the Process From the historical process database of aero-engine blade cladding repair, 10 sets of optimal process-path parameter combinations that have been verified by engineering were selected as empirical solutions to ensure that the initial population contains high-quality feasible solutions. Step 2.2, Generation of Chaotic Mapping Solutions: The remaining individuals in the population are generated using a Logistic chaotic mapping. The randomness and ergodicity of the chaotic variables ensure population diversity. The Logistic mapping expression is as follows: （11） In the formula, the control parameters =4, the system is in a completely chaotic state; the chaotic variable (z_n∈(0,1)) is transformed into the range of values ​​of each decision variable through linear mapping: （12） Step 2.3, Population Merging and Screening The empirical solution and the chaotic solution are combined, and the top N individuals are selected as the initial population through non-dominated sorting, where N is the preset population size.

4. The method for planning the repair path of aero-engine blade cladding according to claim 1, characterized in that, In step 3, an adaptive crossover and mutation operator is designed. Based on the convergence of the population and the fitness of the individual, the crossover probability Pc and the mutation probability Pm are dynamically adjusted to optimize the algorithm performance. Based on the evolutionary state of the population, the crossover probability Pc and the mutation probability Pm are dynamically adjusted to balance the global exploration and local development capabilities. Dynamically adjust the crossover probability: This is done by dynamically adjusting the fitness of the two individuals crossing over and the average fitness of the population. The expression is: （13） In the formula, , (f') represents the larger fitness value among the two crossover individuals; The average fitness of the population; The maximum fitness of the population; Minimum fitness of the population; Mutation probability: dynamically adjusted based on the fitness of the mutated individual and the average fitness of the population, expressed as: （14） In the formula, , f represents the fitness value of the mutated individual; By using dynamically adjusted crossover and mutation probabilities, simulated binary crossover and polynomial mutation operations are performed on the parent population to generate the offspring population.

5. The method for planning the repair path of aero-engine blade cladding according to claim 1, characterized in that, Step 4 is implemented in the following steps: Step 4.1: Generation of the starting reference point Initial reference points are generated using a uniform design method. The number of reference points H is determined by the number of targets M and the number of segments p, and the calculation formula is as follows: （15） With target number M=5 and segmentation number p=4, the initial number of reference points is calculated to be 126. Step 4.2, Dynamic Adjustment of Reference Points After each generation of evolution is completed, the number of individuals associated with each reference point is counted; for reference points with 0 associated individuals, they are moved towards the nearest non-dominated solution to fill the missing solution region in the target space; for reference points with too many associated individuals, new reference points are generated nearby to avoid excessive concentration of solutions. Step 4.3: Improve non-dominated sorting We introduce a weighted sum of crowding distance and reference point distance as the basis for individual selection, and combine it with non-dominated ranking to screen the merged population of parents and offspring, retaining N individuals to form a new generation of parents.

6. The method for planning the repair path of cladding on aero-engine blades according to claim 1, wherein step 5 is specifically implemented according to the following steps: Step 5.1, Constraint Violation Calculation: Calculate the constraint violation degree for each individual in the population, quantifying the extent to which an individual violates the constraints. The expression is: （16） In the formula, For inequality constraints, Equality constraint; ( When CV(X) = 0, the individual is a feasible solution; when CV(X) > 0, the individual is an infeasible solution. The larger the value, the more severe the violation of the constraint. Step 5.2, Dynamic Penalty Coefficient: The penalty coefficient is dynamically adjusted based on the proportion of feasible solutions in the population. The expression is: （17） In the formula, the initial penalty coefficient =10; The number of feasible solutions in the population; This represents the total population size. Step 5.3: Fitness Correction for Infeasible Solutions For infeasible solutions, the modified fitness value is used in population selection, expressed as: （18）。 7. The method for planning the repair path of cladding on aero-engine blades according to claim 1, characterized in that, In step 6, a dual termination condition is set: the maximum number of iterations and the convergence threshold. When the number of iterations reaches the preset maximum value, or the change in the hypervolume index of the population is less than the convergence threshold for several consecutive generations, the iteration is terminated and the current Pareto optimal solution set is output; otherwise, the process returns to step 3 to continue evolution.

8. The method for planning the repair path of aero-engine blade cladding according to claim 1, characterized in that, Step 7 is implemented in the following steps: Step 7.1: Construct the fuzzy judgment matrix Based on the engineering requirements of cladding repair for aero-engine blades, the importance of five optimization objectives is compared pairwise to construct a fuzzy judgment matrix; Step 7.2, Weight Calculation The consistency of the fuzzy judgment matrix is ​​checked using the fuzzy hierarchical analysis method, and the weight vector of each objective is calculated. ; Step 7.3: Optimal Solution Selection The objective value of each Pareto optimal solution is normalized to eliminate the influence of dimensions. The weighted objective sum is then calculated, and the solution with the smallest weighted sum is selected as the optimal compromise solution. The corresponding cladding path parameters and process parameters are then output.

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