Compressor blade milling-laser-shot peening strengthening-service life integrated design method
Through rate-dependent constitutive model and multi-island genetic-NLPQLP combination optimization algorithm, a process parameter-surface integrity feature neural network is constructed, which solves the problem of low efficiency of surface integrity feature simulation and parameter optimization after milling in the existing technology, and realizes the High-precision surface integrity calculation and process parameter optimization are used to improve the fatigue resistance of the blade.
Patent Information
- Application Number
- CN202411286103.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-09-13
- Publication Date
- 2024-12-27
AI Technical Summary
The prior art is difficult to accurately simulate the surface integrity characteristics and stress distribution of compressor blades after milling. In addition, traditional methods are inefficient and costly when optimizing parameters, and cannot effectively improve the fatigue resistance of the blades.
Using numerical simulation based on rate-dependent constitutive model combined with multi-island genetic-NLPQLP combination optimization algorithm, a neural network agent model is constructed to realize efficient calculation of surface integrity features and optimization of process parameters, and simulate milling processing and laser-shoot peening process to obtain the optimal process parameter combination.
Improve the accuracy of surface integrity feature simulation calculation, suitable for different materials, quantify the impact of process parameters on blade deformation and fatigue life, and obtain the optimal milling processing and laser-shoot peening strengthening process parameters combination within blade deformation error, improving The global search capability and solution accuracy of process parameters are obtained.
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Figure CN119203668A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of aerospace engines, and in particular relates to a compressor blade milling-laser-shot peening-life integrated design method. Background Art
[0002] Compressor blades, as important load-bearing components of aircraft engines and gas turbines, are listed as key parts of military engines. During their service, they are subjected to the combined effects of centrifugal and vibration loads for a long time, and fatigue fracture is their main failure mode. Many accidents at home and abroad are caused by fatigue cracks initiating from the blade surface. Therefore, characterizing the surface integrity of compressor blades after milling and, when necessary, introducing laser-shot peening to eliminate defects such as tool marks caused by milling are the main ways to improve the fatigue resistance of parts. In addition, compressor blades generally adopt a thin-walled structure, and the blade body surface is mostly a free surface. As the cold end component material, titanium alloy and other difficult-to-process materials are often used, which are very easy to deform during processing. Therefore, its deformation error also needs to be strictly controlled. Considering the high cost and long cycle of surface integrity characterization and fatigue testing, it is necessary to carry out milling, shot peening, laser strengthening and laser-shot peening composite strengthening process simulations, quantify the distribution law of surface integrity characteristics of key parts of the blade under different process conditions, and establish a fatigue life prediction model considering the influence of surface integrity characteristics. Based on this, an integrated design of milling and laser-shot peening processes with life as the goal can be carried out to obtain the optimal milling and laser-shot peening process parameters while meeting the blade deformation error requirements.
[0003] Chinese patent application CN201110359576.3, "Method for Simulating Three-Dimensional Surface Topography of Workpieces Based on Ball-End Milling," describes the kinematics of the cutting edge during machining, expressing the three-dimensional surface topography using discrete point cloud data. While this method accurately simulates the post-milling 3D surface topography, it fails to describe the residual stress field introduced by milling, which affects the initial stress distribution during subsequent composite strengthening processes.
[0004] Chinese patent application CN201910887404.X, "A Strengthening Method by Optimizing the Combination of Laser Strengthening and Shot Peening," combines laser strengthening and shot peening processes to strengthen titanium alloy test pieces, seeking the optimal parameter combination. However, this method is phenomenological, requiring numerous experiments, resulting in a long cycle and high costs.
[0005] Chinese patent application CN202010168795.2, "A Shot Peening Surface Integrity Prediction Method Based on BP Neural Network," uses a neural network trained on shot peening test data, with shot peening process parameters as input and residual stress and surface roughness as output, to establish a proxy model for residual stress and surface roughness in shot peening. However, the training model's accuracy is limited by the test data, making it less applicable to different materials.
[0006] The existing paper, "Research on Optimization of Laser Shot Peening Process for Ribbed Siding Strips Based on Genetic Algorithms," proposes a genetic algorithm-based method for optimizing process parameters for laser shot peening of ribbed siding strips, based on a finite element model of laser shot peened ribbed siding. As a global probabilistic search method, genetic algorithms do not rely on function gradients for optimization, but they suffer from low efficiency when performing detailed optimization. Summary of the Invention
[0007] In order to overcome the shortcomings of the existing methods, the present invention provides a compressor blade milling-laser-shot peening-life integrated design method, which provides a reference for the selection of aero-engine compressor blade milling and laser-shot peening process parameters.
[0008] In order to achieve the above object, the present invention adopts the following technical solutions: The present invention provides an integrated design method for compressor blade milling, laser-shot peening, and lifespan. This method simulates the milling and laser-shot peening processes to accurately calculate surface integrity characteristics and blade deformation. A neural network proxy model of process parameters and surface integrity characteristics is constructed to efficiently calculate surface integrity characteristics. Taking into account blade processing error constraints, the milling and laser-shot peening process parameters are optimized using a multi-island genetic-NLPQLP combined optimization algorithm to obtain the optimal process parameter combination. The specific implementation steps are as follows: Step (1): Based on the rate-dependent constitutive model of the compressor blade material, numerical simulation of the milling process and laser-shot peening process of the key parts of the compressor blade is carried out to achieve accurate quantification of the surface integrity characteristics and blade deformation after the milling process and laser-shot peening process; the key part is the position of the maximum stress point of the blade; the rate-dependent constitutive model is a high strain rate constitutive model, which is used to describe the high strain rate and large plastic deformation behavior of the material during the milling process and laser-shot peening process; the surface integrity characteristics include residual stress and surface roughness; Step (2): Build an automated process for milling and laser-shot peening simulation, sample in the feature space, and construct a process parameter-surface integrity feature database; further establish a process parameter-surface integrity feature neural network to achieve efficient calculation of surface integrity features; the feature space is determined according to the range of commonly used process parameters in engineering; the process parameters of the milling process include feed rate, milling speed, milling width, and back cutting amount; the process parameters of the laser-shot peening include laser strengthening process parameters and shot peening process parameters; the neural network wheel is obtained by training the process parameters and surface integrity features generated by the automated process; Step (3): Use the multi-island genetic-NLPQLP combined optimization algorithm to find the best in the feature space, optimize the milling and laser-shot peening process parameters, and obtain the optimal process parameters.
[0009] Furthermore, in step (1), the specific steps of the simulation are as follows: Step 1.1 Establish a rate-dependent constitutive model for the blade material, such as the Johnson-Cook high strain rate constitutive model, to simulate the relationship between stress and strain under high strain rates, and establish a damage model, such as the Johnson-Cook damage model, to simulate the chip separation process; Step 1.2: Establish a three-dimensional milling model of the blade. Integrate the rate-dependent constitutive model and damage model established in step 1.1 into the ABAQUS numerical simulation software to implement milling simulation. Extract surface integrity features through Python command stream. Step 1.3: Import the surface integrity features extracted in step 1.2 into the laser shot peening simulation model as the initial state and conduct the laser shot peening simulation. Furthermore, in step (2), the specific steps of the automation process are as follows: Step 2.1 The control program receives the updated geometric model file and the milling and laser-shot peening process parameter data to be simulated, writes the process parameter data into the interactive file, and prepares it for the subroutine to read. The control program starts the Python command script, runs the ABAQUS simulation software, and performs model segmentation, boundary condition definition, and meshing. Solve the initial residual stress field of the blade machined surface according to the milling parameters, call the program to modify the INP file, call the laser loading subroutine, set the shot peening parameters for simulation, read the process parameters from the interactive file, generate new loads and simulate. Use the Python command script to read the result file, extract the surface integrity parameters including residual stress and roughness according to the post-processing command, and output the results; In step 2.2, in the design space, sample the milling and laser-shot peening process parameters. Obtain the corresponding surface integrity features obtained in step 2.1. A deep neural network is trained using the milling and laser-shot peening process parameters as input and the surface integrity features as output to obtain a neural network proxy model for milling and laser-shot peening process parameters and surface integrity features. Furthermore, in step (3), the specific steps of the optimization process are as follows: Step 3.1 Use the multi-island genetic algorithm to roughly locate the optimal solution in the design space, and the optimal individual or optimal population is used as the roughly located optimal solution. , and the corresponding optimized value f( ).
[0010] Step 3.2: Use the optimized value of the multi-island genetic algorithm as the initial value of the NLPQLP numerical algorithm, and use the NLPQLP numerical algorithm (such as gradient-based optimization method or solver) to further optimize the optimal solution. , in order to improve the optimization accuracy of process parameters and meet the constraints to obtain the final optimization solution , and the corresponding optimized value f( ).
[0011] The beneficial effects of the present invention compared with the prior art are: (1) The present invention simulates the residual stress distribution and surface roughness of the milling laser-shot peening process, which is close to the actual process flow and improves the accuracy of the simulation calculation of surface integrity characteristics.
[0012] (2) The present invention establishes a mapping relationship between process parameters and surface integrity characteristics through a neural network, which is suitable for the efficient calculation of surface integrity characteristics of different materials.
[0013] (3) The present invention can quantify the effects of milling and laser-shot peening process parameters on blade deformation and fatigue life, and obtain the optimal combination of milling and laser-shot peening process parameters within the blade deformation error.
[0014] (4) Compared with the traditional genetic algorithm, the combined algorithm of I-GA and NLPQLP can provide better global search capability, higher solution accuracy and more effective constraint processing capability when dealing with numerous process parameters. BRIEF DESCRIPTION OF THE DRAWINGS
[0015] Figure 1 This is the finite element three-dimensional model diagram of the blade milling.
[0016] Figure 2 Schematic diagram of discrete element modeling of blade structure nozzle.
[0017] Figure 3 This is a schematic diagram for determining the laser enhancement range.
[0018] Figure 4 Flowchart for the calculation of milling process automation.
[0019] Figure 5 This is the flow chart for the automated calculation of laser shot peening. DETAILED DESCRIPTION
[0020] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only intended to illustrate the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
[0021] The following combination Figure 1-Figure 4 , further illustrate the technical solution of the present invention.
[0022] A compressor blade milling-laser-shot peening-life integrated design method of the present invention comprises the following steps: Step 1: Based on the constitutive model of blade materials under high strain rates, such as the Johnson-Cook model, numerical simulations of milling, shot peening, laser strengthening, and laser-shot peening combined strengthening of key parts of the blade are carried out to accurately quantify parameters such as residual stress and roughness after milling and laser-shot peening.
[0023] Taking the milling process and the numerical simulation of laser-shot peening composite strengthening as an example, the specific steps are as follows: Step 1.1 Establish a finite element simulation method for milling of key parts of the blade.
[0024] During the milling process, the material undergoes severe plastic deformation, and the strain rate reaches 10 5 s -1 Above, the constitutive model of blade material under high strain rate is established, such as Johnson-Cook model, and its applicable strain rate range is 10 3 ~10 7 s -1 , the expression is: (1) Where, is the flow stress, A, B, C are material constants, n is the work hardening coefficient, is the reference plastic strain rate, is the effective plastic strain rate, is the melting point, is room temperature (298K), m is the temperature term coefficient, m=1 at room temperature, is the equivalent plastic strain. T is the temperature.
[0025] The chip formation process is simulated using a damage failure model such as the Johnson-Cook model, which is expressed as: (2) Where, is the failure strain, is the equivalent plastic strain rate at the onset of material damage, d1, d2, d3, d4, and d5 are material failure parameters. p represents the hydrostatic pressure, q is the Mises stress, and p / q represents the stress triaxiality. is a piecewise function representing a dimensionless temperature parameter. exp() represents an exponential function, and ln() represents a logarithmic function.
[0026] The parameter ω is used as the fracture condition to evaluate the Johnson-Cook constitutive model. The expression of ω is: (3) Where, is the incremental value of the equivalent plastic strain in each step of the simulation. The evaluation condition is that when the sum is ω > 1, it indicates that the material has fractured and separated.
[0027] Simulate the structure near the blade interception danger point to improve the calculation efficiency, such as Figure 1 The milling tool is a carbide ball end mill, and the cutting parameters are consistent with the actual cutting parameters of the blade.
[0028] Step 1.2 uses the discrete element (DEM)-finite element (FEM) coupled shot peening method to carry out shot peening strengthening simulation on the blade joint area.
[0029] A particle generator is used for dynamic modeling. At the same time, considering the rotation of the workpiece during the actual shot peening process, a multi-nozzle layout is used in the simulation to evenly arrange multiple nozzles along the rotation axis. The projectiles are incident from all directions at the same time to ensure that all parts of the target material can be impacted. In the FEM module, according to the geometric characteristics of the blade, the reinforcement of the blade root is taken into account and the model is cut to reduce the amount of calculation; at the same time, the nozzle is modeled according to the nozzle size in the actual shot peening process conditions, and further assembled in combination with the relative position relationship between the nozzle and the target material. The target material is given a constitutive model and a multi-scale calculation program, and the network is divided and locally encrypted at the same time, and the boundary conditions of the simulation part are set according to the actual shot peening process test. In the DEM module, activate the ABAQUS keyword The ParticleGenerator is a particle generator. On this basis, the parameters of the particle generator are set, where the projectile velocity is converted based on the shot peening intensity proxy model. After completing the above settings, the contact properties between the projectile and the simulated surface are set, including normal and tangential contact properties. Finally, the two parts are coupled to generate an INP file, which is submitted to the ABAQUS / EXPLICIT module for solution. Figure 2 The numerical simulation model of shot peening strengthening of structural parts constructed in ABAQUS using dynamic modeling method is demonstrated, in which projectiles are continuously generated from the nozzle and impact the target material.
[0030] Step 1.3 performs laser strengthening simulation on the blade joint area.
[0031] Laser hardening simulations primarily consist of two phases: the first, the propagation and interaction of the laser-induced shock wave within the material; and the second, the stabilization and rebound of the residual stress field after the shock wave is unloaded. Because the blade geometry is complex and curved, unlike flat laser hardening, the surface normal varies with geometric position. The laser generates pressures of varying directions and magnitudes on the surface. Furthermore, the projection of the laser onto the surface is influenced by multiple factors, including the laser incident direction, surface shape, and impact point, and is no longer a regular geometric shape. To address several issues that distinguish curved surface laser hardening from flat surface hardening, a discretization approach is employed, decomposing the surface into a large number of small curved surfaces. Each small surface is extremely small relative to the overall size and can be approximated as a small plane. The collection of these small planes approximates the surface's full characteristics. A dynamic pressure applied perpendicular to each small plane simulates the pressure applied during curved surface laser hardening. In finite element calculations, the smallest unit of pressure loading is the loading surface mesh, and the loading locations are mesh integration points. Regarding the accuracy of approximate planes, if the plane size is larger than the grid, a certain calculation error will occur; if it is smaller than the grid, a large number of planes will not be included in the calculation, resulting in data redundancy and not obtaining more accurate calculation results. Therefore, by extracting the grid divided by the finite element model, a set of planes obtained by surface discretization is obtained, and the center point and normal of each small plane are calculated; Combined with the surface discretization method, in the actual calculation process, a large number of small planes that are much smaller than the laser size are pressure-loaded separately. It can be judged whether the plane is within the range of the laser beam. By traversing all the small planes, the judgment result is that the set of planes within the laser beam is the laser irradiation area. This method needs to define the laser beam in three-dimensional space, define the vector of the center line of the laser beam and a point on the laser beam, and obtain a straight line. The spatial geometric relationship is used to determine the distance from the center of the plane to the straight line. If it is less than the laser radius, the plane is within the impact range of the laser beam; otherwise, it is not within the laser strengthening range. Figure 3 shown.
[0032] Step 2: Build an automated process for milling and laser-shot peening simulation, sample in the feature space, and construct a process parameter-surface integrity feature database. Furthermore, establish a process parameter-surface integrity feature neural network to achieve efficient calculation of surface integrity features. The specific steps are as follows: Step 2.1 Based on the established numerical simulation method of milling and laser-shot peening, an automated calculation process of milling and laser-shot peening composite strengthening is constructed, such as Figure 5 As shown in the figure, the control program receives the updated geometric model file and the milling process and laser-shot peening composite strengthening process parameter data to be simulated, writes the process parameter data to the interactive file, and prepares it for the subroutine to read. The control program launches the Python command script, runs the ABAQUS simulation software, and performs pre-processing operations such as model segmentation, boundary condition definition, and meshing. The control program solves the initial residual stress field on the blade surface based on the milling parameters, calls the program to modify the INP file, calls the laser loading subroutine, sets the shot peening parameters for simulation, reads the process parameters from the interactive file, generates new loads, and performs simulation. The control program uses the Python command script to read the result file, extracts surface integrity parameters such as residual stress and roughness according to the post-processing command, and outputs the results.
[0033] Compared with single strengthening, the automated calculation process of laser-shot peening composite strengthening requires setting two dynamic analysis steps. The first dynamic analysis step simulates the laser process, and the second analysis step simulates the shot peening impact process. After the two-step dynamic analysis is completed, a static rebound analysis is performed.
[0034] Step 2.2 In the design space, Latin hypercube sampling is used to sample the milling and laser-shot peening composite strengthening process parameters.
[0035] After step 2.1, the corresponding surface integrity characteristics are obtained. The milling and laser-shot peening composite strengthening process parameters are used as input, and the surface integrity characteristics are used as output. The neural network proxy model is trained using a deep neural network. The main influencing factors of fatigue life after strengthening include residual stress and roughness. The target variable of the proxy model is surface residual stress. , residual stress influence layer depth h and surface stress concentration factor K t .
[0036] Step 3: Compressor blades generally have thin-walled structures. Due to the blade deformation error limit, the multi-island genetic-NLPQLP combined optimization algorithm is used to optimize the milling and laser-shot peening process parameters to obtain the optimal process parameter combination. The specific steps are as follows: Step 3.1 Under given process parameters, the surface residual stress can be predicted using the process parameter-surface integrity parameter proxy model. , residual stress influence layer depth h and surface stress concentration factor K t , substitute the calculated life under the corresponding process parameters, and conduct optimization research under the drive of the multi-island genetic algorithm-NLPQLP combined optimization algorithm. When the multi-island genetic algorithm is combined with the NLPQLP problem, the usual practice is to define a comprehensive fitness function , considering the objective function value and the satisfaction of the constraints, for example: (4) In the formula, α and β are weight coefficients used to balance the importance of constraint functions and constraints. f(x) is the objective function and provides the core evaluation index. g(x) is the constraint condition, which ensures that the generated solution is feasible under the problem constraints. M is the total number of constraints. i is the index value. The multi-island genetic algorithm initializes the population and distributes it in multiple islands; each island independently performs individual selection, crossover and mutation operations to optimize the objective function f(x), and considers the constraint condition as the blade deformation error; individuals are regularly migrated between islands to increase the diversity of the population and the global search capability; the algorithm is stopped when the predetermined number of iterations is reached or the convergence condition is met, and the optimal individual or optimal population is output as the optimal solution for rough positioning. , and the corresponding optimized value f( ). The specific formulas in multi-island genetics can vary depending on the form of the specific problem and the choice of solution strategy.
[0037] Step 3.2 The optimal solution obtained by the multi-island genetic algorithm As the initial value of the NLPQL algorithm; use the NLPQL algorithm to optimize, the goal is to further optimize the optimal solution , in order to more accurately meet complex nonlinear constraints and objective functions; NLPQL algorithms usually use gradient-based optimization methods or solvers to improve the accuracy and stability of the optimization solution; the algorithm is stopped when the convergence condition of the numerical algorithm is reached or the maximum number of iterations is reached to obtain the final optimization solution , and the corresponding optimized value f( ).
[0038] The above embodiments are provided for the purpose of describing the present invention only and are not intended to limit the scope of the present invention. The scope of the present invention is defined by the appended claims. Various equivalent substitutions and modifications made without departing from the principles of the present invention are intended to be within the scope of the present invention.
Claims
1. A compressor blade milling-laser-shot peening-life integrated design method, characterized in that: The steps include: Step (1): Based on the rate-dependent constitutive model of the compressor blade material, numerical simulation of the milling process and laser-shot peening process of the key parts of the compressor blade is carried out to achieve accurate quantification of the surface integrity characteristics and blade deformation after the milling process and laser-shot peening process; the key part is the position of the maximum stress point of the blade; the rate-dependent constitutive model is a high strain rate constitutive model, which is used to describe the high strain rate and large plastic deformation behavior of the material during the milling process and laser-shot peening process; the surface integrity characteristics include residual stress and surface roughness; Step (2): Establish an automated process for milling and laser-shot peening simulation, sample in the feature space, and construct a process parameter-surface integrity feature database; Further establish a process parameter-surface integrity feature neural network to achieve efficient calculation of surface integrity features; The feature space is determined according to the range of commonly used process parameters in engineering; the process parameters of the milling process include feed rate, milling speed, milling width, and back cutting amount; the process parameters of the laser-shot peening include laser strengthening process parameters and shot peening process parameters; the neural network wheel is obtained by training the process parameters and surface integrity features generated by the automated process; Step (3): Use the multi-island genetic-NLPQLP combined optimization algorithm to find the best in the feature space, optimize the milling and laser-shot peening process parameters, and obtain the optimal process parameters.
2. The compressor blade milling-laser-shot peening-life integrated design method according to claim 1, characterized in that: In step (1), the method for accurately quantifying the surface integrity characteristics and blade deformation is: for the residual stress, select the surface residual stress , the residual stress influence layer depth h is used as the quantitative parameter; for roughness, the stress concentration factor K is selected t As a quantitative parameter; For blade deformation, the tip deformation range is selected as the quantitative parameter.
3. The compressor blade milling-laser-shot peening-life integrated design method according to claim 1, characterized in that: The high strain rate constitutive model is the Johnson-Cook high strain rate constitutive model.
4. The compressor blade milling-laser-shot peening-life integrated design method according to claim 1, characterized in that: The laser strengthening process parameters include spot diameter, laser energy, overlap rate, and pulse width; the shot peening strengthening process parameters include shot peening intensity and coverage rate.
5. The compressor blade milling-laser-shot peening-life integrated design method according to claim 1, characterized in that: In step (1), the specific steps of the simulation are as follows: Step 1.1 Establish the material rate-dependent constitutive model of the blade, simulate the relationship between stress and strain under high strain rate, and establish a damage model to simulate the process of chip separation; Step 1.2: Establish a three-dimensional model of blade milling, integrate the rate-dependent constitutive model and damage model established in step 1.1 into ABAQUS numerical simulation software to realize milling simulation, and extract surface integrity features through Python command stream; Step 1.3 imports the surface integrity features extracted in step 1.2 into the laser-shot peening simulation model as the initial state, and carries out the laser-shot peening simulation.
6. The compressor blade milling-laser-shot peening-life integrated design method according to claim 1, characterized in that: In step (2), the specific steps of the automation process are as follows: Step 2.1 The control program receives the updated geometric model file and the milling process and laser-shot peening process parameter data to be simulated, writes the process parameter data into the interactive file, and prepares to be read by the subroutine; the control program starts the Python command script, runs the ABAQUS simulation software, performs model segmentation, boundary condition definition, and meshing; solves the initial residual stress field of the blade machining surface according to the milling parameters, calls the program to modify the INP file, calls the laser loading subroutine, sets the shot peening parameters for simulation, reads the process parameters from the interactive file, generates new loads and performs simulation; uses the Python command script to read the result file, extracts the surface integrity parameters including residual stress and roughness according to the post-processing command, and outputs the results; In step 2.2, in the design space, the milling and laser-shot peening process parameters are sampled, and the corresponding surface integrity characteristics are obtained through step 2.
1. The milling and laser-shot peening process parameters are used as input, and the surface integrity characteristics are used as output. The deep neural network is used for training to obtain the milling and laser-shot peening process parameter-surface integrity characteristics neural network proxy model.
7. The compressor blade milling-laser-shot peening-life integrated design method according to claim 1, characterized in that: In step (3), the specific steps of the multi-island genetic-NLPQLP combined optimization algorithm are as follows: Step 3.1 Use the multi-island genetic algorithm to roughly locate the optimal solution in the design space, and the optimal individual or optimal population is used as the roughly located optimal solution. , and the corresponding optimized value f( ); Step 3.2: Use the optimization value of the multi-island genetic algorithm as the initial value of the NLPQLP numerical algorithm, and use the NLPQLP numerical algorithm to further optimize the optimal solution. , in order to improve the optimization accuracy of process parameters and meet the constraints, and obtain the final optimization solution , and the corresponding optimized value f( ).
