FDM process energy efficiency modeling and multi-objective optimization method based on BP neural network and NSGA-II

Abstract

The invention provides an FDM process energy efficiency modeling and multi-objective optimization method based on a BP neural network and NSGA-II, and relates to the technical field of fused deposition modeling energy efficiency prediction.The FDM process energy efficiency modeling and multi-objective optimization method comprises the steps that an actual measurement processing power curve graph is combined, energy consumption characteristics of the FDM processing process are analyzed, and an energy efficiency function and a printing efficiency function are constructed; designing a five-factor three-level test by using a Box-Behnken method, and researching key factors influencing energy consumption through variance analysis; energy consumption prediction models are respectively established through a back propagation neural network, support vector regression and response surface regression fitting, and an optimal prediction model is determined through analysis and comparison; and on the basis of the optimal prediction model, combining with the actual processing working condition, and comprehensively considering the specific energy consumption, the material deposition rate and the surface roughness, constructing a multi-objective optimization model, and solving the model by adopting an NSGA-II algorithm. According to the method, the energy consumption influence mechanism of the FDM process is researched, relatively accurate energy consumption prediction is realized, and meanwhile, theoretical support and an optimization strategy are provided for parameter optimization of the FDM process.

Description

Technical Field

[0001] This invention relates to the field of fused deposition modeling energy efficiency prediction technology, and in particular to an energy efficiency modeling and multi-objective optimization method for FDM process based on BP neural network and NSGA-II. Background Technology

[0002] Additive manufacturing (AM) is a production method that uses computer-aided design (CAD) models to build solid parts by layering materials. It has shown strong application potential in many high-end manufacturing fields such as aerospace, medical devices, and automotive manufacturing. Among them, fused deposition modeling (FDM), as an important branch of additive manufacturing technology, has gradually become a hot research and application area due to its advantages such as ease of operation, low cost, and strong material adaptability. Compared with traditional subtractive manufacturing processes, FDM can save 30%~50% in processing time and 20%~35% in manufacturing cost, significantly improving production efficiency. However, behind its green manufacturing advantages, the energy efficiency problem of the FDM process is becoming increasingly prominent, becoming a major factor restricting its large-scale promotion. FDM technology typically involves heating and melting thermoplastic materials, nozzle movement, and the operation of a precision control system. These processes consume a lot of energy, especially when the printing time is long or the workpiece volume is large, the energy load rises rapidly, further exacerbating the overall energy efficiency problem.

[0003] Therefore, studying the energy efficiency mechanism in the FDM molding process, analyzing the key factors affecting energy efficiency, establishing an energy efficiency prediction model, and further optimizing the combination of process parameters are of great theoretical and engineering value for reducing energy consumption, improving energy utilization efficiency, extending equipment life, and thus promoting the further sustainable development of additive manufacturing technology.

[0004] However, it should be noted that existing research rarely includes material deposition rate in its predicted targets, and comparisons of the predictive performance between traditional multinomial regression models and machine learning algorithms are also relatively rare. Existing optimization models are mostly based on traditional multinomial models, with fewer employing advanced modeling methods such as neural networks. Furthermore, optimization targets that comprehensively consider specific energy consumption, roughness, and material deposition rate are also uncommon. Summary of the Invention

[0005] To address the problems existing in current technologies, this invention provides an energy efficiency modeling and multi-objective optimization method for FDM processes based on BP neural networks and NSGA-II. First, the energy consumption characteristics of the FDM process are analyzed using measured processing power curves, and energy efficiency and printing efficiency functions are constructed. Second, a five-factor, three-level experiment is designed using the Box-Behnken method in response surface methodology, and key factors affecting energy consumption are studied through variance analysis. Third, energy consumption prediction models are established using backpropagation neural networks (BPNN), support vector regression (SVR), and response surface regression fitting (RSM), and the optimal prediction model is determined through analysis and comparison. Finally, based on the optimal prediction model and considering actual processing conditions, a multi-objective optimization model is constructed, taking into account specific energy consumption, material deposition rate, and surface roughness. The model is then solved using an elite strategy non-dominated genetic algorithm (NSGA-II). This research method studies the energy consumption impact mechanism of the FDM process and achieves relatively accurate energy consumption prediction, while providing theoretical support and optimization strategies for FDM process parameter optimization.

[0006] A method for energy efficiency modeling and multi-objective optimization of FDM process based on BP neural network and NSGA-II includes: S1. Energy efficiency characteristics analysis of FDM process: The energy efficiency characteristics of standby, preheating, printing and reset stages are determined by analyzing the measured power curves of the FDM process.

[0007] Construct energy efficiency functions and printing efficiency functions for FDM process to calculate mass-to-energy consumption and material deposition rate.

[0008] S2. Analysis of factors affecting the energy efficiency of FDM process; selection of FDM 3D printer, printing consumables, nozzle, power analyzer, computer with experimental data analysis software, electronic scale and printed model to construct experimental system.

[0009] A five-factor, three-level experiment was designed using the Box-Behnken method. The five selected process parameters were layer thickness, printing speed, printing temperature, heated bed temperature, and idle speed. Mass-to-energy consumption and material deposition rate were used as the experimental responses.

[0010] A five-factor, three-level experiment was conducted using the constructed experimental system to obtain the experimental responses corresponding to five process parameters and to analyze the degree of influence of process parameters on mass specific energy consumption and material deposition rate.

[0011] S3. Energy efficiency modeling of FDM process based on BP neural network: Based on experimental data, prediction models of mass ratio energy consumption and material deposition rate are established by backpropagation neural network (BPNN) and support vector regression (SVR), respectively. The optimal FDM process energy efficiency prediction model is determined by analyzing and comparing the evaluation indicators of the FDM process energy efficiency prediction models established by backpropagation neural network (BPNN), support vector regression (SVR), and response surface regression (RSM).

[0012] S4, FDM energy efficiency optimization model and solution: Based on the energy efficiency characteristics of each stage of FDM process and the degree of influence of process parameters on mass ratio energy consumption and material deposition rate, the layer thickness, printing speed, printing temperature, hot bed temperature and idle speed are retained as optimization variables, and the constraint range of the optimization variables is set.

[0013] A surface roughness prediction model was constructed based on experimental data.

[0014] An FDM energy efficiency optimization model is constructed with the objectives of minimizing mass-to-specific energy consumption, maximizing material deposition rate, and minimizing surface roughness, as detailed below: ; Where LT is the layer thickness, PS is the printing speed, NT is the printing temperature, BT is the heated bed temperature, TS is the idle speed, SEC is the mass-to-energy ratio, Ra is the surface roughness, and MDR is the material deposition rate.

[0015] The Pareto optimal solution set was obtained by solving the established FDM energy efficiency optimization model using the NSGA-II algorithm, and the global optimal solution was selected by the TOPSIS method.

[0016] Optionally, the expressions for the energy efficiency function and the printing efficiency function are as follows: ; .

[0017] Where SEC is the mass-to-energy ratio, w is the total energy consumption of the printing process, m is the mass of the printed workpiece, MDR is the material deposition rate, m is the mass of the printed workpiece, and t is the total time of the printing process.

[0018] Optionally, the FDM 3D printer is a Giant Shadow T10000 FDM 3D printer, the printing consumable is polylactic acid with a diameter of 1.75mm, the nozzle diameter is 0.4mm, the power analyzer is a YOKOGAWA WT333E power analyzer, the computer is equipped with WTViewerFreePlus software, the electronic scale has a measurement accuracy of 0.01g, and the printed model is a hollow cube structure with an outer dimension of 20mm*20mm*20mm and an inner dimension of 17.6mm*17.6mm*17.6mm.

[0019] Optionally, the analysis of the influence of process parameters on mass-to-energy consumption and material deposition rate includes: using Design-Expert 13 software to perform response surface regression (RSM) fitting on the five process parameters and their corresponding experimental responses to construct a predictive model for mass-to-energy consumption and material deposition rate, and performing variance analysis to evaluate the significance of the main effects and interaction effects of each process parameter.

[0020] Based on the significance of the main and interaction effects of each process parameter, the order of influence on mass specific energy consumption from largest to smallest is: heated bed temperature, layer thickness, printing speed, idle speed, and printing temperature. Similarly, the order of influence on material deposition rate from largest to smallest is: layer thickness, printing speed, heated bed temperature, idle speed, and printing temperature.

[0021] Optionally, based on experimental data, prediction models for mass-to-energy consumption and material deposition rate are established using Backpropagation Neural Network (BPNN) and Support Vector Regression (SVR), respectively. The optimal FDM process energy efficiency prediction model is determined by analyzing and comparing the evaluation indicators of the FDM process energy efficiency prediction models established using BPNN, SVR, and Response Surface Regression (RSM). This includes: Based on the PyCharm 2024.1 integrated development environment, a BP neural network model was built using the Keras API of the TensorFlow 2.12.0 deep learning framework. The BP neural network model adopts the Sequential sequence model. The input layer variables of the BP neural network model include layer thickness, printing speed, heated bed temperature, idle speed, and printing temperature. The output layer variables of the BP neural network model include mass-to-energy consumption and material deposition rate. The BP neural network model consists of three hidden layers with 128, 64, and 32 neurons in each layer, respectively, all using the ReLU activation function. The dataset is divided into training, validation, and test sets at a ratio of 64%, 16%, and 20%, respectively. The parameter settings of the BP neural network model are shown in Table 5.

[0022] Table 5 BP Neural Network Model Parameter Settings

[0023] A prediction model for mass-to-energy consumption and material deposition rate was established using support vector regression (SVR). The parameter settings for SVR are shown in Table 6.

[0024] Table 6 Support Vector Regression (SVR) Parameter Settings

[0025] Select the percentage error (PE), mean absolute error (MAE), mean square error (MSE), and coefficient of determination (R). 2 As an evaluation index, the FDM process energy efficiency prediction models established by backpropagation neural network (BPNN), support vector regression (SVR), and response surface regression (RSM) were evaluated, and the FDM process energy efficiency prediction model established by BPNN was determined to be the optimal FDM process energy efficiency prediction model.

[0026] Optionally, the step of constructing a surface roughness prediction model based on experimental data includes: Using the Box-Behnken experimental design method, with layer thickness LT, printing speed PS, printing temperature NT, and heated bed temperature BT as key process parameters, a second-order polynomial prediction model for surface roughness was established by fitting the four key process parameters and their corresponding surface roughness using Response Surface Methodology (RSM) with Design-Expert 13 software. The specific expression is as follows: Ra=102.21212+170.45832LT+0286418PS-0.998533NT-0.280567BT-0.243842LT*PS-0.114613LT*NT+0.447006 LT*BT-0.000218PS*NT+0.000378PS*BT+0000330NT*BT-362.27834LT-0.002454PS+0.002426NT-+0.001286BT.

[0027] Optionally, the step of using the TOPSIS (Top-Side Solution Distance) method to select the globally optimal solution includes: The TOPSIS (Top-Side Distance Method) is used to comprehensively rank the Pareto solution set. Production efficiency is selected as a positive indicator, while cutting ratio energy consumption and drum wear depth are selected as negative indicators. After finding the optimal and worst matrix vectors, the distance between the Pareto non-dominated solution and the positive or negative ideal solution is calculated to obtain the comprehensive score. The process parameter combination with the highest comprehensive score is determined as the global optimal solution.

[0028] Compared with the prior art, the present invention has the following beneficial effects: (1) By combining Box-Behnken experimental design with variance analysis, the influence of process parameters such as layer thickness, printing speed, printing temperature, hot bed temperature and idle speed on energy consumption and material deposition rate was systematically revealed. The order of importance of key influencing factors was clarified, avoiding the high cost of traditional full factorial experiments. This provides a basis for key parameter control for subsequent energy efficiency modeling and optimization of FDM process.

[0029] (2) In view of the nonlinear characteristics of specific energy consumption and material deposition rate, a prediction model based on BP neural network was constructed. By comparing and verifying with support vector regression (SVR) and response surface methodology (RSM) models, it was proved that BP neural network can accurately capture the complex mapping relationship between process parameters and energy consumption target, and achieve relatively accurate energy consumption prediction, providing a reliable foundation for subsequent multi-objective optimization.

[0030] (3) Based on the BP neural network prediction model, a multi-objective optimization model is established by comprehensively considering the objectives of minimizing specific energy consumption, maximizing material deposition rate and minimizing surface roughness. The Pareto optimal solution set is solved by the non-dominated sorting genetic algorithm (NSGA-II) with elite strategy, and the global optimal solution is screened by TOPSIS comprehensive evaluation. This achieves the coordinated optimization of energy consumption, efficiency and surface quality, and provides theoretical support and optimization strategy for FDM process parameter optimization. Attached Figure Description

[0031] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0032] Figure 1 This is a flowchart illustrating an FDM process energy efficiency modeling and multi-objective optimization method based on BP neural network and NSGA-II, provided in an embodiment of this disclosure.

[0033] Figure 2 This is the measured power curve of an FDM 3D printer.

[0034] Figure 3 This is a physical diagram of the experimental system.

[0035] Figure 4The following charts compare the evaluation indices for energy consumption prediction and material deposition rate prediction of the three models BPNN, SVR and RSM: (a) compares the evaluation indices for energy consumption prediction of the three models BPNN, SVR and RSM, and (b) compares the evaluation indices for material deposition rate prediction of the three models BPNN, SVR and RSM.

[0036] Figure 5 This is a comparison chart between the optimized solution and the empirical solution obtained after optimization.

[0037] Figure 6 This is the Pareto optimal frontier plot. Detailed Implementation

[0038] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0039] like Figure 1 As shown, this disclosure provides a method for FDM process energy efficiency modeling and multi-objective optimization based on BP neural network and NSGA-II, including: S1, FDM process energy efficiency characteristics analysis.

[0040] 1. Energy efficiency characteristics analysis of FDM process.

[0041] The energy consumption of an FDM 3D printer is mainly concentrated in the standby, preheating, printing, and reset phases, exhibiting significant phased characteristics that reflect the power requirements and energy consumption characteristics under different operating states. The measured power curve is shown below. Figure 2 As shown, during the standby phase, the printer performs software initialization and path calculation. The main components are in standby or ready state, with low and stable power consumption, a smooth curve, and the lowest energy consumption percentage. The preheating phase mainly includes the heating process of the printhead and heated bed. The power rises rapidly, and the heating power of the heated bed fluctuates periodically, resulting in a significant increase in energy consumption. This is the main energy-consuming phase of the heating system. During the printing phase, energy consumption mainly comes from the continuous heating of the printhead and heated bed, the periodic movement of the drive motor, the operation of the cooling fan and lighting, and is significantly affected by process parameters. The reset phase is the process of the device returning to its original position after printing. It mainly involves mechanical movement, with low overall power consumption, short duration, and a small energy consumption percentage.

[0042] 2. Mass-to-energy consumption and material deposition rate.

[0043] Numerous indicators are used to evaluate the energy efficiency of manufacturing processes, among which specific energy consumption and energy utilization rate are commonly used. Specific energy consumption is further divided into mass specific energy consumption and volume specific energy consumption, which measure energy consumption from the perspectives of unit mass and unit volume, respectively. For the energy consumption of FDM equipment, mass specific energy consumption is used as an evaluation indicator to characterize the printing energy efficiency of FDM equipment. The lower the mass specific energy consumption, the lower the energy consumed by the FDM equipment in printing a unit mass of consumables, indicating higher energy efficiency. An energy efficiency function is constructed to calculate mass specific energy consumption, as detailed below: ; Where SEC is the energy consumption per unit mass, w is the total energy consumption of the printing process, and m is the mass of the printed workpiece.

[0044] Material deposition rate was selected as a key indicator for measuring printer printing efficiency. This indicator represents the amount of material successfully deposited onto the build platform per unit time, reflecting the printer's material output capability and is an important parameter for evaluating printing efficiency. Unlike the theoretical extrusion rate, material deposition rate more accurately reflects the material utilization efficiency in the actual printing process. A printing efficiency function was constructed to calculate the material deposition rate, as follows: ; Where MDR is the material deposition rate, m is the mass of the printed workpiece, and t is the total time of the printing process.

[0045] Analysis of factors affecting the energy efficiency of S2 and FDM processes.

[0046] 1. Test system.

[0047] like Figure 3 As shown, the FDM 3D printer used was a Giant Shadow T10000 model. The printing filament was polylactic acid (PLA) with a diameter of 1.75mm and a nozzle diameter of 0.4mm. A YOKOGAWA WT333E power analyzer was used to measure the total processing energy consumption and total processing time. The computer was equipped with WTViewerFreePlus software to process and analyze the input power and real-time data, generating a power curve in real time. An electronic scale with a measurement accuracy of 0.01g was used to measure the weight of the printed model. The printed model was a hollow cube structure with external dimensions of 20mm*20mm*20mm and internal dimensions of 17.6mm*17.6mm*17.6mm. SolidWorks software was used for modeling, and the model was then exported as an STL file and imported into Cura slicing software for path generation and print settings. Finally, it was imported into the FDM 3D printer for printing. The specific dimensions and three views of the workpiece are shown below. Figure 3 As shown in the bottom right corner (unit: mm).

[0048] 2. Experimental design.

[0049] During the FDM 3D printing process, the following process parameters can be set: layer thickness, printing speed, nozzle temperature, heated bed temperature, idle speed, infill density, and infill pattern. This embodiment selects layer thickness, printing speed, printing temperature, heated bed temperature, and idle speed as the process parameters, while other parameters are left at their default values. Considering the number of experiments, efficiency, and cost, the Box-Behnken experimental design method is chosen, with mass-to-energy consumption and material deposition rate as the experimental responses. The experiment is designed using the Design-Expert 13 software based on the five-factor, three-level Box-Behnken method, comprehensively considering machine performance, safety thresholds, and the optimal operating range of polylactic acid. The process parameters and factor level settings are shown in Table 1.

[0050] Table 1. Process parameters and factor level settings

[0051] 3. Experimental results and analysis of variance.

[0052] To clarify the influence of process parameters on mass-to-energy consumption and material deposition rate, and to obtain the dataset required for subsequent modeling, a five-factor, three-level experiment was conducted using the constructed experimental system, resulting in 46 sets of data. The experimental response results are shown in Table 2.

[0053] Table 2 Experimental Design and Results of the Box-Behnken Method

[0054]

[0055] Using Design-Expert 13 software, response surface regression (RSM) was employed to perform quadratic polynomial fitting on five process parameters and their corresponding experimental responses to construct a predictive model for mass-to-energy consumption and material deposition rate. Analysis of variance was then conducted to evaluate the significance of the main effects and interaction effects of each process parameter. The analysis of variance and significance test results for the mass-to-energy consumption prediction model are shown in Table 3, and those for the material deposition rate prediction model are shown in Table 4.

[0056] Table 3. Analysis of variance and significance test of the mass-to-energy ratio prediction model

[0057] Table 4. Analysis of variance and significance test of the material deposition rate prediction model.

[0058] Tables 3 and 4 show that layer thickness (A) and heated bed temperature (D) are the main factors affecting specific energy consumption, with significance levels (P-values) all less than 0.0001. Regarding material deposition rate, layer thickness (A), printing speed (B), and heated bed temperature (D) have significant effects (P-values ​​less than 0.0001), while the idle speed (E) shows some significance in affecting the material deposition rate (P-value less than 0.1). Printing temperature (C) has no significant main effect in either response model, belonging to a minor influencing factor (P-value greater than 0.1). Furthermore, the analysis of variance also shows that some quadratic terms and interaction terms have significant effects on the response, among which A... 2 These are important factors affecting specific energy consumption, AB, AD, and A. 2 With B 2 These are important factors affecting the material deposition rate, reflecting a certain degree of nonlinear coupling and complex interaction among FDM process parameters. The degree of influence of each process parameter on the response is ranked as follows: The order of the impact of energy consumption from greatest to least is: heated bed temperature (D), layer thickness (A), printing speed (B), idle speed (E), and printing temperature (C).

[0059] The order of influence on material deposition rate from largest to smallest is: layer thickness (A), printing speed (B), heated bed temperature (D), idle speed (E), and printing temperature (C).

[0060] S3. Energy efficiency modeling of FDM process based on BP neural network.

[0061] 1. Backpropagation (BP) neural network and support vector regression (SVR).

[0062] Based on the PyCharm 2024.1 integrated development environment, a BP neural network model was built using the Keras API of the TensorFlow 2.12.0 deep learning framework. The BP neural network model employs a Sequential sequence model. Input layer variables include layer thickness, printing speed, heated bed temperature, idle speed, and printing temperature. Output layer variables include mass-to-energy ratio and material deposition rate. The BP neural network model consists of three hidden layers with 128, 64, and 32 neurons respectively, all using the ReLU activation function. Dropout and L2 regularization are introduced to suppress overfitting. To improve model stability and generalization ability, Z-score normalization is used to normalize the input data. The model integrates an EarlyStopping early termination mechanism and a custom R... 2The evaluation metric callback function uses the Adam optimizer for parameter updates. The dataset is divided into training, validation, and test sets in proportions of 64%, 16%, and 20%. The parameter settings of the BP neural network model are shown in Table 5.

[0063] Table 5 BP Neural Network Model Parameter Settings

[0064] A prediction model for mass-to-energy consumption and material deposition rate was established using support vector regression (SVR). The parameter settings for SVR are shown in Table 6.

[0065] Table 6 Support Vector Regression (SVR) Parameter Settings

[0066] 2. Model comparison and analysis.

[0067] To demonstrate the accuracy of the BP neural network prediction model, the percentage error (PE), mean absolute error (MAE), mean squared error (MSE), and coefficient of determination (R²) were selected. 2 As evaluation indicators, a comparative analysis was conducted on the FDM process energy efficiency prediction models established by backpropagation neural network (BPNN), support vector regression (SVR), and response surface regression (RSM). The evaluation indicators of each model are summarized as follows: Figure 4 As shown.

[0068] Overall, the coefficients of determination (R²) of the response surface model (RSM) and the two machine learning models (BPNN and SVR) on the two prediction targets (SEC: specific energy consumption, MDR: material deposition rate) all exceeded 0.95, indicating that all three models have strong fitting ability in regression prediction tasks.

[0069] In SEC prediction, BPNN exhibits a significant advantage, with its mean squared error (MSE) of 88.56 being 25.5% of RSM and 10.5% of SVR, respectively. Its mean absolute error (MAE) is approximately 73% lower than SVR, and its coefficient of determination (R²) reaches 0.9837, higher than both RSM (0.9683) and SVR (0.9369). Furthermore, BPNN's percentage error (PE) is controlled at 1.62%, demonstrating good predictive stability. This indicates that BPNN has a stronger modeling ability in handling the complex nonlinear relationships implicit in SEC objectives, and its distributed weight adjustment mechanism effectively captures the deep mapping relationship between independent and dependent variables. In contrast, SVR has a larger prediction error (PE of 7.80%) under this objective, possibly due to insufficient generalization ability of its kernel function in high-dimensional feature mapping. However, this superior-inferior relationship changes in MDR prediction: RSM outperforms BPNN and SVR with superior accuracy of MSE=0.0001 and PE=0.01%, and its R² value (0.9990) is close to the theoretical limit. This indicates that when the target variable MDR has a more explicit and simple mathematical relationship, the response surface model based on polynomial expansion can fully leverage the advantages of parametric modeling, while machine learning models (especially BPNN with MAE=0.0104) show a slight performance degradation. However, the coefficient of determination R² of the three prediction models remains relatively consistent. 2 All three models have accuracy scores above 0.99 and differ by no more than 0.003, demonstrating that they all have high accuracy in predicting MDR. This objective-dependent model performance differentiation reveals the robustness of RSM in low-dimensional analytical problems and the adaptive advantages of machine learning models in complex nonlinear scenarios.

[0070] In this experiment, BPNN demonstrated superior generalization performance and fitting ability when dealing with target variables (SEC) exhibiting highly nonlinear characteristics; while RSM showed stronger parameter interpretability and modeling efficiency when handling target variables (MDR) with explicit functional relationships. Considering the prediction performance of the three models on specific energy consumption and material deposition rate, BPNN outperformed the Response Surface Model (RSM) and Support Vector Regression Model (SVR) in terms of fitting accuracy and error control, demonstrating stronger nonlinear modeling capabilities. Therefore, BPNN was selected as the fitness function in the multi-objective optimization model to provide an accurate basis for calculating the objective function value for subsequent optimization models, ensuring the validity and reliability of the Pareto solution set.

[0071] S4, FDM energy efficiency optimization model and solution.

[0072] 1. Construct an FDM energy efficiency optimization model.

[0073] (1) Optimize variables and constraints.

[0074] Based on the energy efficiency characteristics and the impact of process parameters on specific energy consumption and material deposition rate at various stages of FDM process operation, layer thickness and hotbed temperature are significant influencing factors in both specific energy consumption and material deposition rate responses, and are core control parameters for FDM process energy efficiency. In addition, printing speed and idle speed also have some influence on material deposition rate. Although the main effect of printing temperature on the two response variables was not significant under the conditions of this experiment, as a key heat input control parameter in FDM process, its potential impact on actual process stability cannot be ignored. Therefore, layer thickness, printing speed, printing temperature, hotbed temperature, and idle speed are retained as optimization variables to ensure the integrity and operability of the optimization model and to maintain consistency with the variables in the previous modeling.

[0075] When optimizing the energy efficiency of FDM 3D printing, both the forming quality of the parts and the feasibility of the process must be considered. For the optimization variables, the effective printing conditions and process limitations in actual processing must be met. Based on the FDM forming principle and related process specifications, the following constraints are set for the optimization variables: ① The layer thickness LT ranges from 0.1 to 0.2 mm; ②The printing speed of PS is between 50mm / s and 70mm / s; ③ The printing temperature range for NT is 190-210℃; ④ The range of heated bed temperature BT is 30-50℃; ⑤ The range of the idle speed TS is not less than 100mm / s and not more than 120mm / s.

[0076] (2) Surface roughness prediction model.

[0077] Surface roughness (Ra) describes the microscopic morphology of the printed surface and reflects the appearance quality and functional performance of the finished product. Its prediction model is built based on the process test data carried out in the early stage.

[0078] Using the Box-Behnken experimental design method, with layer thickness LT, printing speed PS, printing temperature NT, and heated bed temperature BT as key process parameters, a second-order polynomial prediction model for surface roughness was established by fitting the four key process parameters and their corresponding surface roughness using Response Surface Methodology (RSM) with Design-Expert 13 software. The specific expression is as follows: Ra=102.21212+170.45832LT+0286418PS-0.998533NT-0.280567BT-0.243842LT*PS-0.114613LT*NT+0.447006 LT*BT-0.000218PS*NT+0.000378PS*BT+0000330NT*BT-362.27834LT-0.002454PS+0.002426NT-+0.001286BT.

[0079] (3) FDM energy efficiency optimization model.

[0080] To achieve multi-objective optimization of FDM technology across energy saving, efficiency improvement, and quality assurance, in addition to specific energy consumption and material deposition rate as optimization objectives, surface roughness is also introduced as an optimization objective. Through analysis of the aforementioned optimization variables, objectives, and constraints, an FDM energy efficiency optimization model is constructed with the objectives of minimizing specific energy consumption, maximizing material deposition rate, and minimizing surface roughness. Specific energy consumption and material deposition rate are calculated using the aforementioned BP neural network model, and surface roughness is calculated using the aforementioned second-order polynomial prediction model for surface roughness. The specific FDM energy efficiency optimization model is as follows: ; Where LT is the layer thickness, PS is the printing speed, NT is the printing temperature, BT is the heated bed temperature, TS is the idle speed, SEC is the mass-to-energy ratio, Ra is the surface roughness, and MDR is the material deposition rate.

[0081] 2. Solving the FDM energy efficiency optimization model.

[0082] The NSGA-II algorithm was used to solve the established FDM energy efficiency optimization model. Real-number encoding was employed, the population size was set to 400, and the maximum number of iterations was 200 generations to ensure sufficient coverage of the search space. In the crossover operation, two-point crossover was selected, with a crossover probability set to 0.7. The mutation operation used a custom discrete variable polynomial mutation, with the mutation probability dynamically decreasing with iterations, initially at 0.3 and not lower than 0.1, to balance global exploration and local exploitation capabilities. The selection operator adopted the non-dominated sorting and crowding distance criterion from NSGA-II, and an elitism strategy was introduced in each generation to ensure the retention of superior individuals. Table 7 shows a partial set of Pareto optimal solutions calculated based on the NSGA-II optimization algorithm, listing representative solutions in the Pareto front. As shown in bold in the table, the first set of solutions achieved the lowest surface roughness (Ra = 9.835 μm), representing the optimal quality limit case. Solutions in groups 10 and 11 achieved optimal specific energy consumption (130.244 J / mg) and material deposition rate (1.681 mg / s), respectively, reflecting an emphasis on processing efficiency. Solution group 2, as the preferred solution for TOPSIS, achieves a good balance between objectives (Ra = 10.601 μm) and effectively avoids extreme process parameters that occur in single-objective optimal solutions. The Pareto optimal front is as follows: Figure 6 As shown.

[0083] Table 7 Partial Pareto Optimal Solution Set

[0084] The Pareto optimal solution set provides managers with a flexible and diverse decision-making space. To find the unique superior solution in the Pareto solution set, the Top-Side Distance Method (TOPSIS) is used to comprehensively rank the Pareto solution set and obtain a comprehensive score. Calculations show that the highest comprehensive score is achieved when the layer thickness is 0.10 mm, the printing speed is 70 mm / s, the printing temperature is 207℃, the heated bed temperature is 30℃, and the idle speed is 113 mm / s. At this point, the specific energy consumption is 268.341 J / mg, the material deposition rate is 0.976 mg / s, and the surface roughness is 10.061 μm. The optimized processing scheme A is compared with the processing scheme E under empirical conditions, and the comparison is shown in Table 8.

[0085] Table 8. Comparison of optimized processing scheme A and processing scheme E under empirical conditions.

[0086] Compared with the processing scheme under empirical conditions, the optimized processing scheme reduces energy consumption by 55.6%, increases material deposition rate by 1.9%, and reduces roughness by 4.8%, verifying the effectiveness and feasibility of the present invention.

[0087] The present invention has been described above with reference to the preferred embodiments shown in the accompanying drawings. However, it will be readily understood by those skilled in the art that the scope of protection of the present invention is obviously not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will all fall within the scope of protection of the present invention.

Claims

1. A method for energy efficiency modeling and multi-objective optimization of FDM process based on BP neural network and NSGA-II, characterized in that, include: Energy efficiency characteristics analysis of S1 and FDM processes; The energy efficiency characteristics of the standby, preheating, printing and reset stages were determined by analyzing the measured power curves of the FDM process. Construct energy efficiency and printing efficiency functions for FDM process to calculate mass-to-specific energy consumption and material deposition rate; Analysis of factors affecting the energy efficiency of S2 and FDM processes; Select an FDM 3D printer, printing consumables, nozzles, power analyzer, computer with experimental data analysis software, electronic scale, and printed model to build the experimental system; A five-factor, three-level experiment was designed using the Box-Behnken method. The five selected process parameters were layer thickness, printing speed, printing temperature, hot bed temperature, and idle speed. The mass-to-energy consumption and material deposition rate were used as the experimental responses. Five-factor, three-level experiments were conducted using the constructed experimental system to obtain the experimental responses corresponding to five process parameters and to analyze the degree of influence of process parameters on mass specific energy consumption and material deposition rate. S3. Energy efficiency modeling of FDM process based on BP neural network; Based on experimental data, prediction models for mass-to-energy consumption and material deposition rate were established using Backpropagation Neural Network (BPNN) and Support Vector Regression (SVR), respectively. The optimal FDM process energy efficiency prediction model was determined by analyzing and comparing the evaluation indices of the FDM process energy efficiency prediction models established using BPNN, SVR, and Response Surface Regression (RSM). S4, FDM energy efficiency optimization model and solution; Based on the energy efficiency characteristics of each stage of FDM process and the degree of influence of process parameters on mass ratio energy consumption and material deposition rate, layer thickness, printing speed, printing temperature, hot bed temperature and idle speed are retained as optimization variables, and the constraint range of optimization variables is set. Based on experimental data, a surface roughness prediction model is constructed. An FDM energy efficiency optimization model is constructed with the objectives of minimizing mass-to-specific energy consumption, maximizing material deposition rate, and minimizing surface roughness, as detailed below: ； Where LT is the layer thickness, PS is the printing speed, NT is the printing temperature, BT is the heated bed temperature, TS is the idle speed, SEC is the mass-to-energy ratio, Ra is the surface roughness, and MDR is the material deposition rate. The Pareto optimal solution set was obtained by solving the established FDM energy efficiency optimization model using the NSGA-II algorithm, and the global optimal solution was selected by the TOPSIS method.

2. The method for FDM process energy efficiency modeling and multi-objective optimization based on BP neural network and NSGA-II according to claim 1, characterized in that, The expressions for the energy efficiency function and the printing efficiency function are as follows: ； ； Where SEC is the mass-to-energy ratio, w is the total energy consumption of the printing process, m is the mass of the printed workpiece, MDR is the material deposition rate, and t is the total time of the printing process.

3. The method for FDM process energy efficiency modeling and multi-objective optimization based on BP neural network and NSGA-II as described in claim 2, is characterized in that, The FDM 3D printer used is a Giant Shadow T10000 model FDM 3D printer. The printing consumable is polylactic acid with a diameter of 1.75mm. The nozzle diameter is 0.4mm. The power analyzer used is a YOKOGAWA WT333E power analyzer. The computer is equipped with WTViewerFreePlus software. The electronic scale has a measurement accuracy of 0.01g. The printed model is a hollow cube structure with an outer dimension of 20mm*20mm*20mm and an inner dimension of 17.6mm*17.6mm*17.6mm.

4. The method for FDM process energy efficiency modeling and multi-objective optimization based on BP neural network and NSGA-II according to claim 3, characterized in that, The analysis of the influence of process parameters on mass-to-energy consumption and material deposition rate includes: Using Design-Expert 13 software, response surface regression (RSM) was used to fit five process parameters and their corresponding experimental responses to a quadratic polynomial model. This model was used to predict the relationship between mass ratio energy consumption and material deposition rate. Variance analysis was then performed to evaluate the significance of the main effects and interaction effects of each process parameter. Based on the significance of the main and interaction effects of each process parameter, the order of influence on mass specific energy consumption from largest to smallest is: heated bed temperature, layer thickness, printing speed, idle speed, and printing temperature. Similarly, the order of influence on material deposition rate from largest to smallest is: layer thickness, printing speed, heated bed temperature, idle speed, and printing temperature.

5. The method for FDM process energy efficiency modeling and multi-objective optimization based on BP neural network and NSGA-II according to claim 4, characterized in that, Based on experimental data, prediction models for mass-to-energy consumption and material deposition rate are established using Backpropagation Neural Network (BPNN) and Support Vector Regression (SVR), respectively. The optimal FDM process energy efficiency prediction model is determined by analyzing and comparing the evaluation indicators of the FDM process energy efficiency prediction models established using BPNN, SVR, and Response Surface Regression (RSM). This includes: Based on the PyCharm 2024.1 integrated development environment, a BP neural network model was built using the Keras API of the TensorFlow 2.12.0 deep learning framework. The BP neural network model adopted the Sequential sequence model. The input layer variables of the BP neural network model included layer thickness, printing speed, heated bed temperature, idle speed, and printing temperature. The output layer variables of the BP neural network model included mass-to-energy consumption and material deposition rate. The BP neural network model consisted of three hidden layers with 128, 64, and 32 neurons in each layer, respectively, all using the ReLU activation function. The dataset was divided into training, validation, and test sets at a ratio of 64%, 16%, and 20%, respectively. The parameter settings of the BP neural network model are shown in Table 5. Table 5 BP Neural Network Model Parameter Settings ； A prediction model for mass-to-energy consumption and material deposition rate was established using support vector regression (SVR). The parameter settings for SVR are shown in Table 6. Table 6 Support Vector Regression (SVR) Parameter Settings ； Select the percentage error (PE), mean absolute error (MAE), mean square error (MSE), and coefficient of determination (R). 2 As an evaluation index, the FDM process energy efficiency prediction models established by backpropagation neural network (BPNN), support vector regression (SVR), and response surface regression (RSM) were evaluated, and the FDM process energy efficiency prediction model established by BPNN was determined to be the optimal FDM process energy efficiency prediction model.

6. The method for FDM process energy efficiency modeling and multi-objective optimization based on BP neural network and NSGA-II according to claim 5, characterized in that, The surface roughness prediction model constructed based on experimental data includes: Using the Box-Behnken experimental design method, with layer thickness LT, printing speed PS, printing temperature NT, and heated bed temperature BT as key process parameters, a second-order polynomial prediction model for surface roughness was established by fitting the four key process parameters and their corresponding surface roughness using Response Surface Methodology (RSM) with Design-Expert 13 software. The specific expression is as follows: Ra=102.21212+170.45832LT+0286418PS-0.998533NT-0.280567BT-0.243842LT*PS-0.114613LT*NT+0.447006 LT*BT-0.000218PS*NT+0.000378PS*BT+0000330NT*BT-362.27834LT-0.002454PS+0.002426NT-+0.001286BT.

7. The method for FDM process energy efficiency modeling and multi-objective optimization based on BP neural network and NSGA-II according to claim 6, characterized in that, The method of using the TOPSIS (Top-Side Solution Distance) to select the globally optimal solution includes: The TOPSIS (Top-Side Distance Method) is used to comprehensively rank the Pareto solution set. Production efficiency is selected as a positive indicator, while cutting ratio energy consumption and drum wear depth are selected as negative indicators. After finding the optimal and worst matrix vectors, the distance between the Pareto non-dominated solution and the positive or negative ideal solution is calculated to obtain the comprehensive score. The process parameter combination with the highest comprehensive score is determined as the global optimal solution.

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