Flat wire forming parameter and forming angle quantitative modeling method based on cascade machine learning

Abstract

The invention provides a flat wire forming parameter and forming angle quantitative modeling method based on cascade machine learning, and aims to solve the technical problem that the forming angle is difficult to cooperatively control in a multi-step bending process. The method comprises the following steps: firstly, collecting 2D forming process data of the hairpin winding of the flat wire motor of the new energy automobile, and constructing an input set containing geometric parameters and physical derivative characteristics; then, based on RF, XGBoost and LightGBM algorithms, a three-stage cascade chain type regression model is constructed, three forming angles are predicted step by step, and model optimization and verification are carried out through an independent test set; a dynamic influence mechanism of process parameters in multi-step forming is disclosed by adopting an SHAP method, and a preorder forming angle is found to have a key effect in a subsequent stage. According to the method, the optimal process parameters can be reversely solved based on the target span or the allowable error, the transformation from'trial-and-error 'machine adjustment to'predictive' machine adjustment is realized, and the forming precision and the process development efficiency are remarkably improved.

Description

TECHNICAL FIELD

[0001] The present application relates to a new energy vehicle flat wire motor hairpin winding bending forming parameter prediction method, mainly studies the forming angle prediction of flat wire enameled wire and the mapping relationship between the forming geometric parameters (wire width, thickness, width-thickness ratio) and the forming angle, specifically relates to a quantitative modeling method for flat wire forming parameters and forming angle based on cascading machine learning, and belongs to the technical field of new energy motor manufacturing. BACKGROUND

[0002] With the rapid development of new energy vehicle industry, higher requirements are put forward for the power density, efficiency and reliability of the driving motor. Flat wire motor has become the mainstream choice of the next generation of electric drive system due to its high slot fill rate and significant efficiency advantage. However, in the process of 2D CNC multi-step bending forming of enameled flat wire winding, due to the coupling of material rebound and geometric effect, the final forming angle is difficult to predict and control. At present, the internal influence law and quantitative relationship between flat wire geometric parameters and multi-step forming angle are still blank, which leads to the technical bottleneck of coordinated prediction and control of three forming angles, and seriously restricts the consistency and efficiency of high-end motor mass production.

[0003] At present, the bending forming mechanism of polyimide enameled flat copper wire still stays in the stage of experience cognition, and there is a lack of systematic explanation and quantitative model for how key parameters such as wire width, thickness, width-thickness ratio and cross-sectional moment of inertia affect the forming angle at each stage. This leads to the fact that the process development generally relies on the "trial and error - correction" mode, which not only has a long debugging cycle and high cost, but also the experience formed cannot be transferred across specifications, and it is impossible to build a reusable process knowledge system.

[0004] Therefore, there is an urgent need for a quantitative modeling method for enameled flat copper wire flat wire forming parameters and forming angles that can reveal the complex mapping relationship between geometric parameters and forming angles in the multi-step bending process, in order to fill the gap in mechanism cognition and systematic design methods in this field, and provide a theoretical cornerstone for intelligent design and accurate prediction of the process. SUMMARY

[0005] The present application aims to solve the technical problem that the three forming angles of wire with different geometric parameters are difficult to accurately control in the bending process. By establishing the quantitative mapping relationship between the forming geometric parameters and the three forming angles, the internal influence law is studied, the best process scheme for flat wire bending is provided, and the double improvement of forming precision and stability is realized.

[0006] The technical problem of the present application is solved by adopting the following technical scheme:

[0007] The quantitative modeling method for flat wire forming parameters and forming angles based on cascading machine learning includes the following steps:

[0008] S1: Data acquisition:

[0009] The data is derived from the process data of the bending of enameled flat wire in the 2D forming production process of new energy vehicle flat wire motor hairpin winding;

[0010] S2: Feature engineering:

[0011] On the basis of 10-dimensional original geometric parameters, 3-dimensional physical derived features such as width-thickness ratio, cross-sectional second moment, and arm ratio are constructed to form a 13-15 dimensional cascaded input feature set, which systematically represents the geometric properties and mechanical properties of the multi-step forming process, laying the foundation for the cascaded prediction model;

[0012] S3 Multi-model construction and parameter optimization

[0013] Based on RF, XGBoost and LightGBM algorithms, a cascaded chain regression model is constructed. Through independent test set verification, the model is optimized in stages, and the optimal algorithm is selected independently for each stage. In the first stage, the first forming angle θ1_pred is predicted based on 13-dimensional geometric features, in the second stage, the first forming angle θ1_pred is introduced to construct a 14-dimensional input to predict the second forming angle θ2_pred, and in the third stage, the third forming angle θ3_pred is predicted by fusing the previous prediction results to form a 15-dimensional input. This structure effectively captures the physical correlation and feature dependency in the multi-step forming process by gradually passing on the previous prediction information, ensuring the overall prediction accuracy;

[0014] S4: Model evaluation and optimization:

[0015] Through the Hold-out test method, the entire data set is randomly divided in the ratio of 8:2. Among them, 80% of the data is used as the training set to build and train the model; the other 20% of the data is strictly sealed as the test set during the entire model development period, and is only used for one-time, unbiased evaluation of the performance of the final model;

[0016] S5: Cascaded forming mechanism and feature evolution rule revelation:

[0017] This method uses the SHAP method to analyze the explainability of the cascaded chain regression model, and systematically reveals the influence mechanism of each process parameter in the three-stage forming process. Combined with the Gini feature importance and SHAP analysis results, a deep understanding of the physical mechanism of multi-step bending forming is formed;

[0018] S6: Feature optimization and engineering application:

[0019] By setting the target span or forming angle allowable error, the optimization algorithm is used to solve the optimal bending process parameters in reverse, thereby realizing the transformation from traditional "trial and error" machine adjustment to "prediction", and greatly improving the process development efficiency and forming quality.

[0020] Compared with the prior art, the present application has the following advantages:

[0021] (1) The SHAP explainability analysis is adopted to quantify the dynamic evolution rule from "geometric parameter dominance" to "deformation history dominance" in multi-step forming, such as the influence intensity (SHAP value 0.0637) of the second forming angle θ2_pred on the final result, which is 16.3 times that of the second, providing clear theoretical guidance for process optimization;

[0022] (2) The cascaded chain random forest model is innovatively constructed, and the structure strictly matches the physical time sequence, the importance of the previous forming angle in the subsequent stage is in the front row (such as the Gini importance of the first forming angle θ1_pred in the second stage is 0.3019), which ensures the physical rationality and high precision of the prediction result;

[0023] (3) Strong engineering practicability: based on actual production data modeling, the model has good generalization ability and engineering applicability;

[0024] (4) The cumulative contribution of the top five features in the SHAP importance of the three-stage forming angle prediction model is more than 85%, and the explanation degree of the second forming angle θ2_pred on the final result is 94.94%. BRIEF DESCRIPTION OF DRAWINGS

[0025] Figure 1 is a flowchart of the cascaded flat wire forming geometric parameter and forming angle rule analysis based on machine learning;

[0026] Figure 2 is a comparison diagram of the model prediction results and the true values of the three forming angles;

[0027] Figure 3 is a comparison diagram of the Gini feature importance of the random forest model for three-stage forming angle prediction;

[0028] Figure 4 is a random forest model SHAP feature importance ranking diagram for three-stage forming angle prediction;

[0029] Figure 5 is a random forest model SHAP feature influence analysis for three-stage forming angle prediction;

[0030] Figure 6 is a random forest model SHAP dependence diagram for three-stage forming angle prediction; DETAILED DESCRIPTION

[0031] The present application will be further described in detail below in combination with the drawings and examples.

[0032] This invention utilizes historical process data from a new energy vehicle drive motor production line. The data focuses on polyimide enameled copper flat wire, covering various wire specifications and bending process parameters (wire widths ranging from 3.0 mm to 10.0 mm and wire thicknesses from 1.8 mm to 5.0 mm), totaling 745 sets of valid data. All data was collected using high-precision online measurement equipment, ensuring the authenticity and reliability of the data.

[0033] The 745 sets of data were randomly divided into a training set (596 sets) and a test set (149 sets) in an 8:2 ratio. After standardizing the input features (w, h), the LightGBM, XGBoost, and RF regression algorithms were used to train the model, as follows:

[0034] S1 Data Acquisition:

[0035] The data comes from the process data of enameled flat wire bending in the 2D forming production process of hairpin windings for new energy vehicle flat wire motors;

[0036] S2 Feature Engineering:

[0037] 2.1 Original 10-dimensional geometric parameters:

[0038] Basic geometric parameters: wire width w (mm), wire thickness h (mm), crown section height h1 (mm);

[0039] Bending angles: First bending angle θ1 (°), Second bending angle θ2 (°), Third bending angle θ3 (°);

[0040] Line segment lengths: First line segment b1 (mm), Second line segment b2 (mm), Third line segment b3 (mm), Fourth line segment b4 (mm);

[0041] 2.2 Physical Mechanisms Derived from 3D:

[0042] Basic geometric features: width-to-thickness ratio R, second moment of section I, lever arm ratio ;

[0043] Width-to-thickness ratio: R=w / h, Second moment of section: Lever arm ratio: ;

[0044] 2.3 Three forming angles Input parameter selection, :

[0045] First forming angle Input selection: 13 dimensions, wire width w, wire thickness h, crown segment height h1, first bend angle θ1, second bend angle θ2, third bend angle θ3, first straight segment b1, second straight segment b2, third straight segment b3, fourth straight segment b4, width-to-thickness ratio R, section moment I, lever arm ratio ;

[0046] Second forming angle Input selection: 14 dimensions, wire width w, wire thickness h, crown segment height h1, first bend angle θ1, second bend angle θ2, third bend angle θ3, first straight segment b1, second straight segment b2, third straight segment b3, fourth straight segment b4, width-to-thickness ratio R, section moment I, lever arm ratio First forming angle ;

[0047] Third forming angle Input selection: 15 dimensions, wire width w, wire thickness h, crown segment height h1, first bend angle θ1, second bend angle θ2, third bend angle θ3, first straight segment b1, second straight segment b2, third straight segment b3, fourth straight segment b4, width-to-thickness ratio R, section moment I, lever arm ratio First forming angle Second forming angle ;

[0048] 2.4 Three forming angles As output features :

[0049] First forming angle Second forming angle Third forming angle ;

[0050] S3 Multi-Model Construction and Parameter Optimization:

[0051] S3.1 Multi-Model Construction:

[0052] 3.1.1 Random Forest (RF):

[0053] 1) Single tree splitting criterion

[0054] The single tree splitting criterion is divided into classification tasks and regression tasks;

[0055] Classification task: The single tree uses the classification tree in the Classification and Regression Tree (CART) algorithm, and the splitting criterion is usually Gini impurity to maximize the reduction of impurity;

[0056] Regression task: A single tree is a CART regression tree, and the splitting criterion is usually the mean squared error, in order to minimize the variance after splitting;

[0057] This method uses a CART regression tree, as shown in the following formula: Its splitting objective is to find the features and split points that minimize the sum of the mean square errors of the child nodes after the split, i.e., to maximize the following gain:

[0058]

[0059] The set of samples on the parent node before the split; The set of samples on the left and right child nodes after splitting;

[0060] 2) Forest Prediction

[0061] This method employs a regression task (simple averaging), and the formula is as follows:

[0062]

[0063] M: Number of decision trees; The prediction output of the m-th decision tree for input sample x; The final predicted value of the random forest;

[0064] This model (RF) serves as one of the candidate base learners, participating in model selection at each stage of cascaded regression. Its excellent resistance to overfitting makes it a preferred model when the input feature dimension is low (e.g., the first forming angle θ1_pred) or the amount of data is limited.

[0065] 3.1.2 eXtreme Gradient Boosting (XGBoost):

[0066] 1) Objective function

[0067]

[0068] The total cost of the model at the t-th training round; Let be the loss function of the model for the i-th sample during the t-th round of training; This represents the cumulative prediction results for the first t-1 trees; For the t-th tree being constructed, for sample x i The predicted value; For regularization terms;

[0069] 2) Second-order Taylor expansion

[0070]

[0071] For the first-order gradient, It is a second-order gradient;

[0072] 3) Leaf weight analytical solution

[0073]

[0074] The optimal weight for the j-th leaf node; I j This represents the set of all samples assigned to the j-th leaf node;

[0075] 4) Split gain

[0076]

[0077] The set of samples on the parent node before the split; : The sample sets on the left and right child nodes after splitting; λ: L2 regularization coefficient; γ: minimum splitting gain threshold; λ and γ are adjustable regularization hyperparameters, which together constitute the core implementation of this method to control model complexity and improve generalization ability;

[0078] This model (XGBoost) serves as one of the candidate base learners, participating in model optimization at each stage of the cascaded chain regression. Its regularized split gain criterion is one of the core bases of this method, often demonstrating superior performance when dealing with complex high-dimensional feature interactions (such as the cascaded prediction of subsequent forming angles).

[0079] 3.1.3 Light Gradient Boosting Machine (LightGBM):

[0080] 1) Histogram Algorithm

[0081] LightGBM uses a histogram algorithm to discretize continuous features, reducing the computational complexity of finding split points from depending on the number of unique feature values ​​to depending only on the number of preset buckets, which greatly improves training efficiency.

[0082]

[0083] x: A raw value of feature j; min(j): The minimum value of feature j among all samples; min(x): The maximum value of feature j among all samples; max_bins: The preset maximum number of bins; : The function to round down, ensuring the result is an integer; bin: The calculated bin number, ranging from [0, max_bins-1];

[0084] 2) Leaf-wise Growth Strategy (Leaf-wise for short)

[0085] LightGBM employs the same advanced split gain criterion as XGBoost (as shown in the equation below) to ensure prediction accuracy during node splitting. However, the key efficiency improvement of this method lies in LightGBM's application of this criterion through its unique Leaf-wise growth strategy. Unlike the traditional layer-by-layer growth strategy, Leaf-wise splits only the leaf node with the largest current gain at each layer. This approach allows the loss function to decrease faster and convergence accuracy to be higher with the same model complexity, thus providing a significant efficiency advantage for the cascaded optimization structure of this method.

[0086]

[0087] This model (LightGBM) serves as one of the candidate base learners, participating in model selection at each stage of cascaded regression. Its histogram algorithm and leaf-wise growth strategy are key efficiency improvements, making it highly competitive when dealing with large-scale data or requiring extremely fast training speeds.

[0088] 3.1.4 Cascaded Chain Regression:

[0089] 1) Chained prediction process

[0090] This method not only captures the physical dependencies between angles through a cascaded chain regression structure, using the prediction results of preceding models as incremental features input into subsequent models, but also ensures that each step is driven by the algorithm most suitable for the data characteristics of that stage through a phased model optimization mechanism. This "adaptive chain structure" overcomes the limitation that a single model may perform poorly in certain stages, thus achieving more accurate and robust forming angle prediction overall. The process is as follows:

[0091] Phase 1 (First forming angle θ1_pred):

[0092] Among them, model M1 is selected from the candidate pool [RF, XGBoost, LightGBM] according to the following optimization strategy;

[0093] Phase Two (Second Forming Angle θ2_pred):

[0094] Among them, model M2 is independent of M1 and is selected from the same candidate pool according to the same strategy;

[0095] Phase Three (Third Forming Angle θ3_pred):

[0096] Among them, model M3 was also determined through independent optimization;

[0097] X: Original input feature vector; M: The predicted value of the i-th forming angle predicted by the model in the i-th stage; k The regression model ultimately determined in the k-th stage through a systematic optimization process;

[0098] 2) Phased model optimization strategy

[0099] The core of the optimization strategy is to independently select the model with the smallest validation error for each stage k, directly calculate the mean absolute error (MAE) of each candidate model on the validation set, and select the model with the smallest MAE as the optimal model for that stage.

[0100] The formula for selecting the model for stage k is:

[0101]

[0102] M k : The optimal model selected for the k-th stage; : The mean absolute error of model M on the validation set A in the k-th stage;

[0103] S4 Model Evaluation and Optimization:

[0104] 4.1 Model Evaluation Metrics:

[0105] This method uses the mean absolute error (MAE) and root mean square error (RMSE) as accuracy evaluation indicators, as shown in the following formulas:

[0106] (Average absolute value)

[0107] (Root Mean Square Error)

[0108] : The true value of the i-th sample; : The predicted value of the i-th sample; n: The number of samples;

[0109] 4.2 Comparative Analysis and Optimal Selection of Cascade Models:

[0110] This embodiment uses 745 sets of sample data extracted from the 2D forming production process of hairpin windings for new energy vehicle flat wire motors during bending of enameled flat wires. Using the hold-out test method, the entire dataset was randomly divided in an 8:2 ratio. 80% of the data was used as the training set for building and training the model; the remaining 20% ​​was used as the test set, strictly sealed throughout the model development cycle and used only for a one-time, unbiased evaluation of the final model's performance. Evaluation metrics were calculated according to S4.1. The results are shown in Table 1 and... Figure 2 As shown;

[0111] Figure 2 A scatter plot showing the predicted and actual values ​​of the three forming angles is presented. Figure 2 In the middle (A), (D), and (G), the predicted values ​​and the actual values ​​of the LightGBM model are scatter plots. Figure 2 In the middle (B), (E), and (H), the plots are scatter plots of the predicted and actual values ​​of the XGBooet model. Figure 2 In the diagram, (C), (F), and (I) are scatter plots showing the predicted and actual values ​​from the RF model. Figure 2 As shown, all data points are closely distributed on both sides of the ideal diagonal of y=x, forming a clear linear distribution band. This result strongly demonstrates from a qualitative perspective that the model of this method has successfully learned the complex law of forming angle springback, and its predicted values ​​have extremely high consistency with the true values ​​and extremely low systematic bias.

[0112] Table 1. Performance metrics of the three candidate models on the independent test set.

[0113] In this method, the Mean Absolute Error (MAE), as the core indicator directly measuring prediction bias, is given the highest weight and is further validated by the Root Mean Square Error (RMSE). Table 1 shows that for the first shaping angle θ1_pred: Random Forest (RF) leads comprehensively in both MAE=0.109° and RMS=0.145°, significantly outperforming other candidate models and clearly the best choice. For the second shaping angle θ2_pred: the performance of the three models is very close, with RF performing best at MAE=0.140°, and its RMSE of 0.192° also matching the optimal value, making RF the optimal choice for this stage. For the third shaping angle θ3_pred: RF and XGBoost have the best RMSE (0.122°), while RF's MAE (0.089°) is slightly better than LightGBM (0.091°), making it the best among all models. Therefore, RF also demonstrates the best overall performance in this stage.

[0114] Based on the comprehensive analysis centered on MAE above, the optimal cascaded model combination determined by this method is: M1=RF, M2=RF, M3=RF. The results show that the mean absolute error (MAE) of the prediction of all three forming angles is less than 0.15°, as shown in Table 1. Under the specific dataset and feature engineering of this embodiment, the RF model provides the most consistent and accurate solution for the three forming angle prediction tasks.

[0115] The mechanism and characteristic evolution of S5 cascade molding are revealed:

[0116] 5.1 SHAP Importance Quantification:

[0117] This method employs the Shapley Additive Interpretation (SHAP) approach to analyze the interpretability of a cascaded chain regression model, systematically revealing the influence mechanism of various process parameters in the three-stage forming process. Combining the importance of Gini features with the SHAP analysis results, a deeper understanding of the physical mechanism of multi-step bending forming is achieved.

[0118] See Figure 3 As shown in Table 2, the cascaded regression model proposed in this method has been rigorously isolated and verified, confirming its significant effect and physical rationality in predicting the bending forming angle in multi-step bending.

[0119] Table 2. Importance of Gini features in the three-stage forming angle prediction random forest model (top five features)

[0120] As shown in Table 2, the test data of the importance of Gini impurity features (top five features) of the random forest model for three-stage forming angle prediction shows that at the first forming angle θ1_pred, the crown height h1 is the most critical influencing factor with an importance of 33.75%. The wire thickness h (19.95%), the second moment of the cross section I (19.24%), and the width-to-thickness ratio R (17.07%) together constitute the core feature set. The cumulative contribution of these four geometric parameters is as high as 90.01%, which fully verifies the fundamental and dominant role of geometric parameters in the initial forming stage.

[0121] When entering the second forming angle θ2_pred, the model successfully captured the cumulative effect of the preceding deformation. The first forming angle θ1_pred ranked first with an importance of 30.19%. At the same time, the original geometric parameters such as crown segment height h1 (19.09%) and cross section second moment I (17.29%) still maintained a significant influence, forming a hybrid mode of "preceding deformation effect and original geometric parameters driving together", which accurately reflects the physical nature of the transition stage in multi-step forming.

[0122] Most importantly, in the third forming angle θ3_pred, the model reveals a strong physical law: the second forming angle θ2_pred determines the final forming result with an absolute dominance of 94.94%. This discovery confirms that in the process system of this method, there is a near-deterministic physical correlation between the third forming angle and the second forming angle, and the later forming state is completely dominated by the preceding deformation path. This discovery not only verifies the theoretical basis of the cascaded chain structure, but also provides a clear direction for process optimization—the final forming accuracy can be effectively guaranteed by precisely controlling the preceding forming stages.

[0123] The Gini importance built into random forests essentially measures the intrinsic splitting utility of features during model construction, evaluating their discriminative ability by calculating the cumulative reduction in impurity during node splitting. However, this metric has inherent limitations: first, it is susceptible to interference from feature dimensions and numerical scales; second, it is sensitive to multicollinearity; and third, and most importantly, it cannot fairly distribute the interaction effects between features, often attributing the gains from interactions solely to the feature performing the split. Given these limitations, Gini importance cannot truly reflect the independent contribution of each feature to the prediction results; therefore, its analysis results can only serve as auxiliary verification for understanding the internal mechanisms of the model. To achieve a shift in perspective from "how the model is built" to "how predictions are generated," and to accurately quantify the true physical impact of each feature on the final forming angle, this method introduces the Shapley Additive Explanation (SHAP) attribution framework based on federated game theory.

[0124] The three-stage forming angle prediction model was analyzed based on the Shapley Additive Interpretation (SHAP) method, systematically revealing the influence mechanism and evolution law of each process parameter in different forming stages. The analysis results are shown in Table 3 and... Figure 4 , Figure 5 and Figure 6 This indicates that the importance of SHAP features and the direction of their influence exhibit significant systematic changes at different stages;

[0125] Table 3. Ranking of the importance of SHAP features in the three-stage shaping angle prediction random forest model (top five features)

[0126] Table 4 Summary of the Influence Laws of Key Features of the Three-Stage Formation Angle

[0127] In the first forming angle θ1_pred stage, the model identified the fundamental dominant role of geometric parameters. As shown in Table 3, wire thickness h ranked first with a SHAP importance of 0.0306. Combined with... Figure 5 (A) Figure 6As shown in (A) and Table 4, SHAP analysis reveals a stable negative correlation between wire thickness h and the first forming angle θ1_pred, indicating that for every 1 mm increase in wire thickness h, the first forming angle θ1_pred decreases by 0.0372°. The larger the second moment of the cross section I (importance 0.0213), the smaller the first forming angle θ1_pred. Similarly, the width-to-thickness ratio R (importance 0.0176) shows a positive correlation; the larger the width-to-thickness ratio R, the larger the first forming angle θ1_pred. For the crown section height h1 (importance 0.0170), for every 1 mm increase in crown section height h1, the first forming angle θ1_pred increases by 0.0064°. These four geometric parameters are the dominant contributors, accurately reflecting the decisive influence of material geometric properties on deformation behavior in the initial forming stage.

[0128] Entering the second forming angle θ2_pred stage, the model captures the cascading effects of the process, achieving a crucial transition from "geometry-driven" to "deformation history-driven." The first forming angle θ1_pred, with a SHAP importance of 0.0374, ranks first (see Table 3), becoming the most critical influencing factor. According to... Figure 5 (B) shows that the first forming angle θ1_pred and the second forming angle θ2_pred are positively correlated, combined with Figure 6 (B) and Table 4 show that for every 1° increase in the first forming angle θ1_pred, the second forming angle θ2_pred increases by 0.2803°, reflecting the amplification effect of the preceding deformation on the subsequent process. Meanwhile, the influence of the original geometric parameters still exists but is weakening; for example, the importance of the wire thickness h decreases from 0.0306 to 0.0205, representing a 33% reduction in its influence.

[0129] In the final third forming angle θ3_pred stage, the model reveals a near-deterministic physical law: the later forming state is entirely dominated by the preceding deformation path. Table 3 shows that the second forming angle θ2_pred, with a SHAP importance of 0.0637, achieves the highest proportion, reaching 16.3 times that of the second-ranked first forming angle θ1_pred (0.0039). Figure 5 (C) Figure 6 As shown in (C) and Table 4, the second forming angle θ2_pred and the third forming angle θ3_pred exhibit a very strong positive correlation. For every 1° increase in the second forming angle θ2_pred, the third forming angle θ3_pred increases by 0.8568°, demonstrating a strong deformation accumulation and amplification effect. In stark contrast, the importance of all original geometric parameters (such as wire thickness h and cross-sectional moment I) has been reduced to an extremely low level (<0.0032).

[0130] This SHAP analysis not only verifies the theoretical basis of the cascaded chain regression model, but also quantitatively characterizes the evolution of the inherent physical mechanism in the multi-step molding process, providing reliable data support and theoretical guidance for the precise control and optimization of process parameters.

[0131] This method constructs a cascaded random forest model and combines SHAP and Gini perspectives to analyze the characteristic influence mechanism in the three-stage hairpin wire forming process. Specifically, in the initial stage, at the first forming angle θ1_pred, geometric parameters such as wire thickness h and cross-sectional moment I are the decisive factors (both Gini and SHAP importance points to crown section height h1 and wire thickness h). As forming progresses, the influence of the first forming angle θ1_pred becomes prominent (SHAP importance ranks first in the second forming angle θ2_pred stage). By the third forming angle θ3_pred, the second forming angle θ2_pred becomes dominant with a significant advantage (SHAP importance reaches 0.0637, 16.3 times that of the second-ranked angle), while the influence of the original geometric parameters becomes negligible. SHAP analysis further quantifies the direction and intensity of the characteristic influence, confirming the existence of significant deformation accumulation and amplification phenomena in the cascade effect. This conclusion not only verifies the physical rationality of the cascade chain model from a data perspective, but also provides clear guidance for the molding control of multi-step molding processes: in the early stage, the focus should be on the geometric accuracy of raw materials and initial bending, while in the later stage, the focus should be on the precise monitoring and control of the deformation state of the preceding steps.

[0132] S6 Feature Optimization and Engineering Applications:

[0133] Based on the above feature importance analysis results, the engineering application strategy proposed by this method is as follows: First, implement a differentiated data acquisition scheme, that is, in practical applications, prioritize the measurement accuracy of high-importance features (such as wire thickness, crown section height, and preceding forming angle), while using standard values ​​or estimated values ​​for low-importance features, thereby significantly reducing data acquisition costs and complexity while maintaining high model accuracy; Second, use the trained high-precision cascaded model as a digital proxy model for rapid optimization of process parameters for new wire specifications. By setting the allowable error of the target span or forming angle, the optimization algorithm is driven to solve for the optimal bending process parameters in reverse, thereby realizing the transformation from traditional "trial and error" machine adjustment to "predictive" control, and greatly improving process development efficiency and forming quality.

[0134] In summary, this method establishes a quantitative prediction model for the multi-step bending process of enameled flat wire, elevating the traditional experience-based process to a new stage of calculability and predictability. This method achieves accurate prediction of the three forming angles, providing theoretical support for the precision manufacturing and stable mass production of flat wire motor windings.

Claims

1. A quantitative modeling method for flat wire forming parameters and forming angle based on cascaded machine learning, characterized in that... Includes the following steps: S1 Data Acquisition: The data comes from the process data of enameled flat wire bending in the 2D forming production process of hairpin windings for new energy vehicle flat wire motors; S2 Feature Engineering: Based on the original 10-dimensional geometric parameters, 3-dimensional physical derived features such as width-to-thickness ratio, cross-sectional second moment, and lever arm ratio are constructed to form a 13-15 dimensional cascaded input feature set; S3 Multi-Model Construction and Parameter Optimization Based on three types of algorithms—RF, XGBoost, and LightGBM—a cascaded chain regression model is constructed. The model is optimized in stages through independent test set validation, with the optimal algorithm selected independently for each stage. The first stage predicts the first forming angle θ1_pred based on 13-dimensional geometric features. The second stage introduces the first forming angle θ1_pred to construct a 14-dimensional input to predict the second forming angle θ2_pred. The third stage integrates the previous prediction results to form a 15-dimensional input to predict the third forming angle θ3_pred. S4 Model Evaluation and Optimization: Using the hold-out test method, the entire dataset was randomly divided in an 8:2 ratio, with 80% of the data used as the training set to build and train the model, and the remaining 20% ​​used as the test set. The mechanism and characteristic evolution of S5 cascade molding are revealed: The SHAP method was used to conduct interpretability analysis on the cascaded chain regression model, revealing the influence mechanism of each process parameter in the three-stage forming process; combined with the importance of Gini features and the results of SHAP analysis, a deep understanding of the physical mechanism of multi-step bending forming was formed. S6 Feature Optimization and Engineering Applications: By setting the target span or forming angle allowable error, the optimization algorithm is driven to solve the optimal bending process parameters in reverse, thereby realizing the transformation from the traditional "trial and error" machine adjustment to "predictive" adjustment, improving process development efficiency and forming quality.

2. The method for quantitative modeling of flat wire forming parameters and forming angle based on cascaded machine learning according to claim 1, characterized in that... S2 feature engineering is as follows: 2.1 Original 10-dimensional geometric parameters: Basic geometric parameters: wire width w, wire thickness h, crown section height h1; Bending angles: First bending angle θ1, second bending angle θ2, third bending angle θ3; Line segment lengths: first line segment b1, second line segment b2, third line segment b3, fourth line segment b4; 2.2 Physical Mechanisms Derived from 3D: Basic geometric features: width-to-thickness ratio R, second moment of section I, lever arm ratio ; Width-to-thickness ratio: R=w / h, Second moment of section: Lever arm ratio: ; 2.3 Three forming angles Input parameter selection, : First forming angle Input selection: 13 dimensions, wire width w, wire thickness h, crown segment height h1, first bend angle θ1, second bend angle θ2, third bend angle θ3, first straight segment b1, second straight segment b2, third straight segment b3, fourth straight segment b4, width-to-thickness ratio R, section moment I, lever arm ratio ; Second forming angle Input selection: 14 dimensions, wire width w, wire thickness h, crown segment height h1, first bend angle θ1, second bend angle θ2, third bend angle θ3, first straight segment b1, second straight segment b2, third straight segment b3, fourth straight segment b4, width-to-thickness ratio R, section moment I, lever arm ratio First forming angle ; Third forming angle Input selection: 15 dimensions, wire width w, wire thickness h, crown segment height h1, first bend angle θ1, second bend angle θ2, third bend angle θ3, first straight segment b1, second straight segment b2, third straight segment b3, fourth straight segment b4, width-to-thickness ratio R, section moment I, lever arm ratio First forming angle Second forming angle ; 2.4 Three forming angles As output features : First forming angle Second forming angle Third forming angle .

3. The method for quantitative modeling of flat wire forming parameters and forming angle based on cascaded machine learning according to claim 1, characterized in that... The S3 multi-model construction and parameter optimization are as follows: S3.1 Multi-Model Construction: 3.1.1 Random Forest: 1) Single tree splitting criterion Using a CART regression tree, the formula is as follows: Its splitting objective is to find the feature and split point that minimizes the sum of the mean square errors of the child nodes after the split, i.e., to maximize the following gain: ； The set of samples on the parent node before the split; The set of samples on the left and right child nodes after splitting; 2) Forest Prediction Using a regression task, the formula is as follows: ； M: Number of decision trees; The prediction output of the m-th decision tree for input sample x; The final predicted value of the random forest; 3.1.2 Limit Gradient Boosting Machine: 1) Objective function ； The total cost of the model at the t-th training round; Let be the loss function of the model for the i-th sample during the t-th round of training; This represents the cumulative prediction results for the first t-1 trees; For the t-th tree being constructed, for sample x i The predicted value; For regularization terms; 2) Second-order Taylor expansion ； For the first-order gradient, It is a second-order gradient; 3) Leaf weight analytical solution ； The optimal weight for the j-th leaf node; I j This represents the set of all samples assigned to the j-th leaf node; 4) Split gain ； The set of samples on the parent node before the split; : The sample sets of the left and right child nodes after splitting; λ: L2 regularization coefficient; γ: Minimum splitting gain threshold; λ and γ are adjustable regularization hyperparameters; 3.1.3 Light Gradient Lift: 1) Histogram Algorithm LightGBM uses a histogram algorithm to discretize continuous features, reducing the computational complexity of finding split points from depending on the number of unique feature values ​​to depending only on the number of preset buckets, thus improving training efficiency. ； x: A raw value of feature j; min(j): The minimum value of feature j among all samples; min(x): The maximum value of feature j among all samples; max_bins: The preset maximum number of bins; : A floor function that ensures the result is an integer; bin: The calculated bucket number, ranging from [0, max_bins-1]; 2) Leaf-first growth strategy LightGBM employs the same advanced split gain criterion as XGBoost to ensure prediction accuracy when splitting nodes. ； 4-stage chain regression model: 1) Chained prediction process Phase 1 (First forming angle θ1_pred): ; Among them, model M1 is selected from the candidate pool [RF, XGBoost, LightGBM] according to the following optimization strategy; Phase Two (Second Forming Angle θ2_pred): ; Among them, model M2 is independent of M1 and is selected from the same candidate pool according to the same strategy; Phase Three (Third Forming Angle θ3_pred): ; Among them, model M3 was also determined through independent optimization; X: Original input feature vector; M: The predicted value of the i-th forming angle predicted by the model in the i-th stage; k The regression model ultimately determined in the k-th stage through a systematic optimization process; 2) Phased model optimization strategy The core of the optimization strategy is to independently select the model with the smallest validation error for each stage k, directly calculate the mean absolute error (MAE) of each candidate model on the validation set, and select the model with the smallest MAE as the optimal model for that stage. The formula for selecting the model for stage k is: ； M k : The optimal model selected for the k-th stage; : The mean absolute error of model M on the validation set A in the k-th stage.

4. The method for quantitative modeling of flat wire forming parameters and forming angle based on cascaded machine learning according to claim 1, characterized in that... The S4 model was evaluated and optimized as follows: 4.1 Model Evaluation Metrics: This method uses the mean absolute error (MAE) and root mean square error (RMSE) as accuracy evaluation indicators, as shown in the following formulas: (Average absolute value) (Root Mean Square Error) : The true value of the i-th sample; : The predicted value of the i-th sample; n: The number of samples; 4.2 Comparative Analysis and Optimal Selection of Cascade Models: Using the Hold-out test method, the entire dataset was randomly divided in an 8:2 ratio; 80% of the data was used as the training set to build and train the model; the other 20% of the data was used as the test set, and the evaluation metric was calculated according to S4.

1. Random Forest leads in both MAE=0.109° and RMS=0.145°. For the second shaping angle θ2_pred, RF performs best at MAE=0.140°, and its RMSE of 0.192° is also on par with the best value, so RF is the optimal choice for this stage. For the third shaping angle θ3_pred, RF and XGBoost are tied for the best at RMSE=0.122°, while RF's MAE=0.089° is better than LightGBM=0.091°. Therefore, RF also shows the best overall performance in this stage. Based on the comprehensive analysis centered on MAE above, the final cascaded model combination determined by this method is: M1=RF, M2=RF, M3=RF.

5. The method for quantitative modeling of flat wire forming parameters and forming angle based on cascaded machine learning according to claim 1, characterized in that... The mechanism and characteristic evolution of S5 cascade molding are revealed as follows: 5.1 SHAP Importance Quantification: This method uses the SHAP method to perform interpretability analysis on the cascaded chain regression model, revealing the influence mechanism of each process parameter in the three-stage molding process; and combines the importance of Gini features with the SHAP analysis results. Test data shows that at the first forming angle θ1_pred, the crown section height h1 becomes the most critical influencing factor with an importance of 33.75%. The wire thickness h (19.95%), the second moment of the cross section I (19.24%), and the width-to-thickness ratio R (17.07%) together constitute the core feature set. The cumulative contribution of these four geometric parameters is as high as 90.01%, which verifies the fundamental and dominant role of geometric parameters in the initial forming stage. When entering the second forming angle θ2_pred, the model successfully captured the cumulative effect of the preceding deformation. The first forming angle θ1_pred ranked first with an importance of 30.19%, while the original geometric parameters such as crown segment height h1 19.09% and cross section second moment I 17.29% still maintained their influence. Most importantly, in the third forming angle θ3_pred, the model reveals a physical law: the second forming angle θ2_pred determines the final forming result with an absolute dominance of 94.94%; In the first forming angle θ1_pred stage, the model identified the fundamental dominant role of geometric parameters; wire thickness h ranked first with a SHAP importance of 0.0306; wire thickness h was negatively correlated with the first forming angle θ1_pred, indicating that for every 1 mm increase in wire thickness h, the first forming angle θ1_pred decreased by 0.0372°; the larger the second moment I of the section, the smaller the first forming angle θ1_pred; the width-to-thickness ratio R also showed a positive correlation, the larger the width-to-thickness ratio R, the larger the first forming angle θ1_pred; for the crown section height h1, for every 1 mm increase in crown section height h1, the first forming angle θ1_pred increased by 0.0064°; Entering the second forming angle θ2_pred stage, the model captures the cascading effect of the process; the first forming angle θ1_pred ranks first with a SHAP importance of 0.0374, becoming the most critical influencing factor; the first forming angle θ1_pred and the second forming angle θ2_pred are positively correlated, and for every 1° increase in the first forming angle θ1_pred, the second forming angle θ2_pred increases by 0.2803°; In the final third forming angle θ3_pred stage, the second forming angle θ2_pred achieved the first proportion with a SHAP importance of 0.0637, which is 16.3 times that of the second-ranked first forming angle θ1_pred. The second forming angle θ2_pred and the third forming angle θ3_pred are positively correlated. For every 1° increase in the second forming angle θ2_pred, the third forming angle θ3_pred increases by 0.8568°.

6. The method for quantitative modeling of flat wire forming parameters and forming angle based on cascaded machine learning according to claim 1, characterized in that... The S6 feature optimization and engineering applications are as follows: Implement differentiated data acquisition schemes, that is, ensure the measurement accuracy of high-importance features in practical applications, while using standard values ​​or estimated values ​​for low-importance features, thereby reducing data acquisition costs and complexity while maintaining high model accuracy; then use the trained high-precision cascaded model as a digital proxy model for rapid optimization of process parameters for new specification wires. By setting the allowable error of the target span or forming angle, the optimization algorithm is driven to solve the optimal bending process parameters in reverse, realizing the transformation from traditional "trial and error" machine adjustment to "predictive" adjustment, improving process development efficiency and forming quality.

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