A physical information neural network-based micro-milling machining quality index prediction rapid modeling method

Abstract

The application discloses a kind of physical information neural network-based micro-milling machining quality index prediction rapid modeling method, belong to mechanical processing quality prediction and artificial intelligence cross technical field.The method is first obtained by structured experiment design processing data, and fitting prior equation is used as experience prior, to replace the complex physical equation that needs to be derived in traditional physical information neural network;Then construct multilayer perceptron neural network, for learning the residual between the predicted value of prior equation and measured value, rather than complete nonlinear mapping relationship;Secondly, construct the double-item loss function consisting of data residual loss and configuration point regular loss, utilize configuration point to constrain the residual correction behavior of network in the whole design space, prevent overfitting in sparse area of data;The present application takes prior guidance and configuration point regular constraint as core, realizes high-precision, strong generalization machining quality index prediction under limited sample condition, modeling efficiency is high, implementation threshold is low, and by adjusting experiment design and prior equation form, can be flexibly extended to machining quality index prediction task in a variety of mechanical processing scenes.

Description

Technical Field

[0001] This invention relates to the field of interdisciplinary technology of machining quality prediction and artificial intelligence, specifically to a rapid prediction and modeling method for machining quality indicators in micro-milling, which is particularly suitable for accurate prediction of machining quality of complex micro-scale parts in fields such as aerospace, precision molds, biomedicine, and microelectromechanical systems. Background Technology

[0002] With the advancements in aerospace, precision mold making, biomedicine, and microelectromechanical systems (MEMS) fields towards miniaturization, lightweighting, and high performance, the demand for high-quality machining of complex micro-scale components continues to increase. Micromilling, characterized by its strong material adaptability, flexible forming capabilities, and high machining efficiency, is a crucial process for manufacturing complex three-dimensional microstructures. Machining quality directly impacts the service performance and reliability of parts, and accurate prediction of machining quality indicators can provide a reference for process parameter selection, quality control, and the manufacturing of high-precision micro-parts.

[0003] Existing methods for modeling processing quality indicators mainly include empirical formulas, response surface models, pure data-driven neural networks, and physical information neural networks.

[0004] Empirical formulas and response surface models have clear structures and are easy to interpret, but their expressive power is limited. They are difficult to fully describe the high-order nonlinearity, local fluctuations, and multi-factor coupling in the micro-milling process, and their prediction accuracy is limited.

[0005] Pure data-driven neural networks can fit complex nonlinear relationships, but they are prone to overfitting and generalization instability when the sample size is limited or the experimental cost is high, and the model interpretation is insufficient.

[0006] Physical information neural networks (PINs) can balance prior constraints and nonlinear fitting capabilities by incorporating mechanistic knowledge into neural network training. However, existing PIN methods still have the following shortcomings: First, modeling efficiency is low and implementation threshold is high. The micro-milling process is affected by tool geometry, material microstructure, process parameters, size effects, and local deformation behavior. Establishing a rigorous physical equation covering all influencing factors is usually difficult, requiring deep knowledge of physical mechanisms and a lengthy equation derivation process. Especially when introducing new factors, if the complete physical equation needs to be re-derived each time, it will significantly reduce modeling efficiency and engineering applicability. Second, prediction accuracy is limited under limited sample conditions. Existing physical information neural networks usually rely on a large amount of high-quality training data to achieve an accurate approximation of the physical equations. However, in micro-milling, the cost of acquiring experimental data is high and the cycle is long, and the number of samples is often limited, making it difficult for the model to fully learn complex mapping relationships. Third, the model's generalization ability is insufficient. Existing methods often lack effective constraint mechanisms in sparse regions of training samples, and the network is prone to generating excessive prediction biases without physical basis, making it difficult to guarantee the model's generalization ability and stability under small sample conditions. Fourth, hyperparameter setting depends on human experience. The key hyperparameters of existing physical information neural networks, such as network structure, learning rate, and regularization weights, are usually determined through manual trial and error or grid search, which is inefficient and highly dependent on engineering experience, making it difficult to guarantee the global optimality of model performance. Fifth, the model interpretability is poor. Pure data-driven neural networks and existing physical information neural networks are mostly black-box models, lacking explicit mathematical expressions to reveal the influence of various factors on processing quality indicators, making it difficult to meet the interpretability requirements of engineering practice. Sixth, the method architecture is closed, making it difficult to flexibly adapt to different processing scenarios. Existing methods are mostly designed for specific processing conditions or specific materials. When the processing method or influencing factors change, it is often necessary to redesign the network architecture or re-derive the physical equations, lacking the ability to universally adapt to various machining scenarios.

[0007] The aforementioned problems result in significant shortcomings in current micro-milling machining quality index prediction methods in terms of modeling efficiency, prediction accuracy, generalization ability, interpretability, and scenario adaptability. There is an urgent need for a machining quality index prediction method that can balance physical consistency with data-driven flexibility, has rapid modeling capabilities, and broad applicability. Summary of the Invention

[0008] To address the aforementioned shortcomings, this invention proposes a systematic solution from four aspects: prior model construction, residual learning network design, bivariate loss function construction, and hyperparameter adaptive optimization. This aims to solve the technical problems of existing methods for predicting micro-milling machining quality indicators, such as the need to pre-derive complex physical equations for physical information neural networks, low modeling efficiency, and difficulty in flexibly introducing new influencing factors. To achieve the above objectives, this invention adopts the following technical solution: A rapid modeling method for predicting micro-milling machining quality indicators based on physical information neural networks includes the following steps: S1: Implement experimental design and obtain modeling data. Based on the actual process requirements of micro-milling, determine the main influencing factors affecting a certain machining quality index; the modeling data includes a prior dataset for fitting the prior equation and a training dataset for training the residual network. A structured experimental design method is used to formulate a prior experimental plan and obtain a prior dataset; based on this, further full-factor or high-density experimental designs are carried out to obtain a training dataset that covers a more comprehensive design space. Micro-milling experiments are conducted according to all experimental plans, and the machining quality index value is measured to construct an original dataset containing inputs (influencing factors) and outputs (machining quality index values).

[0009] S2: Constructing an empirical prior model Using the prior dataset obtained in step S1, a prior equation is fitted to characterize the overall trend of the processing quality index as a function of various influencing factors. The model is simplified through significance testing, and insignificant terms are removed to obtain a concise prior equation.

[0010] S3: Construct residual labels and generate placement points The training dataset obtained in step S1 is divided into a training set, a validation set, and a test set according to a preset ratio. For each sample in the training set, the difference between its actual processing quality index value and the predicted value of the prior equation is used as the residual label. Simultaneously, configuration points are obtained within the design space using a spatial uniform sampling method for global constraints on subsequent model behavior.

[0011] S4: Constructing a residual learning neural network A multilayer perceptron neural network is constructed as the residual learning network. Its input layer receives influencing factors, and its output layer outputs residual correction terms. The final predicted value of the processing quality index is obtained by superimposing the predicted value of the prior equation and the residual correction terms output by the network.

[0012] S5: Constructing a bidirectional target loss function A bivariate loss function is constructed, consisting of a data residual loss term and a placement point regularization loss term. The data residual loss is used to measure the deviation between the network-corrected residual and the true residual label; the placement point regularization loss is used to constrain the residual correction amount of the network throughout the entire design space, with the regularization weight coefficient serving as a hyperparameter to be optimized.

[0013] S6: Automatic global hyperparameter optimization The set of hyperparameters to be optimized includes at least the network structure parameters, learning rate, and regularization weight coefficients. Using the prediction error on the validation set as the objective function, a global hyperparameter automatic optimization algorithm iteratively searches within a preset search space to obtain the optimal hyperparameter combination.

[0014] S7: Training the final residual correction model Based on the optimal hyperparameter combination, the multilayer perceptron neural network is retrained on the complete training set to obtain the final residual correction model.

[0015] S8: Construct a complete prediction model The final residual correction model is combined with the prior equation to form a complete processing quality index prediction model. For any given combination of influencing factors, the prior predicted value and the residual correction term are calculated sequentially, and the two are added together to obtain the final predicted value.

[0016] S9: Model Validation and Performance Evaluation The complete prediction model is validated using reserved test set data. The prediction accuracy and generalization ability of the model are comprehensively evaluated by calculating evaluation indicators such as root mean square error, mean absolute error, and coefficient of determination.

[0017] Preferably, the main influencing factors mentioned in step S1 include, but are not limited to, spindle speed, feed per tooth, and depth of cut. The structured experimental design method can be flexibly adjusted according to the changes in the influencing factors. When it is necessary to introduce new influencing factors, it is only necessary to incorporate them into the experimental design and refit the prior equations and retrain the residual network, without having to re-derive the physical equations.

[0018] Preferably, the prior equation in step S2 is a quadratic polynomial that includes a constant term, a linear term, a quadratic term, and an interaction term between factors. The insignificant terms with a significance level greater than a preset threshold are removed by analysis of variance to obtain a simplified prior equation.

[0019] Preferably, the ratio of the training set to the test set and the parameter range in step S3 both ensure effective coverage of the design space; the configuration point is used to calculate the configuration point regularization loss, and its residual correction target value is set to 0.

[0020] Preferably, the multilayer perceptron network in step S4 adopts a fully connected structure, the activation function of the hidden layer is a non-linear activation function, and the output layer adopts a linear activation function; the number of hidden layers and the number of neurons in each layer are adaptively determined by the subsequent hyperparameter optimization process.

[0021] Preferably, the data residual loss in step S5 is in the form of mean square error; the regularization loss of the placement points is the square mean of the network residual correction values ​​at each placement point; the regularization weight coefficient is used to balance the data fitting accuracy and prior consistency constraints, and its value is determined by adaptive search in the subsequent global hyperparameter automatic optimization process.

[0022] Preferably, the hyperparameter set in step S6 includes at least the number of hidden layers, the number of neurons in each hidden layer, the learning rate, and the regularization weights; the global hyperparameter automatic optimization algorithm based on the surrogate model includes, but is not limited to, a Bayesian optimization algorithm based on Gaussian processes and a sequence model optimization algorithm based on random forests for sequential iterative search.

[0023] Preferably, in step S7, an optimizer is used to update the network parameters, the model parameters are saved periodically during training, and the parameters with the smallest error on the validation set are selected as the final model.

[0024] Preferably, the verification process in step S9 further includes constructing a model containing only prior equations and a direct data-driven neural network model as a comparison benchmark to verify the superiority of the method of the present invention in terms of prediction accuracy and generalization ability.

[0025] Preferably, the method is not only applicable to the prediction of quality indicators in micro-milling, but can also be extended to the prediction of quality indicators in other machining methods. By adjusting the experimental design and the form of the prior equation, it can be adapted to different combinations of machining conditions and influencing factors.

[0026] Compared with the prior art, the present invention has the following beneficial effects: 1. Prior equations replace physical equations, significantly improving modeling efficiency. This invention uses prior equations fitted from experimental data as the source of physical constraints, replacing the complex physical equations that need to be derived in traditional physical information neural network methods. It can quickly build a predictive model without delving into the full complex physical mechanisms of surface formation. When new influencing factors need to be introduced, the model can be updated simply by incorporating them into the experimental design, refitting the prior equations, and retraining the residual network, without needing to re-derive the physical equations. Only a small amount of prior experimental data is needed to fit usable prior equations, and a finite number of samples is sufficient for complete modeling. The experimental cost is far lower than the hundreds of experiments required by traditional physical modeling methods. Furthermore, the global hyperparameter automatic optimization algorithm can complete the hyperparameter search with only a few iterations, while traditional grid search requires traversing hundreds to thousands of combinations, significantly reducing the time cost of model tuning.

[0027] 2. The explicit residual learning strategy significantly outperforms traditional methods in prediction accuracy. This invention employs an explicit residual learning strategy. The neural network learns only the residuals between the prior equation and the true values, rather than the complete mapping relationship. This significantly reduces the network output range and learning difficulty, allowing the network to focus on compensating for higher-order nonlinearities, local fluctuations, and complex coupling effects that are difficult for the prior model to express. The data residual loss term uses the mean squared error form, directly driving the network to approximate the true residual distribution. Test set validation results show that the prediction accuracy of the model in this invention is significantly better than that of pure prior models and directly data-driven neural network models, verifying the effectiveness and superiority of the residual learning strategy under limited sample conditions.

[0028] 3. The design space is constrained by the configuration point regularization constraint, significantly enhancing the generalization ability. This invention introduces a placement point regularization loss term into the loss function, using the sum of squared residual correction values ​​from spatially uniformly sampled placement points as a penalty term. This constrains the network to minimize residual corrections across the entire design space, effectively preventing excessive and physically unfounded corrections in sparse training regions, thus enhancing the model's generalization ability and stability under small sample conditions. Setting the residual correction target value for placement points to 0 ensures the dominance of the prior equation across the entire design space. Regularization weights are automatically optimized within a preset range using global hyperparameters, avoiding over-regularization or under-regularization issues caused by improper manual settings.

[0029] 4. Automatic global hyperparameter optimization significantly improves hyperparameter tuning efficiency. This invention employs a global hyperparameter automatic optimization algorithm to adaptively determine key hyperparameters such as network structure, learning rate, and regularized weights. It requires only a few iterations to search for the globally optimal hyperparameter combination, avoiding the inefficiencies and experience-dependent problems of traditional manual trial-and-error or grid search methods. The model parameters are saved after a certain number of training epochs, and the parameters with the smallest validation set error are selected as the final model, further ensuring the acquisition of a superior parameter combination.

[0030] 5. Prior equations dominate the trend, achieving both model interpretability and physical consistency. The coefficients of the prior equation have clear physical meanings. Both the coefficient of determination and the adjusted coefficient of determination indicate that the prior equation can explain the vast majority of the total variation of the target variable, providing a solid physical foundation for the model. The analysis of variance results are consistent with the physical mechanism of processing, verifying the effectiveness of the prior equation. The neural network residual correction term only compensates for local biases in the prior model without disrupting the dominant trend of the prior. The combination of these two approaches achieves a balance between physical consistency and data-driven flexibility, giving the model both clear physical interpretability and data-driven adaptive correction capabilities.

[0031] 6. The experimental design is flexible and adaptable, covering a wide range of processing scenarios. This invention is not only applicable to predicting the quality indicators of micro-milling machining, but can also be extended to predicting the surface quality of other machining methods such as milling, turning, and grinding. By incorporating new influencing factors into the experimental design, the invention's ability to flexibly introduce new influencing factors is verified. Through adjusting the experimental design and the form of the prior equations, the method of this invention can be flexibly adapted to different machining scenarios and combinations of influencing factors. Furthermore, only a small amount of prior experimental data is required to obtain effective priors, resulting in low experimental costs, high operability, and broad engineering promotion value and industrial application prospects. Attached Figure Description

[0032] Figure 1 This is a schematic diagram of the overall process of the rapid modeling method for predicting micro-milling machining quality indicators based on physical information neural networks provided in the embodiments of the present invention, showing the complete technical route of steps S1 to S9 from top to bottom.

[0033] Figure 2 The diagram below illustrates the overall architecture of the model provided in this embodiment of the invention, showcasing the "prior + residual correction" dual-branch prediction architecture and the forward propagation and backward propagation paths of data in a modular manner.

[0034] Figure 3 This is a schematic diagram of the Bayesian optimization hyperparameter adaptive search process provided in an embodiment of the present invention, illustrating the hyperparameter iterative optimization mechanism driven by the Gaussian process surrogate model and the desired improved acquisition function.

[0035] Figure 4 This bar chart compares the evaluation metrics of different prediction models provided in the embodiments of the present invention, visually demonstrating the performance of the P-RMLP model of the present invention in RMSE, MAE, and R... 2 It outperforms the RSM-only and Direct MLP models in all three metrics. Detailed Implementation

[0036] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings and specific examples. This embodiment uses the prediction of surface roughness in micro-milling of a certain metal material as an example to illustrate the present invention in detail. However, the application of the present invention is not limited to this. It is also applicable to micro-milling of other metal materials such as aluminum alloys, stainless steel, and high-temperature alloys, as well as other machining methods such as turning and grinding, and the prediction and modeling of other machining quality indicators such as machining accuracy, residual stress, and burrs. Equivalent substitutions or modifications made by those skilled in the art based on the technical solutions provided by the present invention are all within the protection scope of the present invention.

[0037] This embodiment takes the prediction of surface roughness in micro-milling as an example, and fully presents the entire process from experimental design, data acquisition, model building to verification and comparison. It proposes a rapid modeling method for predicting micro-milling quality indicators based on physical information neural networks to verify the effectiveness of the modeling method proposed in this invention, including the following steps: S1: Identify influencing factors and implement DOE experimental design. In this embodiment, three core process parameters that have the most significant impact on the surface roughness of micro-milling are selected as input variables: spindle speed n (r / min), milling depth ap (μm), and feed per tooth fz (μm / z). Meanwhile, to demonstrate the technical advantage of this invention in flexibly introducing new influencing factors, the average equivalent grain size dg (μm) of the material is included as a fourth influencing factor in the model.

[0038] To obtain the prior dataset, the D-optimal design method was used to arrange the experimental scheme. Each influencing factor was selected at three levels: high, medium, and low, and coded with the codes -1, 0, and +1.

[0039] The experiment was conducted using selected metallic material samples, and the sample surfaces were uniformly ground before the experiment. Micro-milling equipment was used, and the experiment was carried out according to the actual machining parameters corresponding to the above-mentioned coding level. After the experiment, a surface profilometer was used to measure the roughness value of the machined surface. Measurements were taken at multiple different locations for each sample, and the average value was taken as the surface roughness value of that sample.

[0040] In this embodiment, the aforementioned D-optimal experimental data serves as a prior dataset for fitting the response surface prior equation (step S2). Based on this, to fully train the residual learning network and ensure effective coverage of the design space, experiments are further conducted according to a four-factor, three-level full factorial design to construct a complete training dataset for subsequent residual label construction (step S3), network training (step S7), and hyperparameter optimization (step S6). The full factorial experimental data covers all level combinations of each influencing factor, providing sufficient training samples for the residual learning network.

[0041] S2: Fitting the prior equation of the quadratic term of the response surface Using the D-optimal experimental data obtained from S1, a quadratic equation of the response surface is fitted in the following form:

[0042] In the formula, This represents the predicted surface roughness value output by the response surface model; There are p influencing factors; For constant terms, , and These are the coefficients of the linear term, the quadratic term, and the interaction term, respectively.

[0043] After fitting, the significance of the response surface equation is tested using analysis of variance (ANOVA) to obtain the regression coefficients for each term. Based on the results of ANOVA and the significance test of the regression coefficients, insignificant terms are removed, and the model is refitted to obtain a simplified model.

[0044] It should be emphasized that this quadratic formula for the response surface does not attempt to fully characterize all the complex physical mechanisms in the micro-milling process, but rather serves as an empirical statistical prior to extract the overall trend of surface roughness as a function of various influencing factors.

[0045] S3: Construct residual labels and split the dataset The training dataset obtained in S1 is randomly divided proportionally into a training set and an independent test set. The training set is further divided into a training subset and a validation set. The training subset is used for updating residual network parameters, the validation set is used for hyperparameter evaluation and model parameter selection during the Bayesian optimization process, and the independent test set is used only for final model performance validation.

[0046] For the i-th sample in the training set, its true roughness is The response surface prior prediction value is The residual label is then defined as:

[0047] The residual label characterizes the biases that cannot be explained by the prior model of the response surface, including higher-order nonlinear effects, local fluctuations, and complex coupling effects.

[0048] To further constrain the model's behavior throughout the design space, this embodiment employs the Latin hypercube sampling method to randomly sample configuration points within the design space:

[0049] In the formula, Represents the number of configuration points; This represents the number of influencing factors. Configuration points are not included in the calculation of data residual loss; their residual correction target value is set to 0, and they are only used for the calculation of subsequent configuration point regularization loss.

[0050] S4: Constructing the MLP residual correction network The input layer of the network contains neurons corresponding to the number of influencing factors. The number of hidden layers L and the number of neurons per layer are determined by subsequent Bayesian optimization. The output layer contains one neuron and outputs the residual correction term. .

[0051] The MLP network uses a fully connected structure, and the ReLU function is selected as the activation function for the hidden layer.

[0052] The output layer uses a linear activation function.

[0053] For the i-th training sample, the forward propagation process of the MLP network is represented as:

[0054] in, represents all trainable parameters of the network; L represents the number of hidden layers. and Here, represents the weight matrix and bias vector of the Lth layer, respectively. The final predicted surface roughness value is obtained by adding the response surface prior term and the network residual correction term:

[0055] S5: Constructing a bivariate loss function The total loss function of this invention consists of two parts: a data residual loss term and a placement point regularization loss term.

[0056] Data residual loss The mean squared error (MSE) is used to measure the difference between the predicted residuals and the actual residuals of the MLP.

[0057] Where N is the number of training samples currently used for network parameter updates. Where M is the number of configuration points.

[0058] Configuration point regularization loss To constrain the residual correction amount of the MLP network within the design space to be as small as possible:

[0059] in, In this embodiment, the number of configuration points is specified. =200, For the first One configuration point, This represents the residual correction value of the MLP network at the configuration point.

[0060] The configuration point regularization loss constrains the residual correction of the network to be as small as possible throughout the entire design space (including regions without training samples), preventing the network from generating excessive and physically unfounded corrections in sparse data regions, thereby enhancing the model's generalization ability and physical consistency. In the formula, λ is the regularization weight coefficient, determined by subsequent Bayesian optimization adaptive search.

[0061] S6: Adaptive determination of MLP hyperparameters using Bayesian optimization The set of MLP hyperparameters to be optimized is defined as follows:

[0062] Where L is the number of hidden layers; This represents the number of neurons in the first hidden layer. η is the number of neurons in the second hidden layer (empty when L=1); η is the learning rate; λ is the weight of the placement point regularization loss.

[0063] The objective function of Bayesian optimization is to minimize the residual corrected mean square error on the validation set.

[0064] in, , The number of samples in the validation set.

[0065] S7: Training the final MLP residual model based on optimal hyperparameters After determining the hyperparameters and selecting the model parameters, the final MLP residual model is retrained using all the modeling data, and the retrained model parameters are used as the final model parameters. The optimal hyperparameter combination H and the final MLP residual model are output. .

[0066] S8: Construct a complete surface roughness prediction model The final trained MLP residual model is combined with the response surface prior equation to obtain a complete surface roughness prediction model:

[0067] For any given combination of process parameters x=(n,fz,ap,dg), first convert each parameter into coded values ​​according to the coding formula, and then calculate the prior prediction values ​​using the response surface prior equation. Then, the residual correction term is calculated using the MLP residual model. The sum of the two values ​​is the final predicted surface roughness value.

[0068] S9: Test Set Validation and Comparative Analysis The fully trained prediction model was validated using the test set data reserved in S3. Three comparative models were also constructed for performance comparison: (1) RSM-only model: only the response surface prior equation fitted by S2 is used for prediction, without any residual correction; (2) Direct MLP model: The MLP neural network is used directly to learn the complete mapping from input parameters to surface roughness. The response surface prior and residual learning strategies are not adopted. The network structure is also determined by Bayesian optimization (λ is not included in the optimization hyperparameters, and the loss function is only the data fitting loss). (3) P-RMLP model (this invention): response surface prior, MLP residual learning, placeholder regularization and Bayesian optimization.

[0069] This invention uses the quadratic equation of the response surface fitted from DOE experimental data as a prior, replacing the complex physical equations that need to be derived in the traditional PINN method. It allows for rapid construction of a predictive model without delving into the full complex physical mechanisms of micro-milled surface formation. When new influencing factors need to be introduced, the model can be updated simply by incorporating them into the DOE experimental design, refitting the response surface equation, and retraining the MLP residual network, without needing to re-derive the physical equations. Only a small amount of D-optimal experimental data is needed to fit a usable response surface prior equation, and a finite number of samples is sufficient for complete modeling. The experimental cost is far lower than the hundreds of experiments required by traditional physical modeling methods. Furthermore, Bayesian optimization can complete hyperparameter search with a small number of iterations, while traditional grid search requires traversing hundreds to thousands of combinations, significantly reducing the time cost of model tuning.

[0070] This invention employs an explicit residual learning strategy. The MLP learns only the residuals between the response surface prior and the true values, rather than the complete mapping relationship. This significantly reduces the network output range and learning difficulty, allowing the network to focus on compensating for higher-order nonlinearities, local fluctuations, and complex coupling effects that are difficult for the prior model to express. The data residual loss term uses mean squared error, directly driving the network to approximate the true residual distribution. Test set validation results show that the prediction accuracy of the P-RMLP model of this invention is significantly better than that of the pure RSM method and the direct MLP method, verifying the effectiveness and superiority of the residual learning strategy under limited sample conditions.

[0071] This invention introduces a placement point regularization loss term into the loss function, using the sum of squared residual correction values ​​of Latin hypercube sampling placement points as a penalty term. This constrains the residual correction amount of the MLP network to be as small as possible across the entire design space, effectively preventing the network from generating excessive and physically unfounded corrections in sparse regions of the training samples, thus enhancing the model's generalization ability and stability under small sample conditions. The residual correction target value for placement points is set to 0, ensuring the dominance of the prior equation across the entire design space. Regularization weights are adaptively searched within a preset range using Bayesian optimization, avoiding over-regularization or under-regularization problems caused by improper manual settings.

[0072] This invention employs an adaptive optimization algorithm to determine key hyperparameters such as network structure, learning rate, and regularized weights. It requires only a few iterations to search for the globally optimal hyperparameter combination, avoiding the inefficiencies and experience-dependent problems of traditional manual trial-and-error or grid search methods. The model parameters are saved after a certain number of training epochs, and the parameters with the smallest validation set error are selected as the final model, further ensuring the global optimality of the model parameters.

[0073] The coefficients of the response surface prior equations have clear physical meanings. Both the coefficient of determination and the adjusted coefficient of determination indicate that the response surface prior can explain the vast majority of the total variation in surface roughness, providing a solid physical foundation for the model. The MLP residual correction term only compensates for local biases in the prior model without disrupting the dominant trend of the prior. The combination of the two achieves a unity of physical consistency and data-driven flexibility, enabling the model to have both clear physical interpretability and data-driven adaptive correction capabilities.

[0074] This invention is not only applicable to surface roughness prediction in micro-milling, but can also be extended to the prediction of machining quality in other machining methods such as milling, turning, and grinding. By incorporating new influencing factors into the experimental design, the invention's ability to flexibly introduce new influencing factors is verified. By adjusting the DOE experimental design, the form of the response surface prior equation, and the network structure search space, the method of this invention can flexibly adapt to different machining scenarios and combinations of influencing factors. Furthermore, only a small number of D-optimal design experiments are required to obtain effective priors, resulting in low experimental costs, high operability, and broad engineering promotion value and industrial application prospects.

[0075] Those skilled in the art can make adaptive adjustments to the range of process parameters, the specific scheme of D-optimal design, the network structure search space, the number of training rounds, and the iteration convergence tolerance in each of the above steps according to the actual processing conditions, material properties, and precision requirements. All of these adjustments fall within the scope of protection of this invention.

Claims

1. A rapid modeling method for predicting micro-milling machining quality indicators based on physical information neural networks, characterized in that, Includes the following steps: S1: Implement the experimental design and obtain modeling data, which includes a prior dataset for fitting the prior equation and a training dataset for training the residual network. S2: Construct an empirical prior model and fit the prior equation using the prior dataset obtained in step S1; S3: Construct residual labels and generate configuration points. Divide the training dataset obtained in step S1 into a training set, a validation set, and a test set. Use the difference between the actual processing quality index value and the predicted value of the prior equation as the residual label, and sample configuration points in the design space. S4: Construct a residual learning neural network. Its input layer receives influencing factors, and its output layer outputs residual correction terms. The predicted value of the processing quality index is obtained by superimposing the predicted value of the prior equation and the residual correction terms. S5: Construct a bi-term loss function consisting of a data residual loss term and a placement point regularization loss term; S6: Employ a global hyperparameter automatic optimization algorithm to iteratively search for the optimal hyperparameter combination; S7: Based on the optimal combination of hyperparameters, the residual learning network is retrained on the complete training set to obtain the final residual correction model; S8: Combine the final residual correction model with the prior equation to obtain the complete prediction model; S9: Validate the complete prediction model using the test set and calculate evaluation metrics to assess prediction accuracy and generalization ability.

2. The method according to claim 1, characterized in that, The prior dataset mentioned in step S1 is obtained through structured experimental design, and the training dataset is obtained through full factorial or high-density experimental design.

3. The method according to claim 1, characterized in that, The prior equation in step S2 is a quadratic polynomial containing constant terms, linear terms, quadratic terms and interaction terms, and insignificant terms are removed by analysis of variance.

4. The method according to claim 1, characterized in that, The configuration points mentioned in step S3 are generated using a spatial uniform sampling method, and the residual correction target value of the configuration points is set to 0.

5. The method according to claim 1, characterized in that, The multilayer perceptron network described in step S4 adopts a fully connected structure, with a nonlinear activation function for the hidden layer and a linear activation function for the output layer.

6. The method according to claim 1, characterized in that, The data residual loss in step S5 is expressed in the form of mean square error, and the regularization loss of the placement points is the square mean of the network residual correction values ​​at each placement point.

7. The method according to claim 1, characterized in that, The global hyperparameter automatic optimization algorithm described in step S6 is based on a preset hyperparameter optimization space and uses an optimization algorithm based on a surrogate model to iteratively optimize the hyperparameter set; the hyperparameter set includes at least the number of hidden layers, the number of neurons in each hidden layer, the learning rate, and the regularization weights.

8. The method according to claim 1, characterized in that, In step S7, an optimizer is used to update the network parameters, and the model parameters with the smallest validation set error are selected as the final model.

9. The method according to claim 1, characterized in that, The evaluation metrics mentioned in step S9 include root mean square error, mean absolute error, and coefficient of determination; the verification process further includes constructing a model containing only prior equations and a direct data-driven neural network model as comparison benchmarks.

10. The method according to claim 1, characterized in that, The method can also be extended to predicting the processing quality indicators of other machining methods by adjusting the experimental design and prior equations to adapt to different processing conditions and combinations of influencing factors.

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