A physical information enhanced lightweight surface roughness prediction and edge deployment method based on taylor formula

Abstract

The application discloses a physical information enhanced lightweight surface roughness prediction and edge deployment method based on Taylor formula, and relates to the technical field of intelligent manufacturing and precision machining quality monitoring. The method acquires cutting parameters and target edge device resource upper limit; utilizes a global optimization algorithm to adaptively calibrate Taylor empirical physical model parameters; extracts a physical constraint feature set and explicitly introduces Taylor prediction prior features; generates virtual samples in the cutting parameter space by using linear interpolation to smooth the decision boundary; implements forced structure constraints on the extremely random tree according to the resource upper limit, and trains the tree by fusing physical features to make up for the nonlinear fitting capability; and finally extracts the model decision path, equivalently converts it into conditional branch logic code that is independent of the runtime library, and deploys it to the edge device. The application realizes microsecond-level high-precision surface roughness real-time reasoning under limited hardware resources.

Description

Technical Field

[0001] This invention relates to the field of intelligent manufacturing and precision machining quality monitoring technology, and in particular to a physical information-enhanced lightweight surface roughness prediction and edge deployment method based on Taylor's formula. Background Technology

[0002] Surface roughness is a key indicator for evaluating the quality of precision turning, and its real-time and accurate prediction is of great significance for process control. In past engineering practices, prediction has typically relied on traditional empirical physical models built based on cutting parameters. While these physical models can reflect the fundamental mechanical laws of the machining process, they are prone to prediction errors due to a lack of adaptive capability when faced with multi-physics coupling interference in actual turning.

[0003] With the development of industrial informatization, data-driven machine learning technology is increasingly being applied to machining quality prediction. These algorithms, by constructing complex network topologies, can effectively fit the nonlinear mapping relationship between cutting parameters and surface roughness. However, in actual manufacturing settings, acquiring machining data with real measurement labels is costly, and relying on small samples for training can easily lead to the model getting trapped in local overfitting.

[0004] To meet the real-time monitoring needs of production sites, predictive models typically need to be deployed directly on industrial edge devices close to the data source. These underlying microcontrollers often face physical constraints such as low clock speed and limited storage space. Conventional high-precision data-driven algorithms are complex in structure and have large runtime libraries, making them difficult to directly deploy to microcontrollers. Furthermore, the predictive logic within pure data models lacks transparency and is difficult to verify against the underlying causal laws of cutting mechanics. Therefore, how to balance the accuracy, physical interpretability, and real-time computational efficiency of roughness prediction on edge platforms with limited hardware resources has become a key technical challenge in current manufacturing monitoring. Summary of the Invention

[0005] The purpose of this invention is to provide a lightweight surface roughness prediction and edge deployment method based on Taylor formula with enhanced physical information, in order to solve the problems that high-precision surface roughness prediction models in the prior art are difficult to achieve low-latency local deployment on resource-constrained industrial edge devices, and that pure data-driven algorithms are prone to overfitting under small sample conditions and lack physical causal interpretability.

[0006] This invention provides a physically-informed, lightweight method for predicting surface roughness and deploying edges based on Taylor's formula, comprising the following steps:

[0007] S1, obtain the original cutting parameters during the precision turning process of the target, and obtain the storage space and main frequency computing resource limit of the target edge device that carries the inference calculation;

[0008] S2, based on historical processing datasets, with the goal of minimizing prediction error, uses a global search optimization algorithm to perform data-driven adaptive optimization of the parameters of the preset Taylor empirical physical model, resulting in an optimized Taylor physical model.

[0009] S3, extract cutting mechanics features to construct a multi-dimensional physical constraint feature set, wherein the multi-dimensional physical constraint feature set explicitly includes Taylor prediction prior features directly output by the optimized Taylor physical model;

[0010] S4. For the samples in the historical processing dataset, virtual training samples are generated by linear interpolation between samples in a continuous cutting parameter space to approximate the intermediate state that was not actually sampled and to smooth the decision boundary of the cutting parameter space, thereby obtaining an enhanced dataset.

[0011] S5, Model Structure Reduction and Physical Capability Compensation under Edge Resource Constraints: Based on the resource limit of the target edge device, the upper limit of the number of trees and the upper limit of the maximum depth of the extremely random tree model are forcibly constrained to construct a lightweight edge prediction model with reduced structure; the original cutting parameters in the augmented dataset are fused with the multidimensional physical constraint feature set and input into the lightweight edge prediction model for training; wherein, during the training process of tree node splitting, the Taylor prediction prior features are used to provide physical prior guidance for the splitting criteria of the lightweight edge prediction model, and by introducing physical dimension prior constraints, the nonlinear data fitting ability lost by the lightweight edge prediction model due to the forced reduction of structure is compensated;

[0012] S6. Extract the decision path of the trained lightweight edge prediction model, convert it into conditional branch nested logic code that is independent of the machine learning runtime library, and deploy it to the target edge device so as to receive real-time raw cutting parameters and output surface roughness prediction results through the target edge device.

[0013] Optionally, the preset Taylor empirical physical model defines surface roughness as a product of a power function of a material constant and various cutting process parameters;

[0014] In step S2, the differential evolution algorithm is used as the global search optimization algorithm. Through mutation, crossover and selection operators, adaptive evaluation is performed in a preset continuous search space to determine the material constant and the exponential coefficients corresponding to the depth of cut, cutting speed, feed rate, tool wear state and cutting force, respectively.

[0015] Optionally, the multidimensional physical constraint feature set constructed in step S3 is specifically composed of six-dimensional feature components, including:

[0016] The Taylor predictive prior features serve as physical prior benchmarks;

[0017] The cutting area characteristic is represented by the product of the depth of cut and the feed rate;

[0018] The material removal rate is characterized by the product of the cutting area feature and the cutting speed.

[0019] The specific cutting force characteristic, characterized by the ratio of cutting force to the cutting area characteristic, is used to eliminate the influence of the cutting area size.

[0020] Cutting power characteristics are represented by the product of cutting force and cutting speed;

[0021] And the thermo-mechanical coupling characteristics characterized by the product of tool wear state and cutting force.

[0022] Optionally, the specific implementation of generating virtual training samples in step S4 is as follows:

[0023] Two benchmark samples representing different processing experimental conditions are randomly selected from the historical processing dataset;

[0024] Generate mixing coefficients that follow a beta distribution, and based on the mixing coefficients, perform weighted summation calculations on the feature vectors of the two selected benchmark samples and the true surface roughness labels respectively;

[0025] By utilizing the inherent continuous physical laws of the cutting parameter space, the data representing the smooth and gradual change state generated by weighted summation is added to the augmented dataset as the virtual training samples.

[0026] Optionally, the specific implementation of converting the model into conditional branch nested logic code in step S6 is as follows:

[0027] Analyze the topology of each lightweight decision tree integrated in the lightweight edge prediction model;

[0028] The feature index judgment conditions and segmentation thresholds of the non-leaf nodes inside each lightweight decision tree are mapped layer by layer to the two-branch conditional jump instructions of the underlying programming language.

[0029] The roughness prediction values ​​stored in each leaf node are mapped to variable assignment statements at the end of the corresponding branch paths, and the outputs of all lightweight decision trees are hard-coded and encapsulated with average calculation logic to generate the final device executable code.

[0030] Optionally, before deployment to the target edge device, step S6 further includes a hardware-oriented fixed-point computation optimization step:

[0031] The floating-point segmentation thresholds involved in the two-branch conditional jump instructions are uniformly converted into fixed-point integer format through a left shift and rounding operation of a specific number of bits;

[0032] And while the target edge device is running the logic code to receive the raw cutting parameters in real time, the collected sensor input data is synchronously converted to fixed-point integer format to reduce the time delay of inference.

[0033] Optionally, after step S5 and before step S6, the method further includes a step of performing physical consistency anti-counterfeiting verification on the lightweight edge prediction model:

[0034] Perform physical monotonicity constraint verification: keep the non-target cutting parameters in the test input sample constant at the median value, and obtain the output response of the lightweight edge prediction model by only using a single gradually changing target cutting parameter. Verify whether the output response conforms to the positive monotonicity theory of feed rate, the negative monotonicity theory of cutting speed, and the positive monotonicity theory of tool wear.

[0035] Optionally, the physical consistency anti-counterfeiting verification step further includes performing feature sensitivity collaborative ranking verification:

[0036] The absolute influence weight of each parameter in the original cutting parameters on the output of the lightweight edge prediction model is quantified using the parameter scanning method and then sorted in descending order.

[0037] Extract the exponential coefficients of each cutting process parameter from the optimized Taylor physical model and sort them in descending order of absolute value;

[0038] By comparing the two sorting results, it is determined whether the most sensitive cutting parameter learned in the lightweight edge prediction model coincides with the theoretical dominant parameter with the largest exponential coefficient in the Taylor physical model.

[0039] Optionally, in step S5, in order to achieve the best edge resource adaptation, the upper limit of the number of trees in the lightweight edge prediction model is forcibly constrained to no more than 30 trees, and the upper limit of the maximum depth is forcibly constrained to no more than 8 layers.

[0040] Under this strong constraint, the Taylor prediction prior features rank highly in the importance evaluation of all input features, dominating the core splitting path of the decision tree nodes.

[0041] Optionally, the target edge device in step S6 is an industrial-grade microcontroller with flash memory capacity limited to megabytes and static random access memory limited to kilobytes.

[0042] The conditional branch nested logic code is directly burned and compiled into the microcontroller in the form of a C language header file, enabling real-time monitoring and inference of processing quality at the microsecond level in a purely local environment free from network bandwidth limitations.

[0043] The present invention has achieved the following beneficial effects:

[0044] This invention effectively improves the accuracy and physical interpretability of surface roughness prediction by integrating data-driven algorithms with Taylor's empirical physical formulas. A global search optimization algorithm is used to adaptively calibrate the physical model parameters and extract multi-dimensional physical constraint features, providing clear mechanical guidance for the machine learning decision-making process and compensating for the loss of fitting ability due to model simplification. An enhancement technique based on linear interpolation of continuous parameters between samples smooths the decision boundary of the cutting parameter space, improving the model's generalization performance under small sample conditions. The model is forcibly shrunk based on the resource limits of edge devices, and the decision tree topology is equivalently converted into nested conditional branch logic code at the lower level. Combined with fixed-point integer format optimization, complex runtime library dependencies and floating-point operation overhead are eliminated. This method enables lightweight deployment of the prediction model on resource-constrained microcontrollers, meeting the microsecond-level latency requirements for real-time monitoring of processing quality in industrial settings.

[0045] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the written description and the accompanying drawings.

[0046] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0047] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0048] Figure 1 A flowchart illustrating the overall steps of a physically-informed, lightweight surface roughness prediction and edge deployment method based on Taylor's formula, provided in an embodiment of the present invention.

[0049] Figure 2 A flowchart illustrating the principle of adaptive optimization of preset Taylor empirical physical model parameters provided in this embodiment of the invention;

[0050] Figure 3 A logical block diagram for the derivation and construction of a multidimensional physical constraint feature set provided in this embodiment of the invention;

[0051] Figure 4 This is a flowchart illustrating the generation of an enhanced dataset based on inter-sample linear interpolation within a continuous cutting parameter space, as provided in an embodiment of the present invention.

[0052] Figure 5 This is a schematic diagram illustrating the structural reduction and physical capability compensation training of a lightweight edge prediction model under edge resource constraints provided in an embodiment of the present invention.

[0053] Figure 6 This is an architecture diagram of the lightweight edge prediction model for decision path extraction, logic code conversion, and target edge device deployment provided in this embodiment of the invention. Detailed Implementation

[0054] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0055] This invention discloses a lightweight surface roughness prediction and edge deployment method based on Taylor's formula and enhanced physical information. The method employs a dual-branch parallel architecture, cascading and fusing physical prior knowledge with data-driven learning to achieve high-precision real-time surface roughness inference on resource-constrained target edge devices.

[0056] The overall process of the physically-informed, lightweight surface roughness prediction and edge deployment method based on Taylor's formula of this invention is as follows: Figure 1 As shown, the specific steps include the following:

[0057] Step S1: Obtain the original cutting parameters during the precision turning process of the target, and obtain the storage space and main frequency computing resource limit of the target edge device that carries the inference calculation.

[0058] In precision turning systems, the final surface roughness of a workpiece is influenced by the coupling effects of multiple physical fields, including cutting mechanics, thermodynamics, and mechanical vibration. To establish a high-precision surface roughness prediction input benchmark, it is necessary to acquire raw cutting parameters in real time, comprehensively reflecting the dynamic characteristics of the turning process, using sensor acquisition devices deployed in the machining environment. In this embodiment, the acquired raw cutting parameters specifically include five core parameters across five physical dimensions: depth of cut... Cutting speed Feed rate Tool wear condition and cutting force To provide robust data support for subsequent parameter optimization and model training, this implementation constructs a historical machining dataset containing two independent cutting experiments, totaling 612 valid machining data samples. The core variables in this historical machining dataset exhibit specific statistical distributions, which are fundamental for describing the decision boundaries of the precision turning system.

[0059] Specifically, regarding the original cutting parameters in the historical machining dataset and the surface roughness used as the prediction target... The statistical distribution characteristics are described as follows: for the depth of cut Its physical unit is millimeters. The minimum value recorded in the dataset is 0.25 mm, the maximum value is 0.80 mm, the arithmetic mean over the entire dataset is 0.45 mm, and the standard deviation is 0.198 mm. Regarding cutting speed... Its physical unit is meters per minute (m / min). The lowest value in the dataset is 310 m / min, and the highest is 390 m / min. The arithmetic mean is 350.0 m / min, and the standard deviation is 23.78 m / min. Regarding the feed rate... The physical unit is millimeters per revolution. The lowest limit of the dataset is 0.07 millimeters per revolution, the highest limit is 0.13 millimeters per revolution, the average value is 0.10 millimeters per revolution, and the corresponding standard deviation is 0.024 millimeters per revolution; for tool wear conditions... Its physical unit is millimeters. It is quantitatively characterized by the width of the wear band on the cutting edge. The minimum initial value in the dataset is 0.0 mm, the maximum wear upper limit is 0.3 mm, the average value in the entire sample is 0.063 mm, and the corresponding standard deviation is 0.108 mm. For cutting force... The physical unit is Newton, specifically referring to the main cutting force component during turning. The minimum measured value recorded in the dataset sample was 49.23 Newtons, the maximum measured value was 289.6 Newtons, the overall arithmetic mean was 136.85 Newtons, and the statistical standard deviation was 62.19 Newtons. The workpiece surface roughness is a result of the coupled response of the aforementioned cutting parameters. The physical unit is micrometers. The minimum value measured by precision instruments in the dataset is 0.142 micrometers, and the maximum value is 1.812 micrometers. The arithmetic mean of the entire sample is 0.683 micrometers, and the corresponding standard deviation spatial distribution characteristic value is 0.304 micrometers. In subsequent processing, this historical processing dataset was divided into a training sample set and a test sample set using a stratified random sampling method at a physical ratio of 8:2. The training sample set contains 489 valid samples, and the test sample set contains 123 valid samples to ensure the target variable, surface roughness, is accurately measured. The distribution trends in the two physical subsets are consistent.

[0060] Meanwhile, to achieve microsecond-level localized monitoring and response of machining quality in the production site close to the physical data source of turning operations, it is essential to clearly define the resource boundary constraints of the target edge device carrying the inference computation. In this embodiment, the target edge device is selected as an industrial-grade control microcontroller chip. This industrial-grade microcontroller chip adopts an advanced microprocessor architecture, and its hardware resource limits are subject to stringent process and power consumption constraints. Specifically, the upper limit of the target edge device's clock frequency computing resources is limited to 480 MHz, and its on-chip physical storage space is limited to megabytes of flash memory and kilobytes of static random access memory. In the specific hardware test platform, the target edge device uses an industrial-grade on-chip microcontroller suitable for industrial environments, with the specific hardware configuration parameters limited to 1 megabyte of internal flash memory and 512 kilobytes of internal static random access memory. These extremely limited hardware computing power and storage boundaries constitute the external hard boundary physical constraints for subsequent forced structural reduction of the prediction model.

[0061] Step S2, as follows Figure 2 As shown, based on historical processing datasets, with the goal of minimizing prediction error, a global search optimization algorithm is used to perform data-driven adaptive optimization of the parameters of the preset Taylor empirical physical model, resulting in an optimized Taylor physical model.

[0062] It is understandable that traditional surface roughness prediction mainly relies on pure theoretical expressions derived from ideal tool geometry. However, due to the complex interference of multiple physical fields in actual turning, such as built-up edge, plastic lateral flow of material, tool edge blunt radius, and micro-vibration of the process system, the prediction error of pure theoretical geometric models is too large. The preset Taylor empirical physical model defines surface roughness as the product of the material constant and various cutting process parameters as a power function, which can better capture the power-law sensitivity of the contribution of cutting depth, cutting speed, feed rate, tool wear state, and cutting force to surface roughness. In this embodiment, the mathematical expression of the preset generalized Taylor empirical physical model is shown in formula (1):

[0063] ;

[0064] In the above formula (1), This represents the theoretically predicted surface roughness value output by the Taylor empirical physical model, with its physical unit being micrometers; It represents a comprehensive material constant related to the characteristics of the workpiece material and the machine tool stiffness system, and is a dimensionless amplification factor; This represents the depth of cut in the original cutting parameters, with the physical unit being millimeters. This represents the cutting speed in the original cutting parameters, with the physical unit being meters per minute. This represents the feed rate in the original cutting parameters, with the physical unit being millimeters per revolution. This indicates the tool wear condition in the original cutting parameters, with the physical unit being millimeters. This represents the cutting force in the original cutting parameters, with the physical unit being Newtons. This represents the exponent coefficient of the power function corresponding to the depth of cut; This represents the exponent coefficient of the power function corresponding to the cutting speed; This represents the exponent coefficient of the power function corresponding to the feed rate; This represents the exponent coefficient of the power function corresponding to the tool wear state; This represents the exponential coefficients of the power function corresponding to the cutting force. The physical sign and absolute value of each exponential coefficient directly reflect the sensitivity of surface roughness to that specific process variable.

[0065] To facilitate the subsequent global search optimization algorithm parameter optimization calculation and avoid the computational singularity and high multiplication delay caused by the multivariate nonlinear multiplication form, this implementation method performs a natural logarithmic transformation on both sides of the expression in formula (1) before parameter optimization, transforming it into a linear logarithmic summation expression as shown in formula (2):

[0066] ;

[0067] In the above formula (2), Represented by constants The natural logarithm operator is used as the base, and the sign definitions of other physical parameters and unknown exponential coefficients are completely consistent with those in formula (1) above. Based on the fundamental laws of metal cutting dynamics and historical machining experience values, a continuous physical boundary search space range is pre-set for each coefficient to be optimized before performing global adaptive calibration: comprehensive material constants The physical search space boundary is restricted to ; the exponential coefficient corresponding to the cutting depth sensitivity The physical search space boundary is restricted to Physically, it is set to be a property that maintains a positive correlation with surface roughness; corresponding to the exponential coefficient of cutting speed sensitivity. The physical search space boundary is restricted to In a physical sense, its theoretical trend is set as a negative correlation with surface roughness; corresponding to the exponential coefficient of feed rate sensitivity. The physical search space boundary is restricted to This is used to reflect the strong positive correlation between feed rate and residual area height; the exponential coefficient corresponding to the sensitivity of tool wear condition. The physical search space boundary is restricted to ; the exponential coefficient corresponding to the cutting force-dominant sensitivity The physical search space boundary is restricted to .

[0068] Furthermore, to ensure that the Taylor empirical physical model can accurately adapt to the specific machine tool-workpiece system and eliminate the problem of low generalization due to fixed parameters caused by consulting manuals in traditional methods, this implementation uses the differential evolution algorithm as the global search optimization algorithm. By performing population initialization, mutation, crossover, and selection operator operations within a preset continuous search space, it performs data-driven adaptive iterative evolution of the above six formula parameters. During the differential evolution calculation process, minimizing the prediction error is the core guiding principle, and its optimization iteration objective is the cost loss function. The mathematical expression for is shown in formula (3):

[0069] ;

[0070] In the above formula (3), This represents a six-dimensional optimization parameter vector constructed from six unknown constants to be optimized and exponential coefficients, which satisfies... Physical matrix representation; This represents the root mean variance objective cost score of the differential evolution algorithm under the current parameter vector, and its physical unit is the same as that of surface roughness, which is micrometers. This represents the total number of samples in the historical processing dataset that participated in the calculation. In the adaptive calibration process of this implementation, the value is set to enhance the sample capacity in the dataset. This represents the physical index value of the current sample during traversal. Represents the first in the historical processing dataset The actual label measurement value of surface roughness corresponding to each physical sample, in micrometers; Indicates the first The original cutting parameter input vector corresponding to each physical sample; This represents the current decision parameter vector. Under constraints, the input vector is processed by the physical model of formula (1). The calculated theoretical prediction of surface roughness is expressed in micrometers.

[0071] Specifically, the differential evolution algorithm performs optimization on an interpolated and enhanced training sample set, sets its evolutionary population size to 20 individuals, limits the maximum number of generations to 200, and sets its mutation operator scaling factor. The value is set to 0.5, and the crossover probability of the crossover operator is... The value was set to 0.9. This differential evolution algorithm achieved stable convergence of the root mean variance of its objective cost loss function around generation 40, with a total physical computation time of 1.8 seconds. The final converged adaptive parameter optimization result shows significant differences from the empirical parameters recommended by traditional cutting theory. The specific comparison parameters and their physical interpretations are detailed below:

[0072] For dimensionless comprehensive material constants The theoretical initial setting recommended by traditional cutting manuals or literature is 3.200, while after adaptive data-driven optimization and calibration according to this invention, the optimal solution value is 9.986, with a positive physical rate of change of 212.1%. This physically characterizes the systematic positive shift in baseline surface roughness caused by the specific fundamental vibration and stiffness defects of the current turning system; regarding the depth of cut exponent coefficient... The traditional theoretical and empirical recommended value is 0.320. After global optimization, the specific value decreases by 0.050, with a change rate of negative 84.4%. The corresponding physical explanation is that, under this precision turning condition, the sensitivity of a slight increase in the depth of cut to the microscopic scratches and plastic deformation of the machined surface is significantly reduced; regarding the cutting speed exponential coefficient... The traditional initial theoretical value was -0.180, while the optimized final value was 0.011, with a rate of change of -106.0%. This change in physical parameters reveals that in the current high-speed cutting range of 310 to 390 meters per minute, further increases in cutting speed have significantly weakened and approached zero in their effect on suppressing built-up edge or smoothing the cutting zone. The response of surface roughness to cutting speed has entered a physical plateau. Regarding the feed rate exponent coefficient... The traditional initial theoretical value was 0.750, while the final value after adaptive optimization was significantly improved to 1.200, with a positive rate of change of 60.0%. This physical result is highly consistent with the second-order power law in classical cutting geometry, where the residual area height is proportional to the square of the feed rate. This fully demonstrates that the feed rate plays a decisive and absolutely dominant role in the formation of surface roughness in this precision machining system. Regarding the tool wear state index coefficient... The traditional theoretical initial value is 0.080, while the final value after optimization and calibration is -0.011, with a numerical physical change rate of -114.3%, exhibiting a weakly coupled, inverse effect in a physical sense; regarding the cutting force exponent coefficient... The traditional theoretical value is -0.120, while the optimized value is -0.016. The rate of change of the numerical physical change is negative 86.8%, which shows that the direct thermodynamic coupling contribution of the macroscopic cutting force to the microscopic surface morphology has weakened to a certain extent under high speed.

[0073] After data-driven adaptive optimization and calibration, the Taylor physical model's predicted root mean variance index recorded a physical value of 0.209 micrometers on the independent test sample set, while the classical Taylor model, which directly uses theoretical and empirical parameters from the literature, has a predicted root mean variance as high as 0.3520 micrometers. Through the adaptive optimization mechanism of this invention, the fitting error of the Taylor empirical physical model was significantly reduced by 40.7%. Although this pure physical model is limited by the fixed linear logarithmic structure of power product, and the independent determination coefficient recorded on the entire test set is only 0.5317, it cannot directly meet the sub-micrometer level industrial control prediction accuracy requirements on its own. However, its optimal exponential parameters after local workpiece-machine tool system calibration successfully lock the core causal dynamic physical laws of turning, and can provide extremely robust physical prediction prior features for subsequent machine learning algorithm splitting and discrimination.

[0074] Step S3, as follows Figure 3 As shown, cutting mechanics features are extracted to construct a multidimensional physical constraint feature set, which explicitly includes Taylor prediction prior features directly output by the optimized Taylor physical model.

[0075] To explicitly transfer classical engineering prior knowledge from the field of cutting mechanics to the data-driven model, this implementation method, based on the original five-dimensional cutting parameter input space and constitutive relations of turning dynamics, systematically extracts six dimensions of derived mechanical feature components, constructing a multi-dimensional physical constraint feature set through feature concatenation. This multi-dimensional physical constraint feature set is not an arbitrary combination of statistical features, but rather possesses a clear physical deductive basis. The specific mathematical construction formulas and actual physical descriptions of each dimension of feature components are as follows:

[0076] The first feature component is the Taylor prediction prior feature. The feature component is the surface roughness physical prediction value directly calculated by the Taylor physical model optimized in step S2, and its mathematical construction calculation formula is shown in formula (4):

[0077] ;

[0078] In the above formula (4), the values ​​of each symbol and the adaptive optimization coefficient are completely consistent with the optimal solution specified in formula (1) and step S2. The physical unit of this feature component is micrometer, which is used as the prior benchmark of the overall physical trend in the feature enhancement space.

[0079] The second-dimensional feature component is the cutting area feature. This feature component is designed to characterize the microscopic cross-sectional area of ​​the metal layer to be removed from a geometric perspective, and its mathematical construction calculation formula is shown in formula (5):

[0080] ;

[0081] In the above formula (5), This represents the physical characteristics of the derived cutting area, with the physical unit being square millimeters. Indicates the depth of cut, in millimeters; This indicates the feed rate, measured in millimeters per revolution. The size of the cutting area directly determines the microscopic length of the cutting edge and the volume of the resulting cutting deformation zone.

[0082] The third feature component is the material removal rate feature. This characteristic component represents the volume of workpiece material removed from the workpiece surface by the machine tool per unit processing time, and its mathematical construction calculation formula is shown in formula (6):

[0083] ;

[0084] In the above formula (6), This indicates the physical characteristic of material removal rate, and its physical unit is cubic millimeters per minute. Indicates the depth of cut, in millimeters; This indicates the feed rate, expressed in millimeters per revolution. This represents the cutting speed, measured in meters per minute. This characteristic component constrains the energy intake and material flow scale of the machining system from a dynamic flow perspective.

[0085] The fourth characteristic component is the specific cutting force characteristic. This feature component is specifically extracted to eliminate the interference of absolute geometric dimension changes in the cutting area on mechanical parameters. Its mathematical construction calculation formula is shown in formula (7):

[0086] ;

[0087] In the above formula (7), It represents the physical characteristic of the specific cutting force per unit cutting area, and its physical unit is Newton per square millimeter (or megapascal). This represents the physical value of the main cutting force obtained from the data collection, in Newtons; the denominator term consists of the depth of cut. With feed rate The product of these factors constitutes the cutting force characteristic. This specific cutting force characteristic eliminates the absolute force changes caused by fluctuations in feed rate or depth, and can more purely and directly reflect the fact that the workpiece material hardens or the microscopic degradation of the cutting edge sharpness occurs as the tool wears.

[0088] The fifth characteristic component is the cutting power characteristic. This characteristic component represents the total mechanical energy consumption level of the turning system per unit time under the current process conditions, and its mathematical construction calculation formula is shown in formula (8):

[0089] ;

[0090] In the above formula (8), It represents the physical characteristics of cutting power, and its physical unit is watt; This represents the cutting force, measured in Newtons (N). This represents the cutting speed, measured in meters per minute. Cutting power directly reflects the intensity of heat generation during cutting and is a core thermodynamic constraint indicator that induces an increase in physical cutting temperature.

[0091] The sixth eigencomponent is a thermo-coupling feature. This characteristic component is specifically used to quantitatively describe the nonlinear synergistic growth effect between the mechanical wear degradation of the tool flank and the cutting force feedback. Its mathematical construction calculation formula is shown in formula (9):

[0092] ;

[0093] In the above formula (9), It represents the characteristic component of thermo-coupling, and its physical dimensionless unit is millimeter-newton; Indicates the width of the tool wear condition, in millimeters; This indicates the value of the main cutting force, in Newtons.

[0094] After extracting and calculating the above six physical feature components, they are concatenated and physically spliced ​​with the five original cutting parameters obtained in step S1 to assemble and construct the eleven-dimensional enhanced feature vector as shown in formula (10). :

[0095] ;

[0096] In the above formula (10), This represents the constructed eleven-dimensional enhanced physical eigenvector; T represents the transpose operator of the physical matrix; This indicates that it belongs to an eleven-dimensional real-valued grid. By explicitly introducing derived features that incorporate the causal laws of classical mechanics, the original five-dimensional input space is expanded and enhanced into an eleven-dimensional physical feature space, which helps the integrated decision tree model perform node splitting optimization on a better feature dimension.

[0097] Step S4, as follows Figure 4 As shown, for samples in the historical processing dataset, virtual training samples are generated by linear interpolation between samples in a continuous cutting parameter space to approximate the intermediate states that were not actually sampled and to smooth the decision boundary of the cutting parameter space, thus obtaining an augmented dataset.

[0098] It is understandable that collecting real surface roughness label data on the manufacturing site incurs extremely high physical costs. To overcome the overfitting limitations imposed on machine learning models by small sample scenarios, this implementation method does not employ traditional geometric transformations targeting discrete image pixels. Instead, it fully utilizes the inherent physical continuity distribution of the cutting parameter space and introduces Mixup data augmentation technology based on linear interpolation between samples. The specific formulas for constructing and generating virtual training samples are shown in formulas (11) and (12):

[0099] ;

[0100] ;

[0101] In the above formulas (11) and (12), and This represents two baseline feature input vectors randomly and independently selected from the historical processing dataset, representing different processing experimental conditions. They each contain the corresponding original five basic cutting process parameters. and These represent the actual measured label values ​​of surface roughness corresponding to these two random reference samples, in micrometers; This represents the feature vector of the virtual training sample generated through weighted summation interpolation; This represents the corresponding weighted virtual surface roughness prediction label value, in micrometers; The mixing coefficient is a randomly generated scalar weight that is dynamically generated with each interpolation calculation. In this embodiment, the mixing coefficient... Set to obey mathematical parameter configuration The symmetric beta distribution has a random generation probability model as shown in formula (13):

[0102] ;

[0103] In the above formula (13), This represents the standard beta probability density function, whose specified shape parameters are set as follows: This parameter configuration makes the randomly generated mixing coefficients... It exhibits a strong tendency to gravitate towards the endpoints of the interval in its probability distribution. or The physical distribution characteristics of aggregation. The important guiding physical significance of this distribution characteristic in engineering practice lies in ensuring that the position of the virtual training samples derived from interpolation techniques in the parameter space is always closer in physical distance to the actually observed original baseline machining state nodes, avoiding the blind introduction of pseudo-random noise that deviates too much from the actual turning physical state in the central gap area. For specific discrete process step numerical variables such as tool wear states included in the dataset, this implementation method incorporates a decision-making selection strategy based on probability thresholds during interpolation: when the real-time generated mixing coefficients satisfy… When determining physical criteria, the tool wear status value of the first benchmark sample is directly inherited and retained; otherwise, the corresponding value of the second benchmark sample is directly adopted to ensure the physical rationality of the virtual sample in the discrete dimension.

[0104] To comprehensively and quantitatively evaluate the practical engineering contribution of the aforementioned Mixup sample space linear interpolation data augmentation technique, this implementation method conducted rigorous cross-sectional comparative tests on five different typical data processing strategies under the same baseline architecture model. The comprehensive test results are detailed below:

[0105] Without any data augmentation on the baseline, the model's mean squared error of prediction (MSE) on the independent test sample set is 0.003593, corresponding to a test coefficient of determination. The score was 0.9644, and the five-fold cross-validation mean squared error (CV-MSE), representing its physical generalization stability, was recorded as 0.006111. When the same number of virtual samples were generated using a traditional boundary augmentation strategy, the physical value of the mean squared error (MSE) on the test set decreased by 0.003393, and its test determination coefficient was [missing data]. A slight improvement was observed at 0.9663, representing a positive 5.57% improvement in mean squared error accuracy compared to the untreated baseline. However, the corresponding cross-validation mean squared error (CV-MSE) deteriorated significantly to 0.021312 due to boundary noise. When traditional smoothing and optimized sample space sampling techniques (such as SMOTE regression enhancement) were introduced, the measured mean squared error (MSE) of the test set was 0.003345, and the test determination coefficient... The mean squared error (MSE) was 0.9668, representing a positive improvement of 6.91%, with a corresponding five-fold cross-validation stability index (CV-MSE) of 0.004659. When using the Mixup continuous spatial linear interpolation data augmentation scheme proposed in this invention, the model exhibited optimal technical performance, with a reduction of 0.003229 in the prediction mean squared error (MSE) recorded on the test set, and a test coefficient of determination (CCO). The boosted performance was 0.9680, achieving a positive mean squared error improvement contribution of up to 10.14% compared to the untreated baseline, and its five-fold cross-validation mean squared error (CV-MSE) remained robustly at an excellent level of 0.009017; while the hybrid strategy constructed by mechanically combining multiple interpolation strategies showed a prediction mean squared error (MSE) of 0.003430 in the test, and the test determination coefficient was... The score was 0.9660, with a mean squared error improvement of only 4.54 percent, and the cross-validation mean squared error (CV-MSE) was 0.007820.

[0106] Through the detailed test data comparison above, it can be clearly deduced that the Mixup interpolation data augmentation technology based on the continuous physical laws of cutting parameters adopted in this invention has a significant performance advantage over traditional pure feature augmentation methods such as SMOTE. The core constitutive mechanism of this advantage lies in the fact that the surface roughness response function in the turning physical system is essentially a continuous sliding surface that spans the boundaries of continuous parameters such as cutting speed and feed rate. The Mixup strategy of this invention performs synchronous linear physical weighted interpolation on the input feature space vector and the output response label, which essentially approximates a large number of objectively existing but not yet physically sampled intermediate gradual machining conditions, thereby smoothly correcting the sharp waveforms of overfitting that are prone to occur in the cutting parameter space under small sample constraints. This makes the model have stronger extrapolation accuracy on the unseen test set. Through this data augmentation step, the final output is an augmented dataset consisting of 489 original training samples and 100 high-quality virtual training samples, which is used for the subsequent training of the core machine learning prediction model.

[0107] Step S5, as follows Figure 5As shown, this paper illustrates the model structure reduction and physical capability compensation under edge resource constraints: Based on the resource limit of the target edge device, the upper limit of the number of trees and the upper limit of the maximum depth of the extremely random tree model are forcibly constrained to construct a lightweight edge prediction model with a reduced structure; the original cutting parameters in the augmented dataset are fused with the multidimensional physical constraint feature set and input into the lightweight edge prediction model for training; wherein, during the training process of tree node splitting, the Taylor prediction prior features are used to provide physical prior guidance for the splitting criteria of the lightweight edge prediction model, and by introducing physical dimension prior constraints, the nonlinear data fitting ability lost by the lightweight edge prediction model due to the forced reduction of structure is compensated.

[0108] To ensure the trained data-driven algorithm can be perfectly integrated and run smoothly on target edge devices limited by the kilobyte and megabyte hardware physical limits specified in step S1, extremely stringent physical structural simplification must be applied to the machine learning model during the initial training phase. In this embodiment, the core skeleton of the regression predictor is an Extra Trees model. When constructing its internal ensemble decision tree nodes, the Extra Trees model uses a completely randomized approach to divide feature segmentation thresholds, significantly reducing prediction variance under small sample conditions and mitigating overfitting oscillations compared to traditional random forests and other algorithms. To implement an extremely lightweight strategy to adapt to the hardware, this embodiment rigidly constrains the total number of trees in the Extra Trees model to no more than 30 decision trees, and rigidly constrains the maximum compression split depth of each individual decision tree topology to no more than 8 layers.

[0109] Understandably, the highly randomized tree model is essentially a nonlinear regression prediction network assembled from multiple independent decision trees in a parallel ensemble. The integrated first-order decision tree in its topology... Any non-leaf split node inside a lightweight decision tree The local discriminant splitting mathematical decision rule can be formally described explicitly using a two-branch conditional jump instruction as shown in formula (14):

[0110] ;

[0111] In the above formula (14), This represents the eleven-dimensional augmented feature vector of the input; This represents the physical index number of the segmentation feature assigned to the current splitting node after random selection, and its value is limited to a range of natural numbers. ; This represents the real-time numerical input corresponding to that specific feature index; This represents the preset single-precision floating-point segmentation threshold stored in the current non-leaf split node; This represents the memory pointer address pointing to the left child node of the next level; This represents the memory pointer address pointing to the right-hand sub-topology node of the next level. When faced with arbitrary input feature vectors, this lightweight, highly randomized tree ensemble system ultimately performs an average hard-coded encapsulation of the surface roughness to output a predicted value. The mathematical composition formula is shown in formula (15):

[0112] ;

[0113] In the above formula (15), This represents the final predicted surface roughness value output by the extremely random tree system, with its physical unit being micrometers. This represents the upper limit of the total number of integrated lightweight decision trees. Under the strong constraints of this invention, the physical value is rigidly limited to 30. This represents the scalar value of the current decision tree traversal index; Indicates the first Each individual topological regression tree sequentially passes through the branches of formula (14) based on the feature vector input, and then outputs and stores the local prediction of surface roughness at the leaf node it finally reaches.

[0114] To determine the scientific rationale for using an extremely random tree as the core predictor, this implementation method conducted a comprehensive benchmark evaluation of 18 mainstream data-driven machine learning algorithms within the same eleven-dimensional extended feature enhancement space. The detailed performance data of the top 5 classic prediction models are disclosed below:

[0115] The algorithm used in this invention, the Extra Tree (Extremely Random Tree), ranked first in all benchmark evaluations, achieving a full-precision test determination coefficient on the independent test set. The performance score was 0.9703. In extreme anti-interference tests where the workpiece was severely disturbed by up to 15% Gaussian noise, its mean square error (MSE) was only 0.0263. After multi-physical factor weighting, the overall performance score was 0.9319. Furthermore, its model topology can directly extract feature importance, demonstrating high interpretability. The second-ranked algorithm was the nearest neighbor (KNN) regression algorithm, which achieved a test determination coefficient measured on an independent test sample set. The coefficient of determination (COP) was 0.9704. Although it was statistically almost identical to the extremely random tree in a noise-free state, its mean squared error (MSE) rapidly deteriorated to 0.0310 in robustness tests with 15% Gaussian sensor noise interference, resulting in a physical conversion score of 0.8850. Furthermore, it lacked internal physical causal mapping capabilities, leading to a low level of interpretability. The third-ranked algorithm was the traditional Random Forest ensemble, with a COP of 0.9704 in the full-accuracy test. The performance index was 0.9683, the mean square error (MSE) under 15% noise perturbation was 0.0391, and the total score converted to an Equation of Performance was 0.6950, demonstrating a high level of performance in the interpretability dimension. Ranking fourth was the Lightweight Gradient Boosting Machine (Light GBM) decision model, whose measured test determination coefficient was... The performance index was 0.9190, with a corresponding mean square error (MSE) of 0.0499 and a total score of 0.7090, indicating a moderate level of interpretability. At the bottom of the top five was a one-dimensional convolutional neural network (1DCNN) deep learning model, whose test determination coefficient on the full-precision test set was... With a score of only 0.8260, and a noise error (MSE) of 0.1000 under 15 percent Gaussian perturbation, its total score is 0.9130, and its multi-layered black box architecture results in extremely low interpretability.

[0116] The comprehensive and multi-dimensional algorithm evaluation data above demonstrates that the highly randomized tree model, while ensuring extremely high nonlinear prediction accuracy, exhibits a significant technological leap in robustness against sensor random noise compared to KNN or neural networks. This provides crucial protection for real-time monitoring applications in industrial workshops where severe cutting vibration and noise interference exists.

[0117] Next, to precisely quantify the accuracy-saving effect of the physical capability compensation mechanism proposed in this invention on the lightweight model after forced structural reduction, this embodiment specifically designed four integrated configurations at different spatial complexity levels and conducted rigorous ablation science experiments. Detailed comparison data of the accuracy performance of each ablation configuration on the test set are disclosed below:

[0118] Under configuration A with extremely low model space complexity (which imposes a strict limit on the total number of decision trees to 10 and a maximum tree split depth constraint of 5 layers), the test decision coefficient achieved by a purely data-driven baseline model without any physical feature engineering is [not specified]. The coefficient of determination for the physical feature-enhanced model is only 0.7241, while after explicitly cascading and incorporating the six-dimensional physical constraint feature set of this invention for physical capability compensation, the predictive determination coefficient is significantly higher. The jump was 0.7831, with an improvement in absolute accuracy of 8.15 percent. The significance statistical weight value obtained from the two-population heteroscedasticity hypothesis test was... The coefficient of determination was 0.023, reaching a statistically significant level. Under the final configuration B selected as the core deployment in this invention (with a strict hard constraint limiting the total number of decision trees to 30 and the maximum topological depth of the trees to 8 layers), the test determination coefficient was obtained from a pure data-driven regression baseline model without using physical derivation terms. The index is only 0.8812, which cannot break through the 90% accuracy threshold required for industrial quality monitoring. However, by injecting a multi-dimensional physical constraint set, including features such as Taylor priors, into the invention for compensation and to provide physical prior support, the surface roughness prediction test determination coefficient of this lightweight model is improved. Significant performance improvement was achieved, with a final numerical increase of 0.9502. The absolute improvement in accuracy was a positive 7.82%, and the corresponding heteroscedasticity test showed significance. The value represents a highly significant level, less than 0.001; in configuration C with further relaxed complexity (setting the total number of decision trees to 50 and the maximum split depth to 10 layers), the corresponding test determination coefficient of the non-augmented data-driven baseline model is... The recorded value was 0.9579, while the corresponding model prediction determination coefficient after applying physical feature enhancement was 0.9579. The improvement was 0.9696, and the absolute improvement in accuracy was positive 1.22%, as measured by the significance test. The value is 0.004; while in a heavy configuration D with an extremely complex structure and without any edge volume reduction (where the decision tree population size is set to 80 trees, and the maximum depth is allowed to split to 12 levels), the test determination coefficient of the pure data-driven regression model is 0.004. The coefficient of determination for the final test of the physical feature-enhanced model is 0.9690. The numerical value is 0.9705, at which point the marginal improvement in precision narrows to only 0.16 percent, and its significance test is... The value is 0.035.

[0119] Based on the deep-seated nonlinear diminishing returns physical law revealed by the above four sets of ablation experiment test data, it can be seen that the physical constraint feature engineering based on cutting mechanics designed in this invention has the most significant nonlinear compensation and efficiency enhancement value for lightweight edge prediction models with high resource constraints where the volume is rigidly reduced. When the model is forcibly constrained to an extremely low spatial capacity of 30 trees and 8 layers due to the upper limit of external edge hardware resources, the simple parameter memory capability of the data-driven part shows a serious deficiency. At this time, the adaptive optimized Taylor physical prediction prior features directly output by this invention... and specific cutting force characteristics The mechanics-derived terms, inherently containing the deep causal determinant laws of the cutting system, directly serve as the core physical coordinate guide for the dominant splitting path in the low-dimensional tree node splitting discrimination process. This allows the originally mediocre lightweight 30-tree configuration (with a file size of only 56.9KB) to exhibit superior nonlinear fitting accuracy, almost comparable to a heavyweight 80-tree complex configuration (with a file size as high as 154KB and far exceeding the edge flash memory limit). This implementation ultimately locks configuration B (30 trees, maximum depth 8 layers, physically enhanced) as the final edge prediction model instance.

[0120] To further conduct a rigorous industrial engineering feasibility assessment of the final locked physical information-enhanced lightweight model, this implementation introduces a factor of determination. Root mean variance and mean absolute error The multi-physics index system, including the comprehensive performance of the lightweight integrated predictor on 123 independent unseen test sample sets, was statistically summarized. The mathematical evaluation index is defined and calculated as follows: Formula (16), Formula (17) and Formula (18) are shown in sequence:

[0121] ;

[0122] ;

[0123] ;

[0124] In the above formulas (16), (17) and (18), This represents the total capacity of valid validation samples in the independent test set, with a physical value set to 123. Indicates the biased physical traversal index of the test sample; Indicates the first test in the independent test set The actual surface roughness of a workpiece is precisely measured using a label, with the unit being micrometers. The value represents the final predicted surface roughness calculated by the physical enhancement lightweight model using formula (15), in micrometers. The value represents the arithmetic mean center of the actual measured surface roughness labels for all surfaces in the test set, with a statistically significant physical value of 0.683 micrometers. The final macroscopic performance data of the lightweight prediction model, obtained based on the above physical evaluation index system, is summarized and disclosed below:

[0125] The final model of this invention recorded the overall coefficient of determination on the full test sample set. The numerical stability is 0.9502, indicating that the lightweight algorithm is capable of successfully explaining 95.02% of the nonlinear evolution of the total variance of the precision-turned surface roughness system; its final measured root mean variance of the prediction full set is... The physical value was recorded as 0.0709 micrometers; the corresponding mean absolute error (MAE) was as low as 0.0495 micrometers; the maximum absolute prediction error limit recorded in the entire set of test samples was successfully capped within 0.2813 micrometers; the effective working prediction range of the final model fully covered the ultra-wide machining range of surface roughness from 0.172 micrometers to 1.723 micrometers. Considering that the average state of the target variable in this precision turning is as high as 0.683 micrometers, the final root mean variance physical error accounts for only a very low percentage of the machining mean, which demonstrates solid sub-micrometer level engineering application feasibility in the field of industrial precision machining quality control.

[0126] Furthermore, to ensure that the model does not generate counterintuitive predictive responses that violate fundamental physical laws when running inference in an entity-edge environment, this implementation rigorously verifies the monotonicity of the physically enhanced lightweight model. The specific monotonicity verification mechanism is as follows: four variables out of the five basic process parameters—depth of cut, cutting speed, feed rate, and tool wear state—are kept constant at their historical midpoint values. Only the remaining target process variable is allowed to undergo continuous gradient incremental scanning within its legal machining physical range. The proportion of step points violating the theoretical classical monotonicity constraints in the lightweight model's output prediction curve is statistically analyzed. Detailed verification data for the physical monotonicity constraints of all five basic parameters are disclosed below:

[0127] For feed rate parameter The theoretical expectation of monotonicity from metal cutting physics is strong positive monotonicity, meaning that an increase in feed rate inevitably leads to a significant increase in residual height. The actual response of the lightweight model when faced with a feed rate gradient scan exhibits a standard positive monotonic increasing waveform, with a monotonicity violation rate of only 2.0% recorded across the entire range, resulting in a physical consistency pass rating. Regarding the cutting speed parameter... The classical theory of cutting mechanics predicts a weakly negative monotonicity or a plateau, meaning that increasing the cutting speed helps reduce surface roughness by suppressing built-up edge. The actual predicted response curve of the lightweight model exhibits a gently decaying weakly negative monotonicity, with a monotonicity violation rate of 4.1% within its interval. The physical consistency assessment result is satisfactory. Regarding the depth of cut parameter... Theoretically, the expected monotonicity is weakly positive monotonicity, meaning that increased cutting depth leads to increased radial force, resulting in a slight deterioration of the surface morphology. The actual response test curve of the lightweight model exhibits a positive monotonicity upward waveform. The monotonicity violation rate across the entire range was measured to be 6.1%, and the physical consistency judgment result was satisfactory. Regarding the tool wear state parameters... The theoretically presupposes a clear positive monotonicity, meaning that the wider the wear band on the cutting edge and the rougher the surface micro-scratches, the more pronounced the physical prediction response of the lightweight model. The actual physical prediction response exhibits a positive monotonicity with a step-like increasing response, corresponding to a monotonicity violation rate of 9.1%. The physical consistency judgment result is "compliant and passed." However, regarding the main cutting force parameters... The initial theoretical expectation given by metal cutting dynamics is positive monotonicity. However, in the continuous parameter scanning test of the lightweight model of this invention, its output curve shows a reverse weak negative monotonicity characteristic response. The corresponding physical monotonicity violation rate index across the entire range increases to 19.2%, and the physical consistency judgment result is ultimately marked as non-compliant.

[0128] For the main cutting force The aforementioned anomalous phenomena that do not conform to monotonicity are addressed in this embodiment through a deep analysis of the multi-field coupling mechanism of cutting. The underlying physical principle is explained as follows: In the actual precision turning sample data distribution, the main cutting force, as a dynamic derivative physical characteristic, exhibits a very strong intrinsic thermodynamic multi-field positive coupling relationship with cutting speed, feed rate, and severe tool wear at the statistical level. When a massive main cutting force approaching 290 Newtons is collected in actual machining, it is often accompanied by an even higher cutting speed or an extreme abnormal machining condition already in the late stage of deep wear. This results in a very strong physical collinearity constraint between the cutting force and other basic process variables within the high-dimensional topological feature space of multi-dimensional cutting parameters. When the verification program of this invention performs a single-variable manual parameter scan, it forcibly locks the cutting speed and tool wear at the median value, while artificially extrapolating the input main cutting force from 50 Newtons to approximately 290 Newtons over a large range. This effectively causes the input feature vector to slip out of the data flow manifold boundary of the actual turning sample, thereby triggering local nonlinear bias in the model. The emergence of this nonlinear bias precisely confirms, at the dynamic level, the specific cutting force characteristic extracted in step S3 of this invention. and thermo-coupling characteristics The physical necessity of it.

[0129] Next, to further achieve collaborative anti-counterfeiting control across feature dimensions, this implementation method uses the parameter scanning perturbation method to calculate and quantify the sensitivity index of the contribution of five basic cutting parameters to the final predicted output of the lightweight model. The dimensionless mathematical quantification formula for this sensitivity score is shown in formula (19):

[0130] ;

[0131] In the above formula (19), Indicates the first The normalized model decision sensitivity index score corresponding to each basic original cutting parameter; This represents the total number of discrete process step sampling grid points artificially divided within the parameter scanning interval; Indicates the physical index of the step sampling; This represents the baseline predicted surface roughness value output by the model when the target parameters are in the initial grid state of the interval, in micrometers. This indicates that the objective independent variable evolves stepwise to the nth step. When there are physical grid points, the predicted values ​​of the dynamic response of surface roughness output sequentially by the lightweight prediction model are in micrometers. This represents a scalar measure of the average relative physical rate of change of the predicted surface roughness over the entire scanning interval. It is a sensitivity index calculated from the various parameters. A descending physics-level queuing was performed, and a three-way cross-dimensional collaborative comparison was conducted with the arrangement matrix of the unknown exponent absolute values ​​of the Taylor physics model optimized in step S2, and the tree node information entropy feature importance score matrix of the extremely random tree itself. The specific results of each ranking tier are disclosed as follows:

[0132] In the Taylor physics model's descending order of exponential absolute values, the feed rate exponent's absolute value occupies the most dominant position. The rankings from second to fifth place are based on the absolute value of the depth of cut index. Absolute value of cutting force index Absolute value of cutting speed index and the absolute value of the tool wear index In the descending order of the model prediction sensitivity ranking matrix of the lightweight extremely random tree model, the measured sensitivity distribution hierarchy is sequentially represented by the feed rate. Absolute dominance (sensitivity index score normalized to 1.0), depth of cut Ranked second (score normalized to 0.48), main cutting force Ranked third (score normalized to 0.45), cutting speed Ranked fourth (score normalized to 0.19) and tool wear condition Ranked fifth (score normalized to 0.0); and in the core importance score matrix of the extremely randomized tree ensemble, the ranking of the importance of the eleven-dimensional features is also clearly shown as the feed rate. It occupies the most dominant position (feature importance-specificity score as high as 0.403), even higher than the physical feature of cutting force. Occupying the second key position (importance score of 0.180), Taylor predicts prior features. It occupies the third core splitting position (importance score of 0.177), followed by cutting force. (Score 0.049), Cutting speed (Score 0.045), Cutting Power (Score 0.040), Cutting area (Score 0.026), Tool Wear Condition (Score 0.025), thermo-coupling characteristics (Score 0.021), Material removal rate (Score 0.018) and depth of cut (Score 0.017).

[0133] Through the lateral perspective collaboration of the above three-way sorting matrices, it can be seen that the most sensitive process variable (feed rate) learned by the physically enhanced lightweight machine learning algorithm constructed in this invention is... The system achieves 100% complete overlap with the theoretical dominant parameter with the largest absolute value of the exponent in the Taylor empirical physical formula, and the three-dimensional matrix exhibits a completely consistent symmetrical physical manifold trend in the sensitivity ranking of all five subsequent process variables. Furthermore, due to the introduction of six derived physical features, such as the specific cutting force, derived from classical cutting mechanics, the cumulative feature importance score of these six engineering physical features in the final decision of the lightweight model reaches a significant proportion of 46.2%. This detailed and highly collaborative feature sensitivity anti-spoofing comparison data fully demonstrates that the lightweight extremely random tree system of this invention, by ingesting a multi-dimensional physical constraint set, has successfully internalized and reproduced the intrinsic mechanical causal chain of precision turning in a low-capacity tree network topology. Its predictive behavior has a strong physical rationality foundation, completely eliminating the safety risks of pure black-box overfitting.

[0134] Step S6, as follows Figure 6As shown, the decision path of the trained lightweight edge prediction model is extracted, and it is equivalently converted into conditional branch nested logic code that is independent of the machine learning runtime library. This code is then deployed to the target edge device to receive real-time raw cutting parameters and output surface roughness prediction results.

[0135] To completely resolve the sharp obstacle of traditional Python language training models being unable to be directly deployed and run on low-level embedded control chips such as hardware microcontrollers due to the lack of environment library support, this implementation method performs a complete rewrite and deconstruction of the low-level control code of the highly randomized tree integration system containing 30 lightweight decision trees trained and optimized in step S5. The specific conversion logic is as follows: the complete decision path experienced by each lightweight regression tree from the root leaf node to each terminal leaf node is extracted by the parsing program, and the feature index logic of non-leaf nodes and floating-point segmentation threshold are converted into standard low-level conditional jump instructions. In order to eliminate the floating-point pipeline multiplication and division time delay accumulated in the target control microprocessor by multi-layer nested If-Else floating-point comparison operations, this implementation method performs a complete fixed-point integer shift optimization for the entire set of decision topology vectors at the code generation level before code burning and compilation. The mathematical rounding execution formula for this fixed-point conversion is shown in formula (20):

[0136] ;

[0137] In the above formula (20), This represents the segmentation threshold for any single-precision floating-point node extracted from the original extremely random tree model. , or represent single-precision floating-point cutting parameter feature values ​​that are captured in real time by physical sensor acquisition devices, and their physical units are different according to the feature definition; This represents a signed 32-bit fixed-point signed integer in Q16.16 standard format, fully adapted to lossless fast shift calculations of microcontrollers, generated after this optimization step. This represents the standard zero-bias nearest neighbor integer truncation operator; (i.e., the decimal constant 65536) represents the physical left shift factor for fixed-point processing. Using this formula, all floating-point segmentation thresholds originally included in the model are... And the discrimination and comparison boundaries are all uniformly rewritten and encapsulated into a pure fixed-point integer format without floating-point overhead. At the same time, in the C language main control code deployed at the edge, the sensor input cutting parameters (such as real-time cutting force signals) acquired in real time by external sensors through analog-to-digital conversion are synchronously converted into Q16.16 fixed-point integer format using formula (20). This allows the microcontroller to completely break free from the delay of the floating-point arithmetic unit when executing the branch jump comparison of formula (14) in the subsequent process, and can instantly complete the discrimination of the condition jump instruction in a single-cycle hard core displacement and subtraction instruction in a 32-bit general-purpose integer register.

[0138] To comprehensively examine the feasibility and resource optimization gains of the aforementioned hardware-oriented low-latency fixed-point reconfiguration strategy on a physical microcontroller platform, this implementation method conducted comprehensive programming and compilation tests on an STM32H743 microcontroller unit (with a maximum clock speed of 480 MHz and 1 megabyte of on-chip flash memory) for four additional tree models under different physical configurations. The complete set of detailed edge deployment feasibility and technical performance comparison data is disclosed below:

[0139] When using a purely data-driven, heavy-duty configuration D (containing 80 decision trees, with a maximum split depth of 12 layers) for native programming deployment without any physical feature engineering, although its test decision coefficient on the host computer shows... The performance coefficient is 0.9690. However, due to its massive decision tree topology, the static C header file model generated after compilation is as large as approximately 154KB. Although this size can theoretically be squeezed into the 1MB flash memory limit, its dense floating-point multi-layered If-Else nested logic generates significant hardware instruction pipeline branch prediction failure penalty overhead when running inference at a 480MHz clock frequency. The measured single-inference latency is as high as 126 microseconds, posing a very high risk of stability overclocking in industrial high-speed cutting real-time control applications. When using the heavy configuration D (80 trees, maximum depth 12 layers, physically enhanced version) with enhanced physical features of this invention to perform the burning test, although it achieved the highest test decision coefficient on the host computer. However, its static compiled model size remains at a heavy size of 154KB, and the physical hardware single inference latency is measured at 119 microseconds, resulting in significant resource and time overhead, which is not conducive to the coordinated scheduling of other on-chip multitasking operations. When using a purely data-driven lightweight configuration B (containing 30 decision trees, with the maximum split depth strictly constrained to within 8 layers) that has undergone forced structural reduction but has not used any physical compensation for burning, due to the significant reduction in the size of the trees, the size of the compiled static code model is greatly reduced to only 56.9KB, and the physical hardware test single inference latency is reduced to an extremely low 74 microseconds, demonstrating excellent deployment capabilities. However, as disclosed in the ablation experiment data of step S5, its test decision coefficient on the test set is low. The accuracy dropped significantly to 0.8812, which is completely unacceptable in terms of technical performance indicators. Due to the severe lack of accuracy, it loses its practical application feasibility in physical precision manufacturing workshops. However, when the core technical route finally determined by this invention is adopted, namely, a lightweight configuration B (30 trees, maximum depth of 8 layers, physically enhanced fixed-point version) with deep superposition of the above-mentioned multi-dimensional physical constraint feature set cascade compensation and Q16.16 fixed-point shift optimization, based on the strong constraint structural reduction of the model structure, is used to perform the final microcontroller programming, compilation and deployment, the size of the final device executable code file generated after compilation remains robustly at an ultra-lightweight level of 56.9KB. This perfectly and sufficiently passes the physical limit of the on-chip microcontroller's kilobyte-level static random access memory and megabyte-level flash memory. The nonlinear prediction test determination coefficient recorded on the host computer is also high. The model maintained a robust performance at a high level of 0.9502, and thanks to the full hardware shift acceleration of the Q16.16 fixed-point instructions, the average single-entity inference latency was as low as 89 microseconds in the microcontroller chip physical operation test at 480MHz, successfully keeping it within the ultra-fast real-time baseline of 100 microseconds.

[0140] To further clarify the technological position of the Physical Information Enhanced Lightweight Machine Learning Prediction Method (PIML) proposed in this invention within the overall manufacturing technology landscape, this embodiment compares the multidimensional physical cascade method of this invention with three existing conventional surface roughness prediction methods in terms of full-accuracy prediction coefficients. A macro-level methodological test comparison was conducted across three technical dimensions: edge hardware deployment feasibility, and physical causal interpretability. The comprehensive technical performance comparison data is summarized and disclosed below:

[0141] The first conventional method is the traditional Taylor empirical power formula calculation method. However, when faced with real-world, highly variable turning sample data, it cannot handle complex nonlinear dynamic deviations, resulting in a low coefficient of determination for the entire set of tests. The first approach, exhibiting an extremely low coefficient of determination (COP) of 0.53, demonstrates exceptionally high edge computing and deployment capabilities due to its simple formula and high level of physical interpretability. However, its extremely low prediction accuracy renders it impractical for industrial production. The second conventional method is purely data-driven conventional machine learning algorithms (such as heavy-duty random forests or KNN without physical features). While these algorithms can leverage big data to automatically capture nonlinear waveforms and achieve relatively high COPs of determination (0.92 to 0.97) on the test set, they are not widely adopted. However, to maintain this accuracy, it must unrestrainedly expand the tree group size or store massive grid samples, leading to a dramatic increase in model size and latency overhead. Its deployment capability on resource-constrained platforms such as microcontrollers is moderately limited. Furthermore, its complex black-box network completely severs the causal mapping with classical cutting mechanics, resulting in extremely low physical interpretability. The third conventional method is cutting-edge deep learning (such as one-dimensional convolutional neural networks (CNNs) combined with long short-term memory networks (LSTMs)) multi-layered, heavily topological models. However, under the constraint of small-sample manufacturing site datasets, these models are prone to local overfitting oscillations, and the measured test set determination coefficients... The performance degradation of the index is poor, ranging from 0.82 to 0.89. Furthermore, its massive backpropagation matrix and millions of floating-point weight parameters place extremely high demands on the underlying hardware computing power, resulting in very low feasibility for deployment on conventional industrial microcontroller platforms. Additionally, the decision paths of the internal hidden layers are not intuitively understandable to the average person, leading to very low physical interpretability. The fourth method, the Physical Information Enhanced Lightweight Surface Roughness Prediction Method (PIML) based on Taylor's formula proposed in this invention, achieves a robust technical test determination coefficient of 0.95 by performing data-driven differential adaptive optimization and systematically extracting six-dimensional mechanical causal constraints. Even with a forced reduction of the tree network size to 30 trees and a file size of only 56.9KB, it remains hardware-friendly and achieves a high coefficient of determination. The performance demonstrates the highest hardware deployment feasibility rating of less than 100 microsecond real-time inference on an industrial-grade microcontroller chip, while ensuring submicron-level precision machining control prediction accuracy. Furthermore, through the perfect collaborative docking of multiple sensitivity descending teams in step S5, it exhibits high-level physical interpretability that can be intuitively trusted by industrial field engineers, achieving comprehensive methodological optimization and balance across three key technical dimensions.

[0142] In summary, through rigorous and complete data flow between the aforementioned steps and the underlying hardware instruction-level execution guarantee built by Q16.16 fixed-point optimization, the present invention's Taylor-based physical information-enhanced lightweight surface roughness prediction and edge deployment method successfully resolves the technical conflict between high prediction accuracy, small sample size constraints, and low hardware computing power capacity limitations of edge devices in the cutting-edge field of intelligent manufacturing. In actual automated turning machining environments, this industrial microcontroller edge device, programmed with 56.9KB of ultra-lightweight code, receives raw turning process parameters reported by the front-end acquisition device in real time via standard field industrial communication bus interfaces such as USB-UART. In a purely local physical environment, completely independent of any external network bandwidth or cloud-based control computing power, it instantaneously calculates and outputs accurate localized prediction results for workpiece micro-surface roughness with an ultra-high execution frequency of less than 89 microseconds for a single inference iteration. This provides reliable and industrially compliant technical support for online closed-loop quality monitoring and closed-loop adaptive process parameter optimization in precision turning operations.

[0143] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A lightweight surface roughness prediction and edge deployment method based on Taylor's formula with enhanced physical information, characterized in that, Includes the following steps: S1, obtain the original cutting parameters during the precision turning process of the target, and obtain the storage space and main frequency computing resource limit of the target edge device that carries the inference calculation; S2, based on historical processing datasets, with the goal of minimizing prediction error, uses a global search optimization algorithm to perform data-driven adaptive optimization of the parameters of the preset Taylor empirical physical model, resulting in an optimized Taylor physical model. S3, extract cutting mechanics features to construct a multi-dimensional physical constraint feature set, wherein the multi-dimensional physical constraint feature set explicitly includes Taylor prediction prior features directly output by the optimized Taylor physical model; S4. For the samples in the historical processing dataset, virtual training samples are generated by linear interpolation between samples in a continuous cutting parameter space to approximate the intermediate state that was not actually sampled and to smooth the decision boundary of the cutting parameter space, thereby obtaining an enhanced dataset. S5, Model Structure Reduction and Physical Capability Compensation under Edge Resource Constraints: Based on the resource limit of the target edge device, the upper limit of the number of trees and the upper limit of the maximum depth of the extremely random tree model are forcibly constrained to construct a lightweight edge prediction model with reduced structure; the original cutting parameters in the augmented dataset are fused with the multidimensional physical constraint feature set and input into the lightweight edge prediction model for training; wherein, during the training process of tree node splitting, the Taylor prediction prior features are used to provide physical prior guidance for the splitting criteria of the lightweight edge prediction model, and by introducing physical dimension prior constraints, the nonlinear data fitting ability lost by the lightweight edge prediction model due to the forced reduction of structure is compensated; S6. Extract the decision path of the trained lightweight edge prediction model, convert it into conditional branch nested logic code that is independent of the machine learning runtime library, and deploy it to the target edge device so as to receive real-time raw cutting parameters and output surface roughness prediction results through the target edge device.

2. The method according to claim 1, characterized in that, The preset Taylor empirical physical model defines surface roughness as a product of a power function of a material constant and various cutting process parameters. In step S2, the differential evolution algorithm is used as the global search optimization algorithm. Through mutation, crossover and selection operators, adaptive evaluation is performed in a preset continuous search space to determine the material constant and the exponential coefficients corresponding to the depth of cut, cutting speed, feed rate, tool wear state and cutting force, respectively.

3. The method according to claim 1, characterized in that, The multidimensional physical constraint feature set constructed in step S3 is specifically composed of six-dimensional feature components, including: The Taylor predictive prior features serve as physical prior benchmarks; The cutting area characteristic is represented by the product of the depth of cut and the feed rate; The material removal rate is characterized by the product of the cutting area feature and the cutting speed. The specific cutting force characteristic, characterized by the ratio of cutting force to the cutting area characteristic, is used to eliminate the influence of the cutting area size. Cutting power characteristics are represented by the product of cutting force and cutting speed; And the thermo-mechanical coupling characteristics characterized by the product of tool wear state and cutting force.

4. The method according to claim 1, characterized in that, The specific implementation method for generating virtual training samples in step S4 is as follows: Two benchmark samples representing different processing experimental conditions are randomly selected from the historical processing dataset; Generate mixing coefficients that follow a beta distribution, and based on the mixing coefficients, perform weighted summation calculations on the feature vectors of the two selected benchmark samples and the true surface roughness labels respectively; By utilizing the inherent continuous physical laws of the cutting parameter space, the data representing the smooth and gradual change state generated by weighted summation is added to the augmented dataset as the virtual training samples.

5. The method according to claim 1, characterized in that, The specific implementation method for converting the model into conditional branch nested logic code in step S6 is as follows: Analyze the topology of each lightweight decision tree integrated in the lightweight edge prediction model; The feature index judgment conditions and segmentation thresholds of the non-leaf nodes inside each lightweight decision tree are mapped layer by layer to the two-branch conditional jump instructions of the underlying programming language. The roughness prediction values ​​stored in each leaf node are mapped to variable assignment statements at the end of the corresponding branch paths, and the outputs of all lightweight decision trees are hard-coded and encapsulated with average calculation logic to generate the final device executable code.

6. The method according to claim 5, characterized in that, Before deployment to the target edge device, step S6 further includes a hardware-oriented fixed-point computation optimization step: The floating-point segmentation thresholds involved in the two-branch conditional jump instructions are uniformly converted into fixed-point integer format through a left shift and rounding operation of a specific number of bits; And while the target edge device is running the logic code to receive the raw cutting parameters in real time, the collected sensor input data is synchronously converted to fixed-point integer format to reduce the time delay of inference.

7. The method according to claim 1, characterized in that, After step S5 and before step S6, the method further includes a step of performing physical consistency anti-counterfeiting verification on the lightweight edge prediction model: Perform physical monotonicity constraint verification: keep the non-target cutting parameters in the test input sample constant at the median value, and obtain the output response of the lightweight edge prediction model by only using a single gradually changing target cutting parameter. Verify whether the output response conforms to the positive monotonicity theory of feed rate, the negative monotonicity theory of cutting speed, and the positive monotonicity theory of tool wear.

8. The method according to claim 7, characterized in that, The steps of the physical consistency anti-counterfeiting verification also include performing feature-sensitive collaborative sorting verification: The absolute influence weight of each parameter in the original cutting parameters on the output of the lightweight edge prediction model is quantified using the parameter scanning method and then sorted in descending order. Extract the exponential coefficients of each cutting process parameter from the optimized Taylor physical model and sort them in descending order of absolute value; By comparing the two sorting results, it is determined whether the most sensitive cutting parameter learned in the lightweight edge prediction model coincides with the theoretical dominant parameter with the largest exponential coefficient in the Taylor physical model.

9. The method according to claim 1, characterized in that, In step S5, in order to achieve the best edge resource adaptation, the upper limit of the number of trees in the lightweight edge prediction model is forcibly constrained to no more than 30 trees, and the upper limit of the maximum depth is forcibly constrained to no more than 8 layers. Under this strong constraint, the Taylor prediction prior features rank highly in the importance evaluation of all input features, dominating the core splitting path of the decision tree nodes.

10. The method according to claim 1, characterized in that, The target edge device in step S6 is an industrial-grade microcontroller with flash memory capacity limited to megabytes and static random access memory limited to kilobytes. The conditional branch nested logic code is directly burned and compiled into the microcontroller in the form of a C language header file, enabling real-time monitoring and inference of processing quality at the microsecond level in a purely local environment free from network bandwidth limitations.

Images