Feature fusion and refining embedding sparse Bayesian learning method and system for robot curved surface milling contour error monitoring

Abstract

The invention belongs to the technical field of robots, and discloses a feature fusion and refining embedding sparse Bayesian learning method and system for robot curved surface milling contour error monitoring, and the method comprises the steps: carrying out the structural fusion of feature vectors composed of technological parameters, robot rigidity, cutting force and tracking errors into a dictionary matrix; and a sparse Bayesian learning method is combined to realize robot processing error monitoring. During model training, the posterior distribution of the weight variables can be obtained, and the expectation and variance of the posterior distribution of the weight coefficients are estimated by maximizing the posterior probability. Wherein the variance and the hyper-parameter influencing the weight sparsity are estimated by maximizing an edge likelihood function, that is, optimization is carried out by the expectation of a joint likelihood function under maximized weight posterior distribution, and the minimum value solution can be solved for the converted loss function to optimize the hyper-parameter. The posterior expectation and variance of the model weight and the hyper-parameter are iteratively updated in the training process, and the iteration process is terminated according to a set change threshold value so as to realize the sparsification of the model weight vector and the construction of the sparse model. According to the method, robot milling error monitoring of curved surface parts with different features under the variable poses is achieved, and the part measurement cost is effectively reduced.

Description

Technical Field

[0001] The present invention belongs to the field of robot technology, and in particular relates to a feature fusion and refinement embedded sparse Bayesian learning method and system for robot surface milling contour error monitoring. Background Art

[0002] Complex curved surface parts are widely used in aerospace, shipbuilding, nuclear power and other manufacturing fields. The machining trajectory planning of such parts is complex, the load changes frequently during the cutting process, and the coupling of multiple error source factors affects the final machining accuracy. Therefore, the monitoring of machining errors is of great significance for high-precision machining of products and optimization of process parameters.

[0003] Compared with traditional CNC machine tools, industrial robots with serial joints have the advantages of large workspace, high flexibility, strong integrated scalability and good economy, and are gradually applied to the milling and polishing of complex curved parts. However, due to the low stiffness of the robot, it is very easy to flutter under the milling force, resulting in significant force-induced deformation. Under the disturbance of cutting force, the robot control system may produce robot joint servo errors. In addition, factors such as robot linkage and assembly errors can also cause geometric errors of the robot. Combining the above factors, during the robot milling process, undesirable material removal will occur between the workpiece and the tool, resulting in significant contour errors. The rapid prediction and compensation of robot machining errors is an important research topic in machining state monitoring and control.

[0004] The method of predicting machining errors by calculating and simulating the mechanism model is usually complex to model and time-consuming to simulate, and is not suitable for industrial sites with complex working conditions. Many researchers have combined data-driven algorithms to predict the surface roughness and posture of parts, but there is less research on machining error monitoring. Error monitoring methods provide more accurate and faster machining error information. Some scholars have also achieved the prediction and monitoring of thin-walled parts machining errors through statistical methods, but fewer error influencing factors have been considered. The existing machining error prediction model based on deep learning cannot meet actual needs due to its high model complexity and poor real-time performance.

[0005] Therefore, there is an urgent need for a rapid prediction method for machining errors that comprehensively considers the sources of robot machining errors and can monitor the machining errors of the robot under variable working conditions based on the physical quantities of the machining process.

[0006] Through the above analysis, the problems and defects of the prior art are as follows:

[0007] The existing deep learning-based machining error prediction model cannot meet actual needs due to its high model complexity and poor real-time performance. Summary of the invention

[0008] In view of the problems existing in the prior art, the present invention provides a feature fusion and refinement embedded sparse Bayesian learning method and system for robot surface milling contour error monitoring.

[0009] The present invention is implemented as follows: a feature fusion and refinement embedded sparse Bayesian learning method and system for robot surface milling profile error monitoring includes:

[0010] S1, according to the proposed processing parameters, the robot air cutting motion and milling experiments of different processing tasks are carried out, and the joint angle, acceleration signal and cutting force signal are collected at the same time, and the processing error of the workpiece after milling is measured;

[0011] S2, processes and calculates the original signal collected in S1 to obtain the feature vector of the model input, and uses the measured processing error as the model label;

[0012] S3, performs feature weighting and feature fusion on the feature vectors calculated in S2 to construct a dictionary matrix;

[0013] S4, establishing a regression prediction model based on the dictionary matrix and processing error obtained in S3;

[0014] First, it is assumed that the weights between the model input features and labels satisfy the Gaussian prior distribution to promote most coefficient weights to approach 0 and achieve the sparsity of the model weights; according to the Bayesian formula, the posterior distribution of the weight variables is obtained, and the expectation and variance of the posterior distribution of the weight coefficients are estimated by maximizing the posterior probability; the variance and the hyperparameters that affect the sparsity of the weights are estimated by maximizing the marginal likelihood function, that is, maximizing the expectation of the joint likelihood function under the posterior distribution of the weights to optimize, and the minimum solution of the transformed loss function can be found to optimize the hyperparameters; the posterior expectation and variance of the model weights, as well as the hyperparameters are iteratively updated during the training process, and the iterative process is terminated according to the set change threshold to achieve the sparsification of the model weight vector and the construction of a sparse model.

[0015] Furthermore, in step S1, air cutting motion and milling experiments of parts with different processing positions and surface features are carried out according to the designed processing trajectory and process parameters; an acceleration sensor is pasted on the main shaft, and the acceleration and cutting force signals during the milling process are collected through the dynamometer system and the data acquisition system, and the angles of each joint of the robot during the processing are obtained through the robot open data acquisition system, and the workpiece after milling is scanned using a structured light camera to measure the processing error.

[0016] Furthermore, in step S2, the process parameters such as the spindle speed, feed rate and cutting depth of the robot milling experiment are used as static input features of the error monitoring model.

[0017] The robot end stiffness is calculated from the joint stiffness, Jacobian matrix and joint angle:

[0018] K S =J -T (q)K q J -1 (q)

[0019] Where J is the Jacobian matrix, q is the joint angle, and K S and K q are the Cartesian stiffness matrix and joint stiffness respectively; the joint stiffness vector is expressed as: K q =diag(K q1 ,K q2 ,K q3 ,K q4 ,K q5 ,K q6 ), K qi represents the stiffness of the i-th joint, K q Is a 6×6 diagonal matrix, each diagonal item represents the robot joint stiffness; the diagonal matrix K S The first three values ​​represent the three static stiffnesses in the Cartesian coordinate directions. Recorded as

[0020] The difference in tool tip position is taken as the end tracking error of the robot under cutting force disturbance and is expressed as:

[0021] δ tracking =k m (p cutting )-k m (p idlecutting )

[0022] Where k m is the calibrated kinematic model, p cutting and p idlecutting Represent the joint angles of the robot during cutting and empty cutting respectively; the calculated tracking error value is weighted and used as the input feature of the error monitoring model

[0023] Prediction of cutting force migration;

[0024] For the collected original signals of acceleration, cutting force and joint angle, the non-cutting segment data is first removed, and downsampling and timing alignment operations are performed. The relationship between the robot joint angle, acceleration signal and cutting force is characterized as follows:

[0025]

[0026] Among them, k represents the current time, Fa (k) represents the cutting force at the current moment, q1(kj), q2(kj), q3(kj), q4(kj), q5(kj), q6(kj), a(kj), (j=0,1,...,n) represent the angles and acceleration signals of each joint at the previous moment and the current moment; F a (kj), (j = 1, 2, ..., l) represents the predicted cutting force value at the previous moment, n and l represent the time lag order related to the input and output, respectively, f represents the nonlinear relationship between the input and output, and a data-driven model is used to construct f; during model training, the time-series aligned data is converted into multidimensional data according to the above formula;

[0027] The feature extractor is defined as follows:

[0028]

[0029] where F ES is the deep feature expression contained in the extracted input time series signal, A feature extractor representing the source data; x s is the input source data sample, represents the feature extractor parameters;

[0030] The extracted source domain features are then input into the regressor to predict the cutting force, and the output dimension is 1; the regression loss of the regressor is as follows:

[0031]

[0032] where n s is the number of source samples, Represents the calculation of mean square error (MSE): represents the regressor parameters;

[0033] Based on the kernel embedding theory of conditional distribution, a conditional distribution embedding calculation operator is proposed to measure the difference in conditional probability distribution; for O X and O Y The variables X and Y, the corresponding reproducing kernel Hilbert space (RKHS) is and By embedding p(Y|X) into RKHS, the conditional mean embedding can be defined as:

[0034]

[0035] where ψ(x): And φ(Y): and yes The operator characterizes the characteristics of the conditional distribution. When a fixed x is taken, a conditional mean embedding value μ is obtained. Y|x ;

[0036] According to the calculation formula of conditional probability distribution, it is equal to the ratio of joint probability distribution to marginal probability distribution of input; the conditional embedding operator calculation can be defined as the combination of cross covariate operator and independent covariate operator:

[0037]

[0038] When given a data set D = {(x1,y1),(x2,y2),...,(x n ,y n )}hour, The estimated value of can be defined as follows:

[0039]

[0040] Where F=(φ(y1),φ(y2),...,φ(y n )), and is the Gram matrix of the variable sample, with a regularization term added to ensure it is well-posed;

[0041] A conditional distribution embedding operation is designed to estimate the difference between conditional probability distributions; it is defined as follows and used as the loss function for network parameter update to minimize domain differences.

[0042]

[0043] The matrix K XX' Calculation using Gaussian kernel κ:

[0044] K XX' (i,j)=κ(X i ,X j ')= <f(X i ),f(X j ')>

[0045] Where <·,·> represents the vector inner product;

[0046] The conditional embedding distribution difference is calculated using the new features formed by the second fully connected layer of the target pose unlabeled input data features, the predicted value of the regression network, the new features formed by the second fully connected layer of the source pose data features and their label values. The conditional embedding distribution difference is calculated by using the new features formed by the second fully connected layer of the unlabeled input data features, the predicted value of the regression network, the new features formed by the second fully connected layer of the target pose labeled data features and their label values.

[0047] The target domain has labeled data prediction values ​​and their label values ​​to calculate regression loss It can be calculated as:

[0048]

[0049] For the training of the feature extractor of the target data and the task-specific regressor, the following weighted integrated loss function is used for parameter update:

[0050]

[0051] in, is the regression loss of labeled data in the target domain, Represents the difference in conditional distribution measure between source domain data and target domain unlabeled data, represents the difference in conditional distribution between labeled and unlabeled data in the target domain, α s and β t is a trade-off parameter;

[0052] The network is trained by minimizing the target posture regression loss and the difference between the two conditional embedding distributions, and the optimizer is used to update the network parameters. After the iteration, the cutting force prediction model of the target posture is obtained:

[0053]

[0054] Adaptive variational mode decomposition (AVMD) is used to extract time-frequency domain features, which can realize adaptive optimization of the decomposition level K and the penalty factor γ, and improve the performance of cutting force feature extraction. The decomposition level is set according to experience, and the cross-correlation spectrum index (CSI) is used to realize adaptive optimization of the penalty factor, which is described as follows:

[0055]

[0056] Where T is the length of the original signal, i and j are the ordinal numbers of the intrinsic mode functions, and u i and u j is the sub-signal decomposed by the AVMD method; for each penalty factor γ within the set range, the VMD method is used to decompose the original signal, and then its CSI is obtained according to the above formula; the penalty factor corresponding to the minimum CSI value is selected as the optimal value; the original signal is decomposed into several sub-component signals, and the time-frequency domain features are extracted using energy entropy The energy of each sub-signal is calculated as:

[0057]

[0058] The energy entropy of the sub-signal is given by:

[0059]

[0060] Where r i =R i / R is the percentage of each sub-signal energy to the total signal energy.

[0061] Furthermore, in step S3, the tracking error of the robot end under the influence of the cutting force describes the position deviation of the robot end under the action of the cutting force, which is most closely related to the contour error of the final machined workpiece;

[0062] Divide the error value into multiple intervals with fixed width; count the number of error values ​​in each interval and calculate the probability p of each interval i , that is, the number of samples in the interval divided by the total number of samples; the resulting probability distribution can describe the frequency of different error ranges; the information entropy is calculated after discretization:

[0063]

[0064] Among them, n is the number of intervals after discretization, p i is the probability of the i-th interval; the larger the information entropy value, the more dispersed the distribution of the feature and the higher the uncertainty;

[0065] The weight of each column of tracking error values ​​is set to a combination of information entropy and variance ratio:

[0066]

[0067] Among them, α H and β ζ is a parameter that controls information entropy and variance weight; N t The number of feature columns representing the tracking error. The information entropy measures the uncertainty of the tracking error value in each column. The variance measures the discreteness of the tracking error in each column. The weighted method combining the information entropy and variance can more comprehensively measure the importance of the feature.

[0068] Select multiple measurement points at equal distances on each trajectory to form a label data set for the prediction model;

[0069] For the robot end stiffness, cutting force characteristics and weighted tracking error characteristics obtained above, a structured feature row vector is constructed in combination with the machining parameters The feature vectors of multiple samples constitute a feature matrix, and then the feature matrix is ​​normalized to eliminate the influence of large differences in the magnitude of different features;

[0070] The Gaussian kernel distribution can be expressed as:

[0071]

[0072] Where σ is the bandwidth of the Gaussian kernel, which is optimized using a random search algorithm; is the feature row vector. For the regression model of feature fusion and physical knowledge embedding, the feature vector is mapped by kernel function to obtain a feature kernel dictionary matrix with Gaussian distribution. The dictionary matrix is ​​configured as a structured sorting of static features and dynamic features according to the order of measurement points, which not only reflects the trend of the features but also avoids the overlap of feature signals. The feature kernel dictionary matrix Φ is expressed as:

[0073]

[0074] The processing error can be expressed as follows:

[0075] y m =y p +ε;y p =Φω

[0076] Where y m is the measured processing error, y p is the prediction of machining error, ε is the prediction noise caused by uncertainty in machining and measurement; Φ is the constructed dictionary matrix, and ω is the corresponding weight coefficient, which can be expressed as:

[0077] ω=[ω1,ω2,...,ω M-1 ,ω M ,b] T .

[0078] Further, in step S4, a regression prediction model is established according to the dictionary matrix and processing error obtained above; the sparse Bayesian learning method introduces sparsity based on the idea of ​​Bayesian theorem, and assumes Gaussian prior distribution for weights, which can greatly reduce model redundancy and improve computational efficiency, model generalization ability and interpretability; the probability distribution of noise variables can be assumed to be a normal probability density function ε~N(0,λI), where λ is the variance, which is affected by the processing uncertainty caused by vibration and cutting heat and the measurement uncertainty; y m The likelihood function is defined as:

[0079]

[0080] A Gaussian prior distribution is introduced on the weight vector to make most of the weight coefficients approach zero and realize the sparsity of the weight vector. In this way, the processing error can be predicted only by the relevant columns in the dictionary matrix and the corresponding sparse weights, which improves the computational efficiency. Usually, in order to calculate the homogeneous analytical solution of the posterior, the prior distribution is the conjugate prior of the likelihood function, that is:

[0081]

[0082] where ξ i Impact i The probability of approaching zero is used to control the sparsity of the weight coefficient, reduce the complexity of the model, and avoid overfitting. According to the Bayesian formula, the posterior distribution of the weight variable can be expressed as:

[0083]

[0084] In the formula, Λ=diag{ξ1,ξ2,...,ξ N} and P(y m |λ,Λ) represents the marginal distribution of the measured processing error, and N is the number of weights. The posterior expectation and variance of the weight coefficient are estimated by finding the maximum value of the posterior probability, which is expressed as:

[0085] μ ω =λ -1 ∑ ω Φ T y m

[0086] ∑ ω =λ(Φ T Φ+λΛ -1 ) -1

[0087] Then, the hyperparameters λ and Λ are optimized by maximizing the marginal likelihood function. For the convenience of calculation, the logarithm of the likelihood function is taken, i.e., logP(y m |λ,Λ); the optimization of marginal likelihood is equivalent to maximizing its lower bound, the weighted posterior distribution P(ω|y m ,λ k ,Λ k ) can be expressed as:

[0088]

[0089] The above operations can generate the following loss function:

[0090]

[0091] The optimization problem can be solved by making the partial derivative of the loss function with respect to the hyperparameters equal to zero, and the hyperparameters λ and Λ can be updated as follows:

[0092]

[0093] Among them <·> i represents the entry of the ith vector, <·> iirepresents the item in the i-th row and i-th column of the matrix; during the iteration process, when the 1-norm of the weight vector || μ ω When the relative change between ||1 ​​and the standard deviation of the predicted noise and the value of the previous iteration is less than the set threshold for multiple consecutive times, the model is judged to be converged; at this time, the model weights are sparse enough, the noise prediction tends to be stable, and the model prediction performance and reliability are high; the convergence condition is expressed as:

[0094]

[0095] in is the set convergence threshold.

[0096] Another object of the present invention is to provide a feature fusion and refinement embedded sparse Bayesian learning system comprising:

[0097] The acquisition module is used to perform robot air cutting motion and milling experiments for different processing tasks according to the planned processing parameters, and collect joint angles, acceleration signals and cutting force signals at the same time, and measure the processing error of the workpiece after milling.

[0098] The processing module is used to process and calculate the collected original signal to obtain the characteristic vector of the model input, and use the measured processing error as the model label;

[0099] A fusion module is used to perform feature weighting on the calculated feature vectors and perform feature fusion to construct a dictionary matrix;

[0100] A module is established to establish a regression prediction model based on the obtained dictionary matrix and processing errors.

[0101] Another object of the present invention is to provide a computer device, comprising a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the feature fusion and refinement embedding sparse Bayesian learning method.

[0102] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, enables the processor to perform the steps of the feature fusion and refinement embedding sparse Bayesian learning method.

[0103] Another object of the present invention is to provide an information data processing terminal, which is used to implement the feature fusion and refinement embedded in the sparse Bayesian learning system.

[0104] In combination with the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solutions to be protected by the present invention are as follows:

[0105] First, the present invention relates to a feature fusion and refinement embedded sparse Bayesian learning method and system for robot surface milling profile error monitoring. The feature vectors composed of process parameters, robot stiffness, cutting force and tracking error are structured and fused into a dictionary matrix, and the robot processing error monitoring is realized in combination with the sparse Bayesian learning method. Robot milling experiments of different characteristic surface parts under variable postures are carried out, and the robot joint angles, robot spindle acceleration signals and cutting force signals are collected during the cutting process, and the part processing errors are used as labels to construct a data set. The robot end stiffness is calculated by combining the joint stiffness with the Jacobian matrix, and the cutting force is predicted by combining the monitored acceleration and joint angle with the deep migration network. The predicted cutting force is aligned with the processing position point in time and space, and then the time domain, frequency domain and time-frequency domain feature extraction are performed, and the principal component analysis is performed to achieve redundant dimension reduction. After the robot kinematic parameters are calibrated, the end tracking error under the cutting force disturbance is calculated using the joint angles collected under empty cutting and cutting, and unsupervised global feature weighting is performed. The feature matrix constructed by process parameters, robot end stiffness, cutting force characteristics and weighted tracking error characteristics is normalized, and kernel function mapping is performed to achieve feature fusion. Combined with the dictionary matrix and processing error, a regression prediction model is established. First, it is assumed that the weight between the model input feature and the label satisfies the Gaussian prior distribution to promote most coefficient weights to tend to 0 and achieve the sparsity of the model weight. According to the Bayesian formula, the posterior distribution of the weight variable can be obtained, and the expectation and variance of the posterior distribution of the weight coefficient are estimated by maximizing the posterior probability. The variance and the hyperparameters affecting the sparsity of the weight are estimated by maximizing the marginal likelihood function, that is, maximizing the expectation of the joint likelihood function under the posterior distribution of the weight to optimize, and the minimum solution of the converted loss function can be obtained to optimize the hyperparameters. The posterior expectation and variance of the model weights, as well as the hyperparameters are iteratively updated during the training process, and the iterative process is terminated according to the set change threshold to achieve the sparseness of the model weight vector and the construction of a sparse model. The present invention realizes the robot milling machining error monitoring of different characteristic surface parts under variable posture, effectively reducing the part measurement cost.

[0106] The purpose of the present invention is to provide a feature fusion and refinement embedded sparse Bayesian learning method and system for robot surface milling profile error monitoring, which fuses the feature vectors composed of machining process parameters, robot stiffness at the machining position, cutting force characteristics and tracking error characteristics into a dictionary matrix, and constructs a sparse Bayesian regression model to predict robot milling machining errors. It reduces the measurement requirements for workpieces with variable feature surfaces in new postures, and greatly reduces the experimental and measurement costs.

[0107] The method proposed in the present invention uses process parameters, robot stiffness information, cutting force signal and tracking error to monitor the processing error, and realizes the monitoring of processing errors at different positions of the robot and on variable feature surfaces. The stiffness of the robot end is calculated by combining the joint angle collected by the internal sensor during the processing with the Jacobian matrix, and the cutting force is predicted by the acceleration. The installation of the sensor does not affect the processing operation of the robot. It is simple and convenient to use, highly economical, and has the potential to be promoted to actual industrial applications.

[0108] The method proposed in the present invention utilizes a data-driven model to establish a mapping relationship between process parameters, robot stiffness, cutting force, tracking error and machining error, without the need for a complex parameter identification process or compensation strategy.

[0109] The method proposed in the present invention adopts a sparse Bayesian learning algorithm and utilizes machining physical quantities to realize machining error monitoring at different positions of the robot and on variable feature surfaces, thereby reducing the need for measuring parts and thus reducing measurement and time costs.

[0110] Second, the expected benefits and commercial value of the technical solution of the present invention after transformation are:

[0111] The existing method uses sensors or equipment such as scanners or three-coordinate measuring machines to measure the machining errors of complex curved surface parts, which is relatively expensive and its performance is also limited by the size and surface characteristics of the parts. Moreover, complex curved surface parts need to be measured after machining, which makes it difficult to measure them on the machine. After the technical solution of the present invention is transformed, the physical signals in the robot milling process are used to indirectly reflect the machining errors of complex curved surface parts. The machining errors are monitored using process parameters, robot stiffness information, cutting force signals and tracking errors, realizing the machining error monitoring of different positions of the robot and variable feature surfaces. The stiffness of the robot end is calculated by combining the joint angle collected by the internal sensor during the machining process with the Jacobian matrix, and the cutting force is predicted by the acceleration. The installation of the acceleration sensor does not affect the robot machining operation. It is simple and convenient to use, highly economical, and has the potential to be promoted to actual industrial applications. It has the potential to replace commercial sensors and equipment such as scanners and three-coordinate dynamometers for machining error measurement, thereby reducing machining costs and increasing revenue.

[0112] The technical solution of the present invention overcomes technical prejudice: the field of machining error monitoring technology to which the present invention relates currently has problems such as the high prices of commercial sensors and equipment such as scanners and three-coordinate dynamometers used, and certain limitations in usage scenarios. The technical solution proposed by the present invention establishes a mapping relationship between process parameters, robot stiffness, cutting force, tracking error and machining error through a data-driven model, without the need for a complex parameter identification process or compensation strategy. For mass production in actual industrial sites, the trained model can be used to accurately monitor machining errors. It breaks through technical prejudice and is a new machining error monitoring method and monitoring process. The technical prejudices overcome include the simplification of complex process flows, the reduction of machining and measurement costs, and the improvement of machining operation safety and reliability of use. BRIEF DESCRIPTION OF THE DRAWINGS

[0113] Figure 1 It is a flow chart of the feature fusion and refinement embedding sparse Bayesian learning method provided by an embodiment of the present invention.

[0114] Figure 2 It is a structural block diagram of the feature fusion and refinement embedded sparse Bayesian learning system provided by an embodiment of the present invention.

[0115] Figure 3 It is a schematic diagram of the basic method flow provided by an embodiment of the present invention.

[0116] Figure 4 It is a robot kinematics model diagram provided by an embodiment of the present invention.

[0117] Figure 5 1 is a diagram of a robot kinematic parameter calibration experimental platform provided in an embodiment of the present invention.

[0118] Figure 6 It is a comparison diagram of position errors before and after calibration provided by an embodiment of the present invention.

[0119] Figure 7 It is a curved workpiece drawing designed according to a scaled-down part of an aircraft engine casing provided by an embodiment of the present invention.

[0120] Figure 8 It is a diagram of a robot milling and data acquisition system provided by an embodiment of the present invention.

[0121] Fig. 9 This is a diagram of an error measurement experiment of a robot processing a part provided in an embodiment of the present invention.

[0122] Fig.10 It is a stiffness distribution diagram of the robot end at different measurement points provided by an embodiment of the present invention.

[0123] Fig.11 It is a tracking error distribution diagram under three processing tasks designed according to an embodiment of the present invention.

[0124] Fig.12 It is a comparison chart between the predicted and measured cutting force values ​​of BT3 in Task B provided in an embodiment of the present invention.

[0125] Fig.13 It is a comparison chart between the predicted value and the measured value of the cutting force of CT1 in Task C provided in an embodiment of the present invention.

[0126] Fig.14 It is a processing flow chart of the cutting force signal provided by an embodiment of the present invention.

[0127] Fig.15 This is a PCA dimensionality reduction diagram of the cutting force signal provided by an embodiment of the present invention.

[0128] Fig.16 is the accumulated saliency map provided by the embodiment of the present invention.

[0129] Fig.17 It is a distribution diagram of machining errors of workpiece measurement points under three machining tasks provided by an embodiment of the present invention.

[0130] Fig.18 It is a weight vector value diagram after training provided by an embodiment of the present invention.

[0131] Fig.19 It is a comparison chart of the predicted value and the measured value of the test set processing error provided by the embodiment of the present invention.

[0132] Fig. 20 It is a comparison chart of the error measurement value provided by the embodiment of the present invention, the benchmark-1 and the prediction results of the proposed method on the test set.

[0133] Fig.21 It is a comparison chart of the error measurement value provided by the embodiment of the present invention, the benchmark-2 and the prediction results of the proposed method on the test set.

[0134] Fig. 22 It is a comparison diagram before and after the machining error compensation provided by the embodiment of the present invention. DETAILED DESCRIPTION

[0135] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0136] like Figure 1 As shown, a feature fusion and refinement embedding sparse Bayesian learning method provided by an embodiment of the present invention includes the following steps:

[0137] S1, according to the proposed processing parameters, the robot air cutting motion and milling experiments of different processing tasks are carried out, and the joint angle, acceleration signal and cutting force signal are collected at the same time, and the processing error of the workpiece after milling is measured;

[0138] S2, processes and calculates the original signal collected in S1 to obtain the feature vector of the model input, and uses the measured processing error as the model label;

[0139] S3, performs feature weighting and feature fusion on the feature vectors calculated in S2 to construct a dictionary matrix;

[0140] S4, establishing a regression prediction model based on the dictionary matrix and processing error obtained in S3;

[0141] The present invention firstly conducts air cutting motion and milling experiments on the robot according to the proposed processing parameters. During the experiment, multimodal data such as robot joint angle, acceleration signal and cutting force signal are collected simultaneously to reflect the changes in dynamic and mechanical characteristics during the processing. After the milling task is completed, the error of the processed workpiece is measured to obtain the data of actual processing accuracy. The goal of this stage is to provide complete and real experimental data for subsequent analysis and modeling.

[0142] The collected raw signals are processed, including denoising, normalization, time series segmentation, and frequency domain analysis, to improve the quality and characterization of the data. Based on signal processing, the key feature vectors in the machining task are calculated, such as the rate of change of joint angles, acceleration frequency distribution, and cutting force peak. The processed feature vectors will be used as the input of the model, and the annotated machining error data will be used as the output label of the model.

[0143] In order to build a more accurate prediction model, the present invention evaluates the influence weight of each feature after extracting the features, and uses a weighted method to strengthen the contribution of key features to model performance. At the same time, feature vectors of different modes (such as joint angles, acceleration signals, and cutting force signals) are fused to form a unified dictionary matrix. This dictionary matrix can effectively integrate multi-modal feature information and reflect the overall characteristics of the processing process.

[0144] Based on the dictionary matrix and processing error labels obtained by feature fusion, a regression prediction model is established using the sparse Bayesian learning method. The sparse Bayesian method automatically selects the features that have the greatest impact on the processing error through regularization constraints and builds an efficient sparse model. This method can not only improve the prediction accuracy of the model, but also reduce the impact of redundant features, making the model more concise and easy to generalize.

[0145] The dictionary matrix and processing error data are input into the sparse Bayesian model, and the model parameters are optimized through the training process. During the training process, the model continuously adjusts the feature weights and regression coefficients according to the deviation between the actual value and the predicted value of the processing error to achieve higher prediction accuracy. In addition, the model can dynamically adjust the structure for experimental data of different processing tasks, and has strong adaptability.

[0146] The sparse Bayesian prediction model finally established can predict errors for future machining tasks. By inputting new machining parameters and signal features, the model can estimate machining errors in real time and provide reference suggestions for optimizing machining process parameters. This method based on feature fusion and sparse learning significantly improves the efficiency and accuracy of error prediction, while reducing the time cost of experiments and debugging, and has a wide range of industrial application value.

[0147] First, it is assumed that the weights between the model input features and labels satisfy the Gaussian prior distribution to promote most coefficient weights to approach 0 and achieve the sparsity of the model weights; according to the Bayesian formula, the posterior distribution of the weight variables is obtained, and the expectation and variance of the posterior distribution of the weight coefficients are estimated by maximizing the posterior probability; the variance and the hyperparameters that affect the sparsity of the weights are estimated by maximizing the marginal likelihood function, that is, maximizing the expectation of the joint likelihood function under the posterior distribution of the weights to optimize, and the minimum solution of the transformed loss function can be found to optimize the hyperparameters; the posterior expectation and variance of the model weights, as well as the hyperparameters are iteratively updated during the training process, and the iterative process is terminated according to the set change threshold to achieve the sparsification of the model weight vector and the construction of a sparse model.

[0148] As a preferred implementation, in step S1

[0149] In step S1, the milling experiment of air cutting motion and parts with different processing positions and surface features is carried out according to the designed processing trajectory and process parameters. The acceleration sensor is attached to the spindle, and the acceleration and cutting force signals during the milling process are collected through the dynamometer system and the data acquisition system. The angles of each joint of the robot during the processing are obtained through the robot open data acquisition system, and the workpiece after milling is scanned by the structured light camera to measure the processing error.

[0150] As a preferred embodiment, in step S2

[0151] In step S2, the process parameters of the robot milling experiment, such as spindle speed, feed rate and cutting depth, are used as static input features of the error monitoring model.

[0152] The robot end stiffness is calculated from the joint stiffness, Jacobian matrix and joint angle:

[0153] K S=J -T (q)K q J -1 (q)

[0154] Where J is the Jacobian matrix, q is the joint angle, and K S and K q are the Cartesian stiffness matrix and joint stiffness respectively; the joint stiffness vector is expressed as: K q =diag(K q1 ,K q2 ,K q3 ,K q4 ,K q5 ,K q6 ), K qi represents the stiffness of the i-th joint, K q Is a 6×6 diagonal matrix, each diagonal entry represents the robot joint stiffness. The diagonal matrix K S The first three values ​​represent the three static stiffnesses in the Cartesian coordinate directions. Recorded as

[0155] Robot kinematics is a key factor affecting machining errors. The DH (Denavit-Hartenberg) parameter method is used to establish the robot kinematic model. The actual position of the robot end in different postures is measured using a calibration instrument, and the DH parameters are calibrated using a solution algorithm combined with the collected joint angles and kinematic models.

[0156] After calibrating the DH parameters, the influence of the robot geometric error is ignored. Then, the corresponding joint angles are collected in the robot's empty cutting motion and cutting conditions, and the corresponding tool tip position in the workpiece coordinate system is calculated using the calibrated DH parameters in combination with the workpiece coordinate system and the tool coordinate system. The difference in tool tip position is taken as the end tracking error of the robot under cutting force disturbance, expressed as:

[0157] δ tracking =k m (p cutting )-k m (p idlecutting )

[0158] Where k m is the calibrated kinematic model, p cutting and p idle cutting Represent the joint angles of the robot during cutting and empty cutting respectively. The calculated tracking error value is weighted and used as the input feature of the error monitoring model

[0159] The detailed process of cutting force migration prediction can be found in patent application: 202410588786.7. The following is only a brief introduction.

[0160] For the collected original signals of acceleration, cutting force and joint angle, the non-cutting segment data is first removed, and downsampling and timing alignment operations are performed. The relationship between the robot joint angle, acceleration signal and cutting force is characterized as follows:

[0161]

[0162] Among them, k represents the current time, F a (k) represents the cutting force at the current moment, q1(kj), q2(kj), q3(kj), q4(kj), q5(kj), q6(kj), a(kj), (j=0,1,...,n) represent the angles and acceleration signals of each joint at the previous moment and the current moment. F a (kj), (j = 1, 2, ..., l) represents the predicted cutting force at previous moments, n and l represent the time lag order related to input and output, f represents the nonlinear relationship between input and output, and f is constructed using a data-driven model. During model training, the time-series aligned data is converted into multidimensional data according to the above formula.

[0163] The PCA method is used to assign pseudo labels to the test data in the target pose to meet the requirements of the network input dimension. The obtained source domain data and target domain data are input into the proposed deep migration regression model. First, a deep network model is established, including a feature extraction network and a fully connected network to extract time series data features and perform regression prediction on the features. First, the CNN feature extraction network and FC regression prediction module are trained using the source domain data, and then the pre-trained model parameters are migrated to the target domain model with the same structure. Among them, the feature extractor is defined as follows:

[0164]

[0165] where F ES is the deep feature expression contained in the extracted input time series signal, Represents the feature extractor of the source data. s is the input source data sample, Represents the feature extractor parameters.

[0166] The extracted source domain features are then input into the regressor to predict the cutting force, and the output dimension is 1. The regression loss of the regressor is as follows:

[0167]

[0168] where n sis the number of source samples, Represents the calculation of mean square error (MSE): represents the regressor parameters.

[0169] Based on the kernel embedding theory of conditional distribution, a conditional distribution embedding operator is proposed to measure the difference in conditional probability distribution. X and O Y The variables X and Y, the corresponding reproducing kernel Hilbert space (RKHS) is and By embedding p(Y|X) into RKHS, the conditional mean embedding can be defined as:

[0170]

[0171] where ψ(x): And φ(Y): and yes The operator characterizes the characteristics of the conditional distribution. When a fixed x is taken, a conditional mean embedding value μ is obtained. Y|x .

[0172] According to the calculation formula of conditional probability distribution, it is equal to the ratio of joint probability distribution to marginal probability distribution of input. The conditional embedding operator calculation can be defined as the combination of cross covariate operator and independent covariate operator:

[0173]

[0174] When given a data set D = {(x1,y1),(x2,y2),...,(x n ,y n )}hour, The estimated value of can be defined as follows:

[0175]

[0176] Where F=(φ(y1),φ(y2),...,φ(y n )), and is the Gram matrix of the variable samples, with a regularization term added to ensure it is well-posed.

[0177] A conditional distribution embedding operation is designed to estimate the difference between conditional probability distributions. It is defined as follows and used as the loss function for network parameter update to minimize domain differences.

[0178]

[0179] The matrix K XX' Calculation using Gaussian kernel κ:

[0180] K XX' (i,j)=κ(X i ,X j ')= <f(X i ),f(X j ')>

[0181] where <·,·> represents the vector inner product.

[0182] The conditional embedding distribution difference is calculated using the new features formed by the second fully connected layer of the target pose unlabeled input data features, the predicted value of the regression network, the new features formed by the second fully connected layer of the source pose data features and their label values. The conditional embedding distribution difference is calculated by using the new features formed by the second fully connected layer of the unlabeled input data features, the predicted value of the regression network, the new features formed by the second fully connected layer of the target pose labeled data features and their label values.

[0183] The target domain has labeled data prediction values ​​and their label values ​​to calculate regression loss It can be calculated as:

[0184]

[0185] For the training of the feature extractor of the target data and the task-specific regressor, the following weighted integrated loss function is used for parameter update:

[0186]

[0187] in, is the regression loss of labeled data in the target domain, Represents the difference in conditional distribution measure between source domain data and target domain unlabeled data, represents the difference in conditional distribution between labeled and unlabeled data in the target domain, α s and β t is a trade-off parameter.

[0188] The network is trained by minimizing the target posture regression loss and the difference between the two conditional embedding distributions, and the optimizer is used to update the network parameters. After the iteration, the cutting force prediction model of the target posture is obtained:

[0189]

[0190] After changing the robot's posture during actual processing, the monitored robot joint angles and acceleration signals are input into the established prediction model for training and iterative prediction in combination with a small amount of labeled data, so as to obtain the real-time and accurate cutting force in the new posture.

[0191] The predicted cutting force signal is aligned with the workpiece measurement point in space, and the time domain, frequency domain and time-frequency domain features closely related to the part processing error are extracted from the cutting force signal near each measurement point. Converting the dynamic cutting force into structured multi-domain information is conducive to establishing a robot processing error prediction model. Time domain features Include maximum value average value variance Peak-to-Peak RMS value Kurtosis value and skewness value Represents the cutting force components in three directions. The change of cutting force in the time domain reflects the unevenness of material removal during the cutting process, and further reflects the change of machining error. Frequency domain characteristics Including frequency average energy Frequency variance Frequency Center and mean square frequency The characteristics of cutting force in the frequency domain mainly reflect the dynamic stability and have a great influence on the machining error.

[0192] Time-frequency domain analysis methods can mine the joint distribution information between the time domain and the frequency domain. The variational mode decomposition (VMD) method is robust to noise and sampling processes, and decomposes the original signal into sub-signals with specific sparsity for subsequent time-frequency domain feature extraction. The setting of the decomposition layer and the penalty factor has a great influence on its decomposition effect. The adaptive variational mode decomposition method (AVMD) is used to extract time-frequency domain features, which can realize the adaptive optimization of the decomposition layer number K and the penalty factor γ, and improve the performance of feature extraction. The number of decomposition layers is set according to experience, and the cross-correlation spectrum index (CSI) is used to realize the adaptive optimization of the penalty factor. The description formula is as follows:

[0193]

[0194] Where T is the length of the original signal, i and j are the ordinal numbers of the intrinsic mode functions, and u i and u j is the sub-signal decomposed by the AVMD method. For each penalty factor γ within the set range, the VMD method is used to decompose the original signal, and then its CSI is obtained according to the above formula. The penalty factor corresponding to the minimum CSI value is selected as the optimal value. The original signal is decomposed into several sub-component signals, and the time-frequency domain features are extracted using energy entropy. The energy of each sub-signal is calculated as:

[0195]

[0196] The energy entropy of the sub-signal is given by:

[0197]

[0198] Where r i =R i / R is the percentage of each sub-signal energy to the total signal energy.

[0199] These features not only provide a deep understanding of the variations in cutting forces during machining, but also offer a physically interpretable basis for analyzing and optimizing possible errors during machining.

[0200] Considering that all cutting force features contain redundant information, the principal component analysis (PCA) method is used to reduce the redundant dimension of all cutting force features to retain the principal components that reflect the deep feature expression and structure of the data. PCA operations are performed on the cutting forces in three directions. First, the feature matrix composed of time domain, frequency domain and time-frequency domain features is Normalized respectively, the original feature dimension is d o . Then solve the covariance matrix about The calculation result of the characteristic value represents the information contained in the corresponding dynamic feature significance. Then calculate the significance ratio of the dynamic features and sort them in order from large to small. According to the sorting, add up the first m significance ratio values ​​to get the total significance s p If p Less than the set threshold s t , then increase the value of m, if it reaches the set threshold, then output the reduced matrix and the corresponding dimension d after reduction r Finally, the dimension reduction results of the cutting force characteristics in the three directions are integrated to obtain the final cutting force characteristics.

[0201] As a preferred implementation, in step S3

[0202] In step S3, the robot end tracking error under the influence of cutting force describes the position deviation of the robot end under the action of cutting force, which is most closely related to the contour error of the final machined workpiece. Therefore, the features constituted by the tracking error are weighted to emphasize its importance in the feature matrix. A global unsupervised feature weighting method is proposed to adaptively adjust the weights of the tracking error feature terms. The error value is divided into multiple intervals with a fixed width. The number of error values ​​in each interval is counted, and the probability p of each interval is calculated. i, which is the number of samples in the interval divided by the total number of samples. The resulting probability distribution can describe the frequency of different error ranges.

[0203] Calculate the information entropy after discretization:

[0204]

[0205] Among them, n is the number of intervals after discretization, p i is the probability of the ith interval. The larger the information entropy value, the more dispersed the distribution of the feature and the higher the uncertainty.

[0206] The weight of each column of tracking error values ​​is set to a combination of information entropy and variance ratio:

[0207]

[0208] Among them, α H and β ζ is a parameter that controls information entropy and variance weight. N t The number of feature columns representing the tracking error, information entropy measures the uncertainty of each column of tracking error values. Variance measures the degree of dispersion of each column of tracking error. Combining the weighting method of information entropy and variance can more comprehensively measure the importance of features.

[0209] Multiple measurement points are selected at equal distances on each trajectory to form a label dataset for the prediction model.

[0210] For the robot end stiffness, cutting force characteristics and weighted tracking error characteristics obtained above, a structured feature row vector is constructed in combination with the machining parameters The feature vectors of multiple samples constitute a feature matrix, which is then normalized to eliminate the impact of large differences in the magnitude of different features.

[0211] The feature matrix is ​​subjected to feature fusion. In order to overcome the disadvantage that feature information is linearly indistinguishable in low-dimensional space, a kernel function is introduced to map sample features to high-dimensional space. The Gaussian kernel has good nonlinear fitting characteristics and is easy to adjust weights to fit different data distributions to map complex relationships. The Gaussian kernel distribution can be expressed as:

[0212]

[0213] Where σ is the bandwidth of the Gaussian kernel, which is optimized using a random search algorithm. For the regression model of feature fusion and physical knowledge embedding, the feature vector is mapped by a kernel function to obtain a feature kernel dictionary matrix with a Gaussian distribution. The dictionary matrix is ​​configured as a structured sorting of static and dynamic features according to the order of the measurement points, which not only reflects the trend of the features but also avoids the overlap of feature signals. The feature kernel dictionary matrix Φ is expressed as:

[0214]

[0215] The processing error can be expressed as follows:

[0216] y m =y p +ε;y p =Φω

[0217] Where y m is the measured processing error, y p is the predicted processing error, ε is the prediction noise caused by uncertainty in the processing and measurement process. Φ is the constructed dictionary matrix, ω is the corresponding weight coefficient, recorded as:

[0218] ω=[ω1,ω2,...,ω M-1 ,ω M ,b] T

[0219] As a preferred implementation, in step S4

[0220] In step S4, a regression prediction model is established based on the dictionary matrix and processing error obtained in the above steps. The sparse Bayesian learning method introduces sparsity based on the idea of ​​Bayesian theorem and assumes a Gaussian prior distribution for the weights, which can greatly reduce model redundancy and improve computational efficiency, model generalization ability and interpretability. The probability distribution of the noise variable can be assumed to be a normal probability density function ε~N(0,λI), where λ is the variance, which is affected by the processing uncertainty caused by vibration and cutting heat and the measurement uncertainty. m The likelihood function is defined as:

[0221]

[0222] A Gaussian prior distribution is introduced on the weight vector, so that most of the weight coefficients are close to zero, and the sparsity of the weight vector is achieved. In this way, the processing error can be predicted only by the relevant columns in the dictionary matrix and the corresponding sparse weights, which improves the computational efficiency. Usually, in order to calculate the homogeneous analytical solution of the posterior, the prior distribution is the conjugate prior of the likelihood function, that is:

[0223]

[0224] where ξ i Impact i The probability of approaching zero is used to control the sparsity of the weight coefficient, reduce the complexity of the model, and avoid overfitting. According to the Bayesian formula, the posterior distribution of the weight variable can be expressed as:

[0225]

[0226] In the formula, Λ=diag{ξ1,ξ2,...,ξ N} and P(y m |λ,Λ) represents the marginal distribution of the measured processing error, and N is the number of weights. The posterior expectation and variance of the weight coefficient are estimated by finding the maximum value of the posterior probability, which is expressed as:

[0227] μ ω =λ -1 ∑ ω Φ T y m

[0228] ∑ ω =λ(Φ T Φ+λΛ -1 ) -1

[0229] Then the hyperparameters λ and Λ are optimized by maximizing the marginal likelihood function. For convenience of calculation, the logarithm of the likelihood function is taken, i.e. logP(y m |λ,Λ). Optimizing the marginal likelihood is equivalent to maximizing its lower bound, the weighted posterior distribution P(ω|y m ,λ k ,Λ k ) can be expressed as:

[0230]

[0231] The above operations can generate the following loss function:

[0232]

[0233] The optimization problem can be solved by making the partial derivative of the loss function with respect to the hyperparameters equal to zero, and the hyperparameters λ and Λ can be updated as follows:

[0234]

[0235] Among them <·> i represents the entry of the ith vector, <·> ii represents the entry in the i-th row and i-th column of the matrix. During the iteration, when the 1-norm of the weight vector ||μ ω When the relative change value of ||1 and the standard deviation of the prediction noise is less than the set threshold for multiple consecutive times, the model is judged to be converged. At this time, the model weights are sparse enough, the noise prediction tends to be stable, and the model prediction performance and reliability are high. The convergence condition is expressed as:

[0236]

[0237] in is the set convergence threshold.

[0238] like Figure 2 As shown, a feature fusion and refinement embedded sparse Bayesian learning system provided by an embodiment of the present invention includes:

[0239] The acquisition module is used to perform robot air cutting motion and milling experiments for different processing tasks according to the planned processing parameters, and collect joint angles, acceleration signals and cutting force signals at the same time, and measure the processing error of the workpiece after milling.

[0240] The processing module is used to process and calculate the collected original signal to obtain the characteristic vector of the model input, and use the measured processing error as the model label;

[0241] A fusion module is used to perform feature weighting on the calculated feature vectors and perform feature fusion to construct a dictionary matrix;

[0242] A module is established to establish a regression prediction model based on the obtained dictionary matrix and processing errors.

[0243] The present invention uses an acquisition module to perform an empty cutting motion and actual milling experiment performed by the robot according to the set processing parameters. In the experiment, multimodal data such as joint angles, acceleration signals and cutting force signals during the robot movement are collected, and the error of the workpiece is measured after the processing task is completed to obtain the processing error data. The acquisition module ensures the correlation between the dynamic characteristics and processing results during the processing, providing a high-quality experimental basis for subsequent data processing.

[0244] The processing module preprocesses the collected raw multimodal signals, including data denoising, normalization, and feature extraction. By analyzing the time domain and frequency domain features, a feature vector reflecting the robot's motion state and processing mechanical characteristics is generated. In addition, the measured processing error data is associated with the feature vector as a label to form the input data set of the machine learning model. The precise calculation of the processing module ensures the quality of data input and lays the foundation for the establishment of the regression prediction model.

[0245] The fusion module performs weighted processing on the multimodal feature vectors, giving higher weights to the features that have a greater impact on the prediction of processing errors. Subsequently, the fusion module performs feature fusion on the weighted feature vectors to integrate the core information of the multimodal data and construct a high-dimensional dictionary matrix. The dictionary matrix can fully reflect the multimodal characteristics of the processing process and provide an accurate and efficient input feature space for the sparse Bayesian learning model.

[0246] The module establishes a regression prediction model based on the dictionary matrix and processing error data through the sparse Bayesian learning method. The sparse Bayesian method realizes the screening and modeling of key features through regularization constraints, significantly improving the prediction accuracy and generalization ability of the model. In addition, computer equipment and information data processing terminals equipped with memory and processors can load readable storage media storing computer programs, execute the algorithm steps of feature fusion and sparse Bayesian learning, and provide intelligent solutions for error prediction and process optimization in actual industrial applications.

[0247] like Figure 3 A feature fusion and refinement embedding sparse Bayesian learning method and system for robot surface milling contour error monitoring, which uses the process parameters such as spindle speed, feed rate and cutting depth of robot milling experiment as static input features of the error monitoring model

[0248] The robot stiffness includes joint stiffness, link stiffness and end effector stiffness. It contains the robot spatial configuration information, robot motion transfer equation and workpiece position information. The robot end stiffness is calculated by joint stiffness, Jacobian matrix and joint angle:

[0249] K S =J -T (q)K q J -1 (q)

[0250] Where J is the Jacobian matrix, q is the joint angle, and K S and K q are the Cartesian stiffness matrix and joint stiffness respectively; the joint stiffness vector is expressed as: K q =diag(K q1 ,K q2 ,K q3 ,K q4 ,K q5 ,K q6 ), K qi represents the stiffness of the i-th joint, K q is a 6×6 diagonal matrix, each diagonal item represents the joint stiffness of the robot. The specific joint stiffness of the robot used in the experiment is shown in Table 1. The diagonal matrix K S The first three values ​​represent the three static stiffnesses in the Cartesian coordinate directions. Recorded as

[0251] Table 1 COMAU Smart5 NJ220 robot joint stiffness (unit: Nmm / rad)

[0252]

[0253] Robot kinematics is a key factor affecting machining errors. The DH (Denavit-Hartenberg) parameter method is used to establish the robot kinematic model. Figure 4 As shown in Figure 1. The robot arm can be regarded as a kinematic chain consisting of a series of joints and links, with a fixed coordinate system on the links. The transformation relationship between the coordinate systems of adjacent links is determined by the link length a. i , connecting rod torsion angle α i , joint distance d i , joint rotation angle θ i The homogeneous transformation can be described by kinematic parameters such as:

[0254]

[0255] In the formula i-1 T i is the homogeneous transformation matrix of the i-th joint coordinate system relative to the i-1-th joint coordinate system, i is the robot joint number; Rot represents the rotation matrix, and Trans represents the translation matrix.

[0256] For a 6-DOF serial robot, the transformation matrices of adjacent links are multiplied in sequence to obtain the homogeneous transformation relationship between the end flange coordinate system and the robot base coordinate system:

[0257] b T6= b T1 1 T2 2 T3 3 T4 4 T5 5 T6

[0258] Symbols 1-6 represent the number of robot joint angles. The calculated end position can be expressed as:

[0259] P calculated =p(θ,d,α,a)

[0260] The standard DH parameters of the COMAU Smart5NJ220-2.7 robot used in this case are shown in Table 2.

[0261] Table 2 COMAU Smart5 NJ220-2.7 robot standard DH parameters

[0262]

[0263] Due to the manufacturing and assembly errors of the robot links, as well as the deviation caused by the joint clearance, when the end position is calculated using standard DH parameters, there is a large deviation between the calculated result and the planned position. The actual robot end position can be expressed as:

[0264] P measured =p(θ+δθ,d+δd,α+δα,a+δa)

[0265] Therefore, it is necessary to calibrate the DH parameters through calibration experiments to improve the accuracy of the kinematic model. A laser tracker (Leica AT901-MR) is used to measure the actual position of the end effector at different positions of the robot, with a positioning accuracy of 25 μm / m and a posture accuracy of 0.01°. The laser tracker reflector is fixed on the end of the robot, and the laser tracker is used to monitor the position of the reflector. A structured light camera (SCANTECH ReadyScanB11) is used to measure the relative position of the reflector relative to the center of the robot end. The experimental platform is as follows: Figure 5 shown.

[0266] After the robot returns to the zero position, the robot's 1, 3, and 6 axes are uniformly rotated within the range of ±20°, ±20°, and ±180°, respectively, and the actual position of the reflector at each rotation angle is recorded. The three space circles and their normal vectors are fitted using the measured positions to obtain the rotation transformation matrix between the robot base coordinate system and the tracker coordinate system. The translation vector between the robot base coordinate system and the tracker coordinate system is calculated by combining the end flange center position and the measured position at the robot zero position. Then, 64 measurement points are uniformly collected within the range of 900×1200×900mm above the robot workbench, and the corresponding joint angles are recorded for calibrating the DH parameters. According to the relative position of the reflector target ball measured by the structured light camera relative to the center of the robot end, combined with the homogeneous transformation matrix, the tracker measurement data is converted to the robot base coordinate system, and the error between the measured position and the calculated position is calculated and expressed as:

[0267] δP=P measured -P calculated

[0268] When the DH parameter error is small, it can be simplified to the corresponding linear equation. For each measurement point, there are errors in the three directions of X, Y, and Z, which are expressed as follows:

[0269]

[0270] For a multi-joint robot with multiple DH parameters, the above formula can be written in matrix form:

[0271] A.δ DH =B

[0272] Where A is the Jacobian matrix, and every three rows form a group. There are n groups, where n is the number of measurement points. The Jacobian matrix is ​​expressed as follows:

[0273]

[0274] B is the error matrix of n measurement points:

[0275] B=[δp 1x ,δp 1y ,δp 1z ,...δp nx ,δp ny ,δp nz ,] T

[0276] δ DH is the error of the DH parameter to be calibrated:

[0277] δ DH =[δθ0,...δθ6,δd0,...δd6,δα0,...δα6,δa0,...δa6] T

[0278] The least squares method is used to identify the DH parameter error:

[0279] δ DH =(A T A) -1 ·A T ·B

[0280] The obtained parameter error is superimposed on the standard DH parameter to obtain a set of new DH parameters, and then the position error is solved again, and it is iterated repeatedly until the position error is small enough. The calibrated DH parameter error is shown in Table 3. The comparison of position error before and after calibration is shown in Table 3. Figure 6 As shown in the figure, the results show that after calibrating the DH parameters, the geometric error of the robot is effectively reduced, and the average position error is reduced from 3.73mm to 0.69mm, a reduction of 81.5%.

[0281] Table 3 DH parameter errors of COMAU Smart5 NJ220-2.7 robot calibration

[0282]

[0283] Under the disturbance of the milling force at the robot end, the robot joint is affected by the additional load and torque. This will lead to a decrease in the response speed and accuracy of the joint servo system, an increase in the joint servo error, and a deviation of the actual cutting path from the set path, thereby generating an end tracking error. Therefore, the end tracking error under the action of cutting force is of great significance for the analysis and prediction of machining errors.

[0284] After calibrating the DH parameters, the influence of the robot's geometric error is ignored. Then the corresponding joint angles are collected when the robot is in the empty cutting and cutting conditions. Combining the workpiece coordinate system and the tool coordinate system, the calibrated DH parameters are used to calculate the position of the corresponding tool tip in the workpiece coordinate system. The difference in the tool tip position is taken as the end tracking error of the robot under the cutting force disturbance, expressed as:

[0285] δ tracking =k m (p cutting )-k m (p idlecutting )

[0286] Where k m is the calibrated kinematic model, p cutting and p idlecutting Represent the joint angles of the robot during cutting and air cutting, respectively.

[0287] The process of cutting force migration prediction, feature extraction and dimensionality reduction is as follows:

[0288] The detailed process of cutting force migration prediction can be found in patent application: 202410588786.7. The following is only a brief introduction.

[0289] The frequency response function between acceleration and cutting force is expressed in the Laplace domain as:

[0290]

[0291] Where m is the mode number, R k is the model residual, ξ k and ω nk are the k-order damping ratio and natural frequency respectively.

[0292] Converting it into differential equation form, the cutting force can be calculated from the inverse estimate of the acceleration:

[0293]

[0294] Among them A j (j=0,...,n), B j (j=1,...,l) are the coefficients of the differential equation, a j (j=0,...,n) and is the jth derivative with respect to time, n and l are a and F a The order of .

[0295] The data-driven method can be used to establish a dynamic nonlinear relationship between the monitored acceleration signal and joint angle signal and the cutting force. In the nonlinear dynamic prediction model, the relationship between the acceleration monitoring signal and the cutting force is characterized by the following discrete time dynamic system model:

[0296]

[0297] Among them, k represents the current time, F a (k) represents the cutting force at the current moment, q1(kj), q2(kj), q3(kj), q4(kj), q5(kj), q6(kj), a(kj), (j=0,1,...,n) represent the angles and acceleration signals of each joint at the previous moment and the current moment. F a (kj), (j = 1, 2, ..., l) represent the predicted values ​​of cutting force at previous moments, and n and l represent the order of time lag associated with input and output, respectively.

[0298] The PCA method is used to assign pseudo labels to the test data in the target pose to meet the requirements of the network input dimension. The obtained source domain data and target domain data are input into the proposed deep migration regression model. First, a deep network model is established, including a feature extraction network and a fully connected network to extract time series data features and perform regression prediction on the features. The CNN feature extraction network and FC regression prediction module are first trained using the source domain data, and then the pre-trained model parameters are migrated to the target domain model with the same structure. Among them, the feature extractor is defined as follows:

[0299]

[0300] where F ES is the deep feature expression contained in the extracted input time series signal, Represents the feature extractor of the source data. s is the input source data sample, Represents the feature extractor parameters.

[0301] The extracted source domain features are then input into the regressor to predict the cutting force, and the output dimension is 1. The regression loss of the regressor is as follows:

[0302]

[0303] where n s is the number of source samples, Represents the calculation of mean square error (MSE): represents the regressor parameters.

[0304] Based on the kernel embedding theory of conditional distribution, a conditional distribution embedding operator is proposed to measure the difference in conditional probability distribution. X and O Y The variables X and Y, the corresponding reproducing kernel Hilbert space (RKHS) is and By embedding p(Y|X) into RKHS, the conditional mean embedding can be defined as:

[0305]

[0306] where ψ(x): And φ(Y): and yes The operator characterizes the characteristics of the conditional distribution. When a fixed x is taken, a conditional mean embedding value μ is obtained. Y|x .

[0307] According to the calculation formula of conditional probability distribution, it is equal to the ratio of joint probability distribution to marginal probability distribution of input. The conditional embedding operator calculation can be defined as the combination of cross covariate operator and independent covariate operator:

[0308]

[0309] When given a data set D = {(x1,y1),(x2,y2),...,(x n ,y n )}hour, The estimated value of can be defined as follows:

[0310]

[0311] Where F=(φ(y1),φ(y2),...,φ(y n )), and is the Gram matrix of the variable samples, with a regularization term added to ensure it is well-posed.

[0312] A conditional distribution embedding operation is designed to estimate the difference between conditional probability distributions. It is defined as follows and used as the loss function for network parameter update to minimize domain differences.

[0313]

[0314] The matrix K XX' Calculation using Gaussian kernel κ:

[0315] K XX' (i,j)=κ(X i,X j ')= <f(X i ),f(X j ')>

[0316] where <·,·> represents the vector inner product.

[0317] The conditional embedding distribution difference is calculated using the new features formed by the second fully connected layer of the target pose unlabeled input data features, the predicted value of the regression network, the new features formed by the second fully connected layer of the source pose data features and their label values. The conditional embedding distribution difference is calculated by using the new features formed by the second fully connected layer of the unlabeled input data features, the predicted value of the regression network, the new features formed by the second fully connected layer of the target pose labeled data features and their label values.

[0318] The target domain has labeled data prediction values ​​and their label values ​​to calculate regression loss It can be calculated as:

[0319]

[0320] For the training of the feature extractor of the target data and the task-specific regressor, the following weighted integrated loss function is used for parameter update:

[0321]

[0322] in, is the regression loss of labeled data in the target domain, Represents the difference in conditional distribution measure between source domain data and target domain unlabeled data, represents the difference in conditional distribution between labeled and unlabeled data in the target domain, α s and β t is a trade-off parameter.

[0323] The network is trained by minimizing the target posture regression loss and the difference between the two conditional embedding distributions. The number of iterations is set to 100, the initial learning rate of the regressor is set to 0.0001, and the network parameters are updated using the Adam optimizer. After the iteration, the cutting force prediction model of the target posture is obtained:

[0324]

[0325] Then, a milling experiment was conducted to verify that the workpiece shape surface in the experiment was derived from the airway surface shape of the actual industrial aircraft engine case scaled-down part, such as Figure 7 (a). Based on the surface features extracted from the receiver, the following Figure 7(b) shows the workpiece, the material of the workpiece is aluminum alloy 6061. In order to verify the generalization ability of the prediction model, three processing tasks A, B, and C are designed, as shown in Table 4.

[0326] Table 4 Designed robot milling tasks

[0327]

[0328] The generalization performance of the prediction model is reflected in three aspects, namely, the variability of the part surface shape, the size scaling of the corresponding workpiece being processed, and the variability of the robot milling position. The different surfaces and size scales of the workpieces, as well as the different placement positions of the workpieces, enrich the diversity of the process information expression of the relationship between the machining error and the cutting parameters, cutting forces, machining surface features, and robot posture. In Task A, the surface feature is a 40% scaled inner airway surface of the casing, covering 16 machining tracks AS1 to AS16, and processed on two identical workpieces. In Task B, the surface feature is the inner airway surface of the casing and 8 machining tracks BS1-BS4 and BT1-BT4. In Task C, the surface feature is a 25% scaled outer airway surface of the casing, with 6 machining tracks CS1-CS2 and CT1-CT4. The comparison between Task A and Task B shows the model adaptation under size scaling and robot position changes, and the comparison between Task B and Task C shows the model adaptation under part surface shape changes and robot position changes.

[0329] The overall scenario of the robot milling system is as follows Figure 8 As shown. The milling experiment was carried out using a six-degree-of-freedom industrial robot (COMAU Smart5 NJ 220-2.7). The maximum load of the robot is 220 kg and the repeatability is 0.06 mm. The COMAU Robotics open data acquisition system C5G open is used to collect the actual joint angles during robot processing. The maximum speed of the milling spindle (Jaeger Z100-H540.08 S3W2) is 30000 rpm and the maximum torque is 5 Nm. The accelerometer (DYTRAN 3263A2) is magnetically mounted on the spindle with a bandwidth of 4000 Hz. The dynamometer (Kistler 9129AA) is installed on the workbench and the workpiece is fixed on the dynamometer. The acceleration signal and cutting force signal are collected using the NI 9234 data acquisition board. The acquisition software is LabVIEW 2018 with a sampling frequency of 25.6 kHz.

[0330] The milling test was carried out using a double-groove carbide ball-end milling cutter (SANDVIK2B330-1000-NCH10F) with a diameter of 10 mm and a helix angle of 30°. For the three designed machining tasks, each trajectory on the workpiece follows the direction of the extracted characteristic curve. 30 sets of milling tests with different process parameters were carried out on 4 workpieces, and the machining parameters are shown in Table 5. Task A is a three-factor, four-level orthogonal experiment on two workpieces. In the 30 sets of milling trajectories, with different feed speeds and cutting depths, the speed ranges from 5500 to 8000 rpm.

[0331] Table 5 Milling process parameters

[0332]

[0333]

[0334] The milled workpiece is scanned and captured using a structured light camera (SCANTECH ReadyScan B11) to obtain the topographic point cloud data, such as Fig. 9 As shown. The measurement accuracy of the device is 20μm and the resolution is 25μm, which meets the measurement requirements compared with the error of the workpiece being measured. The acquired point cloud data is processed using Geomagic software. First, the reference CAD model and the point cloud data are roughly aligned, and then the optimal fit is precisely aligned. Subsequently, the unprocessed surface is used as the reference for offset, and the cross-sectional profile information of the deepest processing under each trajectory is obtained. The measured profile is compared with the two-dimensional theoretical profile to obtain the profile error of the processed workpiece.

[0335] The robot end stiffness distribution of all measurement points under three processing tasks is calculated based on the actual collected joint angles, joint stiffness and Jacobian matrix, as shown in Fig.10 According to the above-mentioned tracking error calculation method under cutting force disturbance, the tracking error distribution of the robot end under the cutting force disturbance under three machining tasks is shown as follows: Fig.11 shown.

[0336] In Table 5, AS1-AS16, BS1-BS4 and CS1-CS2 groups are used as source domains, and the rest are target domains. First, the non-cutting segment data at the beginning and end of the data are removed, and the outliers are eliminated. Then, a low-pass filter with a cutoff frequency of 1000Hz is used to eliminate the noise fluctuation contained in the original cutting force data. Then, a downsampling operation is performed. The time lag order is n=6, l=5. The time series data is synchronized and processed into a format that conforms to the proposed network architecture according to the discrete time relationship to construct a data set. The transfer learning algorithm proposed above is used to predict the cutting force under different postures and process parameters. The predicted values ​​are compared with the measured values, and MAE and RMSE are used as evaluation indicators of the model prediction performance, which are defined as follows:

[0337]

[0338]

[0339] In the formula, x i and i are the input value and the measured value respectively, n t is the sample size. The evaluation index calculation of the prediction results of some experimental groups is shown in Table 6. The ratio of the predicted RMSE to the cutting force peak is less than 15%. The comparison results between the predicted value and the measured value are shown in Fig.12 and Fig.13 As shown, Fig.12 is the prediction result of BT3 in task B, Fig.13 The prediction results for CT1 in Task C. The peak and phase between the predicted and measured values ​​match well, although there are some deviations in the local area, but they are within the acceptable range. The results show that the proposed migration prediction method has high prediction accuracy.

[0340] Table 6 Results of the prediction performance evaluation indicators of some test sets under Task B and Task C

[0341]

[0342] After obtaining the high-precision cutting force prediction results, the predicted cutting force is processed to obtain the dynamic characteristics of the error prediction model. According to the spatial position of the measurement point, the cutting force is uniformly preprocessed along the cutting trajectory. The cutting segment is evenly divided into 40 segments using the sliding window sampling method and aligned with the selected measurement point in time and space. The processing process is as follows Fig.14 As shown. Before establishing the error prediction model, the time domain, frequency domain and time-frequency domain features of the dynamic cutting force are extracted. The predicted cutting force signal is aligned with the workpiece measurement point in space, and the time domain, frequency domain and time-frequency domain features closely related to the part processing error are extracted from the cutting force signal near each measurement point. Converting the dynamic cutting force into structured multi-domain information is conducive to establishing a robot processing error prediction model. Time domain features Include maximum value average value variance Peak-to-Peak RMS value Kurtosis value and skewness value Represents the cutting force components in three directions. The change of cutting force in the time domain reflects the unevenness of material removal during the cutting process, and further reflects the change of machining error. Frequency domain characteristics Including frequency average energy Frequency variance Frequency Center and mean square frequency The characteristics of cutting force in the frequency domain mainly reflect the dynamic stability and have a great influence on the machining error.

[0343] Time-frequency domain analysis methods can mine the joint distribution information between the time domain and the frequency domain. The variational mode decomposition (VMD) method is robust to noise and sampling processes, and decomposes the original signal into sub-signals with specific sparsity for subsequent time-frequency domain feature extraction. The setting of the decomposition layer and the penalty factor has a great influence on its decomposition effect. The adaptive variational mode decomposition method (AVMD) is used to extract time-frequency domain features, which can realize the adaptive optimization of the decomposition layer number K and the penalty factor γ, and improve the performance of feature extraction. The number of decomposition layers is set according to experience, and the cross-correlation spectrum index (CSI) is used to realize the adaptive optimization of the penalty factor. The description formula is as follows:

[0344]

[0345] Where T is the length of the original signal, i and j are the ordinal numbers of the intrinsic mode functions, and u i and u j is the sub-signal decomposed by the AVMD method. For each penalty factor γ within the set range, the VMD method is used to decompose the original signal, and then its CSI is obtained according to the above formula. The penalty factor corresponding to the minimum CSI value is selected as the optimal value. The original signal is decomposed into several sub-component signals, and the time-frequency domain features are extracted using energy entropy. The energy of each sub-signal is calculated as:

[0346]

[0347] The energy entropy of the sub-signal is given by:

[0348]

[0349] Where r i =R i / R is the percentage of each sub-signal energy to the total signal energy.

[0350] These features not only provide a deep understanding of the variations in cutting forces during machining, but also offer a physically interpretable basis for analyzing and optimizing possible errors during machining.

[0351] Considering that all cutting force features contain redundant information, the principal component analysis (PCA) method is used to reduce the redundant dimension of all cutting force features to retain the principal components that reflect the deep feature expression and structure of the data. PCA operations are performed on the cutting forces in three directions. First, the feature matrix composed of time domain, frequency domain and time-frequency domain features is Normalized respectively, the original feature dimension is d o . Then solve the covariance matrix about The calculation result of the characteristic value represents the information contained in the corresponding dynamic feature significance. Then calculate the significance ratio of the dynamic features and sort them in order from large to small. According to the sorting, add up the first m significance ratio values ​​to get the total significance s p If p Less than the set threshold s t , then increase the value of m, if it reaches the set threshold, then output the reduced matrix and the corresponding dimension d after reduction r Finally, the dimensionality reduction results of the cutting force characteristics in the three directions are integrated, and the overall processing flow chart is as follows: Fig.15 The dynamic cutting force features are reduced from 195 to 57, the cumulative significance threshold is set to 99%, the complexity of dynamic features is reduced by 70.77%, and the cumulative significance is shown in Fig.16 shown.

[0352] Among them, the robot end tracking error under the influence of cutting force describes the position deviation of the robot end under the action of cutting force, which is most closely related to the contour error of the final machined workpiece. Therefore, the features constituted by the tracking error are weighted to emphasize its importance in the feature matrix. A global unsupervised feature weighting method is proposed to adaptively adjust the weights of the tracking error feature terms. The error value is divided into multiple intervals with a fixed width. The number of error values ​​in each interval is counted, and the probability p of each interval is calculated. i , which is the number of samples in the interval divided by the total number of samples. The resulting probability distribution can describe the frequency of different error ranges. After discretization, the information entropy is calculated:

[0353]

[0354] Among them, n is the number of intervals after discretization, p i is the probability of the ith interval. The larger the information entropy value, the more dispersed the distribution of the feature and the higher the uncertainty.

[0355] The weight of each column of tracking error values ​​is set to a combination of information entropy and variance ratio:

[0356]

[0357] Among them, α H and β ζ is a parameter that controls information entropy and variance weight. N tThe number of feature columns representing the tracking error, information entropy measures the uncertainty of each column of tracking error values. Variance measures the degree of dispersion of each column of tracking error. Combining the weighting method of information entropy and variance can more comprehensively measure the importance of features.

[0358] 40 measurement points are selected at equal intervals on each trajectory, and a total of 1200 machining error points are obtained, which constitute the label data set of the prediction model. The machining error distribution of the workpiece measurement points under each machining task is shown in the following figure. Fig.17 shown.

[0359] For the robot end stiffness, cutting force characteristics and weighted tracking error characteristics obtained above, a structured feature row vector is constructed in combination with the machining parameters The feature vectors of multiple samples constitute a feature matrix, and then the feature matrix is ​​normalized to eliminate the influence of large differences in different feature dimensions.

[0360] The feature matrix is ​​subjected to feature fusion. In order to overcome the disadvantage that feature information is linearly indistinguishable in low-dimensional space, a kernel function is introduced to map sample features to high-dimensional space. The Gaussian kernel has good nonlinear fitting characteristics and is easy to adjust weights to fit different data distributions to map complex relationships. The Gaussian kernel distribution can be expressed as:

[0361]

[0362] Where σ is the bandwidth of the Gaussian kernel, which is optimized using a random search algorithm. For the regression model of feature fusion and physical knowledge embedding, the feature vector is mapped by a kernel function to obtain a feature kernel dictionary matrix with a Gaussian distribution. The dictionary matrix is ​​configured as a structured sorting of static and dynamic features according to the order of the measurement points, which not only reflects the trend of the features but also avoids the overlap of feature signals. The feature kernel dictionary matrix Φ is expressed as:

[0363]

[0364] The processing error can be expressed as follows:

[0365] y m =y p +ε;y p =Φω

[0366] Where y m is the measured processing error, y p is the predicted processing error, ε is the prediction noise caused by uncertainty in the processing and measurement process. Φ is the constructed dictionary matrix, ω is the corresponding weight coefficient, recorded as:

[0367] ω=[ω1,ω2,...,ω M-1 ,ω M ,b]T

[0368] A regression prediction model is established based on the dictionary matrix and processing error obtained in the above steps. The sparse Bayesian learning method introduces sparsity based on the idea of ​​Bayesian theorem and assumes a Gaussian prior distribution for the weights, which can greatly reduce model redundancy and improve computational efficiency, model generalization ability and interpretability. The probability distribution of the noise variable can be assumed to be a normal probability density function ε~N(0,λI), where λ is the variance, which is affected by the processing uncertainty caused by vibration and cutting heat and the measurement uncertainty. m The likelihood function is defined as:

[0369]

[0370] A Gaussian prior distribution is introduced on the weight vector, so that most of the weight coefficients are close to zero, and the sparsity of the weight vector is achieved. In this way, the processing error can be predicted only by the relevant columns in the dictionary matrix and the corresponding sparse weights, which improves the computational efficiency. Usually, in order to calculate the homogeneous analytical solution of the posterior, the prior distribution is the conjugate prior of the likelihood function, that is:

[0371]

[0372] where ξ i Impact i The probability of approaching zero is used to control the sparsity of the weight coefficient, reduce the complexity of the model, and avoid overfitting. According to the Bayesian formula, the posterior distribution of the weight variable can be expressed as:

[0373]

[0374] In the formula, Λ=diag{ξ1,ξ2,...,ξ N} and P(y m |λ,Λ) represents the marginal distribution of the measured processing error, and N is the number of weights. The posterior expectation and variance of the weight coefficient are estimated by finding the maximum value of the posterior probability, which is expressed as:

[0375] μ ω =λ -1 ∑ ω Φ T y m

[0376] ∑ ω =λ(Φ T Φ+λΛ -1 ) -1

[0377] Then the hyperparameters λ and Λ are optimized by maximizing the marginal likelihood function. For convenience of calculation, the logarithm of the likelihood function is taken, i.e. logP(y m|λ,Λ). Optimizing the marginal likelihood is equivalent to maximizing its lower bound, the weighted posterior distribution P(ω|y m ,λ k ,Λ k ) can be expressed as:

[0378]

[0379] The above operations can generate the following loss function:

[0380]

[0381] The optimization problem can be solved by making the partial derivative of the loss function with respect to the hyperparameters equal to zero, and the hyperparameters λ and Λ can be updated as follows:

[0382]

[0383] Among them <·> i represents the entry of the ith vector, <·> ii represents the entry in the i-th row and i-th column of the matrix. During the iteration, when the 1-norm of the weight vector ||μ ω When the relative change value of ||1 and the standard deviation of the prediction noise is less than the set threshold for multiple consecutive times, the model is judged to be converged. At this time, the model weights are sparse enough, the noise prediction tends to be stable, and the model prediction performance and reliability are high. The convergence condition is expressed as:

[0384]

[0385] in is the set convergence threshold.

[0386] Specifically, the feature vector constructed for each measurement point and its measured processing error value together form a set of samples. The total number of samples in the data set is 1200, the input space dimension is the number of columns of the dictionary matrix, and the output space dimension is 1. In Table 5, AS1-AS16, BS1-BS4 and CS1-CS2 groups are used as training sets, with a total of 880 sample points, and these samples are randomly shuffled before training. The remaining groups are used as test sets, with a total of 320 sample points, to test the trained model. According to the sparse Bayesian learning method constructed above, the feature matrix in the divided training set is used to iteratively train the model weights and hyperparameters after feature fusion. The width hyperparameter of the Gaussian kernel is optimized and determined to be 1.0. The total number of iterations is set to 300 times, and the termination condition is that the relative error between the 1 norm of the weight vector after this round of iteration and the standard deviation of the predicted noise and the value of the previous round of iteration is less than 1e-4 for five consecutive times. The final model iteration terminates at the 166th time. The standard deviation of the prediction noise converges to about 0.082mm, the training process tends to be stable, and the prediction accuracy and reliability of the model are improved. The values ​​in the weight vector after training are shown in Fig.18 In the figure, the blue stems represent the items in the weight vector that are close to 0, which are set to 0, and the red stems represent the non-zero items. There are 279 items in total, accounting for 31.67% of the total, which indicates that the complexity of the model is reduced by 68.33%, and the sparsity of the model is reflected.

[0387] After the model training is completed, the converged weight vector is obtained. The feature matrix in the test set is used to multiply the weight vector after feature fusion to obtain the error prediction value. The prediction process of the processing error of the 320 measurement points selected under the target task only takes 0.002s, which meets the needs of the actual industrial site. MAE, RMSE and R 2 was used to evaluate the prediction performance, R 2 The definition is as follows:

[0388]

[0389] In the formula, and are the i-th predicted value and measured value respectively, is the mean of the measured values, and n is the sample size. The smaller the MAE and RMSE, the more accurate the prediction. 2 The closer the value is to 1, the more reliable the prediction performance is. The calculation results of the evaluation indicators are listed in Table 7. The comparison results between the predicted values ​​and the measured values ​​are shown in Fig.19 The prediction results show good prediction accuracy and the model has strong generalization ability. MAE, RMSE and R 2 The values ​​are 0.0729mm, 0.0906mm and 0.9496 respectively.

[0390] Table 7 Results of the test set machining error prediction performance evaluation index

[0391]

[0392]

[0393] Two benchmarks are used to compare the performance of error prediction to demonstrate the superiority of the proposed model. (1) Comparison with a deep neural network (DNN) model that directly takes machining parameters, robot stiffness, cutting force dynamic characteristics, and tracking error as input features, referred to as Benchmark-1; (2) Ablation experiment: Comparison with a sparse Bayesian model that does not consider the tracking error under cutting force perturbations, referred to as Benchmark-2.

[0394] (1) After obtaining the above-mentioned feature vector composed of process parameters, robot stiffness and cutting force characteristics, the weighted end tracking error is directly added to the feature vector, and the feature vector is divided into training set and test set according to the processing group. The feature vector is not subjected to feature fusion and is directly used for training and testing DNN. The number of DNN iterations is 100, the number of network layers is 8, the number of neurons in each layer is 32, and the optimization algorithm is Adam. The prediction results of the test set are used to show the comparison of prediction capabilities, such as Fig. 20 As shown. Compared with DNN, the proposed model performs feature fusion on the composed feature vectors, overcoming the shortcomings of feature information overlap and linear indistinguishability in low-dimensional space. The dictionary matrix integrates the comprehensive information contained in different types of features, better expressing the complex state of the processing process. In addition, sparsification retains the most valuable information for error prediction, reduces the model complexity and computational complexity, effectively avoids overfitting, and improves the generalization ability of the model. The proposed model significantly improves the prediction accuracy, with MAE on the test set reduced by 58.32%, RMSE reduced by 61.50%, and R 2 The improvement is 43.88%, as shown in Table 8.

[0395] Table 8 Performance comparison between the proposed model and baseline-1

[0396]

[0397] (2) After constructing the dictionary matrix using process parameters, robot end stiffness and cutting force dynamic characteristics, the influence of servo error is not considered. The sparse Bayesian model is trained by combining the measured machining contour error labels. The comparative prediction results of the test set are as follows: Fig.21As shown. Compared with the benchmark-2, the proposed model takes into account the end tracking error caused by the joint servo error under the cutting force disturbance, which reflects the deviation between the actual position and the expected position of the end caused by the dynamic load change, and is closely related to the final processing error. The proposed model uses the end tracking error calculated at each measurement point as the input feature of the processing error prediction model, and performs unsupervised global feature weighting to highlight its importance. It performs adaptive weight adjustment based on the feature’s own information content and the correlation between features, which is conducive to improving the prediction accuracy. Compared with the ablation model, the proposed model has higher prediction accuracy. As shown in Table 9, the MAE on the test set is reduced by 48.66%, the RMSE is reduced by 52.32%, and the R 2 An increase of 22.03%.

[0398] Table 9 Performance comparison between the proposed model and baseline-2

[0399]

[0400]

[0401] The comparison results with the two methods show that the proposed method has higher prediction accuracy than the deep neural network that considers all features but does not perform feature fusion and sparsification and the sparse Bayesian model that does not consider the tracking error, which verifies the effectiveness and advantages of the proposed method.

[0402] Pre-compensation of machining errors is considered to be an effective method to improve robot machining accuracy. For mass production of parts in actual industrial sites, after the proposed error prediction model is used to predict machining errors, the tool position of subsequent workpieces can be pre-compensated to offset the machining errors caused by multi-factor coupling and improve machining accuracy. For the i-th tool position CL i (x i ,y i ,z i ,α i ,β i ,γ i ), according to the predicted machining error, its spatial position is compensated, and the tool position after compensation The milling experiment is carried out using the compensated tool position, and the scanning measurement of the part processing error is performed. The measurement results are compared with the theoretical contour to obtain the compensated processing error. The comparison of the processing error before and after compensation is as follows: Fig. 22 The results show that after pre-compensation of the machining trajectory, the machining accuracy is significantly improved, and the peak value, mean value and standard deviation of the absolute value of the machining error are reduced by 66.09%, 66.40% and 61.65% respectively. The statistical characteristics are shown in Table 10, which verifies the effectiveness of the pre-compensation method based on the error prediction model.

[0403] Table 10 Statistical characterization of compensation experiment processing error indicators

[0404]

[0405] 1. Specific application fields or related products of the present invention.

[0406] Smart manufacturing and industrial automation

[0407] Data-driven intelligent production: Robot milling error monitoring technology can collect a large amount of data on process parameters, robot stiffness, cutting force signals, tracking errors, etc. in real time. In an intelligent manufacturing environment, these data can be integrated into the company's big data platform, and through data analysis and machine learning algorithms, potential rules and optimization points in the processing process can be excavated. For example, according to the processing error data of different products, the robot's processing path planning and cutting parameter settings can be intelligently adjusted to achieve personalized and precise production plan customization, and promote the transformation of the production process from traditional experience-driven to data-driven.

[0408] Automated production process optimization: This monitoring technology provides an important feedback mechanism for industrial automation. When the processing error is detected to be beyond the preset range, the robot control system can be automatically triggered to make adjustments, such as changing the tool path, adjusting the cutting speed, etc., without manual intervention. This not only improves production efficiency, but also enhances the stability and reliability of the entire automated production process, ensures the consistency of product quality, and enables robot milling to be better integrated into the production line of intelligent manufacturing and industrial automation.

[0409] Precision machining and efficient production areas

[0410] Ensure precision machining accuracy: In the field of precision machining, such as the manufacturing of aerospace parts and high-end medical devices, extremely high machining accuracy is required. Robot milling error monitoring technology can accurately monitor the robot's tiny machining errors at different positions and when processing variable feature surfaces. Through real-time feedback, the operator or control system can take timely measures, such as fine-tuning the robot's motion posture, optimizing cutting force control, etc., to ensure that every machining detail can meet the strict standards of precision machining, thereby ensuring the high performance and high quality of the product.

[0411] Improve efficient production capacity: By timely discovering and correcting processing errors, this technology effectively reduces the scrap rate and rework rate caused by errors. In the production process, it avoids a lot of time and resources being wasted on the treatment of unqualified products, allowing robot milling processing to proceed more smoothly, improving the output rate of qualified products per unit time, achieving the coordinated development of precision processing and efficient production, and meeting the dual needs of modern manufacturing for high-quality and high-efficiency production.

[0412] Real-time monitoring and feedback control areas

[0413] Comprehensive real-time processing monitoring: This technology can monitor all key links of robot milling in real time and continuously. From the dynamic changes of process parameters, to the fluctuation of robot stiffness during processing, to the real-time size of cutting force and the instant evolution of tracking error, all information can be accurately captured and transmitted to the monitoring system. This provides operators and control systems with a comprehensive "window" to understand the processing process, enabling them to grasp the processing status at any time and discover potential problems in a timely manner.

[0414] Precise feedback control implementation: Based on the data obtained from real-time monitoring, a precise feedback control system can be constructed. Once it is found that the processing error has a tendency to exceed the allowable range or has exceeded the standard, the system will quickly feed back the relevant information to the robot's control unit and make real-time adjustments to the processing process based on the pre-set control strategy, such as adjusting the movement angle of the robot joint, changing the cutting parameters, etc., to ensure that the processing error is always controlled within a reasonable range, and to achieve precise control and optimization of the processing process.

[0415] Tool life and resource utilization area

[0416] Extend tool life: Cutting force is one of the key factors affecting tool life, and robot milling error monitoring technology can monitor cutting force signals in real time. By analyzing the relationship between cutting force and processing error, when it is found that excessive cutting force may cause excessive tool wear, cutting parameters can be adjusted in time, such as reducing cutting depth, reducing feed speed, etc., thereby reducing tool load, effectively extending tool life, reducing tool replacement frequency and cost, and improving tool resource utilization efficiency.

[0417] Optimize overall resource allocation: Accurate monitoring of machining errors helps to rationally plan and utilize various production resources. On the one hand, by reducing the waste caused by machining errors, the waste of raw materials is avoided; on the other hand, by optimizing the machining process, the utilization rate of robots, tools and other equipment is improved, so that various resources can play a greater value. In addition, effective control of machining errors can also reduce the additional energy consumption caused by rework, etc., and achieve optimal allocation and efficient utilization of resources.

[0418] Energy conservation, emission reduction and environmental protection

[0419] Reduce energy consumption: In the process of robot milling, unreasonable processing parameter settings (such as too high cutting speed, too large cutting force, etc.) often lead to excessive energy consumption. Through processing error monitoring technology, the processing parameters can be adjusted in real time according to the processing error situation to keep it in the optimal state. For example, when it is found that the increase in processing error may be due to excessive cutting force, the cutting force can be reduced in time, which can not only improve the processing accuracy, but also reduce the additional energy consumption required to overcome the excessive cutting force, thereby achieving the goal of energy conservation and emission reduction.

[0420] Reduce waste discharge: Since the processing error monitoring technology can effectively reduce the scrap rate, it reduces the waste generated by processing unqualified products. At the same time, by optimizing the processing process, the utilization rate of raw materials is improved, the demand for raw materials is further reduced, and the waste discharge generated by raw material mining and processing is indirectly reduced, which plays a positive role in promoting environmental protection.

[0421] In summary, robot milling machining error monitoring technology has extensive and important applications in many important fields, and is of great significance for improving the overall level of manufacturing and achieving sustainable development.

[0422] 2. Relevant evidence of the technical effects obtained by the embodiments of the present invention.

[0423] The processing error predicted by the data-driven model established by the present invention is consistent with the processing error measured by existing high-precision scanners and other sensors, showing good prediction accuracy. Specific evidence is as follows: Fig.19 The results show that the proposed model has effective prediction performance in milling experiments of parts with different machining positions and varying feature surfaces. The MAE, RMSE and R 2 They are 0.0729mm, 0.0906mm and 0.9496 respectively, showing good prediction accuracy. A model comparison was also carried out to prove the superiority of the proposed model. (1) It is compared with the deep neural network model that directly uses processing parameters, robot stiffness, cutting force dynamic characteristics and tracking error as input features, called benchmark-1. Compared with the deep neural network model, the proposed model performs feature fusion on the constituent feature vectors, overcoming the shortcomings of feature information overlap and linear indistinguishability in low-dimensional space, and the dictionary matrix fuses the comprehensive information contained in different types of features to better express the complex state of the machining process. In addition, sparsification retains the most valuable information for error prediction, reduces the model complexity and computational complexity, and effectively avoids overfitting, thereby improving the generalization ability of the model. The comparison of the error measurement value, benchmark-1 and the prediction results of the proposed method on the test set is shown in the figure below. Fig. 20The proposed model significantly improves the prediction accuracy, with MAE on the test set reduced by 58.32%, RMSE reduced by 61.50%, and R 2 An improvement of 43.88%. (2) Ablation experiment: It is compared with a sparse Bayesian model that does not consider the tracking error under cutting force disturbance, called benchmark-2. Compared with benchmark-2, the proposed model takes into account the end tracking error caused by the joint servo error under cutting force disturbance, which reflects the deviation between the actual position and the expected position caused by the dynamic load change of the end, and is closely related to the final processing error. The proposed model uses the end tracking error calculated at each measurement point as the input feature of the processing error prediction model, and performs unsupervised global feature weighting to highlight its importance. It performs adaptive weight adjustment based on the feature's own information content and the correlation between features, which is conducive to improving prediction accuracy. Compared with the ablation model, the proposed model has higher prediction accuracy. The comparison of the error measurement value, the benchmark-2 and the prediction results of the proposed method on the test set is shown in the figure. Fig.21 As shown, the MAE on the test set is reduced by 48.66%, the RMSE is reduced by 52.32%, and the R 2 The improvement was 22.03%. The comparison results with the two methods show that the proposed method has higher prediction accuracy than the deep neural network that considers all features but does not perform feature fusion and sparsification, and the sparse Bayesian model that does not consider tracking errors, which verifies the effectiveness and advantages of the proposed method. For the mass production of parts in actual industrial sites, after the proposed error prediction model is used to predict the machining error, the subsequent workpieces are pre-compensated for the machining tool position points to offset the machining errors caused by the coupling of multiple factors and improve the machining accuracy. The comparison of machining errors before and after compensation is as follows: Fig. 22 As shown, the results show that after pre-compensation of the machining trajectory, the machining accuracy is significantly improved, and the peak value, mean value and standard deviation of the absolute value of the machining error are reduced by 66.09%, 66.40% and 61.65% respectively.

[0424] It should be noted that the embodiments of the present invention can be implemented by hardware, software, or a combination of software and hardware. The hardware part can be implemented using dedicated logic; the software part can be stored in a memory and executed by an appropriate instruction execution system, such as a microprocessor or dedicated design hardware. It can be understood by a person of ordinary skill in the art that the above-mentioned devices and methods can be implemented using computer executable instructions and / or contained in a processor control code, such as a carrier medium such as a disk, CD or DVD-ROM, a programmable memory such as a read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. Such code is provided on the carrier medium. The device and its modules of the present invention can be implemented by hardware circuits such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, etc., or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., can also be implemented by software executed by various types of processors, and can also be implemented by a combination of the above-mentioned hardware circuits and software, such as firmware.

[0425] The above description is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with the technical field within the technical scope disclosed by the present invention and within the spirit and principle of the present invention should be covered by the protection scope of the present invention.

Claims

1. A feature fusion and refinement embedding sparse Bayesian learning method, characterized in that: The following steps are involved: S1, according to the proposed processing parameters, the robot air cutting motion and milling experiments of different processing tasks are carried out, and the joint angle, acceleration signal and cutting force signal are collected at the same time, and the processing error of the workpiece after milling is measured; S2, processes and calculates the original signal collected in S1 to obtain the feature vector of the model input, and uses the measured processing error as the model label; S3, performs feature weighting and feature fusion on the feature vectors calculated in S2 to construct a dictionary matrix; S4, establishing a regression prediction model based on the dictionary matrix and processing error obtained in S3; First, it is assumed that the weights between the model input features and the labels satisfy the Gaussian prior distribution to promote most coefficient weights to approach 0 and achieve the sparsity of the model weights; According to the Bayesian formula, the posterior distribution of the weight variable is obtained, and the expectation and variance of the posterior distribution of the weight coefficient are estimated by maximizing the posterior probability; the variance and the hyperparameters that affect the sparsity of the weight are estimated by maximizing the marginal likelihood function, that is, maximizing the expectation of the joint likelihood function under the posterior distribution of the weight to optimize, and the minimum solution of the transformed loss function can be found to optimize the hyperparameters; the posterior expectation and variance of the model weights, as well as the hyperparameters are iteratively updated during the training process, and the iterative process is terminated according to the set change threshold to achieve the sparsification of the model weight vector and the construction of a sparse model.

2. The feature fusion and refinement embedding sparse Bayesian learning method as claimed in claim 1, characterized in that: In the step S1, air cutting motion and milling experiments of parts with different processing positions and surface features are carried out according to the designed processing trajectory and process parameters; an acceleration sensor is attached to the spindle, and the acceleration and cutting force signals during the milling process are collected through the dynamometer system and the data acquisition system, and the angles of each joint of the robot during the processing are obtained through the robot open data acquisition system, and the workpiece after milling is scanned using a structured light camera to measure the processing error.

3. The feature fusion and refinement embedding sparse Bayesian learning method as claimed in claim 1, characterized in that: In step S2, the process parameters such as the spindle speed, feed rate and cutting depth of the robot milling experiment are used as static input features of the error monitoring model. The robot end stiffness is calculated from the joint stiffness, Jacobian matrix and joint angle: K S =J -T (q)K q J -1 (q) Where J is the Jacobian matrix, q is the joint angle, and K S and K q are the Cartesian stiffness matrix and joint stiffness respectively; the joint stiffness vector is expressed as: K q =diag(K q1 ,K q2 ,K q3 ,K q4 ,K q5 ,K q6 ), K qi represents the stiffness of the i-th joint, K q is a 6×6 diagonal matrix, each diagonal item represents the robot joint stiffness; the diagonal matrix K S The first three values ​​represent the three static stiffnesses in the Cartesian coordinate directions. Recorded as The difference in tool tip position is taken as the end tracking error of the robot under cutting force disturbance and is expressed as: δ tracking h k m (p. 100) cutting )-k m (p. 100) idlecutting ) Where k m is the calibrated kinematic model, p cutting and p idlecutting Represent the joint angles of the robot during cutting and empty cutting respectively; the calculated tracking error value is weighted and used as the input feature of the error monitoring model Prediction of cutting force migration; For the collected original signals of acceleration, cutting force and joint angle, the non-cutting segment data is first removed, and downsampling and timing alignment operations are performed. The relationship between the robot joint angle, acceleration signal and cutting force is characterized as follows: Among them, k represents the current time, F a (k) represents the cutting force at the current moment, q1(kj), q2(kj), q3(kj), q4(kj), q5(kj), q6(kj), a(kj), (j=0,1,...,n) represent the angles and acceleration signals of each joint at the previous moment and the current moment; F a (kj), (j = 1, 2, ..., l) represents the predicted cutting force value at the previous moment, n and l represent the time lag order related to the input and output, respectively, f represents the nonlinear relationship between the input and output, and a data-driven model is used to construct f; during model training, the time-series aligned data is converted into multidimensional data according to the above formula; The feature extractor is defined as follows: Among them, F ES is the deep feature expression contained in the extracted input time series signal, A feature extractor representing the source data; x s is the input source data sample, represents the feature extractor parameters; The extracted source domain features are then input into the regressor to predict the cutting force, and the output dimension is 1; the regression loss of the regressor is as follows: Where n s is the number of source samples, Represents the calculation of mean square error (MSE): represents the regressor parameters; Based on the kernel embedding theory of conditional distribution, a conditional distribution embedding calculation operator is proposed to measure the difference in conditional probability distribution; for O X and O Y The variables X and Y, the corresponding reproducing kernel Hilbert space (RKHS) is and By embedding p(Y|X) into RKHS, the conditional mean embedding can be defined as: in and and yes The operator characterizes the characteristics of the conditional distribution. When a fixed x is taken, a conditional mean embedding value μ is obtained. Y|x ; According to the calculation formula of conditional probability distribution, it is equal to the ratio of joint probability distribution to marginal probability distribution of input; the conditional embedding operator calculation can be defined as the combination of cross covariate operator and independent covariate operator: When given a data set D = {(x1,y1),(x2,y2),...,(x n ,y n )}hour, The estimated value of can be defined as follows: Where F=(φ(y1),φ(y2),...,φ(y n )), γ = (ψ(x1),ψ(x2),...,ψ(x n )),and is the Gram matrix of the variable sample, with a regularization term added to ensure it is well-posed; A conditional distribution embedding operation is designed to estimate the difference between conditional probability distributions; it is defined as follows and used as the loss function for network parameter update to minimize domain differences. The matrix K XX' Calculation using Gaussian kernel κ: K XX' (i,j)=κ(X i ,X′ j )=<f(X i ),f(X′ j )> Where <·,·> represents the vector inner product; The conditional embedding distribution difference is calculated using the new features formed by the second fully connected layer of the target pose unlabeled input data features, the predicted value of the regression network, the new features formed by the second fully connected layer of the source pose data features and their label values. The conditional embedding distribution difference is calculated by using the new features formed by the second fully connected layer of the unlabeled input data features, the predicted value of the regression network, the new features formed by the second fully connected layer of the target pose labeled data features and their label values. The target domain has labeled data prediction values ​​and their label values ​​to calculate regression loss It can be calculated as: For the training of the feature extractor of the target data and the task-specific regressor, the following weighted integrated loss function is used for parameter update: in, is the regression loss of labeled data in the target domain, Represents the difference in conditional distribution measure between source domain data and target domain unlabeled data, represents the difference in conditional distribution between labeled and unlabeled data in the target domain, α s and β t is a trade-off parameter; The network is trained by minimizing the target posture regression loss and the difference between the two conditional embedding distributions, and the optimizer is used to update the network parameters. After the iteration, the cutting force prediction model of the target posture is obtained: The number of decomposition layers is set based on experience, and the cross-correlation spectral index (CSI) is used to achieve adaptive optimization of the penalty factor, which is described by the following formula: Where T is the length of the original signal, i and j are the ordinal numbers of the intrinsic mode functions, and u i and u j is the sub-signal decomposed by the AVMD method; for each penalty factor γ within the set range, the VMD method is used to decompose the original signal, and then its CSI is obtained according to the above formula; the penalty factor corresponding to the minimum CSI value is selected as the optimal value; the original signal is decomposed into several sub-component signals, and the time-frequency domain features are extracted using energy entropy The energy of each sub-signal is calculated as: The energy entropy of the sub-signal is given by: Where r i =R i / R is the percentage of each sub-signal energy to the total signal energy.

4. The feature fusion and refinement embedding sparse Bayesian learning method as claimed in claim 1, characterized in that: In step S3, the robot end tracking error under the influence of the cutting force describes the position deviation of the robot end under the action of the cutting force, which is most closely related to the contour error of the final machined workpiece; Divide the error value into multiple intervals with fixed width; count the number of error values ​​in each interval and calculate the probability p of each interval i , that is, the number of samples in the interval divided by the total number of samples; the resulting probability distribution can describe the frequency of different error ranges; the information entropy is calculated after discretization: Among them, n is the number of intervals after discretization, p i is the probability of the i-th interval; the larger the information entropy value, the more dispersed the distribution of the feature and the higher the uncertainty; The weight of each column of tracking error values ​​is set to a combination of information entropy and variance ratio: Among them, α H and β ζ is a parameter that controls information entropy and variance weight; N t The number of feature columns representing the tracking error. The information entropy measures the uncertainty of the tracking error value in each column. The variance measures the discreteness of the tracking error in each column. The weighted method combining the information entropy and variance can more comprehensively measure the importance of the feature. Select multiple measurement points at equal distances on each trajectory to form a label data set for the prediction model; For the robot end stiffness, cutting force characteristics and weighted tracking error characteristics obtained above, a structured feature row vector is constructed in combination with the machining parameters The feature vectors of multiple samples constitute a feature matrix, and then the feature matrix is ​​normalized to eliminate the influence of large differences in the magnitude of different features; The Gaussian kernel distribution can be expressed as: Where σ is the bandwidth of the Gaussian kernel, which is optimized by a random search algorithm. For the regression model of feature fusion and physical knowledge embedding, the feature vector is mapped by a kernel function to obtain a feature kernel dictionary matrix with a Gaussian distribution. The dictionary matrix is ​​configured as a structured sorting of static and dynamic features according to the order of the measurement points, which not only reflects the trend of the features but also avoids the overlap of feature signals. The feature kernel dictionary matrix Φ is expressed as: The processing error can be expressed as follows: y m =y p +ε;y p =Φω Where y m is the measured processing error, y p is the prediction of machining error, ε is the prediction noise caused by uncertainty in machining and measurement; Φ is the constructed dictionary matrix, and ω is the corresponding weight coefficient, which can be expressed as: ω=[ω1,ω2,...,ω M-1 ,oh M ,b] T 。 5. The feature fusion and refinement embedding sparse Bayesian learning method as claimed in claim 1, characterized in that: In the step S4, a regression prediction model is established according to the dictionary matrix and processing error obtained above; the sparse Bayesian learning method introduces sparsity based on the idea of ​​Bayesian theorem, and assumes Gaussian prior distribution for weights, which can greatly reduce model redundancy and improve computational efficiency, model generalization ability and interpretability; the probability distribution of noise variables can be assumed to be a normal probability density function ε~N(0,λI), where λ is the variance, which is affected by the processing uncertainty caused by vibration and cutting heat and the measurement uncertainty; y m The likelihood function is defined as: A Gaussian prior distribution is introduced on the weight vector to make most of the weight coefficients approach zero and realize the sparsity of the weight vector. In this way, the processing error can be predicted only by the relevant columns in the dictionary matrix and the corresponding sparse weights, which improves the computational efficiency. Usually, in order to calculate the homogeneous analytical solution of the posterior, the prior distribution is the conjugate prior of the likelihood function, that is: where ξ i Impact i The probability of approaching zero is used to control the sparsity of the weight coefficient, reduce the complexity of the model, and avoid overfitting. According to the Bayesian formula, the posterior distribution of the weight variable can be expressed as: In the formula, Λ=diag{ξ1,ξ2,...,ξ N } and P(y m |λ,Λ) represents the marginal distribution of the measured processing error, and N is the number of weights. The posterior expectation and variance of the weight coefficient are estimated by finding the maximum value of the posterior probability, which is expressed as: m ω =λ -1 ∑ ω F T y m ∑ ω =λ(Φ T F+lL -1 ) -1 Then, the hyperparameters λ and Λ are optimized by maximizing the marginal likelihood function. For the convenience of calculation, the logarithm of the likelihood function is taken, i.e., logP(y m |λ,Λ); the optimization of marginal likelihood is equivalent to maximizing its lower bound, the weighted posterior distribution P(ω|y m ,λ k ,Λ k ) can be expressed as: The above operations can generate the following loss function: The optimization problem can be solved by making the partial derivative of the loss function with respect to the hyperparameters equal to zero, and the hyperparameters λ and Λ can be updated as follows: Among them <·> i represents the entry of the ith vector, <·> ii represents the item in the i-th row and i-th column of the matrix; during the iteration process, when the 1-norm of the weight vector || μ ω When the relative change value of ||1 and the standard deviation of the prediction noise is less than the set threshold for multiple consecutive times, the model is judged to be converged; at this time, the model weights are sparse enough, the noise prediction tends to be stable, and the model prediction performance and reliability are high; the convergence condition is expressed as: in is the set convergence threshold.

6. A feature fusion and refinement embedded sparse Bayesian learning system implementing the feature fusion and refinement embedded sparse Bayesian learning method according to any one of claims 1 to 5, characterized in that: The feature fusion and refinement embedding sparse Bayesian learning system includes: The acquisition module is used to perform robot air cutting motion and milling experiments for different processing tasks according to the planned processing parameters, and collect joint angles, acceleration signals and cutting force signals at the same time, and measure the processing error of the workpiece after milling. The processing module is used to process and calculate the collected original signal to obtain the characteristic vector of the model input, and use the measured processing error as the model label; A fusion module is used to perform feature weighting on the calculated feature vectors and perform feature fusion to construct a dictionary matrix; A module is established to establish a regression prediction model based on the obtained dictionary matrix and processing errors.

7. A computer device, characterized in that: The computer device includes a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the feature fusion and refinement embedding sparse Bayesian learning method according to any one of claims 1 to 5.

8. A computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, the processor executes the steps of the feature fusion and refinement embedding sparse Bayesian learning method as described in any one of claims 1 to 5.

9. An information data processing terminal, characterized in that: The information data processing terminal is used to implement the feature fusion and refinement embedded in the sparse Bayesian learning system as described in claim 6.

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