FODPGPFM-based tool remaining service life prediction method

Abstract

The invention discloses a tool remaining service life prediction method based on FODPGPFM, and belongs to the technical field of tool remaining service life prediction. The invention provides a prediction scheme giving consideration to small sample adaptability and nonlinear degradation description capability, effectively solves the problems of low prediction precision and insufficient reliability of the existing method in small sample and nonlinear milling cutter wear scenes, and improves the prediction accuracy of the small samples and nonlinear milling cutter wear scenes through the advantages of processing the small samples and capturing fine nonlinear trends by fusing the fractional derivative grey model. A residual service life prediction model suitable for milling cutter full wear stages (initial stage, middle stage and rapid wear) is constructed according to the ability of particle filtering to deal with dynamic uncertainty in a complex processing environment, and a prediction result with higher precision and narrower confidence interval is realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of tool residual service life prediction, and particularly relates to a tool residual service life prediction method based on a fractional derivative polynomial grey particle filter model (FODPGPFM). BACKGROUND

[0002] In the field of metal manufacturing, high-speed machining has become the mainstream production method. As the core component in high-speed machining, the wear state of the milling cutter has a crucial influence on machining precision and production continuity. Milling cutter wear is affected by many factors, such as machining parameters. If the milling speed and feed rate are not properly matched, it will exacerbate the friction between the tool and the workpiece, accelerating tool wear. The hardness, heat resistance and other properties of the tool material itself also directly determine its wear resistance in high-speed machining. Tool wear not only causes a decline in machining precision and an increase in scrap rate, but also may cause production interruption and increase production costs. Therefore, accurately predicting the residual service life of the milling cutter is of great significance to ensure machining quality, improve production efficiency and reduce costs.

[0003] Currently, the methods for predicting the residual service life of the milling cutter mainly include physical model methods, data-driven methods and hybrid model methods.

[0004] The physical model method uses existing tool wear physical laws to construct a wear evolution state equation to describe the dynamic change process of wear over time. For example, the Paris model is used to depict tool degradation, and the Gaussian importance resampling particle filter is used to iteratively update the parameters to realize the prediction of the residual service life. Or, a wear rate model is derived from the Paris law, which is associated with the stress intensity factor, and then local sampling particle filtering is used to handle noise and improve prediction accuracy. This type of method is based on a state equation derived from physics, which can deeply capture the essence of wear, and uses particle filtering and other techniques to handle uncertainties in the prediction process.

[0005] The data-driven method combines various sensor data with machine learning models and uses particle filtering and other algorithms to handle uncertainties in the prediction process, thereby accurately estimating the tool wear stage and residual service life. For example, particle filtering is combined with support vector regression to first build a degradation stage classification model using clustering and support vector machines, and then real-time prediction of features is performed in actual operation through particle filtering, and the results are input into the support vector regression model. There is also an enhanced particle filter based on virtual sensing and support vector regression, which estimates the degradation state by means of virtual measurement, integrates multi-source data, and uses Bayesian inference for prediction. This type of method deeply excavates the hidden patterns in the data without relying on accurate physical mechanism descriptions, and exhibits strong adaptability and prediction ability in complex and variable machining environments.

[0006] The hybrid model method combines the mechanism knowledge of the physical model and the data analysis ability of the data-driven method, aiming to overcome the limitations of both. On the one hand, the tool remaining useful life is predicted by improving the physical model and combining it with the data-driven method, such as proposing a new exponential degradation model, combining Bayesian inference and particle filtering to handle uncertainty; constructing a hybrid-driven probabilistic state space model and using particle filtering to estimate parameters. On the other hand, the prediction is realized by fusing multi-sensor signals and solving the monitoring cost problem, such as integrating multi-sensor signals and offline information, relying on the state space model and particle filtering framework, and combining sensor selection algorithm to improve prediction accuracy; using spatiotemporal attention multi-feature fusion method, even if part of the signal is missing, the prediction accuracy can still be maintained. In addition, there are also ways to improve the data-driven method and combine it with the physical model to predict, such as using Transformer-GRU and particle filtering to fuse multi-source features and update physical parameters; integrating particle filtering and long short-term memory network into the intelligent system. With the development of digital twin technology, some research combines it with particle filtering, integrating data-driven and simulation-based evaluation; developing a digital twin model, fusing data and mechanism model through particle filtering, improving monitoring efficiency and developing supporting software.

[0007] The gray model is suitable for small sample, information-poor uncertain systems due to its simplicity, low computational complexity, and high short-term prediction accuracy. In the limited data scenario of milling tool remaining useful life prediction, the GM(1, 1) model is a classic single-variable prediction model in the gray model. Since the gray system theory was proposed, the gray model has undergone several improvements. Because the traditional cumulative generating operator does not conform to the new information priority principle of the gray system theory, the fractional order cumulative gray model has better prediction performance in small sample scenarios. In addition, to overcome the limitations of the classic GM(1, 1) model, such as the inability to reflect the new information priority principle and the requirement that the original data must pass the comparison test to obtain ideal modeling results, the fractional derivative gray model was developed, which has significant effects in improving modeling accuracy and adaptability. Particle filtering is a nonlinear, non-Gaussian filtering algorithm based on the Monte Carlo method, which is good at handling noise interference and complex nonlinear characteristics in dynamic systems. It approximates the posterior probability distribution by particle set, realizes accurate estimation and prediction of system state, and has strong adaptability to dynamic changes and uncertainties.

[0008] The closest implementation to the present invention is the gray particle filtering model. This model combines the advantages of gray model in handling small sample data and the ability of particle filtering in handling dynamic uncertainty, but still needs to be further improved in terms of capturing accuracy of nonlinear wear trend and prediction reliability in small sample scenarios.

[0009] In order to solve the above problems, the application provides a tool residual service life prediction method based on a fractional derivative polynomial grey particle filter model (FODPGPFM) which takes into account small sample adaptability and non-linear degradation characterization capability. SUMMARY

[0010] The application aims to provide a tool residual service life prediction method based on FODPGPFM to solve the problems that the existing method is difficult to accurately capture the non-linear wear trend in the small sample and non-linear milling tool wear scene, and the processing capability of dynamic uncertainty is insufficient, the prediction accuracy is low, and the reliability is insufficient, and specifically to solve the following problems in tool residual service life prediction: (1) Milling tool wear data is scarce (often due to limited monitoring resources); (2) The wear process presents non-linear degradation (caused by the coupling effect of milling parameters, workpiece material properties and dynamic cutting conditions, etc.).

[0011] In order to achieve the above purpose, the application adopts the following technical scheme: A tool residual service life prediction method based on FODPGPFM, comprising the following steps: S1, coupling a fractional derivative polynomial grey model and a particle filter deeply to build a fractional derivative grey particle filter model and form a unified state space model; S2, based on the state space model, taking the trend prediction of the fractional derivative polynomial grey model as the core of the state transition equation of the particle filter, so that the particle filter continuously utilizes the mechanism information of the fractional derivative polynomial grey model in the iteration process, and simultaneously corrects the model bias in the reverse through particle weight update, realizing deep fusion of mechanism and data-driven; S3, for the milling tool wear characteristics, a fractional derivative polynomial grey model parameter optimization strategy is designed, and the maximum likelihood estimation is combined with the quasi-Newton algorithm to jointly dynamically optimize the fractional derivative parameters and the particle filter noise parameters, so as to ensure that the parameters are adaptively coordinated in different stages of milling tool wear; S4, based on the optimized parameters, using the multi-state particle distribution output by the particle filter, calculating the probabilistic residual service life to realize tool residual service life prediction, so that the prediction result is more consistent with the uncertainty in actual processing.

[0012] Preferably, the particle filter is a Monte Carlo method for system state estimation with non-linear and non-Gaussian characteristics, which uses a set of random samples to represent the posterior probability distribution of the system state: each particle represents a possible state hypothesis and is assigned a weight representing the credibility, and the true state of the system is dynamically approximated through three recursive steps of prediction, update and resampling; the execution of the particle filter specifically includes the following contents: Suppose a system's state-space model is as follows:

[0013] in, x k express k The system state at any given moment. y k express k Measurement data at any given time; f k and h k These represent the state transition function and the measurement function, respectively. v k-1 express k- Process noise at time 1; n k express k Time-matter noise; Based on a state-space model, state estimation is achieved using Bayesian theory; and the reliability of the current state is obtained by recursively calculating the probability formula through two steps: prediction and update. Specifically, this includes: First, assume that it is known. k The state probability density function at time -1 and state transition probability density function And then, the following prediction formula is used to obtain k Prior probability density function at time t :

[0014] Then, the following update formula is obtained. k posterior probability density function at time t :

[0015] in, Let f(x) be the likelihood function and the normalization constant. ; By using the importance probability density function Extract a set of particles To estimate k The posterior probability density function at time t:

[0016] in, Represents the Dirac function; yes The weights, and their update and normalization process are as follows:

[0017] To simplify calculations, the importance probability density function is chosen as:

[0018] The weight update method then becomes:

[0019] During the weight update process, a cumulative distribution function is used for resampling to avoid the problem of particle weight degradation.

[0020] Preferably, the execution of the fractional derivative polynomial grey model specifically includes the following: Assume the original data sequence of tool wear is ,in yes k The value at time, its r The order of accumulative generation sequence (AGS) is Its function is expressed as:

[0021] Transform it into:

[0022] in, for r An order-order cumulative matrix, denoted as:

[0023] sequence Defined as of r The mean sequence of an AGS (Accumulated Generative Sequence) is represented as:

[0024] sequence Defined as of q A cumulative difference sequence of order 1, where Transform it into the following expression:

[0025] Therefore, the fractional derivative polynomial grey model (FODPGM) is expressed as:

[0026] in, Represents a sequence and The first in k One data point; Let the order be the order of the polynomial. and denote the model parameters obtained by least squares method; P is a parameter column vector; Y P is a column vector composed of dependent variables, B is a design matrix, which is a basic tool in regression analysis, containing the values of independent variables, used to build a linear model; If , and

[0027] the model parameters obtained by least squares estimation satisfy:

[0028] According to formulas (8)-(13), given the initial point satisfying , the numerical solution of the sequence satisfies:

[0029] The reduced value is expressed as: .

[0030] Preferably, based on formula (1) and formula (17), the fractional derivative gray particle filtering model is expressed as:

[0031] wherein, , , , ; V denote the process noise parameters, which are subject to distribution; U denote the measurement noise parameters, which are subject to distribution; unknown parameters in the state space model are important parameters for estimating tool wear, assuming that k dimensional measurement data have been obtained, according to the properties of normal distribution, the multivariate normal distribution of is as follows:

[0032] The mean matrix and covariance matrix of are as follows:

[0033]

[0034] The maximum likelihood function of the multivariate normal distribution is expressed as:

[0035] The optimal initial parameters are obtained by inverting equation (22) and applying the quasi-Newton algorithm :

[0036] In the online prediction process, the observed data is used to estimate and update the unknown parameters represented by the probability density function, which is mathematically expressed as:

[0037] where represents the unknown parameters; represents the observed data; is the likelihood function under the given condition; is the prior function of ; Based on equation (24), equation (7) is generalized as:

[0038] The remaining useful life at the th time point is expressed as:

[0039] where represents the failure threshold preset based on the tool parameters; represents the estimated state from the initial time to the th time point; is the predicted state representing the th time point; The following state transition function is applied to predict the subsequent state of the th particle:

[0040] where is the sampling interval; represents the estimated state of the th particle at the th time point, and ; represents the th row of the r th order cumulative decrease matrix at the th time point; represents the estimated state in the r th order cumulative generation sequence from the initial time to the th time point; ​​The state transition process is terminated when the predicted value exceeds the threshold value; a set of remaining service life is obtained by formula (26) The probability density function of the remaining service life is derived as follows:

[0041] The accuracy of the remaining service life prediction is measured by the mean absolute percentage error (MAPE), and the calculation formula is as follows:

[0042] Wherein, represents the actual value of the first i ; represents the predicted value of the first i ; N represents the number of predicted values.

[0043] The application further protects a computer device, which comprises a processor and a memory, and the memory stores at least one instruction, at least one program, a code set or an instruction set, which is loaded and executed by the processor to realize the above-mentioned tool remaining service life prediction method based on FODPGPFM.

[0044] The application further protects a computer readable storage medium, which stores at least one instruction, at least one program, a code set or an instruction set, which is loaded and executed by the processor to realize the above-mentioned tool remaining service life prediction method based on FODPGPFM.

[0045] Compared with the prior art, the application provides a tool remaining service life prediction method based on FODPGPFM, which has the following beneficial effects: (1) Compared with the prior art, the prediction accuracy of the application in the small sample scene is significantly improved, which is due to the deep fusion mechanism of the fractional derivative polynomial gray model and the particle filter. In the prior art, the physical model method has a sharp decline in accuracy when the data is scarce because it depends on the complete physical model, and the traditional data-driven method is prone to overfitting due to insufficient sample size; while the fractional derivative polynomial gray model in the application captures the nonlinear wear trend under small sample, and the particle filter is used to dynamically correct noise interference, and the average absolute percentage error (MAPE) of the predicted milling cutter remaining service life is much better than similar models.

[0046] (2) The application is more adaptable to the whole wear stage, which is derived from the parameter joint optimization strategy. The existing model is prone to deviation in the initial wear stage due to data fluctuation, and the error rises in the rapid wear stage due to nonlinear aggravation; while the application adjusts the fractional order parameters (a, b) and the particle number (N) in a coordinated manner, and the prediction accuracy is improved. r ,q ) and particle filter noise parameters σ 2 , τ 2 ), let the model rely on the memory stability trend of fractional derivative polynomial grey model in the initial stage, and deal with mutations through particle filtering in the rapid wear stage. Experiments show that the accuracy of the method in each stage remains leading, the prediction confidence interval continuously narrows with data accumulation, and the reliability is better. BRIEF DESCRIPTION OF DRAWINGS

[0047] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiment or prior art description. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0048] Figure 1 The present application provides a kind of based on FODPGPFM's tool residual service life prediction method overall flow chart; Figure 2 It is the milling experiment site map mentioned in embodiment 2 of the present application; Figure 3 It is the relief wear band of milling cutter measured using digital microscope mentioned in embodiment 2 of the present application; Figure 4 It is the relief surface of a blade of milling cutter before and after cutting mentioned in embodiment 2 of the present application, wherein, Figure 4 (a) is before cutting, Figure 4 (b) is after cutting 525 times; Figure 5 It is the prediction result of FODPGPFM mentioned in embodiment 2 of the present application, wherein, (a) initial wear stage (m=1, r=0.33, q=0.72). (b) intermediate wear stage (m=1, r=0.8, q=0.33). (c) rapid wear stage (m=2, r=0.40, q=0.94); Figure 6 It is the prediction result comparison of six models in different stages mentioned in embodiment 2 of the present application; Figure 7 It is the MAPE comparison of prediction results of six models in different stages mentioned in embodiment 2 of the present application. DETAILED DESCRIPTION

[0049] With reference to the accompanying drawings, the technical solutions in the embodiments of the present application will be clearly and completely described below. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application.

[0050] The present application proposes a tool residual useful life prediction method based on a fractional derivative polynomial gray particle filter model (FODPGPFM), aiming to solve the following problems existing in the prior art: 1. The physical model method is difficult to accurately describe the wear process changing with time due to insufficient understanding of the underlying physical law and model simplification; 2. The data-driven method is easily affected by the amount and quality of data, and its performance significantly decreases when the data is scarce; 3. The existing hybrid model has insufficient ability to capture subtle wear trends in small sample nonlinear scenarios, and has a wide prediction confidence interval and limited reliability.

[0051] The causes of the above problems are: 1. The physical model method relies on explicit physical mechanism description, but the milling tool wear is affected by multiple factors coupling (such as milling speed, feed rate, material hardness, etc.), which is difficult to completely describe with a single physical model; 2. The data-driven method relies on a large amount of labeled data to train the model, but the milling tool wear monitoring cost is high in actual production, and the data collection is limited; 3. The gray model in the existing hybrid model mostly uses integer order, which fails to fully utilize the memory and nonlinear description ability of fractional derivative, and the fusion degree with particle filtering is insufficient, which cannot effectively balance the small sample adaptability and dynamic uncertainty processing demand.

[0052] The present application proposes a fractional derivative polynomial gray particle filter model to solve the problems of low prediction accuracy and insufficient reliability of existing methods in small sample and nonlinear milling tool wear scenarios. Specifically, by fusing the advantages of fractional derivative gray model in processing small samples and capturing subtle nonlinear trends, and the ability of particle filtering to cope with dynamic uncertainty in complex processing environment, a residual useful life prediction model suitable for the whole wear stage (initial, intermediate, rapid wear) of milling tool is constructed, and a prediction result with higher precision and narrower confidence interval is realized. The present application proposes a tool residual useful life prediction method based on FODPGPFM, which is described in detail below in combination with relevant drawings and specific examples.

[0053] Embodiment 1: Please refer to Figure 1 The present application proposes a tool residual useful life prediction method based on FODPGPFM, which specifically includes the following contents: 1. Basic principle of particle filtering Particle filtering is a Monte Carlo method for estimating the state of systems with nonlinearity and non-Gaussian properties. Its core idea is to use a set of random samples (called "particles") to represent the posterior probability distribution of the system state: each particle represents a possible state hypothesis and is assigned a weight indicating its confidence level. The algorithm dynamically approximates the true state of the system through three recursive steps: prediction (propagating particles according to the system model), updating (adjusting particle weights based on new observations), and resampling (replicating high-weight particles and discarding low-weight particles to avoid weight degradation).

[0054] Suppose a system has the following state-space model:

[0055] in, x k yes k The system state at any given moment. y k yes k Measurement data at time, f k and h k Let these represent the state transition function and the measurement function, respectively. v k-1 express k- Process noise at time 1 n k yes k Process noise at any given moment.

[0056] Based on the state-space model, state estimation can be achieved using Bayesian theory. The confidence level of the current state is recursively calculated based on a series of existing data, that is, the probability formula is recursively calculated through two steps: prediction and update.

[0057] First, assume that it is known. k The state probability density function at time -1 and state transition probability density function Then, the following prediction formula can be used to obtain... k Prior probability density function at time t :

[0058] Then, the following update formula is obtained. k posterior probability density function at time t :

[0059] in, Let f(x) be the likelihood function and its normalization constant. .

[0060] However, the analytical solution of equations (2) and (3) is difficult to obtain due to the nonlinear and non-Gaussian nature of the system. Therefore, the particle filter estimates the posterior probability density function at time by drawing a set of particles from the importance probability density function k :

[0061] where is the Dirac function, and is the weight of . The update and normalization process of is as follows:

[0062] In practical applications, the importance probability density function is usually chosen as

[0063] Therefore, the weight update method becomes

[0064] However, the problem of particle degeneracy occurs in the weight update process. That is, after several recursive steps, most of the weights are concentrated on a few particles, while the weights of other particles are almost zero. This leads to a waste of a large amount of computing resources in updating these low-weight particles. To solve this problem, this paper uses the cumulative distribution function for resampling.

[0065] 2. Fractional-order derivative polynomial grey model Fractional-order derivative polynomial grey model (FODPGM) is a variant of grey prediction model, which combines fractional-order derivative and polynomial structure. This model inherits the advantages of grey model in dealing with small sample and incomplete data. Among them, fractional-order derivative can capture the memory and nonlinearity of the system, while polynomial enhances the flexibility of fitting complex trends.

[0066] In terms of tool residual life prediction, this model performs well because tool wear data is usually scarce and the wear process has nonlinear characteristics. Fractional-order derivative polynomial grey model (FODPGM) can well fit the limited wear data, capture complex wear patterns through fractional calculus, and has fast calculation speed, which can meet the real-time prediction demand.

[0067] Assume that the original data sequence of tool wear is X (0) ( x(0) (1), x (0) (1),…, x (0) ( n )) T ,in x (0) ( k )yes k The value at time, its r The order of accumulative generation sequence (AGS) is ,Right now:

[0068] It can also be expressed as:

[0069] in, A r for r An order-order cumulative matrix, denoted as:

[0070] sequence Defined as of r The mean sequence of an AGS (Accumulated Generative Sequence) can be represented as:

[0071] sequence Defined as of q A cumulative difference sequence of order 1, where It can also be expressed as:

[0072] Therefore, the fractional derivative polynomial grey model (FODPGM) can be expressed as:

[0073] in, Represents a sequence and The first in k Data points, Let be the order of the polynomial. and These are model parameters obtained using the least squares method.

[0074] P is a parameter column vector; Y P is a column vector consisting of dependent variables, and B is the design matrix, which is a basic tool in regression analysis, containing the values ​​of independent variables and used to construct linear models; like , and

[0075] Then, the model parameters obtained by least squares estimation satisfy equation (15):

[0076] According to equations (8)-(13), when the initial point satisfies , the numerical solution of the sequence satisfies equation (16):

[0077] Then, the restored value can be represented as:

[0078] 3. Fractional order derivative polynomial grey particle filter model (FODPGPFM) The combination of fractional order derivative polynomial grey model (FODPGM) and particle filter has high rationality, and the two can form a complementary relationship in the advantage layer. Specifically, FODPGM has unique advantages in dealing with small samples and incomplete information, enabling it to accurately capture the nonlinear characteristics and memory characteristics of the system. In contrast, particle filtering performs well in dealing with data noise and uncertainty, and can correct model bias by dynamically adjusting particle distribution. This fusion can fully exploit the advantages of both methods and produce a synergistic effect, thereby better adapting to the modeling and prediction needs of complex systems.

[0079] Based on equations (1) and (17), FODPGPFM can be represented as:

[0080] where , and , , the process noise parameter obeys distribution, and the measurement noise parameter obeys distribution.

[0081] The unknown parameters in the state space model are crucial for accurate estimation of tool wear. Assuming that k dimensional measurement data has been obtained, according to the properties of normal distribution, the multivariate normal distribution is as follows:

[0082] The mean matrix and covariance matrix of are as follows:

[0083]

[0084] Then, the maximum likelihood function of the multivariate normal distribution can be expressed as:

[0085] However, formula (22) involves complex matrix operations, so it is quite cumbersome to derive and solve the partial differential equations of formula (22). By performing appropriate transformations on formula (22) - specifically, first inverting formula (22) and then applying the quasi-Newton algorithm - the optimal initial parameters :

[0086] In the online prediction process, the observation data are used to estimate and update the unknown parameters represented by the probability density function, which is mathematically expressed as:

[0087] where represents the unknown parameters, represents the observation data, is the likelihood function under the given condition, is the prior function of . Based on formula (24), formula (7) can be generalized as:

[0088]

[0089] The remaining useful life at the th time point can be expressed as:

[0090] where represents the failure threshold preset based on the tool parameters, is the estimated state from the initial time point to the th time point, is the predicted state at the th time point. Next, the following state transition function can be applied to predict the subsequent state of the th particle:

[0091] where,​ for the sampling interval, denotes the estimated state of the th particle at time , and . denotes the th row of the r th order cumulative reduction matrix at time , and denotes the estimated state of the r th order cumulative generation sequence from the initial time to time . When the prediction value exceeds the threshold value, the state transition process is terminated. A set of remaining useful life can be obtained by formula (26). Finally, the probability density function of the remaining useful life can be derived as follows:

[0092] The accuracy of the remaining useful life prediction is measured by the mean absolute percentage error (MAPE), and the calculation formula is as follows:

[0093] wherein, is the i th actual value, is the i th predicted value, N is the number of predicted values.

[0094] In summary, the focus of the invention mainly includes three aspects: first, the construction and fusion mechanism of the fractional derivative polynomial gray particle filter model, the core of which is to deeply couple the fractional derivative polynomial gray model and the particle filter to form a unified state space model; second, the model parameter optimization strategy for the wear characteristics of the milling cutter, especially the joint dynamic optimization of the fractional derivative parameter and the particle filter noise parameter; third, the remaining useful life prediction decision mechanism based on the fusion model output, focusing on the probabilistic evaluation method combining the particle state distribution and the failure threshold.

[0095] From the technical means, in the prior art, although the fractional derivative gray model has been proposed and used to capture nonlinear trends, it is usually used alone or simply spliced with the filtering algorithm, and does not form a close state space coupling. The present application builds a state space model, uses the trend prediction of the fractional derivative polynomial gray model as the core of the state transition equation of the particle filter, so that the particle filter continuously uses the mechanism information of the fractional derivative polynomial gray model in the iteration process, and at the same time, the model bias is corrected in the reverse direction through the particle weight update, realizing the deep fusion of mechanism and data driven.

[0096] In the aspect of parameter optimization, the existing technology adopts independent setting mode for the fractional order parameters of fractional order derivative polynomial grey model ( r , q ) and the noise parameters of particle filter ( σ 2 , τ 2 ), which may lead to insufficient parameter matching. The present application optimizes the two types of parameters by maximum likelihood estimation combined with quasi-Newton algorithm, ensuring that the parameters can be cooperatively adapted in different stages (initial, medium, and rapid wear) of the milling tool wear. In the aspect of remaining useful life prediction, the existing technology often compares the output value of a single model with a threshold value, while the present application uses the multi-state particle distribution output by the particle filter to calculate the probabilistic remaining useful life, making the result more consistent with the uncertainty in actual processing.

[0097] Embodiment 2 Based on Embodiment 1 but with the difference that an experiment is designed to verify the performance of a tool remaining useful life prediction method based on FODPGPFM proposed by the present application, which specifically includes the following contents: 2.1 Experimental setup To verify the feasibility of the proposed tool remaining life prediction method, a set of tool wear experiments were carried out on a VMC850B vertical CNC machining center in Baoji. As shown in Figure 2 , the workpiece material was 45# steel with dimensions of 125 mm x 125 mm x 100 mm. A four-flute carbide end mill was used for milling experiments, and the detailed cutting parameters and tool parameters are shown in Table 1.

[0098] Table 1 Milling experiment parameters

[0099] During cutting, the tool started from the right end of the workpiece and fed from right to left along the positive direction of the machine tool X-axis, covering the workpiece width (125 mm) in a single milling pass. After completing 25 milling passes, the tool flank face was measured. Due to processing limitations, the tool wear was measured offline, as shown in Figure 3 .

[0100] During measurement, the milling tool was first disassembled from the machining area and removed; then the ViTiny UM06 digital microscope was used to measure the maximum wear width of the tool flank face of the four cutting edges; finally, the average wear width of the four cutting edges was taken as the tool wear value of that pass. Please refer to Figure 4 , Figure 4 (a) is a measurement diagram of the tool flank face of a cutting edge before milling, and Fig. 4 (b) is a measurement diagram of the tool flank face of the same cutting edge after 525 milling passes.

[0101] 2.2 Results and analysis The remaining useful life of the milling cutter is predicted by the particle state estimation function. Figure 5 The prediction results of FODPGPFM in the initial wear stage, the intermediate wear stage and the rapid wear stage are shown respectively. Figure 5 (a) is the prediction curve of the initial wear stage. After 175 milling cycles (i.e. 1544 s of milling time) from the new cutter, the flank wear value is 0.0915 mm. At this time, the model predicts the remaining life of 2585 s, while the actual remaining life is 2647 s. Figure 5 (b) is the prediction curve of the intermediate wear stage. After 275 milling cycles (i.e. 2426 s of milling time), based on the corresponding milling data, the flank wear value is 0.128 mm. At this time, the model predicts the remaining life of 1741 s, while the actual remaining life is 1765 s. Figure 5 (c) is the prediction curve of the rapid wear stage. After 375 milling cycles (i.e. 3308 s of milling time), based on the collected milling data, the flank wear value is 0.18325 mm. In this case, the model predicts the remaining life of 834 s, while the actual remaining life is 883 s. From Figure 5 It can be seen that the prediction values of FODPGPFM for the remaining life of the cutter in different wear stages are not much different. However, as the amount of real data increases, the confidence interval narrows, the prediction accuracy is higher, and the reliability of the model is stronger.

[0102] In order to better explore the effect of FODPGPFM model on the prediction of the remaining useful life of the cutter, this paper compares the prediction effects of the model with five other models, namely polynomial grey model (PGM), polynomial grey particle filter model (PGPFM), fractional order accumulation polynomial grey model (FAPGM), fractional order accumulation polynomial grey particle filter model (FAPGPFM), and fractional order derivative grey model (FODPGM). Figure 6 (a) shows the prediction curves of the six models in the initial wear stage. PGM and PGPFM are limited by the amount of data obtained, and cannot predict the trend of future data from the existing data, so the prediction curve effect is very poor, while the four models of FAPGM, FAPGFM, FODPGM and FODPGPFM can well predict the remaining useful life of the cutter. Figure 6 (b) shows the prediction curves of the six models in the intermediate wear stage. It can be seen that the prediction effect of FODPGPFM and FODPGM is better than that of the other four models. Figure 6(c) shows the prediction curves of these 6 models in the rapid wear stage. Since the models have acquired a considerable amount of real data at this point, the prediction effects of the 6 models are not significantly different, but it can still be seen that FODPGM and FODPGPFM perform better.

[0103] Table 2. Comparison of MAPE of predicted data after obtaining different amounts of data for the six models.

[0104] To further analyze the effectiveness of the above six models in predicting remaining tool life, the MAPE (Modular Value Expiration) of different models at different stages was compared, such as... Figure 5 As shown in Table 2.

[0105] Please see Figure 7 ,from Figure 7 As can be seen, the MAPE generally decreases as more real data is acquired. Compared with the other four models, the FODPGM and FODPGPFM models have relatively smaller overall MAPEs, indicating that these two models have better prediction performance. Table 2 shows that FODPGPFM has a relatively smaller overall MAPE than FODPGM, indicating that the model proposed in this invention has better overall prediction performance.

[0106] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. For those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for predicting the remaining tool life based on FODPGPFM, characterized in that, Includes the following steps: S1. Deeply couple the fractional derivative polynomial grey model with particle filtering to construct a fractional derivative grey particle filter model, forming a unified state space model. S2. Based on the state-space model, the trend prediction of the fractional derivative polynomial grey model is used as the core of the state transition equation of the particle filter, so that the particle filter continuously utilizes the mechanism information of the fractional derivative polynomial grey model during the iteration process. At the same time, the model deviation is corrected in reverse through particle weight update, realizing the deep integration of mechanism and data-driven approaches. S3. To address the wear characteristics of milling cutters, a parameter optimization strategy for the fractional derivative polynomial grey model is designed. By combining maximum likelihood estimation with a quasi-Newton algorithm, the fractional derivative parameters and particle filter noise parameters are jointly and dynamically tuned to ensure that the parameters are adapted in a coordinated manner at different stages of milling cutter wear. S4. Based on the optimized parameters, the multi-state particle distribution output by particle filtering is used to calculate the probabilistic remaining service life, thereby predicting the remaining tool service life and making the prediction results more consistent with the uncertainties in actual machining.

2. The method for predicting remaining tool life based on FODPGPFM according to claim 1, characterized in that, The particle filter is a Monte Carlo method for estimating the state of systems with nonlinearity and non-Gaussian properties. It utilizes a set of random samples to represent the posterior probability distribution of the system state: each particle represents a possible state hypothesis and is assigned a weight indicating its confidence level. The true state of the system is dynamically approximated through three recursive steps: prediction, updating, and resampling. The execution of the particle filter specifically includes the following: Suppose a system's state-space model is as follows: in, x k express k The system state at any given moment. y k express k Measurement data at any given time; f k and h k These represent the state transition function and the measurement function, respectively. v k-1 express k- Process noise at time 1; n k express k Time-matter noise; Based on a state-space model, state estimation is achieved using Bayesian theory; and the reliability of the current state is obtained by recursively calculating the probability formula through two steps: prediction and update. Specifically, this includes: First, assume that it is known. k The state probability density function at time -1 and state transition probability density function And then, the following prediction formula is used to obtain k Prior probability density function at time t : Then, the following update formula is obtained. k posterior probability density function at time t : in, Let f(x) be the likelihood function and its normalization constant. ; By using the importance probability density function Extract a set of particles To estimate k The posterior probability density function at time t: in, Represents the Dirac function; yes The weights, and their update and normalization process are as follows: To simplify calculations, the importance probability density function is chosen as: The weight update method then becomes: During the weight update process, a cumulative distribution function is used for resampling to avoid the problem of particle weight degradation.

3. The method for predicting remaining tool life based on FODPGPFM according to claim 2, characterized in that, The execution of the fractional derivative polynomial grey model specifically includes the following: Assume the original data sequence of tool wear is ,in yes k The value at time, its r The sequence generated by the cumulative generation is Its function is expressed as: Transform it into: in, for r An order-order cumulative matrix, denoted as: sequence Defined as of r The mean sequence of the cumulative generation sequence is represented as: sequence Defined as of q A cumulative difference sequence of order 1, where Transform it into the following expression: Therefore, the fractional derivative polynomial grey model is represented as: in, Represents a sequence and The first in k One data point; k i Indicates the first k Data i Power; Let the order be the order of the polynomial. and This represents the model parameters obtained using the least squares method; P is a parameter column vector; Y P is a column vector consisting of dependent variables, and B is the design matrix, which is a basic tool in regression analysis, containing the values ​​of independent variables and used to construct linear models; like ,and The model parameters obtained through least squares estimation satisfy: According to formulas (8)-(13), given that satisfying initial point At that time, sequence The numerical solution satisfies: Restore value Represented as: 。 4. The method for predicting remaining tool life based on FODPGPFM according to claim 3, characterized in that, Based on equations (1) and (17), the fractional derivative gray particle filter model is expressed as: in, , , , ; V Represents process noise parameters, which follow the rules of... distributed; U Represents the measured noise parameters, which obey... distributed; Unknown parameters in state-space model To estimate key parameters for tool wear, it is assumed that they have been obtained. k Dimensional measurement data According to the properties of the normal distribution, The multivariate normal distribution is as follows: The mean matrix and covariance matrix are as follows: The maximum likelihood function of the multivariate normal distribution is expressed as: Invert equation (22) and then apply the quasi-Newton algorithm to obtain the optimal initial parameters. : In online prediction, observed data is used to estimate and update unknown parameters expressed as a probability density function, the mathematical expression of which is: in, Indicates an unknown parameter; Represents observation data; In order to be in Likelihood function given conditions; yes The prior function; Based on formula (24), formula (7) is generalized as follows: No. Remaining service life at any time Represented as: in, This indicates a failure threshold preset based on tool parameters; Represents from the initial time to time 1 The estimated state; It indicates the time. The predicted state; Apply the following state transition function to predict the first... The subsequent states of the particles: in, The sampling interval; Indicates the first Each particle at time The estimated state, and ; Indicates the first time r The first order of the cumulative decreasing matrix OK; express r The sequence generated by the cumulative generation from the initial time to the time step The estimated state; When the predicted value exceeds the threshold, the state transition process terminates; a set of remaining lifetimes is obtained through formula (26). The probability density function for the remaining useful life is derived as follows: The accuracy of remaining useful life prediction is measured by the mean absolute percentage error, calculated as follows: in, Indicates the first i One actual value; Indicates the first i One predicted value; N This indicates the number of predicted values.

5. A computer device, characterized in that, The computer device includes a processor and a memory, the memory storing at least one instruction, at least one program, code set, or instruction set, the instruction, program, code set, or instruction set being loaded and executed by the processor to implement a tool remaining service life prediction method based on FODPGPFM as described in any one of claims 1-4.

6. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores at least one instruction, at least one program, code set, or instruction set, which is loaded and executed by a processor to implement a tool remaining service life prediction method based on FODPGPFM as described in any one of claims 1-4.

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