Cutter residual life prediction method based on adaptive stage division

Abstract

A cutter residual life prediction method based on adaptive stage division comprises the following steps: firstly, establishing a state space model for cutter residual life prediction so as to comprehensively describe a cutter wear process; secondly, a basis is provided for follow-up analysis by obtaining abrasion data of a current tool and historical tools; then establishing a self-adaptive stage division model, and subdividing the wear stage of the cutter; and finally, accurately obtaining a stage switching point of the current cutter by utilizing the self-adaptive stage division model, and finally predicting the residual life of the cutter through a particle filtering algorithm. The method can adjust the prediction model in real time, adapts to the individual difference of cutter degradation, provides a more accurate residual life prediction result, and has a wide industrial application prospect.

Description

Technical Field

[0001] The invention belongs to the technical field of tool remaining life prediction, and in particular relates to a tool remaining life prediction method with adaptive stage division. Background Art

[0002] As a key component in manufacturing, the health status of the tool directly affects the machining accuracy and production efficiency of mechanical parts. Accurate prediction of the remaining life of the tool is of great significance to improving the reliability and production efficiency of CNC machine tools. The degradation process of the tool can usually be divided into three stages. The initial wear stage changes slowly and is difficult to detect, which may cause the model to underestimate the wear; the rapid changes in the severe wear stage make it difficult for traditional linear predictions to cope with; the stable wear stage may cause prediction errors due to individual differences and changes in processing conditions. Therefore, the main challenge is to accurately identify each degradation stage and adopt an adaptable prediction method.

[0003] Traditional data-driven methods (X.Liu, Y.Lei, N.Li, X.Si, X.Li, RUL prediction ofmachinery using convolutional-vector fusion network through multi-featuredynamic weighting[J]. Mechanical Systems and Signal Processing, 2023, 185: 109788.) mostly rely on high-quality full-life degradation data to train prediction models. However, due to various uncertain factors such as manufacturing process differences and service environment, the degradation process of equipment in the same batch is not always similar. Due to the uncertain and complex degradation process, the accuracy and reliability of the prediction results are limited.

[0004] Although some existing technical methods (N.Li, P.Xu, Y.Lei, X.Cai, D.Kong, A self-data-driven method for remaining useful life prediction of wind turbines considering continuously varying speeds [J]. Mechanical Systems and Signal Processing, 2022, 165: 108315.) can predict the remaining useful life based on the degradation data of the mechanical components themselves, solving the problem of having to rely on large batches of data for training. However, their methods cannot capture the changes in the degradation stage during the degradation process, and there is still a large deviation in the accuracy of the prediction. Summary of the invention

[0005] In order to overcome the shortcomings of the above-mentioned prior art, the purpose of the present invention is to provide a method for predicting the remaining life of a tool with adaptive stage division, which realizes adaptive division of the tool operation stages by real-time monitoring of the tool's operating status and combines multi-source sensor data analysis, and makes accurate remaining life predictions based on the characteristics of each stage; by dynamically adapting to the different degradation stages of the tool, the accuracy and reliability of the prediction are significantly improved.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is:

[0007] A tool remaining life prediction method based on adaptive stage division includes the following steps:

[0008] Step 1: Establish a state space model for tool remaining life prediction:

[0009] x t =f(x t-1 )+ω t (1)

[0010] y t =h(x t )+ν t (2)

[0011] Among them, formula (1) is the state transfer equation, formula (2) is the observation equation, x t is the state vector, f(·) is the state transfer function, ω t is the process noise vector, which is zero-mean Gaussian noise, and its covariance matrix is ​​Σ ω ;y t is the observation vector, h(·) is the observation function, which describes the relationship between the state and the observed value, and v t is the observation noise vector, which is zero-mean Gaussian noise, and its covariance matrix is ​​Σ v ;

[0012] Step 2: Obtain the wear data of the current tool and historical tools: By real-time monitoring of the wear of the current tool and combining it with the wear data of the historical tool, systematically collect the wear information of the tool at different processing stages, and integrate the relevant historical wear data as the basis for establishing an adaptive stage division model to ensure that the wear data covers the entire life cycle of the tool;

[0013] Step 3: Establish an adaptive stage division model: Based on the tool degradation process, establish a model for dynamically dividing different degradation stages;

[0014] Step 4: Obtain the stage switching point of the current tool: In the new tool sample, first use the historical samples to make a preliminary estimate of the switching point threshold; then through online real-time monitoring and judgment, dynamically adjust the switching point threshold to finally determine the switching point;

[0015] Step 5: Use the particle filter algorithm to predict the remaining life of the tool: Use the tool wear value data monitored in real time to predict the remaining life, and substitute these data into the adaptive stage division model, combined with the particle filter algorithm to predict the remaining life of the tool.

[0016] The third step is specifically:

[0017] 3.1) The wear data of historical tools are processed by differential method to generate a new set of differential data. Suppose there are m tools, corresponding to m arrays, each array A i Contains i elements, that is, the array A1, A2, A3, ..., A m ,in The difference operation on these arrays is defined as follows:

[0018]

[0019] Where i = 1, 2, 3, ..., m;

[0020] 3.2) Determine whether there are three points that rise continuously, find the first group of points that meet the condition, and determine whether the final value of these three points exceeds the set threshold. The specific expression is: ((a k+1 -a k )>0)∧((a k+2 -a k+1 )>0)∧(a k+3 -a k+2 )>T) (4)

[0021] The range of k is 1≤k≤n-3, and T is a threshold set greater than zero;

[0022] 3.3) If step 3.2) is satisfied, the point is determined to be a stage switching point, and the ordinate corresponding to the point is the stage switching point threshold;

[0023] 3.4) Iterate steps 3.2) to 3.3) multiple times until the first phase switching point is obtained.

[0024] The fourth step is specifically as follows:

[0025] 4.1) Preliminary estimation of the switching point threshold. When the tool sample is in the early degradation stage, the tool has not yet degraded to the stage switching moment. It is necessary to use historical samples under similar working conditions for preliminary estimation. Assuming there are N historical samples, the switching point threshold of each sample i is T i , by averaging the switching point thresholds of historical samples, preliminarily estimate the switching point threshold T of the current tool E ;

[0026]

[0027] 4.2) Online real-time judgment of the switching point threshold. For the degradation data obtained in real time, it is assumed that the tool wear data point set of the current time step can be {d1, d2, d3, …, d t}; Substitute these wear value data into the adaptive phase division model g, and update the switching point threshold T of the current tool online through the model O ; As time goes by and data points accumulate, T O It will gradually converge to a more accurate switching point;

[0028] T O =g({d1,d2,d3,…,d t}) (6)

[0029] 4.3) Comprehensively consider the preliminary estimation and online judgment, taking into account the preliminary estimation switching point threshold TE 和 Online real-time judgment of the switching point threshold T O The difference between the final switching point threshold T F It is expressed as the weighted average of the two:

[0030] T F =αT E +(1-α)T O (7)

[0031] Among them, α is a weight coefficient, which indicates the degree of trust in the initial estimate and the real-time judgment value. As the real-time data accumulates, α switches between 0 and 1, making T F More dependent on the judgment results of online data.

[0032] The fifth step is specifically as follows:

[0033] 5.1) According to the stage division results of the adaptive stage division model, when the tool is in the initial wear stage, the data of the initial wear stage is ignored during modeling; when the tool enters the normal wear and severe wear stages, the adaptive stage division model will automatically identify the stage switching according to the wear value data monitored in real time, and at this time, the model parameters will be adjusted according to the wear characteristics of different stages;

[0034] 5.2) According to the different wear stages of the tool, the established state space model is used to construct a prediction model suitable for each stage;

[0035] When the tool enters the normal wear stage, the tool wear value increases approximately linearly with time. In this stage, the state transfer equation and observation equation are:

[0036]

[0037] Among them, x t-1 is the state vector of the previous time step, Σ1 is the covariance matrix of the process noise, n1 is the random noise vector of the standard normal distribution, x0, x1, x2, x3 are the components of the state vector, corresponding to different model parameters;

[0038] When the tool enters the severe wear stage, the tool degradation process shows an approximate exponential trend. The state transfer equation and observation equation at this stage are:

[0039]

[0040] Among them, x t-1 It also represents the state vector of the previous time step, Σ2 is the covariance matrix of the process noise of the tool in the severe wear stage, n2 is the random noise vector of the standard normal distribution of the tool in the severe wear stage, and x0, x1, x2, x3 are the components of the state vector;

[0041] 5.3) Use particle filtering algorithm to predict the remaining life of the tool: The particle filtering algorithm approximates the posterior distribution by using a set of weighted random samples, namely "particles", so as to track the system state and make predictions without relying on linearization assumptions.

[0042] The particle filter algorithm is used in step 5.3 to predict the remaining tool life as follows:

[0043] 5.3.1) Initialize particle set: At the beginning of prediction, a particle set is generated, each particle represents a possible tool wear state and is assigned a corresponding weight; the initialization state is set based on historical data or prior knowledge to ensure that the particle set can cover all possible initial wear states;

[0044] 5.3.2) State prediction: Using the state transfer equation established in the above step 5.2), the state of each particle in the particle set is predicted;

[0045] 5.3.3) Weight update: For each particle, calculate its closeness to the actual observed data and update the weight according to the result. The higher the weight, the closer the wear state represented by the particle is to the actual situation.

[0046] 5.3.4) Resampling: Generate a new set of particles by replicating high-weight particles multiple times and discarding low-weight particles;

[0047] 5.3.5) Remaining life prediction: by iterating the above steps 5.3.2) to 5.3.4) multiple times, the future wear state of the tool is gradually predicted; at each time step, the wear state distribution of the tool is estimated based on the particle set, and the remaining life (RUL) of the tool is predicted based on the predefined remaining life index;

[0048] 5.3.6) Adaptive adjustment: When the tool wear state changes significantly, the particle filter reflects the new wear characteristics by updating the parameters of the state transfer equation and the observation equation, thereby improving the prediction accuracy.

[0049] Compared with the prior art, the present invention has the following beneficial effects:

[0050] The present invention proposes a method for predicting the remaining life of a tool with adaptive stage division. Since a stage division model is established, the prediction model can be dynamically adjusted and optimized by monitoring the degradation data of the tool in real time and combining the switching point threshold of historical samples. The present invention can accurately identify the key switching points in the tool degradation process, reducing the dependence on a large amount of training data, thereby significantly improving the accuracy and reliability of the remaining life prediction of the tool. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 The figure is a flow chart of a method according to an embodiment of the present invention.

[0052] Figure 2 Schematic diagram of four groups of tool degradation trajectories in an embodiment of the present invention.

[0053] Figure 3 Result diagram of adaptive stage division of four groups of tool degradation trajectories in an embodiment of the present invention.

[0054] Figure 4 These are the prediction results of four groups of tool trajectories in the entire prediction cycle according to the embodiment of the present invention. DETAILED DESCRIPTION

[0055] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0056] Reference Figure 1 , a tool remaining life prediction method based on adaptive stage division, comprising the following steps:

[0057] Step 1: Establish a state space model for tool remaining life prediction:

[0058] x t =f(xt-1 )+ω t (1)

[0059] y t =h(x t )+v t (2)

[0060] Among them, formula (1) is the state transfer equation, formula (2) is the observation equation, x t is the state vector, f(·) is the state transfer function, ω t is the process noise vector, which is zero-mean Gaussian noise, and its covariance matrix is ​​∑ ω ;y t is the observation vector, h(·) is the observation function, which describes the relationship between the state and the observed value, and v t is the observation noise vector, which is zero-mean Gaussian noise, and its covariance matrix is ​​∑ v ;

[0061] Step 2: Obtain the wear data of the current tool and historical tools: By real-time monitoring of the wear of the current tool and combining it with the wear data of the historical tool, systematically collect the wear information of the tool at different processing stages, and integrate the relevant historical wear data as the basis for establishing an adaptive stage division model to ensure that the wear data covers the entire life cycle of the tool;

[0062] Step 3: Establish an adaptive stage division model: Based on the tool degradation process, establish a model for dynamically dividing different degradation stages; specifically:

[0063] 3.1) The wear data of historical tools are processed by differential method to generate a new set of differential data. Suppose there are m tools, corresponding to m arrays, each array A i Contains i elements, that is, arrays A1, A2, A3, ..., A m ,in The difference operation on these arrays is defined as follows:

[0064]

[0065] Where i = 1, 2, 3, ..., m;

[0066] 3.2) Determine whether there are three points that rise continuously, find the first group of points that meet the condition, and determine whether the final value of these three points exceeds the set threshold. The specific expression is: ((a k+1 -a k )>0)∧((a k+2 -a k+1 )>0)∧((a k+3 -ak+2 )>T) (4) where the range of k is 1≤k≤n-3, and T is a threshold value set to be greater than zero;

[0067] 3.3) If step 3.2) is satisfied, the point is determined to be a stage switching point, and the ordinate corresponding to the point is the stage switching point threshold;

[0068] 3.4) Iterate steps 3.2) to 3.3) multiple times until the first stage switching point is obtained;

[0069] Step 4: Obtain the stage switching point of the current tool: In the new tool sample, first use the historical samples to make a preliminary estimate of the switching point threshold; then through online real-time monitoring and judgment, dynamically adjust the switching point threshold to finally determine the switching point; specifically:

[0070] 4.1) Preliminary estimation of the switching point threshold. When the tool sample is in the early degradation stage, the tool has not yet degraded to the stage switching moment. It is necessary to use historical samples under similar working conditions for preliminary estimation. Assuming there are N historical samples, the switching point threshold of each sample i is T i , by averaging the switching point thresholds of historical samples, preliminarily estimate the switching point threshold T of the current tool E ;

[0071]

[0072] 4.2) Online real-time judgment of the switching point threshold. For the degradation data obtained in real time, it is assumed that the tool wear data point set of the current time step can be {d1, d2, d3, …, d t}; Substitute these wear value data into the adaptive phase division model g, and update the switching point threshold T of the current tool online through the model O ; As time goes by and data points accumulate, T O It will gradually converge to a more accurate switching point;

[0073] T O =g({d1,d2,d3,…,d t}) (6)

[0074] 4.3) Comprehensively consider the preliminary estimation and online judgment, taking into account the preliminary estimation switching point threshold T E and the switching point threshold T for online real-time judgment O The difference between the final switching point threshold T F It is expressed as the weighted average of the two:

[0075] T F =αT E +(1-α)T O (7)

[0076] Among them, α is a weight coefficient, which indicates the degree of trust in the initial estimate and the real-time judgment value. As the real-time data accumulates, α switches between 0 and 1, making T F More dependent on the judgment results of online data;

[0077] Step 5: Use particle filter algorithm to predict the remaining life of the tool: Use the tool wear value data monitored in real time to predict the remaining life, and substitute these data into the adaptive stage division model, combined with the particle filter algorithm to predict the remaining life of the tool; specifically:

[0078] 5.1) According to the stage division results of the adaptive stage division model, when the tool is in the initial wear stage, the data of the initial wear stage is ignored during modeling; when the tool enters the normal wear and severe wear stages, the adaptive stage division model will automatically identify the stage switching according to the wear value data monitored in real time, and at this time, the model parameters will be adjusted according to the wear characteristics of different stages;

[0079] 5.2) According to the different wear stages of the tool, the established state space model is used to construct a prediction model suitable for each stage;

[0080] After the tool has gone through the initial wear stage, the rough surface of the tool has been smoothed, and it enters the normal wear stage. In this stage, the wear value of the tool increases approximately linearly with time. In this stage, the state transfer equation and observation equation are:

[0081]

[0082] Among them, x t-1 is the state vector of the previous time step, Σ1 is the covariance matrix of the process noise, n1 is the random noise vector of the standard normal distribution, x0, x1, x2, x3 are the components of the state vector, corresponding to different model parameters;

[0083] When the width of the tool wear zone increases to a certain limit, the tool enters the severe wear stage. In this stage, the wear rate of the tool is significantly accelerated. At this time, the degradation process of the tool presents an approximate exponential trend. The state transfer equation and observation equation in this stage are:

[0084]

[0085] Among them, x t-1 It also represents the state vector of the previous time step, Σ2 is the covariance matrix of the process noise of the tool in the severe wear stage, n2 is the random noise vector of the standard normal distribution of the tool in the severe wear stage, and x0, x1, x2, x3 are the components of the state vector;

[0086] 5.3) Use particle filter algorithm to predict the remaining life of the tool: The particle filter algorithm approximates the posterior distribution by using a set of weighted random samples, namely "particles", so as to track the system state and make predictions without relying on linearization assumptions;

[0087] The particle filter algorithm is used in step 5.3 to predict the remaining tool life as follows:

[0088] 5.3.1) Initialize particle set: At the beginning of prediction, a particle set is generated, each particle represents a possible tool wear state and is assigned a corresponding weight; the initialization state is set based on historical data or prior knowledge to ensure that the particle set can cover all possible initial wear states;

[0089] 5.3.2) State prediction: Using the state transfer equation established in the above step 5.2), the state of each particle in the particle set is predicted;

[0090] 5.3.3) Weight update: For each particle, calculate its closeness to the actual observed data and update the weight according to the result. The higher the weight, the closer the wear state represented by the particle is to the actual situation.

[0091] 5.3.4) Resampling: Generate a new set of particles by replicating high-weight particles multiple times and discarding low-weight particles;

[0092] 5.3.5) Remaining life prediction: by iterating the above steps 5.3.2) to 5.3.4) multiple times, the future wear state of the tool is gradually predicted; at each time step, the wear state distribution of the tool is estimated based on the particle set, and the remaining life (RUL) of the tool is predicted based on the predefined remaining life index;

[0093] 5.3.6) Adaptive adjustment: When the tool wear state changes significantly, the particle filter reflects the new wear characteristics by updating the parameters of the state transfer equation and the observation equation, thereby improving the prediction accuracy.

[0094] Through the above steps, the particle filter algorithm can dynamically track the wear process of the tool and accurately predict its remaining life, especially when dealing with complex wear behaviors and multi-stage wear characteristics.

[0095] In order to prove the effectiveness of the method of the present invention, this embodiment extracts four sets of wear value data of the tool life cycle, and combines the method of the present invention to predict the remaining life. Specifically, the degradation data of the tool is trained by the cross-validation method, such as Figure 2As shown in Figure 2, it can be seen that the degradation trends of the four groups of tools do not have a strong correlation. The difference method is used to determine the stage switching point threshold of the current tool, as shown in Figure 2. Figure 3 As shown in the figure, the switching point of the degradation stage of each tool can be obtained. Subsequently, the model is adaptively switched according to the estimated switching point threshold and the switching point threshold monitored in real time, ensuring that the model can accurately predict the remaining life of the tool at different wear stages.

[0096] The full life cycle prediction results of four sets of tools are calculated according to the method of the present invention, such as Figure 4 As shown, it can be clearly seen that the predicted remaining useful life is very close to the actual remaining useful life, which verifies the effectiveness and accuracy of the method of the present invention in the remaining useful life prediction.

[0097] It should be pointed out that, without departing from the concept of the present invention, adjustments and modifications made to the method of the present invention should also be regarded as within the protection scope of the present invention.

Claims

1. A tool remaining life prediction method based on adaptive stage division, characterized in that: The following steps are involved: Step 1: Establish a state space model for tool remaining life prediction: x t =f(x t-1 )+ω t (1) y t =h(x t )+v t (2) Among them, formula (1) is the state transfer equation, formula (2) is the observation equation, x t is the state vector, f(·) is the state transfer function, ω t is the process noise vector, which is zero-mean Gaussian noise, and its covariance matrix is ​​Σ ω ;y t is the observation vector, h(·) is the observation function, which describes the relationship between the state and the observed value, and v t is the observation noise vector, which is zero-mean Gaussian noise, and its covariance matrix is ​​Σ v ; Step 2: Obtain the wear data of the current tool and historical tools: By real-time monitoring of the wear of the current tool and combining it with the wear data of the historical tool, systematically collect the wear information of the tool at different processing stages, and integrate the relevant historical wear data as the basis for establishing an adaptive stage division model to ensure that the wear data covers the entire life cycle of the tool; Step 3: Establish an adaptive stage division model: Based on the tool degradation process, establish a model for dynamically dividing different degradation stages; Step 4: Obtain the stage switching point of the current tool: In the new tool sample, first use the historical samples to make a preliminary estimate of the switching point threshold; then through online real-time monitoring and judgment, dynamically adjust the switching point threshold to finally determine the switching point; Step 5: Use the particle filter algorithm to predict the remaining life of the tool: Use the tool wear value data monitored in real time to predict the remaining life, and substitute these data into the adaptive stage division model, combined with the particle filter algorithm to predict the remaining life of the tool.

2. The method for predicting the remaining tool life according to claim 1, characterized in that: The third step is specifically: 3.1) The wear data of historical tools are processed by differential method to generate a new set of differential data. Suppose there are m tools, corresponding to m arrays, each array A i Contains i elements, that is, the array A1, A2, A3, ..., A m ,in The difference operation on these arrays is defined as follows: Where i = 1, 2, 3, ..., m; 3.2) Determine whether there are three points that rise continuously, find the first group of points that meet the condition, and determine whether the last value of these three points exceeds the set threshold. The specific expression is: ((a k+1 -a k )>0)∧((a k+2 -a k+1 )>0)∧((a k+3 -a k+2 )>T) (4) The range of k is 1≤k≤n-3, and T is a threshold value set to be greater than zero; 3.3) If step 3.2) is satisfied, the point is determined to be a stage switching point, and the ordinate corresponding to the point is the stage switching point threshold; 3.4) Iterate steps 3.2) to 3.3) multiple times until the first phase switching point is obtained.

3. The method for predicting the remaining tool life according to claim 1, characterized in that: The fourth step is specifically as follows: 4.1) Preliminary estimation of the switching point threshold. When the tool sample is in the early degradation stage, the tool has not yet degraded to the stage switching moment. It is necessary to use historical samples under similar working conditions for preliminary estimation. Assuming there are N historical samples, the switching point threshold of each sample i is T i , by averaging the switching point thresholds of historical samples, preliminarily estimate the switching point threshold T of the current tool E ; 4.2) Online real-time judgment of the switching point threshold. For the degradation data obtained in real time, it is assumed that the tool wear data point set of the current time step can be {d1, d2, d3, …, d t }; Substitute these wear value data into the adaptive phase division model g, and update the switching point threshold T of the current tool online through the model O ; As time goes by and data points accumulate, T O It will gradually converge to a more accurate switching point; T O =g({d1,d2,d3,…,d t }) (6) 4.3) Comprehensively consider the preliminary estimation and online judgment, taking into account the preliminary estimation switching point threshold T E and the switching point threshold T for online real-time judgment O The difference between the final switching point threshold T F It is expressed as the weighted average of the two: T F =αT E +(1-α)T O (7) Among them, α is a weight coefficient, which indicates the degree of trust in the initial estimate and the real-time judgment value. As the real-time data accumulates, α switches between 0 and 1, making T F More dependent on the judgment results of online data.

4. The method for predicting the remaining tool life according to claim 1, characterized in that: The fifth step is specifically as follows: 5.1) According to the stage division results of the adaptive stage division model, when the tool is in the initial wear stage, the data of the initial wear stage is ignored during modeling; when the tool enters the normal wear and severe wear stages, the adaptive stage division model will automatically identify the stage switching according to the wear value data monitored in real time, and at this time, the model parameters will be adjusted according to the wear characteristics of different stages; 5.2) According to the different wear stages of the tool, the established state space model is used to construct a prediction model suitable for each stage; When the tool enters the normal wear stage, the tool wear value increases approximately linearly with time. In this stage, the state transfer equation and observation equation are: Among them, x t-1 is the state vector of the previous time step, Σ1 is the covariance matrix of the process noise, n1 is the random noise vector of the standard normal distribution, x0, x1, x2, x3 are the components of the state vector, corresponding to different model parameters; When the tool enters the severe wear stage, the tool degradation process shows an approximate exponential trend. The state transfer equation and observation equation at this stage are: Among them, x t-1 It also represents the state vector of the previous time step, Σ2 is the covariance matrix of the process noise of the tool in the severe wear stage, n2 is the random noise vector of the standard normal distribution of the tool in the severe wear stage, and x0, x1, x2, x3 are the components of the state vector; 5.3) Use particle filtering algorithm to predict the remaining life of the tool: The particle filtering algorithm approximates the posterior distribution by using a set of weighted random samples, namely "particles", so as to track the system state and make predictions without relying on linearization assumptions.

5. The method for predicting the remaining life of a tool according to claim 4 is characterized in that the prediction of the remaining life of the tool by using a particle filter algorithm in step 5.3) is specifically as follows: 5.3.1) Initialize particle set: At the beginning of prediction, a particle set is generated, each particle represents a possible tool wear state and is assigned a corresponding weight; the initialization state is set based on historical data or prior knowledge to ensure that the particle set can cover all possible initial wear states; 5.3.2) State prediction: Using the state transfer equation established in the above step 5.2), the state of each particle in the particle set is predicted; 5.3.3) Weight update: For each particle, calculate its closeness to the actual observed data and update the weight according to the result. The higher the weight, the closer the wear state represented by the particle is to the actual situation. 5.3.4) Resampling: Generate a new set of particles by replicating high-weight particles multiple times and discarding low-weight particles; 5.3.5) Remaining life prediction: by iterating the above steps 5.3.2) to 5.3.4) multiple times, the future wear state of the tool is gradually predicted; at each time step, the wear state distribution of the tool is estimated based on the particle set, and the remaining life (RUL) of the tool is predicted based on the predefined remaining life index; 5.3.6) Adaptive adjustment: When the tool wear state changes significantly, the particle filter reflects the new wear characteristics by updating the parameters of the state transfer equation and the observation equation, thereby improving the prediction accuracy.

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