Tool wear prediction method based on physics-guided Gaussian process of free energy theory

Abstract

The present invention discloses a tool wear prediction method based on a physics-guided Gaussian process of free energy theory, the steps of which include: 1. establishing a cutting signal-wear-wear rate data set based on the collected cutting force signal; 2. establishing equations between tool wear, wear rate, and signal characteristics using the free energy theory in statistical mechanics; 3. performing data-driven proxy modeling on the free energy and temperature of the system through a physics-guided Gaussian process; 4. establishing a second constraint relationship by taking the derivative of the physics-guided Gaussian process and making it equal to the wear rate; 5. performing Bayesian optimization on the model to obtain the optimal tool wear; 6. directly predicting the wear value using the model. The present invention has the characteristics of easy implementation, good robustness, and high reliability, and can improve the accuracy and interpretability of tool wear prediction, thereby improving the efficiency of milling processing and the quality of produced parts.

Description

Technical Field

[0001] The present invention belongs to the field of tool condition monitoring, and in particular is a tool wear prediction method based on a physically guided Gaussian process of free energy theory. Background Art

[0002] Tool wear is an inevitable natural phenomenon in milling, impacting part quality and machining efficiency. Monitoring tool wear to accurately estimate tool wear and enable timely tool changes is crucial for improving machining quality and efficiency. The most commonly used tool wear monitoring method is the indirect method, which infers tool wear values ​​through real-time acquisition of sensor signals. With the advent of the concept of "smart manufacturing," indirect methods, combined with artificial intelligence (AI), have become more intelligent and automated. Machine learning methods can directly map machining signals to tool wear values ​​without requiring any knowledge of the underlying milling process. However, most existing methods are purely data-driven, overly relying on machine learning methods and ignoring the internal connections between milling signals and the relationship between machining signals and tool wear. On the one hand, these tool wear estimation methods, based solely on "black-box" models, are difficult to guarantee accuracy across diverse scenarios and working conditions, limiting their generalizability and robustness. On the other hand, their lack of understanding of the underlying machining process mechanisms undermines the reliability of such methods, limiting their application in practical production tasks. Summary of the Invention

[0003] In order to address the shortcomings of the above-mentioned existing technologies, the present invention proposes a tool wear prediction method based on a physically guided Gaussian process of free energy theory, in order to achieve a stable and accurate estimation of the tool wear value during milling processing, thereby overcoming the problems of poor generalization, robustness and low reliability of traditional methods in predicting tool wear values ​​under different scenarios and working conditions.

[0004] In order to achieve the above-mentioned object, the present invention adopts the following technical solutions:

[0005] The tool wear prediction method of the present invention based on the physical guided Gaussian process of free energy theory is characterized in that it includes the following steps:

[0006] Step 1: Perform milling on the tool and collect the i-th segment cutting signal sequence of the tool in the X, Y, and Z directions at a fixed frequency , the i-th segment spindle vibration acceleration signal in the X, Y, and Z directions And the i-th segment acoustic emission signal of the tool , while collecting the current signal of the machine tool in section i ; The actual tool wear value of the i-th segment of the tool is recorded as , and calculated using the difference between adjacent wear values Tool wear rate ; Thus forming the milling processing data set ;in, represents the milling processing data of the i-th segment of the tool, and , represents the wear label of the i-th segment of the tool, and , T represents transpose, express time series; N represents the total number of time series;

[0007] Step 2: Extract the signal characteristics of milling processing based on the theory of statistical mechanics;

[0008] Step 3: Use the Gaussian process surrogate model to establish the tool wear equation:

[0009] Step 3.1: Construct a mean function that conforms to the physical process of tool wear;

[0010] Step 3.2: Construct a kernel function that conforms to the physical process of tool wear;

[0011] Step 3.3: Construct tool wear equation based on signal characteristics, mean function and kernel function;

[0012] Step 3.4: Based on D, use the Bayesian optimization algorithm to optimize the mechanical energy of the tool wear equation to obtain the tool wear equation under the optimal hyperparameters;

[0013] Step 4: Collect the milling processing data of the current period in real time and input it into the tool wear equation under the optimal hyperparameters after processing according to the process of step 2. Use the 4th-order Runge-Kutta method to integrate the equation to obtain the predicted tool wear value in the current period.

[0014] The tool wear prediction method based on the physical guided Gaussian process of free energy theory of the present invention is also characterized in that the step 3 includes the following steps:

[0015] Step 2.1: After normalization, the dimensionless milling processing data of the i-th segment is obtained , and use the variational mode decomposition method to Decomposed into n intrinsic mode function components, we get The eigenmode function component matrix of the cutting signal with rows and k columns is ;

[0016] Step 2.2: Importance weight vector ,in, The number of rows and The number of rows is equal, The number of columns is 1;

[0017] Step 2.3: Calculate using formula (1) Enthalpy , thus obtaining the enthalpy vector :

[0018] (1)

[0019] In formula (1), t represents The index of the cutting signal sequence of each row at a discrete moment; express The cutting signal sequence of column t in ;

[0020] Step 2.4: Calculate using formula (2) The energy probability corresponding to the jth row in :

[0021] (2)

[0022] In formula (2), Indicates the set constant, express The cutting signal of row j and column t in ; express The j-th importance weight value in ;

[0023] Step 2.5: Calculate using formula (3) Entropy :

[0024] (3).

[0025] Furthermore, the step 3.1 includes the following steps:

[0026] Step 3.1.1: Use Fourier series to Perform fitting to obtain the fitted wear rate curve , thereby setting the wear rate mean function ;

[0027] Step 3.1.2: Use Fourier series to Perform fitting to obtain the fitted wear value curve , thereby setting the wear value mean function .

[0028] Furthermore, the step 3.2 includes the following steps:

[0029] Step 3.2.1: Use Equation (4) to construct a kernel function that conforms to the tool wear rate change process :

[0030] (4)

[0031] In formula (4), Indicates the tool's Segment milling processing data The corresponding tool wear rate, express The corresponding timing, 、 、 、 、 There are 5 hyperparameters respectively;

[0032] Step 3.2.2: Use Equation (7) to construct a kernel function that conforms to the physical process of tool wear :

[0033] (7)

[0034] In formula (7), express The corresponding free energy, 、 、 、 There are 4 hyperparameters respectively.

[0035] Furthermore, the step 3.3 includes the following steps:

[0036] Step 3.3.1: Use Equation (9) to construct the tool wear equation:

[0037] (9)

[0038] In formula (9), Represents a wear value mean function , kernel function Gaussian process; Represents a wear rate mean function , kernel function Gaussian process;

[0039] Step 3.3.2: Use equation (10) to establish the constraint equation of tool wear equation:

[0040] (10)

[0041] In formula (10), Represents the derivative operator.

[0042] The electronic device of the present invention includes a memory and a processor, wherein the memory is used to store a program that supports the processor to execute the tool wear prediction method, and the processor is configured to execute the program stored in the memory.

[0043] The present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program executes the steps of the tool wear prediction method when the computer program is executed by a processor.

[0044] Compared with the prior art, the present invention has the following beneficial effects:

[0045] 1. The present invention has the advantages of easy extraction of data features and clear physical meaning of the features. It uses free energy theory to extract tool characteristic enthalpy and entropy. Compared with the traditional machine learning module automatic feature extraction method, the features extracted by the method of the present invention are more relevant to the tool wear process and more robust.

[0046] 2. This method treats the cutting signal and actual tool wear values ​​as a dynamic system characterized by free energy G and temperature T, and constructs a tool wear equation based on this. This approach, compared to traditional purely data-driven tool wear prediction methods, has a deeper underlying logic, making the tool wear estimation results more reliable and interpretable, thus resolving the uninterpretable nature of traditional purely data-driven tool wear prediction methods.

[0047] 3. The present invention embeds the known prior knowledge of the milling process into the data-driven method, providing the Gaussian process with a mean function and kernel function that conform to the physical process of tool wear. Compared with the traditional purely data-driven tool wear value prediction method, the learning efficiency is higher and the training and prediction process is more stable. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 It is a schematic diagram of the overall framework of the present invention;

[0049] Figure 2 A schematic diagram of the installation of the sensing equipment in the implementation process of the present invention;

[0050] Figure 3 A schematic diagram of the milling process system constructed for the present invention;

[0051] Figure 4 Schematic diagram of comparison between tool wear prediction value and actual value according to an embodiment of the present invention. DETAILED DESCRIPTION

[0052] The present invention will be described in further detail below with reference to the accompanying drawings. The specific embodiments described herein are only for explanation and are not intended to limit the present invention.

[0053] In this embodiment, a tool wear prediction method based on a physical guided Gaussian process of free energy theory is implemented to achieve a highly robust and reliable tool wear value prediction by combining free energy theory with a data driven method. Figure 1 This is a schematic diagram of the overall framework of the present invention, which is specifically carried out according to the following steps:

[0054] Step 1: The sensor device of this embodiment is installed as follows Figure 2 As shown, the tool is milled and the cutting signal sequence of the tool in the X, Y, and Z directions is collected at a fixed frequency. , the i-th segment spindle vibration acceleration signal in the X, Y, and Z directions And the i-th segment acoustic emission signal of the tool , while collecting the current signal of the machine tool in section i After each cutting step, an optical microscope is used to obtain an image of the cutting edge of the tool and calculate the wear value. The actual tool wear value of the i-th segment of the tool is recorded as , and calculated using the difference between adjacent wear values Tool wear rate ; Thus forming the milling processing data set ;in, represents the milling processing data of the i-th segment of the tool, and , represents the wear label of the i-th segment of the tool, and , T represents transpose, express The timing sequence is as follows: N represents the total number of timing sequences. In this embodiment, the machine tool used is a high-speed CNC milling machine DX-650, the data acquisition card used is a Dewesoft SIRIUSi-HS-8xACC, the sampling frequency is 50kHz, and the duration of each cutting signal collected is 5 seconds. The sensors used are a Kistler 9129AA dynamometer, a Kistler 8763B three-axis vibration sensor, and a Sunderg SS430 acoustic emission sensor. The tool used is a Sanco four-tooth carbide end mill with a helix angle of 48° and a diameter of 6mm. The workpiece material being milled is aluminum alloy 7030.

[0055] Step 2: Extract the signal characteristics of milling processing based on the theory of statistical mechanics:

[0056] like Figure 3As shown in the figure, based on free energy theory, the milling tool and workpiece are constructed as a system. The free energy of the system is equal to the system's enthalpy minus the product of the system's entropy and temperature. The tool wear value is defined as the actual internal state of the system and is related to the free energy, while the tool wear rate is related to the system temperature. The sensor signal is defined as an external representation of the actual state of the system, and the entropy and enthalpy of the milling signal are extracted as features.

[0057] Step 2.1: After normalization, the dimensionless milling processing data of the i-th segment is obtained , and use the variational mode decomposition method to Decomposed into n intrinsic mode function components, we get The eigenmode function component matrix of the cutting signal with rows and k columns is In this embodiment, the matrix is decomposed into 60 components.

[0058] Step 2.2: Importance weight vector ,in, The number of rows and The number of rows is equal, The number of columns is 1;.

[0059] Step 2.3: Calculate using formula (1) Enthalpy , thus obtaining the enthalpy vector :

[0060] (1)

[0061] In formula (1), t represents The index of the cutting signal sequence of each row at a discrete moment; express The cutting signal sequence of column t in ;

[0062] Step 2.4: Calculate using formula (2) The energy probability corresponding to the jth row in :

[0063] (2)

[0064] In formula (2), Indicates the set constant, express The cutting signal of row j and column t in ; express The jth importance weight value in ; In this embodiment, the setting , the importance weight vector is set to a periodic exponential decay form: .

[0065] Step 2.5: Calculate using formula (3) Entropy :

[0066] (3)

[0067] Step 3: Use the Gaussian process surrogate model to establish the tool wear equation:

[0068] Step 3.1: Construct a mean function that conforms to the physical process of tool wear:

[0069] Step 3.1.1: Use Fourier series to Perform fitting to obtain the fitted wear rate curve , thereby setting the wear rate mean function ;

[0070] Step 3.1.2: Use Fourier series to Perform fitting to obtain the fitted wear value curve , thereby setting the wear value mean function ;

[0071] Step 3.2: Construct a kernel function that conforms to the physical process of tool wear:

[0072] Step 3.2.1: Use Equation (4) to construct a kernel function that conforms to the tool wear rate change process :

[0073] (4)

[0074] In formula (4), Indicates the tool's Segment milling processing data The corresponding tool wear rate, express The corresponding timing, 、 、 、 、 There are 5 hyperparameters respectively;

[0075] Step 3.2.2: Use Equation (7) to construct a kernel function that conforms to the physical process of tool wear :

[0076] (7)

[0077] In formula (7), express The corresponding free energy, 、 、 、 There are 4 hyperparameters respectively.

[0078] Step 3.3: Based on the fact that the free energy of the system is equal to the product of enthalpy minus entropy and temperature, the tool wear equation is constructed using Equation (9):

[0079] (9)

[0080] In formula (9), Represents a wear value mean function , kernel function Gaussian process; Represents a wear rate mean function , kernel function Gaussian process;

[0081] Step 3.4: Use equation (10) to establish the constraint equation of tool wear equation:

[0082] (10)

[0083] In formula (10), represents the derivative operator; in this embodiment, the derivative is specifically to use automatic gradient to obtain the model output mean The gradient of , this calculation can also be replaced by theoretical derivation, through The mixed covariance function between and its first-order partial derivatives is obtained.

[0084] Step 3.5: Based on D, use the Bayesian optimization algorithm to update the hyperparameters in equation (9) under equation (10), thereby obtaining the tool wear equation under the optimal hyperparameters; this embodiment uses the Bayesian Optimization object provided by Python to create an instance and solve it.

[0085] Step 4: Collect the milling processing data of the current period in real time and process it according to the process of step 2. Input it into the tool wear equation under the optimal hyperparameters and integrate the equation using the 4th-order Runge-Kutta method. The tool wear value in the i+1th milling period is ,in, , , , , f represents the function represented by tool wear equation (9). h represents the time period, which is 5 seconds in this embodiment. Thus, the wear value predicted for the tool in the current time period is obtained. The comparison of the wear prediction value and the actual value in this embodiment is visualized as follows: Figure 4 As shown;

[0086] In this embodiment, an electronic device includes a memory and a processor, wherein the memory is used to store a program that supports the processor to execute the above method, and the processor is configured to execute the program stored in the memory.

[0087] In this embodiment, a computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the above method are executed.

[0088] In summary, the prediction results of the cases of the present invention prove that the method combining free energy theory and Gaussian process proxy model can accurately and stably predict tool wear values. This method can improve the accuracy of traditional tool wear prediction methods, further ensure the safe progress of the machining process, and help improve the quality of parts and machining efficiency; the data used in the present invention is easy to obtain, easy to process, and easy to extract features, which alleviates the need for traditional complex manual extraction of time, frequency, and time-frequency domain features, and is more physically meaningful than the features automatically extracted by machine learning, which enhances the reliability of the features. The present invention combines the free energy theory that conforms to the physical process of tool wear with the Gaussian process proxy model, enhances the interpretability of the tool wear prediction method, and provides machine tool users with a more reliable way to predict tool wear values.

Claims

1. A tool wear prediction method based on a physical guided Gaussian process of free energy theory, characterized in that: The following steps are involved: Step 1: Perform milling on the tool and collect the i-th segment cutting signal sequence of the tool in the X, Y, and Z directions at a fixed frequency , the i-th segment spindle vibration acceleration signal in the X, Y, and Z directions And the i-th segment acoustic emission signal of the tool , while collecting the current signal of the machine tool in section i ; The actual tool wear value of the i-th segment of the tool is recorded as , and calculated using the difference between adjacent wear values Tool wear rate ; Thus forming the milling processing data set ;in, represents the milling processing data of the i-th segment of the tool, and , represents the wear label of the i-th segment of the tool, and , T represents transpose, express time series; N represents the total number of time series; Step 2: Extract the signal characteristics of milling processing based on the theory of statistical mechanics; Step 3: Use the Gaussian process surrogate model to establish the tool wear equation: Step 3.1: Construct a mean function that conforms to the physical process of tool wear; Step 3.2: Construct a kernel function that conforms to the physical process of tool wear; Step 3.3: Construct tool wear equation based on signal characteristics, mean function and kernel function; Step 3.4: Based on D, use the Bayesian optimization algorithm to optimize the mechanical energy of the tool wear equation to obtain the tool wear equation under the optimal hyperparameters; Step 4: Collect the milling processing data of the current period in real time and input it into the tool wear equation under the optimal hyperparameters after processing according to the process of step 2. Use the 4th-order Runge-Kutta method to integrate the equation to obtain the predicted tool wear value in the current period.

2. The tool wear prediction method based on the physical guided Gaussian process of free energy theory according to claim 1 is characterized in that: The step 3 comprises the following steps: Step 2.1: After normalization, the dimensionless milling data of the i-th segment is obtained , and use the variational mode decomposition method to Decomposed into n intrinsic mode function components, we get The eigenmode function component matrix of the cutting signal with rows and k columns is ; Step 2.2: Importance weight vector ,in, The number of rows and The number of rows is equal, The number of columns is 1; Step 2.3: Calculate using formula (1) Enthalpy , thus obtaining the enthalpy vector : (1) In formula (1), t represents The index of the cutting signal sequence of each row at a discrete moment; express The cutting signal sequence of column t in ; Step 2.4: Calculate using formula (2) The energy probability corresponding to the jth row in : (2) In formula (2), Indicates the set constant, express The cutting signal of row j and column t in ; express The j-th importance weight value in ; Step 2.5: Calculate using formula (3) Entropy : (3)。 3. The tool wear prediction method based on the physical guided Gaussian process of free energy theory according to claim 2 is characterized in that: The step 3.1 includes the following steps: Step 3.1.1: Use Fourier series to Perform fitting to obtain the fitted wear rate curve , thereby setting the wear rate mean function ; Step 3.1.2: Use Fourier series to Perform fitting to obtain the fitted wear value curve , thereby setting the wear value mean function .

4. The tool wear prediction method based on the physical guided Gaussian process of free energy theory according to claim 3 is characterized in that: The step 3.2 includes the following steps: Step 3.2.1: Use Equation (4) to construct a kernel function that conforms to the tool wear rate change process : (4) In formula (4), Indicates the tool's Segment milling processing data The corresponding tool wear rate, express The corresponding timing, 、 、 、 、 There are 5 hyperparameters respectively; Step 3.2.2: Use Equation (7) to construct a kernel function that conforms to the physical process of tool wear : (7) In formula (7), express The corresponding free energy, 、 、 、 There are 4 hyperparameters respectively.

5. The tool wear prediction method based on the physical guided Gaussian process of free energy theory according to claim 4 is characterized in that: The step 3.3 includes the following steps: Step 3.3.1: Use Equation (9) to construct the tool wear equation: (9) In formula (9), Represents a wear value mean function , kernel function Gaussian process; Represents a wear rate mean function , kernel function Gaussian process; Step 3.3.2: Use equation (10) to establish the constraint equation of tool wear equation: (10) In formula (10), Represents the derivative operator.

6. An electronic device comprising a memory and a processor, characterized in that: The memory is used to store a program that supports the processor to execute the tool wear prediction method according to any one of claims 1 to 5, and the processor is configured to execute the program stored in the memory.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the tool wear prediction method according to any one of claims 1 to 5 are executed.

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