Alloy processing workshop scheduling method based on real-time monitoring of physical neural network
By adopting a real-time monitoring method based on physical neural networks in the alloy processing workshop, combining deep operator networks and genetic algorithms and reinforcement learning, the problems of tool status monitoring and life prediction are solved, and efficient machining task scheduling and resource optimization are achieved.
Patent Information
- Application Number
- CN202510167743.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-02-14
- Publication Date
- 2025-05-27
- Estimated Expiration
- 2045-02-14
AI Technical Summary
The prior art is difficult to effectively monitor the tool status and predict its fatigue life in alloy processing workshops, resulting in reduced processing accuracy and waste of resources.
Real-time monitoring method based on physical neural network is adopted to collect physical signal data of the machine tool (such as vibration, cutting force and temperature) in real time, perform preprocessing and feature extraction, combine with the depth operator network to predict the remaining tool life, and optimize the scheduling scheme through genetic algorithms and reinforcement learning.
Real-time monitoring of tool status and accurate life prediction are achieved, machining task allocation and tool replacement plan are optimized, production efficiency and resource utilization are improved, and production costs are reduced.
Smart Images

Figure CN120044904A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of intelligent scheduling in alloy processing workshops, and particularly relates to a scheduling method for alloy processing workshops based on real-time monitoring of physical neural networks. Background Technique
[0002] The processing of alloy materials usually requires high precision and high efficiency. Especially when processing complex parts, extremely high performance requirements are imposed on numerically controlled machine tools. The cutting tools of numerically controlled machine tools are the core tools in the processing process, and their service life directly affects the quality and cost of the processed products. However, due to the fact that the tools work under high-temperature and high-speed cutting conditions, wear and fatigue phenomena are inevitable. This wear process will not only lead to a decline in processing accuracy, but may also cause tool failure or even breakage, causing irreversible damage to the equipment and products. How to effectively monitor the tool state and predict its fatigue life has become a key technology to ensure the stability and economy of the processing process.
[0003] In recent years, with the development of sensor technology, physical parameters such as machine tool vibration signals, cutting force signals, and temperature signals can be obtained in real time, providing a rich data basis for tool wear monitoring. At the same time, the emergence of artificial intelligence technology, especially deep learning models, has provided a powerful tool for extracting potential laws from these complex data. These technologies can use a large amount of historical data to model and predict the wear trend of tools, so as to provide data support for timely tool replacement and optimization of processing parameters. However, the "black box" prediction method that simply relies on deep learning models often lacks physical interpretability and is difficult to combine the processing mechanism with the data model, restricting its popularization and application in industrial scenarios.
[0004] In addition, the coupling problem between workshop production scheduling and tool life prediction has not been effectively solved. Most traditional scheduling methods are based on empirical rules and lack the ability to dynamically respond to the real-time state of tools, easily leading to overuse or premature replacement of tools, thereby reducing production efficiency and resource utilization rate. Therefore, deeply integrating tool life prediction with intelligent scheduling and optimizing the allocation of processing tasks and tool replacement plans through real-time monitoring of tool states has become an important direction to solve the bottleneck problem in alloy processing workshops. The existing technologies have the following defects:
[0005] 1. Disadvantages of the method based on empirical formulas:
[0006] First of all, the accuracy is low. This method relies on empirically set formulas by humans and fails to fully consider the dynamic changes in the processing process. Secondly, the flexibility is poor. It is difficult to adapt to the processing conditions of different machine tools and tools, especially in complex processing scenarios. Finally, there is resource waste. It may lead to premature tool replacement or overuse, reducing production efficiency.
[0007] 2. Disadvantages of the data-driven method:
[0008] Data dependency during model training. Data-driven models require a large amount of high-quality historical data as training samples. Insufficient data or low data quality will affect model performance.
[0009] Poor model interpretability. Traditional deep learning models lack the ability to directly interpret the physical characteristics of cutting tools and only rely on data features, which may not be able to capture key information in physical signals well.
[0010] High requirements for real-time performance: Most existing deep learning models are offline trained, and there is still a certain lag in meeting the requirements of real-time monitoring and scheduling in the workshop.
[0011] Low degree of integration with the scheduling system: The current tool life prediction model and the workshop scheduling system are usually separated, resulting in the prediction results being unable to be efficiently applied to the optimized scheduling of actual production tasks. Summary of the Invention
[0012] In view of the above problems, the present invention proposes an alloy processing workshop scheduling method based on real-time monitoring of physical neural networks, including the following processes:
[0013] S1. Real-time collect the physical signal data of the machine tool, including vibration, cutting force and temperature data;
[0014] S2. Preprocess the collected data, and obtain enhanced time-domain feature data and frequency-domain feature data through Fourier transform feature extraction, and fuse them as the data input of the tool remaining life prediction model;
[0015] S3. The tool remaining life prediction model predicts and outputs the tool fatigue life result; the model adopts a deep operator network guided by physical information, including a backbone network and a branch network, which respectively process tool wear information and physical signal data, and perform feature combination through a fusion module;
[0016] S4. Model the tool scheduling optimization problem, use the tool remaining life prediction results of each machine tool, the processing time of each machining task, the life parameters of the tool consumed by the machining task, and the requirements of each machining task for machining accuracy as input data, and set the objective function and constraint function; obtain the global optimal machining scheduling plan through the genetic algorithm, and then use the global optimal machining scheduling plan as the initial state, and use reinforcement learning to dynamically enhance the scheduling plan, so as to obtain the dynamically optimized optimal scheduling plan.
[0017] Preferably, the extracted time-domain feature data includes:
[0018] The mean value μ of the tool wear signal, which reflects the overall level of the signal;
[0019] The standard deviation σ of the tool wear signal measures the volatility of the signal;
[0020] The root mean square value RMS of the vibration signal measures the energy level of the signal;
[0021] The peak factor τ is used to detect minor chipping of the tool;
[0022] The finally extracted time-domain feature data is output as
[0023] Preferably, the fast Fourier transform is used to extract frequency-domain features. The extracted frequency-domain feature data includes:
[0024] The main frequency feature f peak , which is used to monitor tool resonance. When the tool is approaching failure, the main frequency will shift and the amplitude will increase;
[0025] The kurtosis SC of the cutting force signal is used to measure the energy concentration of the spectrum and reflect the energy center of gravity of the spectrum. After tool wear, the high-frequency components increase, resulting in an increase in SC;
[0026] The energy consumption value E during the cutting process is used to measure the total energy of the signal. When the vibration and cutting force of the tool increase, the total energy E also increases;
[0027] The output after frequency-domain feature extraction is
[0028] Preferably, the backbone network is used to process tool wear information, extract high-level features related to tool life, and enhance the expression ability through non-linear transformation. Its input is the extracted wear features The wear features are:
[0029] Time-domain features and frequency-domain features are combined to form a complete feature vector Among them, the time-domain features reflect the influence of tool wear on signal volatility, and the frequency-domain features reflect the influence of tool wear on signal spectrum. To better capture non-linear relationships, some features are transformed to obtain enhanced features
[0030]
[0031] Among them, log(σ + 1) represents taking the logarithm of the standard deviation, and e -τ is the negative exponential transformation, is the square root of the spectrum center to make the data distribution more uniform;
[0032] The backbone network uses a multi-layer fully connected neural network to extract deep features:
[0033]
[0034] Among them, represents the weight matrix of the i-th layer, represents the bias term of the i-th layer, is the output feature of the i-th layer, and σ(·) is the ReLU activation function.
[0035] Preferably, the branch network adopts a CNN+Transformer combined architecture, and the CNN module is used to extract features from the output feature Z of the backbone network T The core calculation formula is:
[0036] Z C =σ(W C *Z T +b C )
[0037] Among them, W C is the convolution kernel of the CNN, * represents the convolution operation, b C is the bias term, and Z C is the local temporal feature extracted by the CNN; σ(·) is the ReLU activation function; multi-layer convolutional CNN is used to extract features of different scales:
[0038]
[0039] The final output feature of the CNN is:
[0040]
[0041] Among them, N is the number of CNN layers, and Flatten(·) represents flattening into a vector to adapt to the Transformer input;
[0042] To capture the long-term dependence of physical signals, Transformer is used for global time series modeling:
[0043]
[0044] Among them, Q, K, and V are linear transformation matrices; W Q , W K , W V are weight matrices; Z B is the extracted time series feature; among them, the attention mechanism in Z B is calculated through multi-head attention as:
[0045]
[0046] Among them, d kRepresents the key feature dimension; finally, Z is processed through layer normalization C and Z B The final model prediction output obtained through processing is:
[0047]
[0048] Among them, Represents the predicted tool fatigue life.
[0049] Preferably, to enhance the physical consistency of the branch network, a cutting force model is used for physical constraint optimization:
[0050] F c = k c a p f
[0051] F t = k t a p f
[0052] Among them, F c , F t Represents the main cutting force and the feed force, k c , k t Represents the cutting force sparsity, a p Is the cutting depth, and f represents the feed rate; define the physical consistency loss Lphys:
[0053] L phys = ||Z B - [F c , F t || 2
[0054] The final optimization objective consists of the prediction error loss L MSE , the physical consistency loss L phys and the regularization loss L reg Nonlinearly:
[0055]
[0056] Among them, λ 1 λ 2 λ 3 Represents a hyperparameter that controls the relative importance of each loss term, N is the number of training samples, Y i Represents the true remaining tool life, Represents the predicted remaining tool life, and W represents all the trainable parameters of the model.
[0057] Preferably, the modeling of the tool scheduling optimization problem is specifically:
[0058] First, variable definitions and scheduling problem modeling are carried out; it is defined that there are M machine tools in the workshop, and each machine tool is equipped with a cutting tool. The remaining life of each cutting tool has been predicted and is expressed as:
[0059]
[0060] Among them, represents the predicted remaining life of the cutting tool on the j-th machine tool; the workshop needs to complete N machining tasks, and each task i requires a cutting tool life of L i , i = 1, 2,..., N; set T i as the machining time required for task i, and P i as the accuracy requirement for task i. Define the scheduling decision variable:
[0061]
[0062] Among them, X ij represents a binary variable indicating whether task i is assigned to machine tool j. The problem objective is to find an optimal task assignment scheme X = {X ij}, to minimize the total task cost while ensuring the cutting tool service life and task requirements.
[0063] Preferably, the objective function is set, and the optimization objective is to minimize the comprehensive scheduling cost, including cutting tool replacement cost, task delay cost, and accuracy loss cost, as follows:
[0064]
[0065] Among them, C replace,j represents the cost of cutting tool replacement on machine tool j, C delay,i represents the cost of task i being delayed, and C precision,ij represents the accuracy loss cost caused by cutting tool wear when task i is executed by machine tool j;
[0066] The set constraint conditions are specifically:
[0067] Task assignment constraint, each task must be assigned to and only assigned to one machine tool;
[0068] Cutting tool remaining life constraint, the total service life of the cutting tool on machine tool j cannot exceed its predicted remaining life;
[0069] Task execution time constraint, after task i is assigned to machine tool j, its deadline must be met.
[0070] Preferably, in S4, the task assignment and cutting tool replacement strategies are optimized and solved through an adaptive genetic algorithm:
[0071] First, initialize pop chromosome encodings, where each chromosome encoding F represents a scheduling scheme:
[0072] F = [X 11 , X 12 ,..., X NM
[0073] Among them, each parameter X ij takes a value of 0 or 1, indicating whether task i is assigned to machine tool j;
[0074] Secondly, the fitness function is calculated from the optimization objective C. The smaller C is, the better the scheduling scheme:
[0075] Fitness(F) = -C(F)
[0076] Thirdly, adopt the adaptive roulette wheel selection strategy, where the selection probability is proportional to the individual fitness:
[0077]
[0078] Among them, F k is the task assignment scheme of the k-th individual, and P(F k ) is the probability that individual F k is selected. Through this step, a new chromosome encoding population F se is obtained:
[0079]
[0080] Among them, select() represents the chromosome selection operation. After that, the present invention proposes to perform a crossover operation on the chromosomes using adaptive two-point crossover, and the crossover rate P c is dynamically adjusted:
[0081]
[0082] Among them, t max is the maximum number of iterations, t is the current number of iterations, P c_min represents the minimum crossover probability, P c_max is the maximum crossover probability. Randomly select two chromosome individuals se from the population F and as the parents and perform the crossover operation:
[0083]
[0084] Among them, r is a random number r ~ U(0, 1); the new offspring population F cr generated after crossover: After that, the new population enters the mutation stage;
[0085] The mutation operation is used to enhance the diversity of the population and avoid premature convergence. An adaptive mutation method is adopted:
[0086]
[0087] Among them, P m represents the adaptive mutation probability, Fitness avg is the average fitness of the population, P m_min represents the minimum mutation probability, P m_max is the maximum mutation probability. The mutation process is as follows: randomly select some tasks i*, and randomly adjust their assigned machine tools j*: F i*j = 0, F i*j* = 1, j*≠j; the individuals of the new population generated after compilation are: The solution of the new population is the global optimal scheduling scheme.
[0088] Preferably, the use of reinforcement learning to dynamically enhance the scheduling scheme in S4 is specifically as follows:
[0089] The mutated new population obtained by the adaptive genetic algorithm is used as the initial scheme to be locally optimized, that is, the initial state of reinforcement learning. Combining the predicted remaining tool life and setting the task queuing time of machine tool j to optimize the task scheduling scheme, including:
[0090] Define the state space: at time step t, the state variable of reinforcement learning
[0091] Define the action space A t : Task reassignment is to adjust tasks to different machine tools: X ij ←X ik , k≠j; the tool replacement decision is to replace the tool in advance if the tool life is lower than the threshold: Task priority adjustment is to reduce the impact on tasks with high precision requirements: P i = max(P i -δ, 0);
[0092] Design a reward function, and continuously optimize the scheduling scheme by updating the Q value.
[0093] Compared with the prior art, the present invention has the following beneficial effects:
[0094] 1. Physics Information - Guided Deep Operator Network: The present invention proposes a deep operator network that combines physical information with a deep learning model for tool life prediction. This network can not only learn the dynamic changes of tool wear from data but also enhance the interpretability and prediction ability of the model through physical signals (such as cutting force, vibration, temperature). Through physical constraint optimization, it ensures that the prediction results conform to actual physical laws, improving the robustness and accuracy of the model.
[0095] 2. Deep Integration of Real - Time Monitoring and Intelligent Scheduling: By deeply integrating tool life prediction with workshop production scheduling, an intelligent scheduling method based on the remaining tool life is proposed. By real - time monitoring the tool status, dynamically adjusting the allocation of machining tasks and the tool replacement plan, it avoids over - using or premature replacement of tools, optimizes the workshop production efficiency, and reduces production costs.
[0096] 3. Hybrid Optimization Strategy of Adaptive Genetic Algorithm and Reinforcement Learning: A hybrid optimization strategy combining an adaptive genetic algorithm and reinforcement learning is proposed to solve the workshop task scheduling problem. Through global optimization by the genetic algorithm and local optimization by combining reinforcement learning, it can dynamically respond to changes in the workshop environment (such as sudden drop in tool life, task delay), ensuring the real - time and high - efficiency of the scheduling scheme. It can continuously optimize the scheduling scheme according to real - time monitoring data, ensuring that the task allocation is always in the optimal state. Reducing the number of tool replacements, optimizing the tool usage method, reducing maintenance costs, and improving resource utilization. BRIEF DESCRIPTION OF THE DRAWINGS
[0097] Figure 1 It is the overall method flow chart of the present invention.
[0098] Figure 2 It is the schematic diagram of the physical signal acquisition and language processing module of the present invention.
[0099] Figure 3 It is the schematic diagram of the structure of the tool remaining life prediction model guided by physical information of the present invention.
[0100] Figure 4 It is the design flow chart of the intelligent scheduling and real - time monitoring module of the present invention.
[0101] Figure 5 It is the analysis diagram of the predicted values of tool life prediction by the algorithm of the present invention in the embodiment of the present invention.
[0102] Figure 6 It is the comparison diagram of the scheduling costs between the algorithm of the present invention and the traditional algorithm. DETAILED DESCRIPTION OF THE INVENTION
[0103] The present invention proposes a scheduling method for an alloy processing workshop based on real - time monitoring of a physical neural network, and the overall process is as Figure 1 shown.
[0104] The invention will be further described below in conjunction with specific embodiments.
[0105] I. Physical signal acquisition and preprocessing
[0106] During the alloy processing, the wear and fatigue life of the cutting tool have a crucial impact on the processing quality and production efficiency. To achieve precise monitoring of the tool state, real-time acquisition and processing of physical signal data are crucial steps. By installing sensors such as vibration, cutting force, and temperature sensors, multi-dimensional physical signals of the cutting tool during processing can be obtained. These signals provide basic data for the evaluation of the tool wear state and life prediction. As Figure 2 shown.
[0107] 1. Data acquisition
[0108] In the alloy processing workshop, the first step in real-time monitoring of the tool state is to acquire physical signals from the machine tool. To accurately capture the wear characteristics of the cutting tool and the minute changes during the processing, multiple high-precision sensors are used for data acquisition, mainly including the following types of equipment:
[0109] (1) Vibration sensor: Installed near the machine tool spindle or the cutting tool, it is used to acquire the vibration signal V(t) generated by the cutting tool during processing. The vibration signal can reflect the change in the cutting force between the cutting tool and the workpiece, so it has a strong indication effect on the tool wear state. The sensor uses an accelerometer, and the sampling frequency is set to 50 kHz.
[0110] (2) Cutting force sensor: Installed on the tool fixture, it can real-time monitor the cutting force F(t) exerted on the cutting tool during processing. This sensor can simultaneously measure the cutting force components in three directions: F x (t), F y (t), F z (t). They represent the cutting forces in the X, Y, and Z axis directions of the cutting tool respectively. The cutting force signal is sensitive to the tool wear state and can effectively indicate the load condition of the cutting tool. The sampling frequency is set to 20 kHz.
[0111] (3) Temperature sensor: Since the high-temperature environment during processing has an important impact on tool wear, a temperature sensor installed in the cutting area of the tool is used to measure the working temperature T(t) of the cutting tool in real-time. This sensor uses an infrared thermometer for non-contact measurement, and the sampling frequency is set to 1 kHz.
[0112] The analog signals of all sensors are connected to the computer system through a data acquisition card (DAQ), converted into digital signals, and then stored. The data collected by each sensor signal is stored in the form of a time series. Therefore, the final signal vector is:
[0113] X(t) = [V(t), F x (t), F y (t), F z (t), T(t)] (1)
[0114] Among them, X(t) is the multi-channel signal data collected by all sensors, and t is the time variable.
[0115] 2. Data preprocessing
[0116] Due to the existence of noise, offset, and data scale differences in the sensor signals, preprocessing must be carried out to improve the data quality and prepare for subsequent feature extraction. The input of data preprocessing is the original signal X(t), and the processed signal X p (t) is obtained after data preprocessing.
[0117] First, filtering and noise reduction are performed. Sensor noise and mechanical vibration interference are removed to improve the signal stability. In the present invention, a second-order Butterworth low-pass filter is used to remove high-frequency noise, and the cut-off frequency f c = 5 kHz is set. The transfer function of the filter:
[0118]
[0119] Among them, X fliter (t) represents the filtered signal, h(t) is the impulse response of the low-pass filter, and γ is the time variable. Then, the data obtained through filtering and noise reduction in combination with formula 1 is:
[0120] X fliter (t) = [V filter (t), F x,filter (t), F y,filter (t), F z,filter (t), T filter (t)] (3)
[0121] Secondly, detrending and normalization are performed on the data to map the data to the same scale range, improving the stability and convergence speed of subsequent modeling. In the present invention, the slow-changing trend in the signal is first eliminated through a linear detrending method to make the data more in line with the requirements of short-time dynamic analysis. Then, the min-max normalization method is used to standardize the data so that all input data is mapped between [0, 1] to eliminate the scale influence of different signals, providing high-quality input data for subsequent feature extraction and model training.
[0122] Specifically, linear detrending Trend(X(t)) is adopted:
[0123] X detrend (t) = X fliter(t)-Trend(X fliter (t)) (4)
[0124] Trend(X fliter (t)) = at + b (5)
[0125] In the formula, X detrend (t) represents the detrended signal, and a and b represent the fitting parameters calculated by the least squares method. Then, normalization is performed. Since the physical dimensions of cutting force, vibration, and temperature are different, min-max normalization is used:
[0126]
[0127] Among them, X norm (t) represents the normalized signal, and the finally obtained output data is:
[0128] X norm (t) = [V norm (t), F x,norm (t), F y,norm (t), F z,norm (t), T norm (t)] (7)
[0129] 3. Feature Extraction
[0130] The health state and fatigue life of the tool not only depend on the instantaneous signal value, but also on the overall statistical characteristics and frequency distribution information of the signal. Therefore, the main frequency components of the signal are extracted by the fast Fourier transform (FFT), and the spectral energy is calculated to reflect the change in the vibration mode during the tool wear process. Finally, all features are combined into a multi-dimensional feature vector to provide input data for the subsequent deep operator network.
[0131] Specifically, the extracted features are as follows:
[0132] The mean value of the tool wear signal, which reflects the overall level of the signal:
[0133]
[0134] Among them, μ represents the average value of the signal, N represents the number of sampling points, and X norm (i) is the normalized signal value at the i-th time step.
[0135] The standard deviation of the tool wear signal, which measures the volatility of the signal:
[0136]
[0137] Among them, σ represents the standard deviation of the signal, reflecting the stability of the tool operation.
[0138] The root mean square value of the vibration signal measures the energy level of the signal. A higher root mean square value indicates that the tool is subjected to a greater cutting force or increased vibration:
[0139]
[0140] The peak factor is used to detect minute chipping of the tool. When local chipping occurs on the tool, the peak value of the vibration signal rises, resulting in an increase in the peak factor.
[0141]
[0142] According to the above description of time-domain characteristics, the finally extracted characteristic output is: These characteristics can characterize the variation of the signal in the time domain during the tool wear process.
[0143] Furthermore, frequency-domain feature extraction is carried out to analyze the influence of tool wear on the signal spectrum. During the actual machining process, the vibration signal of the tool usually contains periodic components, and the main frequency and energy distribution of the signal will change under different wear states. Therefore, the fast Fourier transform is used to extract frequency-domain features to capture the spectral changes of tool wear.
[0144] Fast Fourier transform processing function:
[0145]
[0146] where, X FFT (f) is the spectrum of the normalized signal at frequency f, j represents the imaginary unit, and N is the number of sampling points.
[0147] Main frequency feature f peak Extraction: It is used to monitor tool resonance. When the tool is approaching failure, the main frequency will shift and the amplitude will increase;
[0148]
[0149] Obtaining the kurtosis SC of the cutting force signal: It is used to measure the energy concentration of the spectrum and reflect the energy center of gravity of the spectrum. After tool wear, the high-frequency components increase, resulting in an increase in SC;
[0150]
[0151] Obtaining the energy consumption value E during the cutting process: It is used to measure the total energy of the signal. When the vibration and cutting force of the tool increase, the total energy E also rises.
[0152] E = ∑ f |X FFT (f)| 2 (15)
[0153] Output after the above frequency-domain feature extraction: These features are used to describe the spectral changes of the tool state over time.
[0154] Furthermore, finally, the time-domain features and the frequency-domain features are combined to form a complete feature vector:
[0155]
[0156] Among them, the time-domain features reflect the influence of tool wear on the signal volatility, and the frequency-domain features reflect the influence of tool wear on the signal spectrum. To better capture the non-linear relationship, some features are transformed to obtain enhanced features
[0157]
[0158] Among them, log(σ + 1) represents taking the logarithm of the standard deviation to prevent the influence of excessive changes on model convergence, and e -τ is the negative exponential transformation to avoid the excessive influence of the peak factor on the training process, is the square root of the spectral center to make the data distribution more uniform. The input feature dimension of the final backbone network is: Therefore, the output feature vector is used in the tool fatigue life prediction model.
[0159] II. Design of Tool Remaining Life Prediction Model Based on Physics-Informed
[0160] In the tool life prediction task, traditional machine learning methods have limitations in dealing with high-dimensional time series data and are difficult to effectively capture the dynamic changes of tool wear. Although deep learning methods can learn the temporal features in the data, they lack the physical mechanism modeling of tool wear and are easily affected by data noise. The present invention designs a physics-informed deep operator network (DeepOperator Network, DON) for tool remaining life prediction. This method can not only learn data-driven features but also combine physical information to enhance the interpretability and prediction ability of the model. DON mainly includes a backbone network and a branch network, and through an innovative physical-guided feature fusion strategy, it realizes high-precision tool fatigue life prediction.
[0161] The deep operator network is modeled as Figure 3 shown below:
[0162] DON is composed of a backbone network and a branch network, which respectively process tool wear information and physical signal data, and combine features through a fusion module to finally predict the tool fatigue life.
[0163] Specifically, first, the backbone network is designed. The backbone network is used to process the tool wear information, extract high-level features related to tool life, and enhance the expression ability through non-linear transformation. Its input comes from the extracted wear features This network uses a multi-layer fully connected neural network to extract deep features:
[0164]
[0165] Among them, represents the weight matrix of the i-th layer, represents the bias term of the i-th layer. is the output feature of the i-th layer. σ(·) is the ReLU activation function.
[0166] Secondly, the branch network is designed. Since physical signal data usually has temporal correlation, the present invention adopts a CNN+Transformer combined architecture to achieve local temporal pattern extraction and long-term dependence modeling, and enhance the model's ability to analyze dynamic signals. Specifically, the CNN module is used to process the output feature Z of the backbone network T for feature extraction, and the core calculation formula is as follows:
[0167] Z C =σ(W C *Z T +b C ) (19)
[0168] Among them, W C is the convolution kernel of the CNN, * represents the convolution operation, b C is the bias term, and Z C is the local temporal feature extracted by the CNN. σ(·) is the ReLU activation function. Multiple layers of convolutional CNN are used to extract features of different scales:
[0169]
[0170] Finally, the output feature of the CNN is:
[0171]
[0172] Among them, N is the number of CNN layers, and Flatten(·) represents flattening into a vector to adapt to the input of the following Transformer.
[0173] Furthermore, in order to capture the long-term dependence of physical signals, Transformer is used for global time series modeling:
[0174]
[0175] Among them, Q, K, and V are linear transformation matrices. W Q , W K , W V are weight matrices. Z B is the extracted time series feature. Among them, the attention mechanism in Z B is calculated as follows:
[0176]
[0177] Among them, d k represents the key feature dimension to prevent gradient explosion. Finally, through layer normalization of Z C and Z B the final model prediction output obtained by processing is:
[0178]
[0179] Among them, represents the final predicted tool fatigue life.
[0180] In addition, to enhance the physical consistency of the branch network, the cutting force model is used for physical constraint optimization:
[0181] F c = k c a p f(25)
[0182] F t = k t a p f(26)
[0183] Among them, F c , F t represent the main cutting force and the feed force, k c , k t represents the cutting force sparsity, a p is the cutting depth, and f represents the feed rate. Define the physical consistency loss L phys :
[0184] L phys = ||Z B - [F c , F t || 2 (27)
[0185] The final optimization objective is non-linearly composed of the prediction error loss L MSE , the physical consistency loss L phys and the regularization loss L reg :
[0186]
[0187] Among them, λ 1 λ 2 λ 3 represents a hyperparameter that controls the relative importance of each loss term. N is the number of training samples, and Y i represents the true remaining tool life, represents the predicted remaining tool life, and W represents all the trainable parameters of the model.
[0188] The training and optimization process of this part is as follows:
[0189] 1) Initialize the parameters, set the hyperparameters λ 1 , λ 2 , λ 3 and the learning rate;
[0190] 2) Forward propagation, calculate the outputs of the backbone network and the branch network. Calculate the fused features and obtain the life prediction value
[0191] 3) Calculate the loss function, calculate L MSE , L phys , L reg . Calculate the total loss L.
[0192] 4) Backward propagation, calculate the gradients, and update the network parameters.
[0193] 5) Convergence judgment, observe the change of the loss, adjust the hyperparameters until the convergence condition is met.
[0194] Through the above process, not only can the tool life be accurately predicted during the training process but also it can ensure that the prediction results conform to the physical laws, and at the same time prevent the model from overfitting to ensure the generalization ability.
[0195] III. Design of the Intelligent Scheduling and Real-Time Monitoring Module
[0196] As Figure 4 shown, the present invention constructs an intelligent scheduling model based on the predicted remaining tool life to optimize the machining tasks of the CNC machine tools in the alloy processing workshop. The core objectives of intelligent scheduling are:
[0197] Avoid the risk of tool failure. When the remaining life of the tool on a certain machine tool is approaching exhaustion, replace the tool in advance to prevent the machining task from being interrupted or causing product scrap.
[0198] Optimize the task allocation, give priority to the high-precision machining tasks to the tools with longer life to improve the product quality.
[0199] Dynamically adjust the scheduling strategy, combine real-time monitoring data, and timely adjust the task arrangement to ensure the efficient completion of processing tasks under resource constraints.
[0200] Based on the above objectives, the present invention designs and establishes an optimization model, and minimizes the total cost of processing tasks through a scheduling algorithm while ensuring the constraint conditions of task completion time and tool service life. The present invention will adjust the scheduling plan based on the prediction results of the remaining tool life and in combination with real-time monitoring data to ensure the efficient execution of workshop processing tasks under resource constraints.
[0201] 1. Modeling of the tool scheduling optimization problem
[0202] First, perform variable definition and scheduling problem modeling. Define that there are M machine tools in the workshop, and each machine tool is equipped with a tool. The current remaining life of each tool has been predicted and is expressed as:
[0203]
[0204] Among them, represents the predicted remaining life of the tool on the jth machine tool. The workshop needs to complete N processing tasks, and each task i requires a tool life consumption of L i , i = 1, 2,..., N. Set T i as the processing time required for task i, and P i as the accuracy requirement for task i. Define the scheduling decision variable:
[0205]
[0206] Among them, X ij represents a binary variable indicating whether task i is assigned to machine tool j. The problem objective is to find the optimal task assignment scheme X = {X ij} to minimize the total task cost while ensuring tool service life and task requirements.
[0207] 2. Setting of the objective function
[0208] Set the objective function. The optimization objective is to minimize the comprehensive scheduling cost, including tool replacement cost, task delay cost, and accuracy loss cost, as follows:
[0209]
[0210] Among them, C replace,j represents the cost of tool replacement on machine tool j, C delay,i represents the cost of task i being delayed, and C precision,ij represents the accuracy loss cost caused by tool wear when task i is executed by machine tool j.
[0211] Specifically, when the remaining tool life is insufficient to complete the task, a new tool needs to be replaced, and the loss of tool replacement is set as follows:
[0212]
[0213] Among them, C tool is the fixed cost of replacing a new tool.
[0214] If task i fails to be completed within the specified time, a task delay loss will occur:
[0215] C delay,i = α(T i - D i ) + (33)
[0216] Among them, D i represents the deadline of task i, and α represents the penalty factor for task delay.
[0217] High-precision tasks should be assigned to tools with less wear as much as possible, otherwise it may affect product quality, that is, precision loss:
[0218]
[0219] Among them, β represents the weight factor of precision loss, and θ represents the exponential decay parameter of precision loss, that is, the more severe the wear, the greater the precision loss.
[0220] 3. Constraint setting
[0221] (1) Task assignment constraint: Each task must be assigned to and only assigned to one machine tool:
[0222]
[0223] (2) Remaining tool life constraint: The total service life of the tool on machine tool j cannot exceed its predicted remaining life:
[0224]
[0225] (3) Task execution time constraint: After task i is assigned to machine tool j, its deadline must be met:
[0226]
[0227] 4. Obtaining the global optimization scheme for machining scheduling
[0228] Since the scheduling problem involves integer decision variable task assignment X ij and continuous variable tool life The present invention adopts a hybrid solution strategy. First, the task allocation and tool change strategy are optimized and solved through an adaptive genetic algorithm, and then a reinforcement learning method is used for local dynamic optimization to ensure balanced task allocation and reduce the task scheduling cost.
[0229] First, initialize pop chromosome encodings, where each chromosome encoding F represents a scheduling scheme:
[0230] F = [X 11 , X 12 ,..., X NM (38)
[0231] Among them, each parameter X ij takes a value of 0 or 1, indicating whether task i is assigned to machine tool j.
[0232] Secondly, the fitness function is calculated from the optimization objective C according to formula 33 (the smaller C is, the better the scheduling scheme):
[0233] Fitness(F) = -C(F) (39)
[0234] Thirdly, adopt the adaptive roulette wheel selection strategy, and the selection probability is proportional to the individual fitness:
[0235]
[0236] Among them, F k is the task allocation scheme of the k-th individual, and P(F k ) is the probability that individual F k is selected. Through this step, a new population of chromosome encodings F se is obtained:
[0237]
[0238] Among them, select() represents the chromosome selection operation. After that, the present invention proposes to perform a crossover operation on the chromosomes using adaptive two-point crossover, and the crossover rate P c is dynamically adjusted:
[0239]
[0240] Among them, t max is the maximum number of iterations, t is the current number of iterations, P c_min represents the minimum crossover probability, and P c_max is the maximum crossover probability. Randomly select two chromosome individuals se from the population F and as the parents and perform the crossover operation:
[0241]
[0242] where r is a random number, r ~ U(0, 1). The new offspring population F generated after crossover cr : After that, the new population enters the mutation stage.
[0243] The mutation operation is used to enhance the diversity of the population and avoid premature convergence. An adaptive mutation method is adopted:
[0244]
[0245] where P m represents the adaptive mutation probability, Fitness avg is the average fitness of the population, P m_min represents the minimum mutation probability, and P m_max is the maximum mutation probability. The mutation process is as follows: Randomly select some tasks i*, and randomly adjust their assigned machine tools j*: F i*j = 0, F i*j* = 1, j* ≠ j. The individuals of the new population generated after compilation are: The solution of the new population is the global optimal scheduling scheme.
[0246] After that, reinforcement learning is used to locally enhance the global optimal scheduling scheme. Since the genetic algorithm only optimizes in a static task scheduling environment and does not consider the dynamic changes in the workshop environment (sudden drop in tool life, task delay, emergency task insertion), the present invention further introduces reinforcement learning and uses a deep Q-network to locally optimize the task scheduling scheme of the genetic algorithm to achieve dynamic intelligent scheduling.
[0247] Take the mutated new population obtained by the adaptive genetic algorithm as the initial scheme to be locally optimized, that is, the initial state of reinforcement learning. Combine the predicted remaining tool life and set the task queuing time of machine tool j to optimize the task scheduling scheme. The specific steps are as follows:
[0248] (1) Define the state space: At time step t, the state variable of reinforcement learning
[0249] (2) Define the action space A t : Task reassignment (adjust the task to a different machine tool): X ij ←X ik , k ≠ j; Tool replacement decision (if the tool life is lower than the threshold, replace it in advance): The task priority is adjusted to (reduce the impact on tasks with high precision requirements): P i = max(P i - δ, 0). Each action corresponds to a different task scheduling adjustment method, and the reinforcement learning model selects the optimal action through training (i.e., performs real-time optimization and adjustment for different local situations).
[0250] (3) Design the reward function: The reward function R of reinforcement learning t Based on the task scheduling optimization objective, it is the same as formula (41):
[0251] R t = -C(F)(45)
[0252] The goal of reinforcement learning is to maximize the Q value and minimize the scheduling cost. By updating the Q value, the scheduling scheme is continuously optimized. The Q value update formula is as follows:
[0253]
[0254] Among them, ∈ represents the learning rate, which is used to control the Q value update step size. R t is the immediate reward, which calculates the immediate optimization effect of the task scheduling scheme; θ represents the discount factor, which is used to balance the current reward and future rewards; is the maximum Q value of the next state. Q(s t , A t ) represents the Q value after the state s t executes the action A t , that is, the quality of this scheduling scheme. After updating the Q value, the Q value is used to adjust the scheduling scheme:
[0255]
[0256] The training process of reinforcement learning based on Q learning is as follows:
[0257] ① Input the global scheme to be locally optimized, that is, the mutated population
[0258] ② Calculate the Q value: (s t , A t , R t , s t+1 ) ~ D;
[0259] ③ Update the Q network parameters: L(ω) is the loss function:
[0260]
[0261] Among them, ω represents the parameters in the current Q network, ω -Denote the target Q-network parameters, which are updated periodically. η is the learning rate of the optimizer, and D is the experience replay pool responsible for storing historical decision-making data.
[0262] ④ Update the scheduling strategy according to formula (47) to obtain the final locally optimized optimal task scheduling plan.
[0263] IV. Model Deployment
[0264] To achieve intelligent workshop management, the present invention deploys physical signal acquisition, deep operator network, tool remaining life prediction model and task scheduling strategy to an integrated management platform to realize the closed-loop management of real-time monitoring-intelligent prediction-optimized scheduling. The specific implementation applications after deployment include the following steps:
[0265] Physical signal acquisition: Real-time collect data such as machine tool vibration, cutting force, temperature, etc., and use the above data processing operations (including filtering, detrending, Fourier transform feature extraction) to obtain enhanced time-domain feature data and frequency-domain feature data, and fuse them as the data input of the tool remaining life prediction model;
[0266] Tool remaining life prediction: Use the deep operator network model based on physical signals to predict the remaining life of the tool and provide data support to the task scheduling module;
[0267] Task scheduling optimization module: This part includes obtaining the overall global optimal scheduling plan based on the genetic algorithm, and locally optimizing the optimal scheduling plan through reinforcement learning to achieve dynamic task scheduling; specifically, first use ① the predicted results of the remaining life of the tool for each machine tool, ② the processing time of each machining task to be processed, ③ the life parameters of the tool consumed by the machining task to be processed, and ④ the requirements of each machining task for machining accuracy as input data, and obtain the global optimal machining scheduling plan through the genetic algorithm; then, use the global optimal machining scheduling plan as the initial state, and use reinforcement learning to dynamically enhance the scheduling plan, so as to obtain the dynamically optimized optimal scheduling plan. Thus, the machining tasks are intelligently allocated to ensure that the tasks are completed on schedule and the utilization rate of the machine tools is maximized.
[0268] In addition, the present invention evaluates the proposed method to verify the accuracy and rationality of the method, including the following evaluation indicators specifically.
[0269] Tool remaining life prediction accuracy evaluation: Obtain the true wear data Y of the tool through the physical signal acquisition module i,j and the life predicted by the deep operator network for evaluation:
[0270]
[0271] where, E jIt is the prediction error of the tool at the machine tool j, which reflects the accuracy of the model prediction.
[0272] Furthermore, based on the scheduling cost of the final solution, the algorithm designed in the present invention is compared with the traditional GA algorithm and the fixed threshold strategy algorithm to verify the performance of the scheduling strategy based on the genetic algorithm and reinforcement learning proposed in the present invention. Finally, the comparison results of the tool remaining life prediction accuracy and the scheduling scheme cost are as shown in the appendix Figure 5 and 6 shown; the results show that the method proposed in the present invention has higher prediction accuracy and lower scheduling cost.
[0273] The foregoing is only the preferred embodiment of the present application and is not intended to limit the present application. For those skilled in the art, the present application may have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included within the protection scope of the present application.
[0274] Although the specific implementation manners of the present invention are described above, they are not limitations on the protection scope of the present invention. Those skilled in the art should understand that, based on the technical solutions of the present invention, various modifications or deformations that can be made by those skilled in the art without creative efforts are still within the protection scope of the present invention.
Claims
1. A scheduling method for alloy processing workshop based on real-time monitoring of physical neural network, characterized in that: The process includes: S1, real-time collection of machine tool physical signal data, including vibration, cutting force and temperature data; S2, preprocessing the collected data, and obtaining enhanced time domain feature data and frequency domain feature data through Fourier transform feature extraction, and fusing them as data input for the tool remaining life prediction model; S3, tool remaining life prediction model predicts and outputs tool fatigue life results; the model uses a deep operator network guided by physical information, including a backbone network and a branch network, which process tool wear information and physical signal data respectively, and combine features through a fusion module; S4, tool scheduling optimization problem modeling, using the remaining tool life prediction results of each machine tool, the processing time of each task to be processed, the life parameters of the tool consumed by the task to be processed, and the requirements of each task to be processed for processing accuracy as input data, setting the objective function and constraint function; obtaining the global optimal processing scheduling plan through genetic algorithm, and then taking the global optimal processing scheduling plan as the initial state, using reinforcement learning to dynamically enhance the scheduling plan, so as to obtain the optimal scheduling plan after dynamic optimization.
2. The alloy processing workshop scheduling method based on real-time monitoring of physical neural network as claimed in claim 1 is characterized in that: The extracted time domain feature data include: The mean μ of the tool wear signal reflects the overall level of the signal; The standard deviation σ of the tool wear signal measures the volatility of the signal; The root mean square value (RMS) of the vibration signal measures the energy level of the signal; Peak factor τ, used to detect tiny chipping of tool edges; The final extracted time domain feature data output is 3. The alloy processing workshop scheduling method based on real-time monitoring of physical neural network as claimed in claim 1, characterized in that: The frequency domain features are extracted using fast Fourier transform. The extracted frequency domain feature data include: Main frequency characteristic f peak , used to monitor tool resonance. When the tool is close to failure, the main frequency will shift and the amplitude will increase; The kurtosis SC of the cutting force signal is used to measure the energy concentration of the spectrum and reflects the energy center of the spectrum. After the tool is worn, the high-frequency components increase, resulting in an increase in SC. The energy consumption value E during the cutting process is used to measure the total energy of the signal. When the vibration and cutting force of the tool increase, the total energy E will also increase; The output after frequency domain feature extraction is 4. The method for scheduling an alloy processing workshop based on real-time monitoring of a physical neural network as claimed in claim 1, characterized in that: The backbone network is used to process tool wear information, extract high-level features related to tool life, and enhance the expression ability through nonlinear transformation. Its input is the extracted wear features. The wear characteristics for: Time domain characteristics and frequency domain characteristics Combined to form a complete feature vector The time domain features reflect the impact of tool wear on signal volatility, and the frequency domain features reflect the impact of tool wear on signal spectrum. In order to better capture the nonlinear relationship, some features are transformed to obtain enhanced features. Where log(σ+1) represents the logarithm of the standard deviation, e -τ is a negative exponential transformation, Take the square root of the center of the spectrum to make the data distribution more even; The backbone network uses a multi-layer fully connected neural network to extract deep features: in, represents the weight matrix of the i-th layer, represents the bias term of the i-th layer, is the output feature of the i-th layer, and σ(·) is the ReLU activation function.
5. The method for scheduling an alloy processing workshop based on real-time monitoring of a physical neural network as claimed in claim 1, characterized in that: The branch network adopts the CNN+Transformer combination architecture, and uses the CNN module to output the feature Z of the main network. T For feature extraction, the core calculation formula is: WITH C =σ(W C *WITH T +b c ) Among them, W C is the convolution kernel of CNN, * indicates the convolution operation, b C is the bias term, Z C is the local temporal feature extracted by CNN; σ(·) is the ReLU activation function; multi-layer convolutional CNN is used to extract features of different scales: The final output features of CNN are: Where N is the number of CNN layers, and Flatten(·) means flattening into a vector to adapt to the Transformer input; In order to capture the long-term dependencies of physical signals, Transformer is used for global time series modeling: Among them, Q, K, V are linear transformation matrices; W Q , W K , W V is the weight matrix; Z B is the extracted time series feature; where Z is obtained through multi-head attention B The attention mechanism in is calculated as: Among them, d k represents the key feature dimension; finally, Z is normalized by layer C and Z B The final model prediction output obtained after processing is: in, Represents the final predicted tool fatigue life.
6. The method for scheduling an alloy processing workshop based on real-time monitoring of a physical neural network as claimed in claim 5, characterized in that: To enhance the physical consistency of the branch network, the cutting force model is used for physical constraint optimization: F c =k c a p f F t =k t a p f Among them, F c , F t Indicates the main cutting force and feed force, k c , k t Indicates that the cutting force is sparse, a p is the cutting depth, f is the feed rate; the physical consistency loss L is defined phys : L phys =||Z B -[F c ,F t ]|| 2 The final optimization target is the prediction error loss L MSE , physical consistency loss L phys and the regularization loss L reg Non-linear composition: Among them, λ1λ2λ3 represent hyperparameters that control the relative importance of each loss term, N is the number of training samples, and Y i Indicates the actual remaining tool life. represents the predicted remaining tool life, and W represents all trainable parameters of the model.
7. The alloy processing workshop scheduling method based on physical neural network real-time monitoring as claimed in claim 1, characterized in that: The tool scheduling optimization problem is modeled as follows: First, define variables and model the scheduling problem. Define that there are M machine tools in the workshop, each of which is equipped with a tool. The current remaining life of each tool has been predicted, expressed as: in, It is expressed as the predicted remaining life of the tool of the jth machine tool; the workshop needs to complete N processing tasks, and each task i consumes L tool life i , i = 1, 2, ..., N; set T i is the processing time required for task i, P i Define the scheduling decision variables for the accuracy requirement of task i: Among them, X ij A binary variable indicating whether task i is assigned to machine tool j. The problem goal is to find the optimal task allocation solution X = {X ij } to minimize the total cost of the task while ensuring tool life and task requirements.
8. The method for scheduling an alloy processing workshop based on real-time monitoring of a physical neural network as claimed in claim 7, characterized in that: The objective function is set to optimize the cost of minimizing the comprehensive scheduling cost, including tool replacement cost, task delay cost and precision loss cost, as follows: Among them, C replace,j represents the cost of tool replacement for machine tool j, C delay,i represents the cost of delay in task i, C precision,ij represents the cost of precision loss due to tool wear when task i is performed by machine tool j; The setting constraint conditions are specifically: Task allocation constraints: each task must be assigned to and only to one machine tool; Tool remaining life constraint: the total tool life of machine tool j cannot exceed its predicted remaining life; Task execution time constraint: After task i is assigned to machine tool j, its deadline must be met.
9. The method for scheduling an alloy processing workshop based on real-time monitoring of a physical neural network as claimed in claim 1, characterized in that: In S4, the task allocation and tool replacement strategy are optimized and solved by an adaptive genetic algorithm: First, initialize pop chromosome codes, where each chromosome code F represents a scheduling scheme: F=[X 11 ,X 12 ,...,X NM ] Among them, each parameter X ij The value is 0 or 1, indicating whether task i is assigned to machine tool j; Secondly, the fitness function is calculated by the optimization target C. The smaller C is, the better the scheduling scheme is: Fitness(F)=-C(F) Again, an adaptive roulette selection strategy is adopted, and the selection probability is proportional to the individual fitness: Among them, F k is the task allocation plan for the kth individual, P(F k ) is the individual F k The probability of being selected, through this step to obtain a new chromosome encoding population F se : Wherein, select() represents the chromosome selection operation. After that, the present invention proposes to use adaptive two-point crossover to perform a crossover operation on the chromosome, and the crossover rate P c Dynamic Adjustment: Among them, t max is the maximum number of iterations, t is the current number of iterations, P c_min represents the minimum crossover probability, P c_max is the maximum crossover probability, from population F se Randomly select two chromosome individuals and As a parent, perform a crossover operation: Where r is a random number r~U(0,1); the new offspring population F generated after crossover cr : Afterwards, the new population enters the mutation phase; The mutation operation is used to enhance the diversity of the population and avoid premature convergence, using an adaptive mutation method: Among them, P m Expressed as adaptive mutation probability, Fitness avg is the average fitness of the population, P m_min represents the minimum mutation probability, P m_max is the maximum mutation probability, and the mutation process is as follows: randomly select some tasks i* and randomly adjust their assigned machine tools j*: F i*j =σ,F i*j *=1,j*≠j;The new population individuals generated after compilation are: The solution of the new population is the global optimal scheduling solution.
10. The alloy processing workshop scheduling method based on physical neural network real-time monitoring as claimed in claim 1, characterized in that: The scheduling scheme is dynamically enhanced by using reinforcement learning in S4 as follows: The new population obtained by adaptive genetic algorithm As the initial solution to be locally optimized, that is, the initial state of reinforcement learning, combined with the predicted remaining tool life And set the task queue time of machine tool j Optimize the task scheduling scheme, including: Define the state space: At time step t, the state variables of the reinforcement learning Define the action space A t :Task redistribution is to adjust tasks to different machines: X ij ←X ik , k≠j; the tool replacement decision is to replace the tool in advance if the tool life is lower than the threshold: Task priority is adjusted to reduce the impact on tasks with high precision requirements: P i =max(P i -δ, 0); Design a reward function and continuously optimize the scheduling plan by updating the Q value.
Citation Information
Patent Citations
Method for predicting abrasion loss and residual life of cutter
CN113458873A
Turbocharging blade quality control method
CN113947821A
Cutter residual life prediction method based on deep learning and time sequence regression model
CN114749996A
Cutter residual life prediction method based on CNN-SBULSTM-Attention
CN118349831A
Flexible material pressing numerical control machining method based on data processing
CN118657056A
Cited By
Intelligent cutting process for aerospace titanium alloy cutter
CN120734434A
Resource state prediction and deep reinforcement learning scheduling fused workshop active scheduling method and device, and readable storage medium
CN120764935A
Tire rubber mixing process control method and system based on spatial-temporal characteristics and physical information
CN121091829A
Numerical control energy efficiency adaptive planning method based on physical information neural network
CN122449907A
Numerical control energy efficiency adaptive planning method based on physical information neural network
CN122449907B