Ceramic polishing machine real-time energy consumption prediction method based on Lyapunov width learning

Abstract

The invention relates to the technical field of energy consumption prediction, and provides a real-time energy consumption prediction method for a ceramic polishing machine based on Lyapunov width learning, which comprises the following steps: acquiring input parameters of the ceramic polishing machine at a plurality of historical moments to form an input parameter matrix; performing dimension reduction processing on the input parameter matrix by using a principal component analysis method to obtain a dimension-reduced feature vector; using a width learning system to take the dimensionality-reduced feature vector as input and the polishing energy consumption as output, and establishing an energy consumption prediction model which has an output weight; and when a new input parameter and a corresponding real energy consumption value are received, updating the output weight according to the new input parameter and the real energy consumption value by using a model updating strategy based on the Lyapunov theory to obtain real-time energy consumption prediction.

Description

Technical Field

[0001] This invention relates to the field of energy consumption prediction technology, and in particular to a real-time energy consumption prediction method for ceramic polishing machines based on Lyapunov width learning. Background Technology

[0002] Ceramic polishing is a key process in tile production, and its energy consumption accounts for 30% to 40% of the total electricity cost of tile production, highlighting the problems of high energy consumption and large resource consumption.

[0003] Currently, energy consumption modeling methods for ceramic polishing machines are mainly divided into two categories: mechanistic analysis-based methods and data-driven methods. In existing technologies, some studies have identified high-energy-consuming components and established corresponding energy consumption models by analyzing the energy flow during the idle phase of the polishing machine; other studies have established energy consumption models based on the motion law of the grinding disc and material removal theory; and still others have established parameter configuration strategy models using the controlled variable method.

[0004] However, these methods all belong to mechanism-based offline modeling methods, which have the following prominent problems: First, the computational complexity of mechanism models is high, relying on a precise mathematical description of the physical process, making them difficult to apply in actual industrial environments; second, existing methods cannot track and predict energy consumption changes in the polishing process in real time, making it difficult to adapt to the dynamic changes in working conditions in actual production; in addition, ceramic polishing machines have multiple mutually coupled operating parameters (such as grinding head speed, indentation depth, crossbeam swing speed, etc.), and the strong nonlinear coupling relationship between parameters further increases the difficulty of establishing an accurate energy consumption model.

[0005] Therefore, developing a method that can accurately predict the energy consumption of a polishing machine in real time is of great significance for improving the energy utilization efficiency of the polishing process. Summary of the Invention

[0006] To address the aforementioned shortcomings, the present invention aims to propose a real-time energy consumption prediction method for ceramic polishing machines based on Lyapunov width learning, which aims to achieve real-time and dynamic prediction of energy consumption in the ceramic polishing process and overcome the limitations of existing offline models that cannot adapt to dynamic changes in operating conditions.

[0007] To achieve this objective, the present invention adopts the following technical solution: A real-time energy consumption prediction method for ceramic polishing machines based on Lyapunov width learning, the method comprising: S1: Obtain the input parameters of the ceramic polishing machine at multiple historical moments and form an input parameter matrix; S2: Use principal component analysis to reduce the dimensionality of the input parameter matrix to obtain the dimensionality-reduced feature vector; S3: Using a width learning system, the dimensionality-reduced feature vector is used as input and polishing energy consumption is used as output to establish an energy consumption prediction model, wherein the energy consumption prediction model has output weights; S4: When new input parameters and corresponding real energy consumption values ​​are received, a model update strategy based on Lyapunov theory is used to update the output weights according to the new input parameters and the real energy consumption values ​​to obtain real-time energy consumption prediction.

[0008] Preferably, the input parameter matrix includes the grinding head rotation speed, the grinding head indentation depth, the crossbeam oscillation speed, and the tile feed speed.

[0009] Preferably, step S2 includes: For the input parameter matrix Perform zero-mean normalization: ; in, This represents the input parameter matrix. This indicates the total number of time points measured by the sensor. Indicates the first A vector consisting of all parameters measured at each time point; Calculate the covariance matrix of the matrix after zero-mean normalization. : ; in, Representation matrix transpose, The calculated covariance matrix is ​​used to characterize the degree of linear correlation between the parameters. Using singular value decomposition to analyze the covariance matrix Decompose to obtain eigenvalues and eigenvectors ,in This indicates the number of polishing machine heads. This represents the nth eigenvalue. This represents the nth eigenvector, with a total of eigenvalues. ; eigenvalues Sort in descending order and select the top... Construct an eigenvector matrix from the eigenvectors corresponding to the largest eigenvalues. ; Through projection transformation Converted to dimensionality-reduced feature vectors The following relation is satisfied: .

[0010] Preferably, step S3 includes constructing the mapping features: The dimensionality-reduced feature vectors are converted into mapped features, satisfying the following relationship: ; in, Let s represent the s-th mapping feature matrix. Let represent the activation function of the s-th group of mapped features. and Let represent the randomly generated input weights and biases, respectively, and r represent the number of sets of mapped features. Denotes the input matrix, and ; The r sets of mapping feature matrices are integrated into an output matrix of mapping features. The following relation is satisfied: .

[0011] Preferably, step S3 includes enhancing node construction: After obtaining the mapped feature output matrix M, the augmentation nodes are calculated: ; in, Indicates the first Group enhancement node matrix, Indicates the first The activation function for group-enhanced nodes. and These represent the randomly generated input weights and biases, respectively. Indicates the number of augmented node groups; Will Grouped enhanced node matrices are integrated into an enhanced node matrix. The following relation is satisfied: .

[0012] Preferably, step S3 includes calculating the output weights: By connecting the mapping features and the enhancement nodes, the output of the energy consumption prediction model is represented as follows: ; in, This represents the concatenation matrix of the mapping feature matrix M and the augmentation node matrix E. This represents the output weights of the width learning system; With the goal of minimizing prediction error, the following objective function is introduced: ; in, The ridge regression parameters are represented by the objective function, which is then solved to obtain... The solution is: ; in, Represents the identity matrix. This represents the transpose of matrix D; Based on the obtained output weights Predicted polishing energy consumption at time i+1 Satisfying the relation: ; in, Let the concatenation matrix at time i satisfy the following condition: , This represents the mapping feature matrix at time i. Let i represent the augmentation node matrix at time i; in and Satisfying the relation: ; ; in, This represents the eigenvector after dimensionality reduction at time i. Let x be the activation function of the x-th mapping feature. and This represents the random weights and biases corresponding to the x-th augmentation node. and Let r represent the random weights and biases corresponding to the x-th mapping feature group, and r represent the number of feature groups.

[0013] Preferably, step S4 includes: When new input data is acquired from the sensor At that time, among them Calculate the dimensionality-reduced feature vectors and actual energy consumption value ; Update the output weights according to Lyapunov theory. The following relation is satisfied: ; in, express The updated output weights at each step express Output weights at time 10:00 express The adaptive gain vector at time step 1. Indicates use The prediction error of the weight calculation is output at each time step; The adaptive gain vector Satisfying the relation: ; in, Indicates the learning rate. Describes the 2-norm of a matrix. Indicates use The prediction error of the weight calculation is output at each time step. express The concatenation matrix at time t, satisfies ; The prediction error and The calculation formula is: ; ; Based on the updated output weights , Predicted energy consumption for polishing at any time Satisfying the relation: ; in, and They represent The mapping feature matrix and the enhanced node matrix at each time step.

[0014] One of the above technical solutions has the following advantages or beneficial effects: This invention utilizes principal component analysis to reduce the dimensionality of the input parameter matrix, obtaining effective feature vectors, removing noise and unimportant coupling features from the input data, improving the speed and accuracy of data modeling, and reducing the impact of parameter coupling on the energy consumption prediction model. This effectively solves the problem of modeling difficulties caused by parameter coupling in traditional methods. A width learning system is used as input to establish an energy consumption prediction model with polishing energy consumption as output. As a data-driven method, the width learning system avoids the problem of excessively high computational costs in traditional mechanism-based modeling methods and has a simple and easy-to-implement structure. When new input parameters and corresponding actual energy consumption values ​​are received, a model update strategy based on Lyapunov theory is used to update the output weights, achieving real-time energy consumption prediction. The model accuracy can be adaptively adjusted based on real-time sensor data, enabling the model to adapt to the dynamic changes of the polishing machine in real time. This overcomes the limitation of existing offline models that cannot predict real-time energy consumption and meets the need for real-time energy consumption prediction in the ceramic polishing process. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0016] Figure 1This is a flowchart of a real-time energy consumption prediction method for ceramic polishing machines based on Lyapunov width learning, provided in an embodiment of the present invention. Detailed Implementation

[0017] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0018] In this invention, the terms "comprising," "including," or any other variations thereof are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0019] A real-time energy consumption prediction method for ceramic polishing machines based on Lyapunov width learning, such as Figure 1 As shown, in a preferred embodiment of the present invention, the real-time energy consumption prediction method for the ceramic polishing machine includes: S1: Obtain the input parameters of the ceramic polishing machine at multiple historical moments and form an input parameter matrix; It should be noted that in the real-time energy consumption prediction method for ceramic polishing machines, the input parameter matrix refers to a matrix composed of the input parameters of the ceramic polishing machine at multiple historical moments. This matrix reflects the operating status of the ceramic polishing machine and will be used for subsequent energy consumption prediction analysis.

[0020] S2: Use principal component analysis to reduce the dimensionality of the input parameter matrix to obtain the dimensionality-reduced feature vector; It should be noted that dimensionality reduction refers to the process of using principal component analysis (PCA) to process the input parameter matrix to extract key feature vectors. In this embodiment, PCA can remove noise and unimportant coupling features from the original parameter vectors by performing operations such as zero-mean normalization, covariance matrix calculation, and singular value decomposition on the input parameter matrix, thereby reducing the impact of parameter coupling on the energy consumption prediction model. Principal component analysis (PCA) is a commonly used statistical method to reduce the dimensionality of data while preserving its main features, thus improving the efficiency and accuracy of data processing.

[0021] Understandably, the purpose of dimensionality reduction is to reduce the dimension of the input parameter matrix without affecting key information, thereby reducing the complexity and computational cost of the subsequent energy consumption prediction model. By extracting the principal components, i.e., key feature vectors, from the input parameter matrix, the main factors reflecting the changes in the energy consumption of ceramic polishing machines can be highlighted, while removing some redundant information and noise interference.

[0022] S3: Using a width learning system, the dimensionality-reduced feature vector is used as input and polishing energy consumption is used as output to establish an energy consumption prediction model, wherein the energy consumption prediction model has output weights; Understandably, the purpose of establishing an energy consumption prediction model is to construct a mapping relationship between the input parameters of a ceramic polishing machine and its energy consumption through a data-driven approach, thereby achieving accurate prediction of polishing energy consumption. Width learning systems, as efficient machine learning algorithms, can quickly learn the complex relationship between input and output from data, and enhance the model's expressive power and generalization performance through the construction of mapping features and augmenting nodes. By minimizing the objective function of prediction error, the difference between the model's predicted energy consumption and the actual energy consumption can be minimized, thus improving the model's prediction accuracy.

[0023] S4: When new input parameters and corresponding real energy consumption values ​​are received, a model update strategy based on Lyapunov theory is used to update the output weights according to the new input parameters and the real energy consumption values ​​to obtain real-time energy consumption prediction.

[0024] It should be noted that real-time model parameter updates refer to updating the output weights of the energy consumption prediction model based on a Lyapunov theory-based model update strategy when new input parameters and corresponding actual energy consumption values ​​are received. This allows the model to adapt to the dynamic changes of the ceramic polishing machine in real time, improving the model's real-time performance and prediction accuracy. Lyapunov theory is a control theory method used to analyze system stability and dynamic behavior. In this embodiment, by designing update rules based on Lyapunov theory, the model's output weights can be adaptively adjusted according to newly arrived data, thereby achieving real-time model updates.

[0025] Understandably, the purpose of real-time model parameter updates is to enable the energy consumption prediction model to dynamically adapt to changes in the operating conditions of the ceramic polishing machine during actual operation, thereby maintaining high prediction accuracy. Since the energy consumption of the ceramic polishing machine is affected by various factors, and these factors change dynamically in actual production, traditional offline models are insufficient to meet the needs of real-time prediction. The model update strategy based on Lyapunov theory, by introducing the concept of system stability, ensures that when new data arrives, the model parameters can be adjusted in a stable and efficient manner, thus enabling the predicted energy consumption output by the model to reflect the actual energy consumption changes of the polishing machine in a timely manner.

[0026] Preferably, the input parameter matrix includes the grinding head rotation speed, the grinding head indentation depth, the crossbeam oscillation speed, and the tile feed speed.

[0027] It should be noted that the grinding head rotation speed refers to the number of revolutions the polishing machine's grinding head makes per unit time, measured in revolutions per minute (RPM). It directly affects the relative speed between the polishing head and the tile, thus influencing material removal rate and energy consumption. The grinding head penetration depth refers to the depth to which the grinding head penetrates the tile surface during polishing, measured in millimeters (mm). It determines the contact area and force between the grinding head and the tile, significantly impacting polishing effect and energy consumption. The crossbeam oscillation speed refers to the distance the polishing machine's crossbeam oscillates left and right per unit time, measured in millimeters per second (mm / s). It determines the lateral movement speed of the grinding head on the tile surface, affecting the polishing area and energy consumption distribution. The tile feed speed refers to the distance the tile moves along the conveying direction per unit time, measured in millimeters per second (mm / s). It determines the relative speed between the grinding head and the tile, affecting polishing efficiency and energy consumption.

[0028] Preferably, step S2 includes: For the input parameter matrix Perform zero-mean normalization: ; in, This represents the input parameter matrix. This indicates the total number of time points measured by the sensor. Indicates the first A vector consisting of all parameters measured at each time point; Calculate the covariance matrix of the matrix after zero-mean normalization. : ; in, Representation matrix transpose, The calculated covariance matrix is ​​used to characterize the degree of linear correlation between the parameters. Using singular value decomposition to analyze the covariance matrix Decompose to obtain eigenvalues and eigenvectors ,in This indicates the number of polishing machine heads. This represents the nth eigenvalue. This represents the nth eigenvector, with a total of eigenvalues. ; eigenvalues Sort in descending order and select the top... Construct an eigenvector matrix from the eigenvectors corresponding to the largest eigenvalues. ; Through projection transformation Converted to dimensionality-reduced feature vectors The following relation is satisfied: .

[0029] It's important to note that zero-mean normalization is a data preprocessing technique that reduces the mean of the data to zero by subtracting the mean from each parameter value, thereby eliminating data bias and improving the accuracy of subsequent covariance analysis. The covariance matrix B is used to quantify the linear correlation between parameters in the input parameter matrix; its elements represent the covariance between different parameters. Singular value decomposition (SVD) is a matrix factorization technique that decomposes the covariance matrix into eigenvalues ​​and eigenvectors. Eigenvalues ​​represent the magnitude of the data variance along the corresponding eigenvector direction, while eigenvectors indicate the main direction of data variation. Projective transformation is the process of projecting the original data onto a low-dimensional space composed of selected eigenvectors, achieving dimensionality reduction while preserving key feature information. The dimensionality-reduced eigenvectors are the representation of the original data in the low-dimensional space, reducing data dimensionality, lowering data complexity, and improving the efficiency of subsequent processing.

[0030] Based on principal component analysis, zero-mean normalization is used to remove data bias, ensuring that the covariance matrix accurately reflects the correlation between parameters. Singular value decomposition is used to identify the directions with the largest variance in the data, i.e., the principal component directions, which contain the most information. The eigenvectors corresponding to the top q largest eigenvalues ​​are selected for projection transformation, mapping the original high-dimensional data to a low-dimensional feature space, resulting in dimensionality-reduced eigenvectors. This process removes noise and redundant information from the original data, reduces the impact of parameter coupling on the energy consumption prediction model, and thus improves the model's training efficiency and prediction accuracy.

[0031] For example, suppose parameter acquisition was performed on a ceramic polishing machine, acquiring relevant data at five historical moments. At each moment, parameters such as the rotational speed of grinding head 1, the indentation depth of grinding head 1, the rotational speed of grinding head 2, the indentation depth of grinding head 2, the oscillation speed of the crossbeam, and the tile feed speed were collected. First, this data was organized into an input parameter matrix A. Then, the average value of each parameter was calculated, such as the average rotational speed of grinding head 1 being 1215 rpm and the average indentation depth of grinding head 1 being 2.0 mm. Next, matrix A was zero-mean normalized to obtain a zero-mean matrix. Then, the covariance matrix B of this matrix was calculated. Assuming that after obtaining the covariance matrix, singular value decomposition was used to decompose it, obtaining eigenvalues ​​and eigenvectors, the eigenvalues ​​are arranged in descending order as 120, 110, 100, 0.015, 0.012, 0.01, 0.009, and 0.6, and the corresponding eigenvectors are as follows: , , Etc. Select the eigenvectors corresponding to the first 3 eigenvalues ​​to form an eigenvector matrix. = , , Finally, the parameter vector a(1) at the first time step is compared with... Multiplying by transpose yields the eigenvector c(1) after dimensionality reduction.

[0032] Preferably, step S3 includes constructing the mapping features: The dimensionality-reduced feature vectors are converted into mapped features, satisfying the following relationship: ; in, Let s represent the s-th mapping feature matrix. Let represent the activation function of the s-th group of mapped features. and Let represent the randomly generated input weights and biases, respectively, and r represent the number of sets of mapped features. Denotes the input matrix, and ; The r sets of mapping feature matrices are integrated into an output matrix of mapping features. The following relation is satisfied: .

[0033] It's important to note that the dimensionality-reduced feature vectors are low-dimensional data representations processed by PCA, used to remove redundant information and noise while retaining key features. Mapped features are feature representations obtained by performing a non-linear transformation on the input data using activation functions, used to capture complex patterns in the data. Activation functions are a class of mathematical functions used to introduce non-linearity, such as ReLU and Sigmoid, which enable the model to learn more complex feature relationships. Input weights and biases are parameters in the neural network used to perform a linear transformation on the input data; they are usually randomly generated in the initial stage. The mapped feature output matrix is ​​the result of integrating all mapped feature matrices and is used for subsequent model output calculations.

[0034] By applying nonlinear transformations to the input data using activation functions, the model can capture complex nonlinear relationships within the data, thereby enhancing its expressive power and predictive performance. Different sets of mapping features can be implemented using different activation functions and randomly generated weights and biases, increasing model diversity. Integrating these mapping feature matrices into an output matrix provides rich feature representations for subsequent energy consumption prediction models, helping to improve the model's sensitivity to energy consumption changes and its prediction accuracy.

[0035] For example, suppose we have already reduced the dimensionality of the input parameters of the ceramic polisher to a 3×5 matrix (3 feature dimensions, 5 samples) using PCA. Now we need to construct the mapping features, setting the number of mapping feature groups r=2. First, we randomly generate two sets of input weights. and bias Assuming each group's weight matrix has a dimension of 3×4 and its bias vector has a dimension of 1×4, and then choosing the ReLU function as the activation function, the following calculations are performed on the mapping features of each group. and All dimensions are 5×4. Finally, and Concatenate the columns to obtain the mapped feature output matrix. Its dimensions are 5×8.

[0036] Preferably, step S3 includes enhancing node construction: After obtaining the mapped feature output matrix M, the augmentation nodes are calculated: ; in, Indicates the first Group enhancement node matrix, Indicates the first The activation function for group-enhanced nodes. and These represent the randomly generated input weights and biases, respectively. Indicates the number of augmented node groups; Will Grouped enhanced node matrices are integrated into an enhanced node matrix. The following relation is satisfied: .

[0037] It's important to note that augmentation nodes in a wide-learning system are used to further enhance the model's expressive power. By introducing additional non-linear transformations, they can capture more complex feature relationships. Activation functions are mathematical functions used to introduce non-linearity, such as ReLU and Sigmoid, which enable the model to learn more complex feature patterns. Input weights and biases are model parameters used to perform linear transformations on the input data; they are typically randomly generated initially. The augmentation node output matrix is ​​the result of integrating all augmentation node matrices and is used for subsequent model output calculations.

[0038] Understandably, augmentation nodes, by introducing additional nonlinear transformations, can capture more complex feature relationships in the data. The activation function performs a nonlinear transformation on the input data, enabling the model to learn richer feature representations. Different groups of augmentation nodes can be implemented using different activation functions and randomly generated weights and biases, increasing model diversity. Integrating the matrices of each augmentation node group into an output matrix provides a more powerful feature representation for the subsequent energy consumption prediction model, helping to improve the model's prediction accuracy.

[0039] Preferably, step S3 includes calculating the output weights: By connecting the mapping features and the enhancement nodes, the output of the energy consumption prediction model is represented as follows: ; in, This represents the concatenation matrix of the mapping feature matrix M and the augmentation node matrix E. This represents the output weights of the width learning system; With the goal of minimizing prediction error, the following objective function is introduced: ; in, The ridge regression parameters are represented by the objective function, which is then solved to obtain... The solution is: ; in, Represents the identity matrix. This represents the transpose of matrix D; Based on the obtained output weights Predicted polishing energy consumption at time i+1 Satisfying the relation: ; in, Let the concatenation matrix at time i satisfy the following condition: , This represents the mapping feature matrix at time i. Let i represent the augmentation node matrix at time i; in and Satisfying the relation: ; ; in, This represents the eigenvector after dimensionality reduction at time i. Let x be the activation function of the x-th mapping feature. and This represents the random weights and biases corresponding to the x-th augmentation node. and Let r represent the random weights and biases corresponding to the x-th mapping feature group, and r represent the number of feature groups.

[0040] It should be noted that the augmentation node matrix is ​​a matrix obtained from the augmentation node construction process, used to further enhance the model's expressive power. The concatenation matrix is ​​formed by concatenating the mapping feature matrix and the augmentation node matrix column-wise, used to integrate all feature information. Output weights are the parameters connecting the feature layer and the output layer in the width learning system, used to map feature information to energy consumption prediction values. The objective function is the function to be minimized during optimization, used to measure the difference between the model's predicted values ​​and the true values, as well as the model's complexity. Ridge regression parameters are hyperparameters used to control model complexity and prevent overfitting. The identity matrix is ​​a matrix with diagonal elements of 1 and all other elements of 0, used as the unit element in matrix operations. The transpose matrix is ​​a matrix obtained by interchanging the rows and columns of the original matrix, used for transpose operations in matrix operations.

[0041] Understandably, based on a width-based learning system, by concatenating mapped features and augmented nodes to form a complete feature representation, and using ridge regression to solve for the output weights, the model can minimize prediction error when predicting energy consumption, while controlling model complexity and preventing overfitting. This ensures that the model has a good fit on the training data and also has good generalization ability on new data, thereby improving the accuracy and reliability of energy consumption prediction.

[0042] Preferably, step S4 includes: When new input data is acquired from the sensor At that time, among them Calculate the dimensionality-reduced feature vectors and actual energy consumption value ; Update the output weights according to Lyapunov theory. The following relation is satisfied: ; in, express The updated output weights at each step express Output weights at time 10:00 express The adaptive gain vector at time step 1. Indicates use The prediction error of the weight calculation is output at each time step; The adaptive gain vector Satisfying the relation: ; in, Indicates the learning rate. Describes the 2-norm of a matrix. Indicates use The prediction error of the weight calculation is output at each time step. express The concatenation matrix at time t, satisfies ; The prediction error and The calculation formula is: ; ; Based on the updated output weights , Predicted energy consumption for polishing at any time Satisfying the relation: ; in, and They represent The mapping feature matrix and the enhanced node matrix at each time step.

[0043] It should be noted that the new input data consists of the input parameters of the ceramic polishing machine collected by sensors at the current moment, reflecting its current operating status. The dimensionality-reduced feature vector is a feature representation obtained by principal component analysis (PCA) after dimensionality reduction of the input data, used to reduce data dimensionality while retaining key information. The actual energy consumption value is the actual energy consumed by the ceramic polishing machine at the current moment, used for model updates and validation. The output weights are the parameters connecting the feature layer and the output layer in the wide learning system, used to map feature information to energy consumption prediction values. Lyapunov theory, a control theory used to construct energy functions to ensure system stability, is used here to guide the updating of model parameters. The adaptive gain vector is a vector dynamically adjusted based on the current prediction error and historical prediction errors, used to control the update step size. The prediction error is the difference between the model's predicted value and the true value, used to measure the model's predictive performance. The concatenation matrix is ​​a matrix formed by column-wise concatenation of the mapped feature matrix and the enhancement node matrix, used to integrate all feature information. This process employs an online learning method based on Lyapunov theory, which adapts to the dynamic changes of the polishing machine by updating the output weights in real time.

[0044] Based on Lyapunov theory, an energy function is constructed to measure changes in prediction error, ensuring that model parameter updates stabilize the system. Specifically, when new input data and actual energy consumption values ​​arrive, the prediction error at the current moment is first calculated, and then the output weights are updated according to Lyapunov theory. The adaptive gain vector dynamically adjusts its update step size based on current and historical prediction errors, ensuring the model can quickly respond to the dynamic changes of the polishing machine while avoiding instability caused by over-adjustment. In this way, the model can capture the energy consumption changes of the polishing machine in real time, providing accurate energy consumption predictions and supporting energy-saving optimization decisions.

[0045] At any moment The sensor collected new input data. and actual energy consumption value First, using the eigenvector matrix Will Converted to dimensionality-reduced feature vectors Then, calculate the prediction error at the current time. and use Prediction error of weight calculation at time step Assuming and The output weights at times 5 and 4 are respectively. This is the concatenated matrix at time 6. The learning rate is set. Calculate the adaptive gain vector ,in This represents the prediction error at time 5. Finally, update the output weights. And predict the energy consumption at the next moment. Through this process, the model can adjust its parameters in real time to adapt to the dynamic changes of the polishing machine and improve prediction accuracy.

[0046] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "illustrative embodiment," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0047] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims

1. A method for real-time energy consumption prediction of a ceramic polishing machine based on Lyapunov width learning, characterized in that, The real-time energy consumption prediction method of the ceramic polishing machine comprises: S1: Obtain input parameters of the ceramic polishing machine at multiple historical time points to form an input parameter matrix; S2: Perform dimension reduction processing on the input parameter matrix using a principal component analysis method to obtain a dimension-reduced feature vector; S3: Use a width learning system to take the dimension-reduced feature vector as input and take polishing energy consumption as output to establish an energy consumption prediction model, wherein the energy consumption prediction model has output weights; S4: When receiving new input parameters and corresponding real energy consumption values, use a model update strategy based on Lyapunov theory to update the output weights according to the new input parameters and the real energy consumption values to obtain real-time energy consumption prediction.

2. The ceramic polisher real-time energy consumption prediction method according to claim 1, characterized in that, The input parameter matrix includes the rotation speed of the grinding head, the pressure depth of the grinding head, the beam swing speed, and the tile feeding speed.

3. The ceramic polishing machine real-time energy consumption prediction method according to claim 2, characterized in that, Step S2 comprises: zero-meaning the input parameter matrix zero-meaning ； wherein, a matrix of input parameters, denotes the total number of time points measured by the sensors, denotes the vector of all parameters measured at the time instant. computing a covariance matrix of the zero-mean matrix : ； wherein denotes the transpose of the matrix , denotes a calculated covariance matrix, which is used to characterize the degree of linear correlation between parameters; Using singular value decomposition to analyze the covariance matrix Decompose to obtain eigenvalues and eigenvectors ,in This indicates the number of polishing machine heads. This represents the nth eigenvalue. This represents the nth eigenvector, with a total of eigenvalues. ; The characteristic values are sorted in descending order, and the eigenvectors corresponding to the first The characteristic values are sorted in descending order, and the eigenvectors corresponding to the first The characteristic values are sorted in descending order, and the eigenvectors corresponding to the first ; Through projection transformation Converted to dimensionality-reduced feature vectors The following relation is satisfied: .

4. The ceramic polishing machine real-time energy consumption prediction method according to claim 3, characterized in that, Step S3 comprises mapping feature construction: Convert the dimension-reduced feature vector into a mapping feature to satisfy the relationship: ； wherein, denotes the st mapping feature matrix, denotes the activation function of the st mapping feature, and denotes the randomly generated input weight and bias, respectively, and r denotes the number of groups of mapping features, denotes the input matrix, and ; integrating the r sets of mapping feature matrices into an output matrix of mapping features , satisfying the relationship: .

5. The ceramic polishing machine real-time energy consumption prediction method according to claim 4, characterized in that, Step S3 comprises enhanced node construction: After obtaining the mapping feature output matrix M, calculate the enhanced node: ； wherein, represents the group of enhanced node matrix, represents the activation function of the group of enhanced nodes, and respectively represent randomly generated input weights and biases, represents the number of groups of enhanced nodes; Will The group enhanced node matrix is integrated into an enhanced node matrix , satisfying the relationship: .

6. The ceramic polisher real-time energy consumption prediction method according to claim 5, characterized in that, Step S3 comprises output weight calculation: By connecting the mapped features and the augmented nodes, the output of the energy consumption prediction model is represented as ; wherein, denotes a concatenated matrix of the mapping feature matrix M and the enhancement node matrix E, denotes the output weight of the wide learning system; Take the minimum prediction error as the target to introduce the following objective function: ； wherein, denotes a ridge regression parameter, and the solution of the objective function is given by ； wherein denotes the identity matrix, denotes the transpose of the matrix D; based on the obtained output weight the polishing predicted energy consumption at the i+1 time satisfies the relationship ； wherein, represents a series matrix at time i, satisfying , represents a mapping feature matrix at time i, represents an augmented node matrix at time i; wherein and satisfies the relationship: ； ； wherein, represents the feature vector after dimension reduction at time i, represents the activation function of the xth group of mapped features, and represents the random weight and bias corresponding to the xth group of enhanced nodes, and represents the random weight and bias corresponding to the xth group of mapped features, and r represents the number of feature groups.

7. The real-time energy consumption prediction method of a ceramic polishing machine according to claim 6, characterized in that, Step S4 comprises: When new input data is acquired from the sensor , wherein , a reduced dimension feature vector and a real energy consumption value are calculated; updating the output weight values in accordance with Lyapunov theory satisfying the relationship ； wherein, denotes the output weight updated at the time instant, denotes the output weight at the time instant, denotes the adaptive gain vector at the time instant, denotes the prediction error calculated using the output weight at the time instant. the adaptive gain vector satisfies the relation: ； wherein, denotes a learning rate, denotes a two-norm of a matrix, denotes using a prediction error of the output weight computation at time t, denotes a concatenated matrix at time t, satisfying ; The prediction error And The calculation formula is: ； ； based on the updated output weights , polishing prediction energy consumption at the moment satisfies the relationship ； wherein, and respectively represent mapping feature matrix and augmented node matrix at the time instant.

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