Copper Foil Resistivity and Surface Treatment Process Parameter Correlation Prediction Algorithm System

Abstract

This invention relates to the field of electro-digital data processing, specifically to a predictive algorithm system for the correlation between copper foil resistivity and surface treatment process parameters. The system includes: a process topology graph construction component, which constructs a directed acyclic graph based on the physical process sequence, where nodes represent process segments, edges represent the substrate flow direction, and node feature vectors are time series of process parameters; a spatiotemporal feature extraction component, which embeds a temporal convolutional network into node feature extraction, extracts the time lag effect of parameter changes through dilated causal convolution, and aggregates cross-process parameter coupling features based on flow direction features in the graph convolutional layer; and a resistivity dynamic prediction component, which maps the cross-process parameter coupling features through a fully connected layer to output predicted values. This invention solves the problem that existing static models cannot characterize the nonlinear coupling between continuous processes and the inaccurate resistivity prediction caused by parameter delays, reduces prediction bias caused by transient fluctuations, and improves prediction stability.

Description

Technical Field

[0001] This invention relates to the field of electronic digital data processing, specifically to a prediction algorithm system for the correlation between copper foil resistivity and surface treatment process parameters. Background Technology

[0002] Copper foil, as a fundamental material in the electronics industry, directly impacts the conductivity and energy consumption of downstream products due to its resistivity. In copper foil manufacturing, surface treatment is the core stage determining the final resistivity, involving multiple continuous processes such as electroplating passivation, extrusion, and drying. Existing technologies typically employ data-driven static prediction schemes to establish the mapping relationship between surface treatment process parameters and resistivity. These schemes collect historical process parameters for each step, including physical quantities such as treatment solution temperature, current density, and reaction time. The average of all process parameters within the same production batch over time, or the instantaneous values ​​of specific time slices, are then combined into a flattened high-dimensional feature vector. This feature vector is input into a regression model such as a fully connected neural network or support vector machine, and the model calculates the corresponding predicted resistivity value. However, this scheme assumes that the process state within the same batch is under static and constant conditions, ignoring the objective laws governing the dynamic evolution of various parameters on the production line over time.

[0003] The aforementioned static prediction schemes face structural limitations in practical industrial applications. Copper foil surface treatment production lines involve a continuous, dynamic physicochemical process. The substrate sequentially passes through various treatment tanks, and changes in process parameters from one step are carried into subsequent steps as the substrate is physically transferred, continuously impacting the subsequent chemical reactions. This impact exhibits a significant lag effect over time. Furthermore, there is a non-linear coupling relationship between chemical deposition and electrochemical reactions between adjacent steps. For example, the chromium deposition state in the electroplating passivation process directly affects the liquid film peeling effect in the extrusion process. Existing static schemes flatten multidimensional parameters and fragment the temporal sequence, directly mapping features within the same time slice without considering the physical flow direction and time delay of chemical reactions between steps. This prevents the model from capturing the dynamic characteristics of parameter fluctuations and from reflecting the true physical process of parameter transfer across steps.

[0004] Based on the specific implementation methods and limitations of the existing technologies, there are technical problems with the inability to characterize the nonlinear coupling between continuous processes and the inaccurate resistivity prediction caused by parameter delays. Because the flattened feature input method severs the temporal dependence and spatial flow correlation of process parameters, when transient fluctuations or time-series drift occur in the production environment, the static model cannot perceive the lag effect of current parameter changes in the time dimension or the coupling transmission path in the process topology dimension. This leads to a disconnect between the distribution of model input features and the actual physicochemical process, resulting in serious deviations in the predicted output results. This makes it impossible to provide a reliable basis for closed-loop control of process parameters, thus limiting the fine-tuning capability of copper foil surface treatment processes. Summary of the Invention

[0005] The purpose of this invention is to provide a prediction algorithm system for the correlation between copper foil resistivity and surface treatment process parameters, which can solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A prediction algorithm system for the correlation between copper foil resistivity and surface treatment process parameters includes: a process topology graph construction component, configured to construct a directed acyclic graph based on the physical process sequence of the copper foil surface treatment production line, wherein nodes represent each process segment, edges represent the flow direction of the copper foil substrate, and the node feature vector of the node is a sequence of process parameters of the corresponding process segment changing over time; The spatiotemporal feature extraction component is configured to embed a temporal convolutional network into the node feature extraction of the directed acyclic graph, extract the time lag effect of the change of process parameters on subsequent processes and final resistivity by expanding causal convolution, and perform feature aggregation in the graph convolutional layer according to the flow direction to obtain cross-process parameter coupling features. The resistivity dynamic prediction component is configured to map the cross-process parameter coupling features through a fully connected layer to output a dynamic prediction value of the target copper foil resistivity.

[0007] Preferably, in the process topology graph construction component, for the node feature vector being a sequence of process parameters changing over time for the corresponding process segment, the process topology graph construction component is further configured to: perform a normalization operation on the heterogeneous process parameters in the node feature vector, mapping physical parameters of different dimensions to a unified numerical range; For the missing sampling points in the node feature vector, interpolation reconstruction is performed based on the adjacent known sampling points of the missing sampling points on the time axis to generate a continuous and complete node feature vector. The interpolation reconstruction adopts linear interpolation or spline interpolation.

[0008] Preferably, in the spatiotemporal feature extraction component, for the extraction of the time lag effect of the process parameter change on subsequent processes and final resistivity by dilated causal convolution, the temporal convolutional network includes multiple stacked dilated causal convolutional layers, each of which adopts a progressively increasing dilation rate, so that the temporal convolutional network can obtain a temporal receptive field of different scales. The output features of each layer in the multi-layered stacked dilated causal convolutional layer are concatenated along the channel dimension to generate a multi-scale temporal feature vector that includes the effects of multiple time lags.

[0009] Preferably, in the spatiotemporal feature extraction component, for the feature aggregation in the graph convolutional layer based on the flow direction to obtain cross-process parameter coupling features, the graph convolutional layer is further configured to: introduce an attention weight coefficient calculation mechanism in the flow direction, and calculate the spatial correlation score of the upstream adjacent process node to the current process node based on the node feature vectors of the current process node and the upstream adjacent process node; The features of the upstream adjacent process nodes are weighted and summed based on the spatial correlation score. The weighted summation result is then fused with the features of the current process node to generate the cross-process parameter coupling feature.

[0010] Preferably, in the resistivity dynamic prediction component, for the dynamic prediction value of the target copper foil resistivity output by mapping the cross-process parameter coupling feature through the fully connected layer, the resistivity dynamic prediction component is further configured to: before the mapping of the fully connected layer, perform residual connection between the cross-process parameter coupling feature and the baseline process parameter feature initially input by the process topology graph construction component, and input the fused feature after residual connection to the fully connected layer; The fully connected layer comprises a hidden mapping layer and a linear output layer connected in sequence, and the hidden mapping layer uses a non-linear activation function to process the fused features.

[0011] Preferably, for calculating the spatial correlation score between the upstream adjacent process node and the current process node, the graph convolutional layer is further configured to: extract the temporal query vector of the current process node and the temporal key vector of the upstream adjacent process node, and calculate the dot product between the temporal query vector and the temporal key vector; The dot product result is input into the softening function to obtain the spatial correlation score. During the iterative training of the graph convolutional layer, based on the deviation between the dynamic predicted value of the target copper foil resistivity and the true resistivity label, the weight matrix of the time-series query vector and the time-series key vector is updated through backpropagation.

[0012] Preferably, for generating multi-scale temporal feature vectors containing the effects of multiple time lags, the temporal convolutional network is further configured with a gating filtering mechanism: constructing a gating vector with the same dimension as the multi-scale temporal feature vector, wherein each element of the gating vector takes a value between zero and one; The gate vector is multiplied element-wise with the multi-scale temporal feature vector to filter out the hysteresis feature components in the multi-scale temporal feature vector that are weakly correlated with the change in copper foil resistivity. The filtered feature vector is then output as the final output of the temporal convolutional network.

[0013] Preferably, for the interpolation reconstruction to generate continuous and complete node feature vectors, the process topology graph construction component is further configured to: obtain the physical allowable extreme value boundaries of each process parameter in the node feature vectors; When performing the interpolation reconstruction, a truncation constraint is applied to the intermediate reconstruction value obtained by interpolation calculation. When the intermediate reconstruction value exceeds the physical allowable extreme value boundary, the intermediate reconstruction value is corrected to the corresponding physical allowable extreme value. The corrected node feature vector is input into the spatiotemporal feature extraction component.

[0014] Preferably, it also includes a physical mechanism constraint component, which is configured to: during the model training phase, obtain the physical calculation formula of resistivity corresponding to the copper foil material, wherein the physical calculation formula of resistivity characterizes the parallel relationship between the inherent resistance of the copper foil substrate and the additional resistance of the surface treatment deposition layer; A regularization penalty term is constructed based on the physical calculation formula of resistivity. The regularization penalty term is then combined with the supervision loss function corresponding to the dynamic prediction value of the target copper foil resistivity to construct the total loss function. The network parameters of the spatiotemporal feature extraction component and the resistivity dynamic prediction component are adjusted according to the total loss function.

[0015] Preferably, it also includes an online incremental update component, which is configured to continuously collect newly generated surface treatment process parameters and corresponding real copper foil resistivity data pairs at the production site, and construct a sliding time window of fixed length; When the number of data pairs accumulated within the sliding time window reaches a preset number, the network parameters of the graph convolutional layer in the spatiotemporal feature extraction component are frozen, and only the parameters of the fully connected layer in the resistivity dynamic prediction component are fine-tuned. The fine-tuning loss is calculated based on the latest data within the sliding time window, and the parameters of the fully connected layer are updated by gradient descent.

[0016] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. By constructing a directed acyclic graph (DAG) consistent with the physical process sequence of a copper foil surface treatment production line, each process segment is treated as a graph node, the substrate flow direction as an edge, and the sequence of process parameters changing over time for each corresponding process segment is used as the node feature vector, thus reconstructing the spatiotemporal distribution of process parameters. In the feature extraction stage, a temporal convolutional network is embedded into the feature extraction of the graph nodes. Expanded causal convolutions are used to extract the time-lag effect of process parameter changes on subsequent processes and the final resistivity. Simultaneously, feature aggregation is performed in the graph convolutional layer based on the flow direction to obtain cross-process parameter coupling features. This approach deeply binds the time-dimensional lag effect with the spatial-dimensional process flow topology, changing the static and flat feature mapping logic of existing technologies and solving the technical problems of inaccurate resistivity prediction caused by the inability to characterize nonlinear coupling between continuous processes and parameter delays. When process parameters fluctuate dynamically, the model can track the lag propagation path of parameter changes based on the flow direction. Combined with cross-process parameter coupling features, it reconstructs the real interaction process of chemical reactions, improving the consistency between prediction results and actual physicochemical processes, reducing prediction bias caused by transient fluctuations, and enhancing the stability and reliability of the prediction system.

[0017] 2. When aggregating features based on flow direction in the graph convolutional layer, an attention weight coefficient calculation mechanism is introduced. Spatial correlation scores are calculated based on the node feature vectors of the current process node and its upstream neighboring process nodes, and then weighted and summed. This achieves a differentiated measurement of the influence of different upstream processes, eliminating the interference of weakly correlated process features on the aggregation results. The temporal convolutional network uses a layer-by-layer increasing expansion rate to obtain temporal receptive fields of different scales and concatenates them to generate multi-scale temporal feature vectors. Combined with a gating screening mechanism, it filters out lagging feature components weakly correlated with resistivity changes, reducing irrelevant noise input and feature dimension redundancy. The physical mechanism constraint component constructs a regularization penalty term based on the resistivity physical calculation formula to participate in the calculation of the total loss function, limiting the risk of network parameter updates deviating from the physical conductivity mechanism and ensuring the physical rationality of the predicted output under boundary conditions. The online incremental update component continuously accumulates data on the production site, freezes the feature extraction network parameters, and only fine-tunes the prediction layer parameters. This reduces the computational resource consumption and time delay of model reconstruction when facing production condition drift, ensuring the tracking and prediction capabilities of the prediction system in long-cycle continuous production environments. Attached Figure Description

[0018] Figure 1 This is a flowchart of the entire operation of the copper foil resistivity and process parameter correlation prediction algorithm system. Figure 2 A flowchart for the entire process of preprocessing component node feature vectors for constructing the process topology diagram; Figure 3 Flowchart for feature extraction and gating filtering using temporal convolutional networks, a component for spatiotemporal feature extraction. Figure 4 The graph convolutional layer generates a flowchart based on the cross-process parameter coupling features of process flow and attention weights; Figure 5 Flowchart for residual fusion and hierarchical fully connected prediction output of resistivity dynamic prediction component; Figure 6 A flowchart illustrating the entire process of model parameter optimization and control that coordinates physical mechanism constraints with online incremental updates. Detailed Implementation

[0019] In one embodiment, append Figure 1 The copper foil resistivity and surface treatment process parameter correlation prediction algorithm system runs on the industrial control computer of the copper foil surface treatment production line. The system establishes data communication connections with sensors and controllers at each stage of the production line via industrial Ethernet, collecting process parameter data from each stage in real time. The system first constructs a directed acyclic graph (DAG) based on the physical process sequence of the copper foil surface treatment production line using a process topology graph construction component. The physical process sequence of the copper foil surface treatment production line is as follows: electroplating and passivation, extrusion, drying, and winding. Each of these process stages is treated as an independent node in the DAG. The edges between nodes represent the flow direction of the copper foil substrate on the production line, and the direction of the edges is consistent with the physical movement direction of the substrate, i.e., from the electroplating and passivation node to the extrusion node, from the extrusion node to the drying node, and so on, until the winding node. The node feature vector of each node is a sequence of process parameters changing over time for the corresponding process stage, where the feature dimension of each time step is consistent with the number of process parameters collected for that process stage.

[0020] After the process topology graph construction component completes the construction of the directed acyclic graph (DAG), it inputs the DAG containing node feature vectors into the spatiotemporal feature extraction component. The spatiotemporal feature extraction component embeds a temporal convolutional network into the feature extraction process of each node in the DAG, performing temporal feature extraction operations on the node feature vector of each node separately. The temporal convolutional network adopts a dilated causal convolution structure. Causal convolution ensures that only input data at time t and earlier is used when extracting features at time t, avoiding prediction bias caused by introducing future information. Dilated convolution expands the receptive field by inserting zero values ​​between convolutional kernel elements, capturing the impact of process parameter changes over a longer time span. The dilated causal convolution extracts the time lag effect of process parameter changes in each process segment on subsequent processes and the final resistivity. For example, an increase in current density at time t in the electroplating passivation process will affect the deposition layer growth state in the extrusion process after time t+Δt, and subsequently affect the final copper foil resistivity after time t+2Δt, where Δt is the time required for the copper foil substrate to transfer from the electroplating passivation process to the extrusion process.

[0021] After extracting the temporal features of each node, the spatiotemporal feature extraction component aggregates features based on the flow direction in the directed acyclic graph (DAG). The DAG only propagates features along the edges, allowing features from upstream process nodes to be passed to downstream process nodes, while prohibiting features from downstream process nodes from being passed to upstream process nodes, in accordance with the physical flow patterns of the production line. For each downstream process node, the DAG aggregates the temporal features of all its directly upstream process nodes and fuses them with the node's own temporal features to generate the node's cross-process parameter coupling features. For example, the cross-process parameter coupling features of the extrusion process node are generated by fusing the temporal features of the electroplating passivation node with the extrusion process node's own temporal features; similarly, the cross-process parameter coupling features of the air-drying process node are generated by fusing the cross-process parameter coupling features of the extrusion process node with the air-drying process node's own temporal features. Finally, the cross-process parameter coupling features of the winding process node contain the temporal information of all upstream process parameters and cross-process coupling information.

[0022] The spatiotemporal feature extraction component outputs the cross-process parameter coupling features of the winding process nodes to the resistivity dynamic prediction component. The resistivity dynamic prediction component contains a fully connected layer. This layer receives the cross-process parameter coupling features as input and, through linear transformation and nonlinear activation of multiple neural networks, maps the high-dimensional cross-process parameter coupling features into a one-dimensional dynamic resistivity prediction value for the target copper foil. The output of the fully connected layer is a continuous time series, with the output at each time step corresponding to the predicted resistivity value of the copper foil substrate that has undergone the winding process at that time step.

[0023] This embodiment fully realizes the technical solution of deeply binding the time dimension lag effect of process parameters with the spatial dimension of process flow topology, reconstructs the spatiotemporal distribution of process parameters, and changes the static and flat feature mapping logic of the existing technology.

[0024] Appendix Figure 2 In a preferred embodiment, the process topology graph construction component performs a normalization operation on the heterogeneous process parameters in the node feature vectors when generating them. This is because different process parameters have different physical dimensions and numerical ranges; for example, the temperature of the processing liquid typically ranges from 20°C to 80°C, and the current density typically ranges from 1 A / dm³. 2 Up to 10A / dm 2 The reaction time typically ranges from 5 to 30 seconds. Directly inputting parameters of different dimensions into the neural network can lead to larger parameters dominating the model's training process, affecting the model's convergence speed and prediction accuracy. Normalization maps physical parameters of different dimensions to a unified numerical range. In this embodiment, the min-max normalization method is used, and its calculation formula is as follows:

[0025] in, These are the original sampled values ​​of the process parameters. This is the minimum value of the process parameter in historical production data. This is the maximum value of the process parameter in historical production data. These are the normalized parameter values. Through the above normalization operation, the values ​​of all process parameters are mapped to the [0,1] interval, eliminating the influence of dimensional differences on model training.

[0026] Furthermore, the process topology graph construction component performs interpolation reconstruction for missing sampling points in the node feature vectors. In actual production, due to sensor malfunctions, network transmission interruptions, or inconsistent data acquisition cycles, some time steps of the node feature vectors may be missing sampling values. Missing sampling points lead to discontinuities in the node feature vectors, affecting the accuracy of subsequent time-series feature extraction. Interpolation reconstruction is performed based on adjacent known sampling points on the time axis of the missing sampling points to generate continuous and complete node feature vectors. This embodiment provides two interpolation methods: linear interpolation and spline interpolation, which can be selected according to the variation characteristics of the process parameters.

[0027] Linear interpolation is suitable for scenarios where process parameters change relatively smoothly, and its calculation formula is as follows:

[0028] in, For the timestamps of missing sampling points, The timestamp of the nearest known sampling point to the left of the missing sampling point. The timestamp of the nearest known sampling point to the right of the missing sampling point. for Parameter sample values ​​at time 10:00 for Parameter sample values ​​at time 10:00 Calculated by interpolation The parameter value at time.

[0029] Spline interpolation is suitable for scenarios where process parameters change drastically and exhibit nonlinear characteristics. In this embodiment, cubic spline interpolation is used. Cubic spline interpolation constructs a cubic polynomial function between adjacent known sampling points, ensuring that the entire interpolation curve is continuous at all sampling points, with continuous first and second derivatives, thus more accurately fitting the nonlinear changes in process parameters. The process segments and corresponding process parameters of the copper foil surface treatment production line are shown in Table 1 below.

[0030] Table 1. Process Sections and Corresponding Process Parameters of Copper Foil Surface Treatment Production Line ; The applicable scenarios for different interpolation methods are compared in Table 2 below.

[0031] Table 2 Comparison of Applicable Scenarios for Different Interpolation Methods ; Furthermore, when performing interpolation reconstruction, the process topology graph construction component applies truncation constraints to the intermediate reconstructed values ​​obtained from the interpolation calculation. Since the values ​​of process parameters are limited by equipment performance and process requirements, there are clear physical allowable extreme value boundaries. For example, the temperature of the processing liquid cannot be lower than the ambient temperature, nor can it be higher than the maximum heating temperature of the heating equipment; the current density cannot be lower than zero, nor can it be higher than the maximum output current of the power supply. If the intermediate reconstructed value obtained from the interpolation calculation exceeds the physical allowable extreme value boundary, it indicates that the interpolation result does not conform to the actual physical situation and needs to be corrected. The process topology graph construction component pre-obtains the physical allowable extreme value boundaries of each process parameter in the node feature vector. When the intermediate reconstructed value is greater than the physical allowable maximum value of the parameter, the intermediate reconstructed value is corrected to the physical allowable maximum value; when the intermediate reconstructed value is less than the physical allowable minimum value of the parameter, the intermediate reconstructed value is corrected to the physical allowable minimum value. The corrected node feature vector is then input to the spatiotemporal feature extraction component.

[0032] This embodiment eliminates the dimensional differences of process parameters through normalization, generates continuous and complete node feature vectors through interpolation reconstruction, and ensures the physical rationality of the interpolation results through truncation constraints of physical extreme value boundaries, thereby improving the quality of input data.

[0033] Appendix Figure 3 In a preferred embodiment, the temporal convolutional network in the spatiotemporal feature extraction component comprises multiple stacked dilated causal convolutional layers. Each dilated causal convolutional layer employs a progressively increasing dilation rate to enable the temporal convolutional network to acquire temporal receptive fields at different scales. In this embodiment, the temporal convolutional network comprises four dilated causal convolutional layers. The dilation rate of the first dilated causal convolutional layer is 1, the second is 2, the third is 4, and the fourth is 8. The receptive field size of the dilated causal convolutional layer with dilation rate d is (k-1)×d+1, where k is the size of the convolutional kernel. In this embodiment, the kernel size is uniformly set to 3. Therefore, the receptive field size of the first dilated causal convolutional layer is 3, which can capture process parameter changes within 3 time steps; the receptive field size of the second layer is 5, which can capture process parameter changes within 5 time steps; the receptive field size of the third layer is 9, which can capture process parameter changes within 9 time steps; and the receptive field size of the fourth layer is 17, which can capture process parameter changes within 17 time steps. The parameter configuration of the dilated causal convolutional layers is shown in Table 3 below.

[0034] Table 3. Parameter Configuration Table for Dilated Causal Convolutional Layers ; The formula for calculating the output features of each dilated causal convolutional layer is:

[0035] in, The output features of the l-th dilated causal convolutional layer at time t. For non-linear activation functions, the ReLU activation function is used in this embodiment. The kernel weights of the l-th dilated causal convolutional layer are... The index of the convolution kernel element. The input features are those of the (l-1)th layer. Let l be the dilation rate of the l-th dilated causal convolutional layer. This is the bias term for the l-th layer of the dilated causal convolutional layer.

[0036] The output features of each layer in a multi-layered dilated causal convolutional layer are concatenated along the channel dimension to generate a multi-scale temporal feature vector containing the effects of multiple time lags. In this embodiment, each dilated causal convolutional layer has 16 output channels, and the concatenated multi-scale temporal feature vector has 4 × 16 = 64 channels, containing time lag effect information at different scales from 3 to 17 time steps.

[0037] Furthermore, the temporal convolutional network is also equipped with a gating mechanism to filter out hysteresis feature components in the multi-scale temporal feature vector that are weakly correlated with the copper foil resistivity change. The gating mechanism first constructs a gating vector with the same dimension as the multi-scale temporal feature vector, and the values ​​of each element of the gating vector are between zero and one. The gating vector is generated through an independent 1×1 convolutional layer, whose input is the multi-scale temporal feature vector, and whose output channel number is the same as that of the multi-scale temporal feature vector. The activation function is the Sigmoid function, which restricts the output value to the interval [0,1].

[0038] The gated vector is multiplied element-wise with the multi-scale temporal feature vector to obtain the filtered feature vector. The formula for calculating the element-wise multiplication operation is as follows:

[0039] in, The values ​​of the filtered feature vector at time t and channel c are... The values ​​of the multi-scale temporal feature vector at time t and channel c are given. Let be the value of the gate vector at time t and channel c. When When the value is close to zero, the corresponding feature components are filtered out; when... As time approaches a certain point, the corresponding feature components are retained. The filtered feature vectors are then used as the final output of the temporal convolutional network and input into the graph convolutional layer for cross-process feature aggregation.

[0040] This embodiment obtains temporal receptive fields at different scales through multi-layered dilated causal convolutional layers with progressively increasing dilation rates. It integrates multi-level temporal lag impact information by splicing multi-scale features and filters out weakly correlated lag feature components through a gating screening mechanism, thereby reducing feature dimension redundancy.

[0041] Appendix Figure 4 In a preferred embodiment, the graph convolutional layer in the spatiotemporal feature extraction component introduces an attention weight coefficient calculation mechanism when aggregating features according to the flow direction. Based on the node feature vectors of the current process node and its upstream neighboring process nodes, it calculates the spatial correlation score of the upstream neighboring process node to the current process node. Different upstream process nodes have different degrees of influence on the current process node. For example, the influence of the electroplating passivation process on the extrusion process is much greater than the influence of indirect processes on the curing process. The attention weight coefficient can be used to achieve differentiated measurement of the degree of influence of different upstream processes.

[0042] Specifically, the graph convolutional layer first extracts the temporal query vector of the current process node and the temporal key vector of the upstream neighboring process nodes. The temporal query vector and temporal key vector are generated through two independent linear transformation layers. The input to the linear transformation layer is the temporal feature vector of the node, and the output is a fixed-dimensional query vector and key vector. The calculation formula for the linear transformation layer is:

[0043]

[0044] in, This is the time-series query vector for the current process node v. To query the weight matrix of the vector linear transformation layer, Let v be the temporal feature vector of the current process node v. To query the bias term of the linear transformation layer of the vector; Let u be the time sequence key vector of the upstream adjacent process node. The weight matrix of the linear transformation layer of the key vectors. Let u be the temporal feature vector of the upstream adjacent process node. This is the bias term for the linear transformation layer of the key vector.

[0045] The dot product between the time-series query vector and the time-series key vector is calculated. The dot product represents the feature similarity between the upstream neighboring process node u and the current process node v. The dot product is then input into a softening function to obtain the spatial relevance score. The softening function maps the dot product results of all upstream neighboring process nodes to weight values ​​between zero and one, and the sum of all weight values ​​is one. The formula for calculating the spatial relevance score is as follows:

[0046] in, The spatial correlation score between the upstream adjacent process node u and the current process node v. Let v be the set of all directly upstream neighboring process nodes of the current process node v. For set Any upstream adjacent process node in the process.

[0047] The features of upstream adjacent process nodes are weighted and summed based on spatial correlation scores to obtain the upstream feature aggregation result. This weighted sum is then fused with the current process node's own features to generate the cross-process parameter coupling feature of the current process node. The formula for feature fusion is as follows:

[0048] in, The cross-process parameter coupling characteristics of the current process node v. This is the linear transformation weight matrix representing the characteristics of the current process node itself. This is a linear transformation weight matrix representing the characteristics of upstream adjacent process nodes. For bias terms, For non-linear activation functions, the ReLU activation function is used in this embodiment.

[0049] During the iterative training of the graph convolutional layer, based on the deviation between the dynamically predicted value of the target copper foil resistivity and the actual resistivity label, the weight matrices of the time-series query vector and the time-series key vector are updated through backpropagation. and and the linear transformation weight matrix and The backpropagation process uses the gradient descent algorithm to calculate the gradient of the loss function with respect to each weight matrix, and updates the weight matrix in the opposite direction of the gradient until the loss function converges.

[0050] This embodiment achieves differentiated measurement of the degree of influence of different upstream processes through the attention weight coefficient calculation mechanism, eliminates the interference of weakly correlated process features on the aggregation results, and improves the characterization ability of cross-process parameter coupling features.

[0051] Appendix Figure 5In a preferred embodiment, before mapping the cross-process parameter coupling features to output the dynamic predicted value of the target copper foil resistivity through a fully connected layer, the resistivity dynamic prediction component performs a residual connection between the cross-process parameter coupling features and the baseline process parameter features initially input by the process topology graph construction component. The baseline process parameter features are the initial settings of the process parameters for each process segment at the start of the current production batch. These initial settings are baseline process conditions determined based on historical production experience and can reflect the basic resistivity level of the copper foil in that batch. The residual connection can fuse the global information of the baseline process parameters with the dynamic fluctuation information in the cross-process parameter coupling features, improving the accuracy of the prediction results.

[0052] The formula for fusion of residual connections is:

[0053] in, The fusion features are those resulting from residual connections. This is due to the cross-process parameter coupling characteristic. This is a linear transformation weight matrix for the baseline process parameter features, used to map the baseline process parameter features to the same dimension as the cross-process parameter coupling features. These are the baseline process parameter characteristics.

[0054] The fused features after residual concatenation are input into a fully connected layer, which contains a hidden mapping layer and a linear output layer connected sequentially. The hidden mapping layer uses a non-linear activation function to process the fused features; in this embodiment, ReLU activation is used. The number of neurons in the hidden mapping layer is set to 128 to map the 64-dimensional fused features to 128-dimensional high-dimensional features, capturing the non-linear relationships in the fused features. The number of neurons in the linear output layer is set to 1 to map the 128-dimensional high-dimensional features to a one-dimensional copper foil resistivity prediction value.

[0055] The forward computation process of the fully connected layer is as follows: First, the fused features are input to the hidden layer mapping layer, and hidden features are obtained through linear transformation and the ReLU activation function; then, the hidden features are input to the linear output layer, and the final resistivity prediction value is obtained through linear transformation. The formula for calculating the linear transformation is:

[0056] in, For the output of the layer, The weight matrix of the layer, For the input of the layer, This is the bias term for the layer.

[0057] This embodiment integrates global information of baseline process parameters with dynamic fluctuation information of cross-process parameter coupling characteristics through residual connections, and realizes the mapping from high-dimensional features to resistivity prediction values ​​through a fully connected layer containing a hidden mapping layer and a linear output layer.

[0058] Appendix Figure 6 In a preferred embodiment, the copper foil resistivity and surface treatment process parameter correlation prediction algorithm system further includes a physical mechanism constraint component. The physical mechanism constraint component runs during the model training phase and is used to introduce the physical conductivity mechanism of copper foil resistivity into the model training process, thereby limiting the risk of network parameter updates deviating from physical laws.

[0059] The resistivity of copper foil is determined by both the inherent resistance of the copper foil substrate and the additional resistance of the surface treatment deposited layer, which are in parallel. The inherent resistance of the copper foil substrate is determined by the material properties and thickness of the substrate and remains relatively constant within the same production batch. The additional resistance of the surface treatment deposited layer is determined by the material properties, thickness, and structure of the deposited layer and is affected by the process parameters of each step in the surface treatment process. The physical formula for calculating the resistivity of copper foil is:

[0060] in, The total resistivity of the copper foil. The inherent resistivity of the copper foil substrate. To improve the resistivity of the surface-treated deposited layer, The thickness of the copper foil substrate. This represents the total thickness of the surface treatment deposition layer.

[0061] The physical mechanism constraint component constructs a regularization penalty term based on the aforementioned physical formula for resistivity. This regularization penalty term characterizes the deviation between the resistivity predicted by the model and the resistivity calculated based on the physical formula. During model training, for each training sample, the thickness of the surface treatment deposition layer is first calculated based on the process parameters of that sample. and resistivity Then, substituting these values ​​into the aforementioned physical calculation formula yields the resistivity calculated based on the physical mechanism. The formula for calculating the regularization penalty term is:

[0062] in, This is a physical regularization penalty term. This represents the number of samples in the training batch. Predict the resistivity of the model for the i-th sample. This is the physical mechanism-based resistivity calculation value for the i-th sample.

[0063] The total loss function is constructed by jointly using the regularization penalty term and the supervised loss function corresponding to the dynamically predicted value of the target copper foil resistivity. The supervised loss function adopts the mean squared error loss function, and its calculation formula is as follows:

[0064] in, For the supervision loss function, is the true resistivity label for the i-th sample.

[0065] The formula for calculating the total loss function is:

[0066] in, For the total loss function, The weighting coefficients for the physical regularization term are used to balance the effects of the supervision loss and the physical regularization loss. In this embodiment... The value is 0.1.

[0067] Table 4 below shows the components of the total loss function.

[0068] Table 4. Components of the Total Loss Function ; The network parameters of the spatiotemporal feature extraction component and the resistivity dynamic prediction component are adjusted based on the total loss function. In each iteration of model training, the value of the total loss function is first calculated through forward propagation, then the gradient of the total loss function with respect to each network parameter is calculated through backpropagation, and finally the network parameters are updated using the gradient descent algorithm until the total loss function converges.

[0069] This embodiment introduces the physical conductivity mechanism of copper foil resistivity into the model training process through a physical mechanism constraint component, constructs a total loss function that includes a physical regularization penalty term, limits the risk of network parameter updates deviating from the physical conductivity mechanism, and ensures the physical rationality of the predicted output under boundary conditions.

[0070] In a preferred embodiment, the copper foil resistivity and surface treatment process parameter correlation prediction algorithm system further includes an online incremental update component. The online incremental update component runs continuously after the system is put into operation on the production site to cope with the slow drift of production conditions and ensure the tracking and prediction capability of the prediction system in a long-cycle continuous production environment.

[0071] The online incremental update component continuously collects newly generated surface treatment process parameters and corresponding actual copper foil resistivity data pairs on the production floor. Surface treatment process parameters are collected in real time from sensors at each stage of the production line via industrial Ethernet. Actual copper foil resistivity data is collected by a resistivity detection device installed after the winding process. The resistivity detection device uses the four-probe method to measure the resistivity of the copper foil, and the measurement results are transmitted to the system via an RS485 interface.

[0072] The online incremental update component constructs a fixed-length sliding time window to store the latest acquired process parameter and resistivity data pairs. The length of the sliding time window is set to 1000 data pairs. When a new data pair is acquired, it is added to the end of the sliding time window, while the oldest data pair at the beginning of the sliding time window is deleted to keep the length of the sliding time window constant.

[0073] When the number of data pairs accumulated within the sliding time window reaches a preset number, an online incremental update operation is triggered. In this embodiment, the preset number is set to 1000 data pairs, meaning that an online incremental update is triggered when the sliding time window is filled. The online incremental update operation adopts a strategy of freezing the feature extraction network parameters and only fine-tuning the prediction layer parameters. That is, the network parameters of the graph convolutional layer in the spatiotemporal feature extraction component are frozen, and only the parameters of the fully connected layer in the resistivity dynamic prediction component are fine-tuned. This is because the spatiotemporal feature extraction component has learned the spatiotemporal feature extraction rules of the process parameters, and these rules remain basically unchanged when the production conditions drift slowly; while the fully connected layer in the resistivity dynamic prediction component is responsible for mapping the spatiotemporal features to the resistivity prediction value, and its parameters need to be adjusted according to the latest production conditions.

[0074] The fine-tuning loss is calculated based on the latest data within the sliding time window. The fine-tuning loss uses the mean squared error loss function, and its calculation formula is as follows:

[0075] in, To fine-tune the loss function, The number of data pairs within the sliding time window. Predict the resistivity of the model for the i-th data pair. is the true resistivity label for the i-th data pair.

[0076] The fully connected layer parameters are updated using gradient descent, employing a mini-batch gradient descent algorithm with a batch size of 32 and a learning rate of 0.0001. In each fine-tuning iteration, 32 data pairs are randomly selected from the sliding time window to form a mini-batch. The fine-tuning loss for this mini-batch is calculated, and then the gradient of the fine-tuning loss with respect to the fully connected layer parameters is calculated via backpropagation. Finally, the fully connected layer parameters are updated in the opposite direction of the gradient. The fine-tuning process continues until the fine-tuning loss converges or the preset maximum number of iterations is reached; in this embodiment, the maximum number of iterations is set to 100.

[0077] This embodiment continuously accumulates the latest data on the production site through an online incremental update component. It adopts a strategy of freezing the feature extraction network parameters and only fine-tuning the prediction layer parameters, which reduces the consumption of computational resources and time delay of model reconstruction when facing production condition drift, and ensures the tracking and prediction capabilities of the prediction system in long-cycle continuous production environments.

Claims

1. A prediction algorithm system for the correlation between copper foil resistivity and surface treatment process parameters, characterized in that, include: The process topology graph construction component is configured to construct a directed acyclic graph based on the physical process sequence of the copper foil surface treatment production line. Nodes represent each process segment, edges represent the flow direction of the copper foil substrate, and the node feature vector of each node is a sequence of process parameters of the corresponding process segment changing over time. The spatiotemporal feature extraction component is configured to embed a temporal convolutional network into the node feature extraction of the directed acyclic graph, extract the time lag effect of the change of process parameters on subsequent processes and final resistivity by expanding causal convolution, and perform feature aggregation in the graph convolutional layer according to the flow direction to obtain cross-process parameter coupling features. The resistivity dynamic prediction component is configured to map the cross-process parameter coupling features through a fully connected layer to output a dynamic prediction value of the target copper foil resistivity.

2. The copper foil resistivity and surface treatment process parameter correlation prediction algorithm system according to claim 1, characterized in that, In the process topology graph construction component, for the node feature vector being a sequence of process parameters changing over time for the corresponding process segment, the process topology graph construction component is further configured to: perform a normalization operation on the heterogeneous process parameters in the node feature vector, mapping physical parameters of different dimensions to a unified numerical range. For the missing sampling points in the node feature vector, interpolation reconstruction is performed based on the adjacent known sampling points of the missing sampling points on the time axis to generate a continuous and complete node feature vector. The interpolation reconstruction adopts linear interpolation or spline interpolation.

3. The copper foil resistivity and surface treatment process parameter correlation prediction algorithm system according to claim 1, characterized in that, In the spatiotemporal feature extraction component, for the extraction of the time lag effect of the process parameter change on subsequent processes and final resistivity by dilated causal convolution, the temporal convolutional network includes multiple stacked dilated causal convolutional layers. Each dilated causal convolutional layer adopts a progressively increasing dilation rate so that the temporal convolutional network can obtain a temporal receptive field of different scales. The output features of each layer in the multi-layered stacked dilated causal convolutional layer are concatenated along the channel dimension to generate a multi-scale temporal feature vector that includes the effects of multiple time lags.

4. The copper foil resistivity and surface treatment process parameter correlation prediction algorithm system according to claim 1, characterized in that, In the spatiotemporal feature extraction component, for the feature aggregation in the graph convolutional layer based on the flow direction to obtain cross-process parameter coupling features, the graph convolutional layer is further configured to: introduce an attention weight coefficient calculation mechanism in the flow direction, and calculate the spatial correlation score of the upstream adjacent process node to the current process node based on the node feature vectors of the current process node and the upstream adjacent process node. The features of the upstream adjacent process nodes are weighted and summed based on the spatial correlation score. The weighted summation result is then fused with the features of the current process node to generate the cross-process parameter coupling feature.

5. The copper foil resistivity and surface treatment process parameter correlation prediction algorithm system according to claim 1, characterized in that, In the resistivity dynamic prediction component, for mapping the cross-process parameter coupling features through the fully connected layer to output the dynamic prediction value of the target copper foil resistivity, the resistivity dynamic prediction component is further configured as follows: before the full connected layer mapping, the cross-process parameter coupling features are residually connected with the baseline process parameter features initially input by the process topology graph construction component, and the fused features after residual connection are input to the fully connected layer. The fully connected layer comprises a hidden mapping layer and a linear output layer connected in sequence, and the hidden mapping layer uses a non-linear activation function to process the fused features.

6. The copper foil resistivity and surface treatment process parameter correlation prediction algorithm system according to claim 4, characterized in that, To calculate the spatial correlation score between the upstream adjacent process node and the current process node, the graph convolutional layer is further configured to: extract the temporal query vector of the current process node and the temporal key vector of the upstream adjacent process node, and calculate the dot product between the temporal query vector and the temporal key vector; The dot product result is input into the softening function to obtain the spatial correlation score. During the iterative training of the graph convolutional layer, based on the deviation between the dynamic predicted value of the target copper foil resistivity and the true resistivity label, the weight matrix of the time-series query vector and the time-series key vector is updated through backpropagation.

7. The copper foil resistivity and surface treatment process parameter correlation prediction algorithm system according to claim 3, characterized in that, To generate multi-scale temporal feature vectors that include the effects of multiple time lags, the temporal convolutional network is also configured with a gating and filtering mechanism: constructing a gating vector with the same dimension as the multi-scale temporal feature vector, wherein the values ​​of each element of the gating vector are between zero and one. The gate vector is multiplied element-wise with the multi-scale temporal feature vector to filter out the hysteresis feature components in the multi-scale temporal feature vector that are weakly correlated with the change in copper foil resistivity. The filtered feature vector is then output as the final output of the temporal convolutional network.

8. The copper foil resistivity and surface treatment process parameter correlation prediction algorithm system according to claim 2, characterized in that, To generate continuous and complete node feature vectors for the interpolation reconstruction, the process topology graph construction component is further configured to: obtain the physical allowable extreme value boundaries of each process parameter in the node feature vectors; When performing the interpolation reconstruction, a truncation constraint is applied to the intermediate reconstruction value obtained by interpolation calculation. When the intermediate reconstruction value exceeds the physical allowable extreme value boundary, the intermediate reconstruction value is corrected to the corresponding physical allowable extreme value. The corrected node feature vector is input into the spatiotemporal feature extraction component.

9. The copper foil resistivity and surface treatment process parameter correlation prediction algorithm system according to claim 1, characterized in that, It also includes a physical mechanism constraint component, which is configured to: during the model training phase, obtain the physical calculation formula of resistivity corresponding to the copper foil material, wherein the physical calculation formula of resistivity characterizes the parallel relationship between the inherent resistance of the copper foil substrate and the additional resistance of the surface treatment deposition layer; A regularization penalty term is constructed based on the physical calculation formula of resistivity. The regularization penalty term is then combined with the supervision loss function corresponding to the dynamic prediction value of the target copper foil resistivity to construct the total loss function. The network parameters of the spatiotemporal feature extraction component and the resistivity dynamic prediction component are adjusted according to the total loss function.

10. The copper foil resistivity and surface treatment process parameter correlation prediction algorithm system according to claim 1, characterized in that, It also includes an online incremental update component, which is configured to continuously collect newly generated surface treatment process parameters and corresponding real copper foil resistivity data pairs at the production site, and construct a sliding time window of fixed length. When the number of data pairs accumulated within the sliding time window reaches a preset number, the network parameters of the graph convolutional layer in the spatiotemporal feature extraction component are frozen, and only the parameters of the fully connected layer in the resistivity dynamic prediction component are fine-tuned. The fine-tuning loss is calculated based on the latest data within the sliding time window, and the parameters of the fully connected layer are updated by gradient descent.

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