LFP positive electrode sheet compaction density optimization method and system

Abstract

The application relates to the technical field of battery positive pole piece manufacturing, and discloses an LFP positive pole piece compaction density optimization method and system. The method comprises the following steps: obtaining a cross-sectional image, and constructing a pole piece cross-sectional particle topological sample; screening target particle diameters, and generating a proportion state vector; constructing particle nodes, pore nodes and connecting edges, and generating a particle-pore dual-phase adjacency graph; constructing a scene constraint loss function according to the area proportion in the proportion state vector; performing layer depth weighted graph propagation on the particle-pore dual-phase adjacency graph according to the layer depth coordinates in the pole piece cross-sectional particle topological sample, and generating a layer depth compaction contribution matrix; inputting the layer depth compaction contribution matrix and the proportion state vector into a pre-trained inversion model, and outputting rolling process parameters and mixing parameters based on the constraint loss function; and performing multistage rule checking, and generating a compaction density optimization instruction when the checking is passed. The application improves the LFP positive pole piece manufacturing process parameter optimization precision.

Description

Technical Field

[0001] This application relates to the field of battery cathode manufacturing technology, and in particular to a method and system for optimizing the compaction density of LFP cathode sheets. Background Technology

[0002] The compaction density of the positive electrode sheet in lithium-ion batteries is a key process parameter that determines the battery's energy density, rate performance, and cycle life. In the manufacturing process of LFP positive electrode sheets, the rolling process applies mechanical pressure to compact the coated electrode sheet to the target thickness and density. The compaction density directly affects the contact resistance between active particles in the electrode sheet, the connectivity of pore channels, and the wetting efficiency of the electrolyte.

[0003] Currently, the compaction density control of LFP cathode sheets mainly relies on the experience-based trial and error of process engineers and adjustment strategies based on macroscopic parameter feedback. Existing methods treat the electrode sheet as a homogeneous medium, approximating the target compaction density by adjusting macroscopic parameters such as roller pressure and roller gap. However, they ignore the objectively existing layer depth structural gradient along the thickness direction of the electrode sheet: the current collector side is fully compacted due to the rigid support of the aluminum foil, the middle layer is prone to particle agglomeration or pore discontinuity under bidirectional extrusion, and the surface layer rebounds due to pressure release. When the particle size distribution is unreasonable, this difference in the layer depth direction is further aggravated, leading to problems such as excessively high or low local compaction density, decreased pore connectivity, and excessive rebound, manifesting as an inconsistent state of "dense surface and loose interior." In addition, there is an inverse relationship between the four process objectives of compaction density accuracy, rational particle size distribution, pore connectivity, and the risk of overpressure rebound. Existing methods lack the technical means to integrate multi-objective synergistic optimization into a unified framework. Summary of the Invention

[0004] To address the aforementioned technical issues, this application provides a method and system for optimizing the compaction density of LFP positive electrode sheets, enabling closed-loop control throughout the entire process, from microscopic particle structure analysis of LFP positive electrode sheets to optimization and recommendation of rolling process parameters.

[0005] In a first aspect, this application provides a method for optimizing the compaction density of LFP positive electrode sheets, the method comprising: Cross-sectional images are obtained by cross-sectional sampling of the LFP positive electrode sheet, and a cross-sectional particle topology sample of the electrode sheet is constructed based on the cross-sectional image. Target particle size particles are selected from the cross-sectional particle topology sample of the electrode sheet, and the area ratio, local aggregation index and interlayer distribution deviation of the target particle size particles in the cross-sectional observation field of view are calculated. The particles are then spliced ​​to generate a ratio state vector. Based on the particle topology sample of the electrode section, particle nodes, pore nodes and connecting edges are constructed to generate a double adjacency graph of particles and pores. Based on the aforementioned proportion state vector, a scenario constraint loss function is constructed by weighted summation of the compaction density error term, the target particle size proportion window penalty term, the pore discontinuity penalty term, and the overpressure rebound penalty term. Based on the particle topology sample of the electrode cross section, layer depth weighted graph propagation is performed on the particle and pore double adjacency map to generate a layer depth compaction contribution matrix; The layer depth compaction contribution matrix and the proportion state vector are input into the pre-trained inversion model, and the rolling process parameters and mixing parameters are output based on the scenario constraint loss function; the rolling process parameters and the mixing parameters are subjected to multi-level rule verification, and when the verification passes, a compaction density optimization instruction is generated.

[0006] Secondly, this application provides an LFP positive electrode compaction density optimization system, the system comprising: The sample construction unit is used to perform cross-sectional sampling on the LFP positive electrode to obtain a cross-sectional image, and construct a cross-sectional particle topology sample of the electrode based on the cross-sectional image; select target particle size particles from the cross-sectional particle topology sample of the electrode, calculate the area ratio, local aggregation index and interlayer distribution deviation of the target particle size particles in the cross-sectional observation field of view, and splice them to generate a ratio state vector; The graph construction unit is used to construct particle nodes, pore nodes and connecting edges based on the particle topology sample of the electrode cross section, and generate a double adjacency graph of particles and pores. The function construction unit is used to construct a scenario constraint loss function based on the proportion state vector by weighted summation of the compaction density error term, the target particle size proportion window penalty term, the pore discontinuity penalty term, and the overpressure rebound penalty term. The graph propagation unit is used to perform layer depth weighted graph propagation on the particle and pore double adjacency graph based on the particle topology sample of the electrode section, and generate a layer depth compaction contribution matrix. The parameter inversion unit is used to input the layer depth compaction contribution matrix and the proportion state vector into the pre-trained inversion model, and output the rolling process parameters and mixing parameters based on the scenario constraint loss function; the rolling process parameters and the mixing parameters are subjected to multi-level rule verification, and a compaction density optimization instruction is generated when the verification passes.

[0007] Compared with the prior art, the beneficial effects of the present invention are at least as follows: First, by constructing a heterogeneous graph structure—a dual-adjacent graph of particles and pores—the compressive topology of particles and the connectivity topology of pores in the electrode cross-section are modeled on the same graph. An explicit information exchange channel is established between particle nodes and pore nodes through a third connecting edge, enabling the transmission of compressive deformation information from particles to adjacent pore nodes and the feedback of pore connectivity information to adjacent particle nodes, thus achieving coupled representation of the two types of structural units at the graph level. Simultaneously, a depth-weighted graph propagation mechanism is introduced, dividing the dual-adjacent graph into three subgraphs—the current collector side, the middle layer, and the surface layer—based on depth coordinates, and assigning differentiated propagation weights to each subgraph. After independently performing information propagation on each subgraph using a graph neural network, pooling and aggregation are used to generate a depth-based compaction contribution matrix, explicitly characterizing the differentiated contributions of different depth regions to compaction density, overcoming the limitation of traditional methods that treat the electrode as a homogeneous medium. Then, the designed scenario-constrained loss function is constructed by weighted summation of the compaction density error term, the target particle size proportion window penalty term, the pore discontinuity penalty term, and the overpressure rebound penalty term. This integrates four mutually constraining process objectives into a single scalar evaluation. The weight coefficients can be flexibly adjusted according to different application scenarios such as high energy density, high rate of change, or long cycle life, achieving multi-objective collaborative optimization. Next, in the inference stage of the inversion model, a conditional modulation latent vector mechanism is adopted to output differentiated combinations of process parameters for the same microstructure under different target compaction densities and pore connectivity threshold constraints. Combined with an adaptive gradient step size, the parameter correction priority is dynamically adjusted according to the value proportion of each penalty term, accelerating the optimization convergence. Finally, after the compaction density optimization command is issued and executed through an iterative closed-loop mechanism, the produced electrode is re-analyzed. Convergence is judged by the Euclidean distance between the proportion state vectors of two adjacent cycles, gradually eliminating model prediction bias and bringing the process parameters closer to the actual optimal values. Attached Figure Description

[0008] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0009] Figure 1 This is a flowchart illustrating a method for optimizing the compaction density of an LFP positive electrode sheet in an embodiment of this application. Figure 2 This is a grayscale heatmap of a layer depth compaction contribution matrix according to an embodiment of this application; Figure 3 This is a schematic diagram of the structure of an LFP positive electrode compaction density optimization system according to an embodiment of this application. Detailed Implementation

[0010] This application provides a method and system for optimizing the compaction density of LFP positive electrode sheets. The terms "first," "second," "third," "fourth," etc. (if present) in the specification, claims, and accompanying drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments described herein can be implemented in a sequence other than that illustrated or described herein. Furthermore, the terms "comprising" or "having" and any variations thereof are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0011] For ease of understanding, the specific process of the embodiments of this application is described below. Please refer to [link / reference]. Figure 1 One embodiment of the LFP positive electrode compaction density optimization method in this application includes: Step S1: Perform cross-sectional sampling on the LFP positive electrode to obtain a cross-sectional image, and construct a cross-sectional particle topology sample based on the cross-sectional image; select target particle size particles from the cross-sectional particle topology sample, calculate the area ratio, local aggregation index and interlayer distribution deviation of the target particle size particles in the cross-sectional observation field, and splice them to generate a proportion state vector.

[0012] Furthermore, a topological sample of the pole piece cross-section is constructed, including: At least three sampling positions are selected at equal intervals along the width direction of the LFP positive electrode sheet. For each sampling position, a cross-sectional image is obtained by slicing the cross-section along the direction perpendicular to the aluminum foil current collector. The contour region of each LFP active particle is identified by denoising, threshold segmentation, and connected component analysis. For each contour region, the equivalent diameter and cross-sectional area of ​​the particle are calculated according to the principle of equal area circles. Roundness and aspect ratio are extracted as morphological features. The thickness and coverage integrity of the carbon coating layer are obtained as carbon coating layer response features. The layer depth coordinates are defined along the thickness direction of the electrode sheet with the surface of the aluminum foil current collector as the zero point. Width weights are assigned according to the width coordinates of each sampling position. The weight of the center position of the electrode sheet width is greater than that of the edge position. The attribute records of all LFP active particles identified at each sampling position are merged into a unified particle set, and the width weights are marked in the corresponding particle records to generate the topological sample of the electrode sheet cross-section particles.

[0013] Furthermore, the proportion state vector is generated by concatenation, including: Target particle size particles with equivalent diameters within the target particle size range are extracted from the topological sample of the electrode cross-section. The total cross-sectional area of ​​the target particle size is obtained by summing the cross-sectional areas of all target particle size particles. The area proportion is calculated by the ratio of the total cross-sectional area of ​​the target particle size to the total area of ​​the cross-sectional observation field. The cross-sectional observation field is divided into equally spaced grids, and the number of target particle size particles in each grid is counted to obtain a distribution series. The ratio of the variance to the mean of the distribution series is used as the local aggregation index. The target particle size particles are grouped into three depth segments: the current collector side, the middle layer, and the surface layer. The range or standard deviation of the three groups is used as the interlayer distribution deviation. The area proportion, local aggregation index, and interlayer distribution deviation are normalized and then spliced ​​to generate the proportion state vector.

[0014] Furthermore, after calculating the local aggregation index, the following is also included: Calculate the center distance between each target particle size and its nearest neighbor of the same type. Compare the mean of all center distances with the expected nearest neighbor distance under an ideal uniform distribution across the entire field of view. Use the ratio of the expected nearest neighbor distance to the mean as an auxiliary verification index. When the auxiliary verification index is less than a preset verification threshold, it is determined that there is a clustering phenomenon of target particles. The preset verification threshold is greater than or equal to 1, and the weight coefficient of the target particle size proportion window penalty term is increased when constructing the scene constraint loss function.

[0015] The active material of the LFP cathode is lithium iron phosphate particles. Its low conductivity needs to be compensated for by conductive agents (such as carbon black and carbon nanotubes), and a binder (such as PVDF) is used to adhere the active particles and conductive agents to the current collector to form a continuous electrode layer. The relationship between compaction density and the LFP cathode sheet lies in the compaction of the coated electrode sheet through a rolling process, establishing a more sufficient conductive contact network between the active particles, while controlling the porosity to not fall below the threshold required for ion transport. The core of this method is to quantify the spatial topological relationship between particles and pores through a graphical model, and optimize the compaction density parameters accordingly to achieve the optimal balance between electronic conductivity and ionic conductivity in the LFP electrode.

[0016] Specifically, the electrode cross-section particle topology sample is a structured dataset of microstructural information on all LFP active particles and pores in the electrode cross-section. Its function is to transform the particle morphology, distribution, and contact relationships at the microscale into a digital representation that can be used for subsequent graphical modeling and numerical calculations. In the cross-section sampling stage, multiple sampling locations are selected along the electrode width direction instead of a single location. This is because the electrode width is typically on the order of hundreds of millimeters, while the field of view of a single cross-section only covers a region of micrometers to tens of micrometers; the particle distribution of a single cross-section is insufficient to represent the macroscopic state of the entire electrode. Each sampling location is sliced ​​along a direction perpendicular to the aluminum foil current collector, allowing simultaneous observation of the bottom layer, intermediate layer, and surface layer particles on one side of the aluminum foil current collector. This provides complete thickness direction information for subsequent particle segmentation by layer depth. After acquiring the cross-section image, denoising, thresholding, and connected component analysis are performed sequentially. The purpose of denoising is to eliminate the interference of imaging noise and powdery debris generated during slicing on subsequent segmentation. Thresholding segmentation divides image pixels into foreground and background based on grayscale values. The foreground corresponds to LFP active particles and conductive agent regions, while the background corresponds to pores and resin-filled regions. Connected component analysis aggregates adjacent foreground pixels into independent regions. Each region corresponds to the contour of a particle identified in the cross-section. The principle is to perform region growing on pixels with foreground values ​​in the binary image, grouping four-connected or eight-connected adjacent foreground pixels into the same connected component, thereby generating an independent contour boundary for each particle.

[0017] Particle attributes are extracted for each contour region. The equivalent diameter of a particle is the diameter value after converting an irregular cross-section into a circle of equal area. Roundness and aspect ratio describe the particle's geometry from two dimensions: the degree to which the shape approximates a sphere and the degree of flatness, respectively. The carbon coating is a conductive carbon film on the surface of LFP particles, compensating for the low conductivity of the LFP material itself. The thickness and coverage integrity of the carbon coating are obtained through energy dispersive spectroscopy (EDS) or Raman imaging. EDS maps the spatial distribution of the coating with the intensity of carbon elements, while Raman imaging uses the D and G peaks of carbon to identify the location of the coating and measure its thickness. Coverage integrity is the ratio of the actual arc length of the coating along the outer edge of the particle to the total arc length of the outer edge. This value directly affects the compressive deformation behavior of the particle during rolling and its rebound tendency after rolling: the higher the coverage integrity, the more uniform the stress on the particle surface and the lower the rebound tendency; when there are gaps or exposed areas in the coating, uneven stress leads to local stress concentration, increasing rebound. The layer depth coordinates are defined along the electrode thickness direction with the surface of the aluminum foil current collector as the zero point. Their function is to provide a positional basis for subsequent grouping of particles according to the three layer depth sections of the current collector side, middle layer and surface layer.

[0018] Data from multiple sampling locations needs to be aggregated into a unified dataset using width-weighted aggregation. The width weighting rule is that the weight of the center position of the electrode width is greater than that of the edge position. This is because the central area is subjected to the most uniform load during actual rolling and corresponds to the main effective area of ​​the electrode, while the edge position is more affected by the edge effect of rolling. After merging all particle attribute records identified from each sampling location, the width weight is marked in the corresponding particle record. In subsequent calculations, the attribute value of each particle will be multiplied by the corresponding width weight to reflect the differentiated contribution of different positions to the overall result. The merged unified particle set is the electrode cross-sectional particle topology sample, where each particle record includes equivalent diameter, cross-sectional area, morphological features, carbon coating layer response features, layer depth coordinates, and the width weight of the source sampling location.

[0019] Based on the topological sample, particles with an equivalent diameter within a preset target particle size range are further screened from all particles. This particle size range is pre-defined according to the particle size requirements of the filling particles in the LFP positive electrode rolling process. Small particles within this range can fill the gaps between large particles during rolling, thereby increasing the compaction density. Their content and distribution directly affect the final compaction effect of the electrode. Three indicators are calculated for the target particle size particles and concatenated into a proportion state vector.

[0020] The area ratio reflects the degree of spatial fullness of target-size particles in the cross-section. Its physical meaning is intuitive: a higher ratio means a more abundant content of target-size particles and a greater potential for filling the gaps between large particles; a low ratio means insufficient filling particles, and more unfilled pores may remain after rolling. The local agglomeration index is obtained by dividing the cross-sectional observation field into equally spaced grids and counting the number of target-size particles in each grid. The ratio of the variance to the mean of the series is used as the index value. The ratio of variance to mean is used instead of variance itself because the variance changes with the total number of particles. Dividing by the mean eliminates the interference of total quantity differences, making the degree of agglomeration between different cross-sections comparable. The larger the agglomeration index, the more uneven the distribution of target-size particles in the cross-section. The harm of agglomeration in the rolling process is that small particles densely accumulate in the agglomeration area, forming local hard spots. The rolling pressure cannot be effectively transmitted to the surrounding large particles, resulting in over-compaction of the agglomeration area itself while the surrounding area is under-compacted, ultimately causing spatial unevenness of compaction density. Interlayer distribution deviation was quantified by grouping the target particle size into three depth segments: the current collector side, the middle layer, and the surface layer, and then using the range or standard deviation of these three groups. The division into these three depth segments is based on the fundamental differences in the stress state experienced by each region during the rolling process: the current collector side experiences bidirectional compression due to the rigid support of the aluminum foil; the middle layer particles are most prone to relative slippage and rearrangement; and the surface layer directly bears the rolling pressure and rebounds due to stress release after rolling. A larger interlayer distribution deviation indicates that the target particle size is concentrated in one depth segment but scarce in others. This skewed distribution leads to differences in filling effects at different depths. The three indicators were normalized to the same numerical range and then arranged in a preset order. Normalization aims to eliminate the phenomenon where one indicator dominates the overall vector due to differences in dimensions and numerical magnitudes. The resulting three-dimensional vector is the proportion state vector. Its function is to provide quantitative input for the calculation of the target particle size proportion window penalty term in the subsequent scene constraint loss function, and at the same time, it serves as one of the conditional inputs of the inversion model to guide the direction of parameter optimization.

[0021] After calculating the local clustering index, the clustering phenomenon is further verified through nearest neighbor distance analysis. For each target particle size, the Euclidean distance between its cross-sectional geometric center and its nearest neighbor particle of the same type is calculated. The mean of all distances is compared with the expected nearest neighbor distance under an ideal uniform distribution across the entire field of view. The expected nearest neighbor distance is the expected distance from each particle to its nearest neighbor, assuming all target particles are distributed in a perfectly uniform grid, given a fixed cross-sectional field of view area and a fixed total number of target particles. The ratio of the expected distance to the actual mean is used as an auxiliary verification index: a ratio close to 1 indicates a distribution close to ideal uniformity; a ratio deviating from 1 indicates abnormal particle spacing; and an actual mean less than the expected distance indicates that the particle spacing is closer than in a uniform distribution, i.e., a clustering tendency exists. When this index exceeds a preset verification threshold, the existence of clustering is confirmed, and the weight coefficient of the target particle size proportion window penalty term is increased when constructing the scene constraint loss function. The purpose of increasing the adjustment is to increase the penalty of the loss function on the aggregation phenomenon, and to guide the inversion model to tend to output the combination of process parameters that can alleviate aggregation during the parameter optimization process. For example, increasing the secondary mixing time to improve the uniformity of particle dispersion, or adjusting the target particle size particle supplementation ratio to reduce the degree of local aggregation.

[0022] Step S2: Construct particle nodes, pore nodes, and connecting edges based on the particle topology sample of the electrode cross section to generate a double adjacency graph of particles and pores.

[0023] Furthermore, a particle-pore double adjacency map is generated, including: For each particle in the topological sample of the electrode cross-section, the convex hull contour is extracted. Adjacent particle pairs with contact arc lengths exceeding a preset arc length threshold are identified as valid contacts. Each particle is abstracted as a particle node, and a first connecting edge is established between particle nodes in valid contact. The cross-sectional image is segmented using multi-threshold segmentation to distinguish the LFP active particle phase, porous phase, and conductive agent interstitial phase. Through connected component analysis, porous clumps are abstracted as porous nodes, and a second connecting edge is established between porous nodes with channel widths greater than a preset connectivity threshold. The nearest distance between the outer contours of particle nodes and porous nodes is calculated, and a third connecting edge is established when the nearest distance is less than a preset proximity threshold. The particle nodes and porous nodes are merged into a unified node set, and the three types of connecting edges are merged into a unified edge set, generating a particle-pore double adjacency graph.

[0024] Specifically, the core of step S2 lies in transforming the microstructural information in the electrode cross-section from the image domain to the graph structure domain. The electrode cross-section contains both solid particles and pores, which play different roles during the rolling process. Particles form the pressure-bearing skeleton and transmit the rolling pressure, while pores determine the electrolyte wetting path and ion transport capability. If both are modeled as the same type of node, the physical meaning carried by the two types of nodes cannot be distinguished during graph propagation. Therefore, a heterogeneous graph structure is used to model particles and pores as particle nodes and pore nodes respectively, and an information exchange channel between them is established through three types of semantically different connecting edges.

[0025] When constructing particle nodes, the convex hull profile is first extracted for each particle in the topological sample of the electrode cross-section. The convex hull profile is the smallest convex polygon that encloses all contour points of the particle cross-section. Its function is to eliminate the concavity and jaggedness caused by segmentation errors at the edge of the particle cross-section, providing a geometrically simple and non-concave outer boundary for subsequent contact judgment. After extraction, candidate particle pairs with a convex hull profile spacing less than the contact threshold are quickly screened using a spatial indexing structure (such as KD-Tree or R-Tree), avoiding the computational explosion caused by performing pairwise comparisons on all particles. The contact arc length on the common boundary is further calculated for the selected candidate particle pairs. Only particle pairs with an arc length exceeding a preset threshold are considered to have valid contact. The logic of this screening is that, due to pixel resolution and segmentation errors in the cross-sectional image, two particles that are not actually in contact may produce extremely short overlapping pixel segments at the boundary. The arc length of these pseudo-contacts is much smaller than that of real contact, and they can be filtered out by the arc length threshold. The physical meaning of a valid contact relationship is that there is a mechanical transmission interface between two particles, and the pressure borne by one particle during the rolling process can be transmitted to the adjacent particle through this interface. Each particle is abstracted as a particle node. The node attributes carry the particle's equivalent diameter, cross-sectional area, morphological characteristics, carbon coating response characteristics, and layer depth coordinates. The effective contact relationship is abstracted as the first connecting edge.

[0026] When constructing pore nodes, it is necessary to first distinguish the phases in the cross-sectional image. There are three phases in the LFP electrode cross-section: the LFP active particle phase, the pore phase, and the conductive agent interstitial phase. These three phases exhibit different grayscale characteristics in the SEM image due to differences in electron scattering ability. By setting multiple thresholds on the grayscale histogram, pixels can be divided into three intervals, each corresponding to one of the three phases. Connectivity analysis is performed on the divided pore phase and conductive agent interstitial phase, aggregating adjacent pixels of the same phase into independent pore clusters. The conductive agent interstitial phase is included in the pore cluster category because in the LFP electrode, conductive agents such as carbon black and carbon nanotubes mainly fill the interstitial regions between particles, spatially interspersed with pores, and together they constitute the interstitial channel network between particles. Each pore cluster is abstracted as a pore node, and the node attributes include the area of ​​the cluster and the narrowest channel width. When there is a narrow-path connection between two pore clusters with a width greater than the connectivity threshold, a second connection edge is established between the corresponding pore nodes. The physical meaning of this connection edge is that there is a sufficiently wide channel between two pore clusters to allow electrolyte wetting and ion transport, belonging to the same connected pore network. The connectivity threshold is set based on the minimum channel width required for effective lithium ion transport in the electrolyte; channels below this threshold are unlikely to play an ion conduction role during actual charging and discharging.

[0027] After constructing the internal connection edges for both particle and pore nodes, cross-type connections between particles and pores need to be established to enable information exchange between the two types of nodes. The mechanical coupling between particles and pores is manifested in the following way: when particles undergo extrusion deformation under roller pressure, adjacent pore channels may be compressed, narrowed, or even completely closed; conversely, the presence of pores also affects the movable space and rearrangement path of particles during compaction. To encode this coupling relationship into the graph structure, the nearest distance between the outer contours of each particle node and each pore node is calculated. When this distance is less than a proximity threshold, a third connection edge is established between them. The physical meaning of the proximity threshold is the effective range of mechanical interaction between particles and pores, within which the deformation behavior of particles and the morphological evolution of pores are strongly correlated.

[0028] Ultimately, particle nodes and pore nodes are merged into a unified node set, and the three types of connecting edges are merged into a unified edge set. Each node and each edge is labeled with a type identifier to distinguish its category. The resulting particle-pore double adjacency graph serves as the input carrier for subsequent depth-weighted graph propagation. The node attributes in the graph provide numerical descriptions of microstructural features, and the edge relationships provide spatial topological connections between particles, between pores, and between particles and pores. Together, they constitute a complete information network describing the microstructural topology of the electrode cross-section. During subsequent graph propagation, information flows along the three types of connecting edges between heterogeneous nodes, enabling each node to integrate the feature information of its neighboring nodes and update its own representation. Finally, through pooling aggregation, a depth-compaction contribution matrix reflecting the structural differences in the depth direction is generated.

[0029] Step S3: Based on the proportion state vector, construct the scenario constraint loss function by weighted summation of the compaction density error term, the target particle size proportion window penalty term, the pore discontinuity penalty term, and the overpressure rebound penalty term.

[0030] Furthermore, a scenario-constrained loss function is constructed, including: The regression model trained using historical rolling process data is used as the forward prediction model. The candidate process parameter group and the proportion state vector are input into the forward prediction model, and the output is the predicted compaction density value. The difference between the predicted compaction density and the preset target compaction density is used as the compaction density error term. The deviation between the area proportion and the preset target particle size proportion window is used as the target particle size proportion window penalty term. The deviation is zero when the area proportion is within the preset target particle size proportion window. The difference between the preset pore connectivity threshold and the proportion of the maximum connected component in the pore node subgraph of the double adjacent graph is used as the pore disconnection penalty term. The difference is zero when the difference is negative. The morphological characteristics of the target particle size particles and the response characteristics of the carbon coating layer in the particle topology sample of the electrode section are combined with the magnitude of the candidate rolling line pressure exceeding the yield pressure of the LFP material. The rebound rate estimated by the rebound rate estimation function is used as the overpressure rebound penalty term. The scenario constraint loss function is constructed by weighted summation after assigning weight coefficients to the four penalty terms.

[0031] Specifically, the design concept of the scenario-constrained loss function originates from an engineering reality: the LFP cathode sheet rolling process needs to simultaneously meet four objectives: achieving the required compaction density, reasonable particle content of the target particle size, good pore connectivity, and controlled overpressure rebound. However, there is an inverse relationship between these four objectives. For example, simply increasing the rolling pressure can improve the compaction density, but it will also compress the pore channels, leading to a decrease in connectivity. Furthermore, excessive pressure can cause the carbon coating layer on the particle surface to rupture, exacerbating rebound. The role of the scenario-constrained loss function is to quantify the deviations corresponding to each of these four objectives as penalty terms, and then combine them into a scalar value through weighted summation. The smaller this value, the better the overall performance of the current candidate process parameter group on the four objectives. Therefore, the inversion model can search for the optimal solution in the parameter space with the objective of minimizing this scalar value.

[0032] Before calculating the penalty terms of the scenario constraint loss function, it is necessary to obtain the predicted compaction density corresponding to the candidate process parameter set. The candidate process parameter set refers to a set of process parameter values ​​currently being considered during the parameter optimization process, which at least includes the rolling pressure, roll gap, secondary mixing time, and target particle size replenishment ratio. The role of the forward prediction model is to predict, based on this set of candidate parameters, what the compaction density of the produced electrode sheet will be if the parameters are actually used for rolling. The forward prediction model is a regression model trained based on historical rolling process data. Its training data comes from the process parameter combinations and their corresponding measured compaction density values ​​recorded in previous rolling production. The input of the model is the candidate process parameter set and the proportion state vector, and the output is the predicted compaction density value. The proportion state vector is also used as input because the same process parameters will produce different compaction results when applied to electrodes with different particle distribution states. Electrodes with a high area proportion have sufficient target particle size content, and it is easier to achieve a high compaction density under the same pressure; electrodes with a high local agglomeration index have uneven particle distribution, and it is easy for local over-compression and local under-compression to coexist during the compaction process. The introduction of the proportion state vector enables the positive prediction model to correct the prediction results based on the current microstate of the electrode, thereby improving the prediction accuracy.

[0033] After the forward prediction model outputs the predicted compacted density, the compacted density error term is first calculated. The compacted density error term is the difference between the predicted compacted density and the preset target compacted density. Its physical meaning is intuitive: a positive difference indicates that the predicted value exceeds the target value, and the current candidate parameter set may lead to overcompression; a negative difference indicates that the predicted value is lower than the target value, and the current parameter set cannot increase the compacted density to the target level. This term contributes to the scenario constraint loss function by forcing the inversion model to tend to output parameter combinations that make the predicted compacted density approach the target value during the optimization process.

[0034] The second penalty is the target particle size ratio window penalty. The preset target particle size ratio window is a reasonable range for the area ratio. The lower and upper limits of this range are determined based on experience with LFP electrode rolling processes. An area ratio below the lower limit means insufficient target particle size content, and the gaps between large particles cannot be effectively filled; an area ratio above the upper limit means excessive small particle content, increasing the contact area between particles and leading to increased internal friction. This makes it difficult for particles to slip and rearrange during rolling, which is also detrimental to improving compaction density. The deviation calculation rule is as follows: when the area ratio is within the window, the deviation is zero, indicating that the current particle content is within a reasonable range and no penalty is required; when the area ratio is below the lower limit, the deviation is the difference between the lower limit and the area ratio; when the area ratio is above the upper limit, the deviation is the difference between the area ratio and the upper limit. The larger the deviation, the stronger the penalty, thus guiding the inversion model to output process parameters that can bring the area ratio back within the window, such as adjusting the secondary mixing time or the target particle size supplementation ratio to change the particle distribution.

[0035] The third penalty is the pore disconnection penalty. This penalty is calculated based on the pore node subgraph in the particle-pore biadjacency graph. The pore node subgraph is a subnetwork formed by retaining only pore nodes and the second connecting edge from the biadjacency graph. This subnetwork reflects the connectivity topology between pores in the cross-section. Connectivity component analysis is performed on this subgraph: a connected component is the set of pore nodes in the subgraph that are connected to each other through the second connecting edge. If the entire subgraph has only one connected component, it means that all pores in the cross-section are connected to form a complete pore network; if the subgraph splits into multiple connected components, it means that there are isolated pore regions in the cross-section that are blocked by particles or conductive agents and cannot be connected. The maximum connected component percentage is the proportion of pore nodes contained in the maximum connected component to the total number of pore nodes. The closer this proportion is to 1, the better the overall connectivity of the pore network. The difference between the preset pore connectivity threshold and the percentage of the maximum connected component is used as a pore disconnection penalty term. When the percentage of the maximum connected component is lower than the threshold, this term is positive, and the larger the difference, the heavier the penalty, indicating that the current candidate parameter set may cause severe pore network disconnection. When the percentage is higher than the threshold, this term is zero or negative (zero), indicating that the connectivity requirement is met. The role of this term in the scene constraint loss function is to prevent the inversion model from outputting parameter combinations that lead to excessive compression or even closure of pore channels in pursuit of high real density.

[0036] The fourth penalty is the overpressure rebound penalty. Roller rebound refers to the phenomenon of increased thickness and decreased density of the electrode sheet after it has been compacted through the roller gap due to the elastic recovery of the material. The rebound rate is the ratio of the increase in thickness after rebound to the immediate thickness after rolling. The higher the value, the more severe the rebound, and the further the actual compacted density deviates from the target value after rolling. The estimation of the rebound rate needs to consider two factors. One is the morphological characteristics of the target particle size and the response characteristics of the carbon coating layer: the lower the particle roundness (the more irregular the shape), the more likely it is to develop microcracks or local breakage due to stress concentration at the corners during rolling. These damages manifest as rebound after the pressure is released. The lower the integrity of the carbon coating layer, the more the exposed area on the particle surface directly bears the pressure during rolling. Due to the lack of buffer and protection from the carbon film, it is more likely to undergo plastic deformation and elastic energy storage. After the pressure is released, the stored energy is released in the form of rebound. On the other hand, there is the relationship between the candidate roll forming pressure and the yield pressure of the LFP material: the yield pressure is the critical pressure value for the LFP material to transition from the elastic deformation stage to the plastic deformation stage. When the roll forming pressure exceeds the yield pressure, the elastic strain energy accumulated inside the particles drives the particles to partially recover deformation after the pressure is released. The greater the excess, the more elastic energy is stored and the higher the rebound rate. The rebound rate is estimated by combining these two factors. The specific estimation method is: based on the particle roundness... and carbon coating coverage integrity Quantify the degree of particle defects and roundness The lower The larger the value, the more severe the morphological defects and the greater the coverage integrity. The lower The larger the value, the more severe the coating defect. The sum of the two values ​​multiplied by the candidate roll pressure line pressure... Exceeding the yield pressure of LFP material relative amplitude Multiply by the preset rebound coefficient The rebound rate estimation function for the rebound rate r is obtained as follows: When the linear pressure does not exceed the yield pressure, the excess is zero and the rebound rate is zero. The physical meaning of this formula is: the greater the particle defect degree and the higher the overpressure amplitude, the higher the rebound rate. If either of these factors is zero, the rebound rate is zero, and this rebound rate is used as the overpressure rebound penalty term. The role of this term in the loss function is to suppress excessively high roller pressure output by the inversion model, preventing the pursuit of high compaction density while ignoring the risk of rebound.

[0037] After calculating the four penalty terms individually, each is multiplied by its corresponding weight coefficient, and then summed to obtain the final value of the scenario constraint loss function. The weight coefficients reflect the relative importance of the four process objectives in the current production scenario. The weight coefficients can be flexibly adjusted under different application scenarios: when the product prioritizes high energy density, the weight coefficient of the compaction density error term can be appropriately increased, allowing for a reasonable sacrifice in pore connectivity; when the product prioritizes high-rate charge / discharge performance, the weight coefficient of the pore disconnection penalty term should be increased to ensure that the pore channels remain unobstructed after rolling to facilitate rapid lithium-ion transport. As a whole, a lower value of the scenario constraint loss function indicates better overall performance of the current candidate process parameter group across the four process objectives. The subsequent inversion model iteratively optimizes this function value.

[0038] Step S4: Based on the particle topology sample of the electrode section, perform layer depth weighted graph propagation on the particle and pore double adjacency map to generate the layer depth compaction contribution matrix.

[0039] Furthermore, a layer depth compaction contribution matrix is ​​generated, including: Based on the layer depth coordinates of each node in the particle topology sample of the electrode cross-section, the double adjacency graph is divided into a current collector side subgraph, a middle layer subgraph, and a surface layer subgraph. The layer depth weight allocation rule determined based on the layer depth stress distribution data of the LFP positive electrode rolling process is obtained, and propagation weights are assigned to the three subgraphs according to the layer depth weight allocation rule. The propagation weights are used as global scaling factors to perform graph neural network propagation operations on the three subgraphs to update the feature representation of each node. The particle node features and pore node features in each layer depth subgraph are pooled respectively, and the pooling results of the three layers depth are arranged in order of layer depth and normalized to generate a layer depth compaction contribution matrix.

[0040] Specifically, this approach addresses a long-standing issue neglected by traditional compaction density control methods: the differences in particle packing state, pressure response, and porosity evolution across different depth regions along the thickness direction of the electrode. The current collector side forms a high-stress zone due to the rigid support of the aluminum foil, where particles are fully compacted. In the middle layer, under bidirectional compression, particles are most prone to relative slippage and rearrangement, making its packing state most sensitive to changes in process parameters. The surface layer directly bears the roller pressure but rebounds after stress release, exhibiting the greatest porosity compression but the worst stability. The purpose of the depth-weighted graph propagation design is to explicitly encode these physical differences along the depth direction into the information propagation process of the graph neural network.

[0041] The input to the layer depth weighted graph propagation is the layer depth coordinate information from the particle-pore double adjacency graph and the particle topology sample of the electrode cross-section. The output is the layer depth compaction contribution matrix. The first step in the propagation process is to divide the double adjacency graph into three subgraphs according to the layer depth coordinates. Each node carries the layer depth coordinate attribute when constructing the particle-pore double adjacency graph. This coordinate is defined along the thickness direction with the aluminum foil current collector surface as the zero point. According to the layer depth coordinates of the node, it is assigned to the corresponding layer depth segment: the current collector side subgraph contains all particle nodes and pore nodes with layer depth coordinates within the range of zero to one-third of the electrode thickness, as well as the connecting edges between them; the middle layer subgraph contains nodes and edges within the range of one-third to two-thirds of the thickness; the surface layer subgraph contains nodes and edges within the range of two-thirds of the thickness to the electrode surface. For connecting edges that cross two layer depth segments, i.e., when the two endpoints of the edge belong to different segments, their assignment is determined by the layer depth coordinates at the midpoint of the edge. The logic behind this partitioning method is that while the double adjacency graph itself is a complete graph describing the topological relationships of the entire cross-section, the stress states and deformation behaviors of different depth regions are drastically different during actual rolling. If uniform information propagation is performed on the entire graph without differentiation, the neighbor information fused by each node after propagation will be mixed with heterogeneous physical signals from different depths, resulting in the final generated features failing to reflect the structural gradient in the depth direction. After partitioning the graph into subgraphs, information propagation is confined to the regions within each depth, allowing each node to fuse only the features of neighbor nodes within the same depth range, thus preserving the differences in the depth direction.

[0042] After the subgraphs are divided, differentiated propagation weights need to be assigned to the three subgraphs. The propagation weight is a global scaling factor that differentiates the update magnitude of node features in the depth dimension during information propagation. The allocation of propagation weights is not arbitrary but determined based on the depth stress distribution data of the LFP positive electrode rolling process. Depth stress distribution data can be obtained by pressure sensors embedded at different depths inside the electrode during rolling, or by finite element simulation of the rolling process. The patterns extracted from the stress distribution data are: the current collector side has a higher average stress level due to the rigid support of the aluminum foil, meaning that the particles in this area have close contact and high force transmission efficiency; therefore, the node features in this subgraph contribute significantly to the compaction density. The surface layer directly bears the rolling pressure and has the largest pore compression amplitude, but it also responds most drastically to changes in process parameters; its propagation weight reflects the sensitivity of this area during parameter adjustment. The stress distribution data can be transformed into weight allocation rules by establishing a mapping relationship between depth coordinates and stress levels, and then normalizing the mapping values ​​so that the sum of the three weights is 1. After the three subgraphs obtain their respective propagation weights, these weights are used as global scaling factors in subsequent graph neural network propagation operations.

[0043] The graph neural network propagation operation is the core computational step in the propagation of a deep weighted graph. Graph neural networks are a type of neural network specifically designed to process graph-structured data. Their basic working principle is a message-passing mechanism: in each round of propagation, each node collects feature messages sent by all its neighboring nodes, aggregates these messages, and merges them with its current features to update the node's feature representation. After multiple rounds of propagation, each node's features no longer contain only its own original attribute information but also incorporate information from its multi-hop neighboring nodes reachable via connecting edges in the graph. This gives the node's feature representation a contextual awareness of the local topology. In this scheme, the graph neural network propagation operation is executed independently on three deep subgraphs. Each subgraph uses its own propagation weight as a global scaling factor. Specifically, during the message aggregation phase, the feature messages sent by neighboring nodes are multiplied by the propagation weight of that subgraph before aggregation. Subgraphs with larger propagation weights experience greater updates to their node features in each round of propagation. The physical implication of this is that regions with high propagation weights contribute more significantly to compaction density during rolling. Therefore, their node features should be updated and strengthened to a greater extent during propagation, allowing the final output feature representation to more fully reflect the microstructural state of that region. In the heterogeneous subgraph where particle nodes and pore nodes coexist, message passing also crosses node types: particle nodes not only receive messages from adjacent particle nodes but also receive messages from adjacent pore nodes through third connecting edges, and vice versa. This cross-type information interaction allows the compressive state information of particles to propagate to adjacent pore nodes, and the connectivity state information of pores to be fed back to adjacent particle nodes. Both achieve mutual influence and coupling at the feature level during propagation.

[0044] After the graph neural network propagation operations on each subgraph are completed, each node obtains an updated feature representation. At this point, pooling operations need to be performed on the node features in each deep subgraph to generate a fixed-dimensional subgraph-level feature vector. Pooling is an operation that compresses a variable number of node features into a fixed-dimensional vector. Common methods include average pooling and max pooling. Average pooling averages the feature vectors of all nodes of the same type (particle nodes or pore nodes) in the subgraph element-wise, and the resulting vector reflects the overall statistical level of particle or pore features in that deep region. Max pooling, on the other hand, takes the maximum value among all node features of the same type element-wise, and the resulting vector reflects the most prominent particle or pore features in that deep region. After performing particle node feature pooling and pore node feature pooling on each deep subgraph, six pooled vectors are obtained (three depths × particle and pore node types). Arrange these six vectors in order of layer depth, namely, the current collector side, the middle layer, and the surface layer, into a two-dimensional matrix. The rows correspond to the layer depth positions, and the columns correspond to the node feature dimensions. Then, normalize the matrix so that each element is within a uniform numerical range, thus obtaining the layer depth compaction contribution matrix.

[0045] The physical meaning of the layer depth compaction contribution matrix is ​​as follows: each row of the matrix represents the contribution of a layer depth region to the compaction density. The column vector corresponding to the particle node reflects the particle packing density and bearing capacity of that layer depth region, while the column vector corresponding to the pore node reflects the pore connectivity and compressible space of that layer depth region. The numerical differences among the three layer depth rows characterize the structural gradient of the electrode along the thickness direction. If the particle characteristic value of the current collector side row is significantly higher than that of the surface row, it indicates that the particle packing on the current collector side is more compact; if the pore characteristic value of the surface row is abnormally low, it indicates that the surface pores have been over-compressed. This matrix serves as one of the core inputs to the subsequent inversion model, enabling the inversion model to perceive the differentiated contributions of different layer depth regions to the compaction density. Therefore, during the parameter optimization process, it outputs a combination of process parameters that can be differentiated and adjusted according to the actual state of each layer depth region.

[0046] For example, Figure 2 This is a grayscale heatmap of a layer depth compaction contribution matrix. The vertical axis represents three layer depth regions, from top to bottom: the current collector side, the middle layer, and the surface layer. The horizontal axis represents multiple microscopic feature dimensions. The first four features (equivalent particle diameter, particle roundness, carbon coating integrity, and particle contact number) are particle node features, while the last two features (pore area and pore channel width) are pore node features. The value in each cell represents the normalized contribution value of the corresponding layer depth region to that feature dimension. The closer the value is to 1 (the darker the grayscale), the greater the contribution of that layer depth region to that feature; the closer the value is to 0 (the lighter the grayscale), the smaller the contribution.

[0047] Step S5: Input the layer depth compaction contribution matrix and the proportion state vector into the pre-trained inversion model, and output the rolling process parameters and mixing parameters based on the scenario constraint loss function; perform multi-level rule verification on the rolling process parameters and mixing parameters, and generate compaction density optimization instructions when the verification passes.

[0048] Furthermore, before inputting the layer depth compaction contribution matrix into the pre-trained inversion model, the training process of the inversion model is as follows: Historical rolling process data and corresponding electrode cross-section particle topology samples are collected as historical samples. For each historical sample, the proportion state vector is calculated, a double adjacency graph is constructed, and a layer depth weighted graph is propagated to obtain a historical feature matrix. The historical feature matrix is ​​used as the training input, and the actual rolling process parameters and mixing parameters corresponding to the historical samples are used as training labels to construct a training set. A neural network with an encoder-decoder structure is used as the basic architecture of the inversion model. The encoder part introduces a conditional input corresponding to the scene constraint loss function, so that the inversion model outputs differentiated combinations of process parameters under different constraints. The inversion model is trained by minimizing the mean square error between the predicted parameters and the actual parameters.

[0049] Furthermore, the output rolling process parameters and mixing parameters also include: The encoder compresses the layer depth compaction contribution matrix into a high-dimensional latent vector. An inversion condition vector is constructed using the area ratio, the target compaction density within the target compaction density range, and a preset pore connectivity threshold. This high-dimensional latent vector is injected into the condition input terminal for conditional modulation to obtain a conditionally modulated latent vector. The decoder decodes the conditionally modulated latent vector and outputs initial candidate parameters. These parameters are then substituted into the scene constraint loss function to calculate the loss value and backpropagate. The gradient step size is adaptively adjusted according to the proportion of each penalty term to update the latent vector and re-decode. This process is repeated until the loss value converges to below the preset threshold. The candidate parameters at convergence are then determined as rolling process parameters and mixing parameters. The rolling process parameters include at least the rolling line pressure and roll gap, while the mixing parameters include at least the secondary mixing time and the target particle size replenishment ratio.

[0050] Furthermore, after generating the compaction density optimization instruction upon successful verification, it also includes: The compaction density optimization command is sent to the rolling mill and mixing equipment for execution. All the above steps are repeated on the LFP positive electrode sheet produced after the execution to obtain a new round of proportion state vector and a new round of compaction density optimization command. The Euclidean distance between the new round of proportion state vector and the previous round of proportion state vector is calculated as the compaction density deviation. It is determined whether the compaction density deviation is less than the preset convergence threshold. If it is less, the current compaction density optimization command is used as the final command output. If it is not less, the command continues to be sent and executed until the compaction density deviation is less than the preset convergence threshold.

[0051] Specifically, the inversion model is a deep learning model that infers macroscopic process parameters from microstructural features. Unlike the forward prediction model, which predicts compaction density from process parameters, the inversion model starts with the microstructural features of the electrode and infers what process parameters should be used to achieve the target compaction state. Training such a model is necessary because the mapping relationship from microstructure to process parameters is highly nonlinear. Different combinations of rows and columns in the layer depth compaction contribution matrix correspond to different particle packing and pore distribution states. These states respond differently to roller pressure, roller gap, mixing time, and replenishment ratio, and are mutually coupled. They cannot be described by simple analytical formulas and require a data-driven approach to learn this mapping relationship from historical samples.

[0052] The training process of the inversion model first requires the construction of training data. Historical rolling process data and corresponding electrode cross-sectional particle topology samples are collected as historical samples. Each set of historical samples contains two parts: one is the actual process parameters used in the rolling production (rolling line pressure, roll gap, secondary mixing time, and target particle size replenishment ratio); the other is the particle topology data obtained by analyzing the electrode cross-section before rolling. For each historical sample, the same processing flow as steps S1 to S4 above is performed: proportion state vector calculation, particle and pore double adjacency graph construction, and layer depth weighted graph propagation, to obtain the layer depth compaction contribution matrix corresponding to the historical sample, which is called the historical feature matrix to distinguish it from the layer depth compaction contribution matrix of the current electrode to be optimized. The historical feature matrix is ​​used as training input, and the corresponding historical actual process parameters are used as training labels. The two are paired to form a set of training samples, and all historical samples constitute the training set.

[0053] The inversion model employs an encoder-decoder neural network as its basic architecture. The encoder-decoder structure is a two-stage network architecture that first compresses the input data into a low-dimensional latent representation and then recovers the output data from the latent representation. The encoder is responsible for compressing the high-dimensional input into an information-dense latent vector, and the decoder is responsible for decoding the target output from the latent vector. In this scheme, the encoder's input is the historical feature matrix, and its output is a high-dimensional latent vector; the decoder's input is the conditionally modulated latent vector, and its output is the predicted combination of process parameters. Because the deep compaction contribution matrix has a high dimension and contains a large amount of redundant local detail information, the encoder compresses this information layer by layer into a compact latent vector representation. The decoder then extracts key information related to process parameters from this latent vector for output. This compression-refinement-recovery process has better generalization ability than directly mapping parameters end-to-end from the original matrix.

[0054] The key design difference between this inversion model and ordinary regression models lies in introducing a conditional input terminal corresponding to the scene constraint loss function in the encoder section. The conditional input terminal is a network module in the encoder that specifically receives external conditional vectors and injects them into the latent vector. The inversion conditional vector consists of three values: area ratio, target compaction density, and pore connectivity threshold. These three values ​​correspond to the core constraints on which the compaction density error term, target particle size ratio window penalty term, and pore discontinuity penalty term in the scene constraint loss function depend, respectively. The working principle of the conditional input terminal is as follows: the inversion conditional vector is mapped to modulation parameters of the same dimension as the high-dimensional latent vector through a linear transformation. These modulation parameters are then injected into the latent vector through element-wise multiplication or addition, thereby changing its numerical distribution without altering the dimension of the latent vector. The technical effect of this design is that the layer depth compaction contribution matrix of the same electrode sheet will produce different process parameter outputs under different inversion conditional vectors. When the target compaction density is increased, the roll pressure output by the inversion model increases accordingly; when the pore connectivity threshold is increased, the output parameters tend to use a smaller roll gap to avoid excessive pore compression. This enables the inversion model to differentiate its output based on the constraints of different production scenarios, rather than outputting fixed parameters for all scenarios. During training, the network weights of the encoder and decoder are optimized by minimizing the mean squared error between the predicted and actual parameters. The mean squared error is the average of the sum of the squares of the differences in each dimension between the predicted and actual parameter vectors. The smaller this value, the closer the model's predicted parameters are to the parameters actually used in history.

[0055] After the inversion model is trained, the inference phase begins, where the trained model is used to optimize the process parameters of the LFP cathode sheet to be optimized. The first step in the inference phase is to compress the layer depth compaction contribution matrix of the current electrode sheet into a high-dimensional latent vector using an encoder. The high-dimensional latent vector is a compact numerical representation of the layer depth compaction contribution matrix obtained after multiple nonlinear transformations by the encoder. Each dimension corresponds to an abstract feature channel. Although it no longer has direct physical interpretability, it encodes all the key information related to process parameters in the original matrix. Subsequently, an inversion condition vector is constructed using the area ratio, target compaction density, and pore connectivity threshold. This high-dimensional latent vector is then injected into the condition input terminal for conditional modulation, resulting in a conditionally modulated latent vector. The difference between the conditionally modulated latent vector and the original high-dimensional latent vector is that the conditionally modulated latent vector retains the information of the original matrix while superimposing the constraint information of the current production scenario. This ensures that subsequent decoding operations are based not only on the microstructural features of the electrode sheet but also on the user-specified compaction density target and pore connectivity requirements.

[0056] The decoder decodes the conditionally modulated latent vector and outputs initial candidate parameters. These initial candidate parameters are the first output of the inversion model before iterative adjustments. At this point, the scene constraint loss function corresponding to these parameters may not have reached its minimum value and requires further optimization. The optimization process substitutes the initial candidate parameters into the scene constraint loss function to calculate the loss value. Specifically, it substitutes the candidate roll pressure, roll gap, secondary mixing time, and replenishment ratio into the scene constraint loss function constructed in step S3. The predicted compaction density is obtained through the forward prediction model, and then the compaction density error term is calculated. Simultaneously, the target particle size distribution window penalty term, pore discontinuity penalty term, and overpressure rebound penalty term are calculated. The weighted sum of these four terms yields the loss value. The loss value is backpropagated to the high-dimensional latent vector, and its gradient is calculated. The gradient indicates the direction in which each dimension of the latent vector should be adjusted to reduce the loss value.

[0057] An adaptive gradient step size mechanism is introduced in the gradient update stage. Adaptive gradient step size refers to dynamically adjusting the update magnitude of each parameter dimension based on the relative proportions of the penalty terms in the scenario constraint loss function, instead of using a uniform learning rate to update all parameter dimensions equally. The logic is as follows: the four penalty terms correspond to four different process objectives. When the value of a penalty term has the highest proportion in the total loss, it means that the current candidate parameter violates that objective most severely, and the parameter dimension most relevant to that objective should be corrected first. This mechanism, which adaptively adjusts the correction magnitude and priority based on constraint violations, enables the optimization process to achieve an unbalanced but more targeted search in multiple directions of the parameter space. Compared to gradient descent with a uniform learning rate, it can converge to a parameter combination that satisfies multiple objective constraints more quickly.

[0058] The latent vector updated by gradients is re-injected into the inverted conditional vector through the conditional input terminal and decoded to obtain the updated candidate parameters. These parameters are then substituted into the scene constraint loss function to calculate the loss value, and this process is repeated iteratively. In each iteration, the loss value gradually decreases, and iteration stops when the loss value converges below a preset threshold. Convergence means that the decrease in the loss value over several consecutive iterations has become extremely small, and further parameter adjustments have no substantial significance in improving the overall performance of the four process objectives. The candidate parameters corresponding to convergence are determined as the final rolling process parameters and mixing parameters.

[0059] After the inversion model outputs process parameters, multi-level rule verification is required to ensure that the parameters are within the engineering-executable range. Multi-level rule verification is a hard safety valve mechanism independent of the scenario-constrained loss function. Unlike the soft constraint nature of the loss function, which uses a penalty term to flexibly constrain the parameter range through gradient guidance, it cannot guarantee that the output parameters absolutely satisfy all engineering boundary conditions. The verification is based on four thresholds: the electrode thickness threshold ensures that the predicted electrode thickness does not exceed the design's upper limit; exceeding the thickness limit means the electrode is too thick to be installed in the battery casing. The porosity threshold ensures that the predicted porosity is not lower than the lower limit; too low porosity means difficulty in electrolyte wetting. The compaction density target range ensures that the predicted compaction density is within the design requirements. The springback threshold ensures that the predicted springback rate does not exceed the upper limit; too high a springback rate means that the actual compaction density after rolling will continue to decrease during storage and use. During verification, based on the inverted output of the rolling process parameters and mixing parameters, combined with the coating surface density and the output of the forward prediction model, the predicted electrode thickness, predicted porosity, predicted compaction density, and predicted springback rate are calculated. It is then determined whether each of the four indicators meets its corresponding threshold requirements. Verification passes when all four conditions are met. The rolling process parameters and mixing parameters are then mapped according to the interface protocol of the rolling and mixing equipment, generating a structured instruction message containing equipment identifier, parameter name, parameter value, and effective timestamp as the compaction density optimization instruction. This message is then sent to the rolling mill and mixing machine for execution via the industrial bus or manufacturing execution system.

[0060] After the compaction density optimization command is issued and executed, the produced electrode sheets enter an iterative closed-loop process. The design of the iterative closed-loop is based on the fact that both the forward prediction model and the inversion model are trained on historical data, and there is an inevitable deviation between the model prediction and the actual production results. A single parameter recommendation cannot guarantee accuracy on the first try. The closed-loop approach is to re-execute all steps from cross-sectional sampling to rule verification on the LFP cathode sheets produced after the initial optimization, resulting in a new round of proportion state vector and a new round of compaction density optimization command. The Euclidean distance between the new round of proportion state vector and the previous round of proportion state vector is calculated as the compaction density deviation. The Euclidean distance is the square root of the sum of the squares of the differences in each dimension of the two vectors. The reason for choosing the Euclidean distance instead of a single dimension difference is that the proportion state vector includes three dimensions: area proportion, local aggregation index, and interlayer distribution deviation. These three dimensions together reflect the microstructure state of the electrode sheet, and the Euclidean distance can synthesize the changes in the three dimensions into a single scalar for judgment. When the distance is less than the preset convergence threshold, it means that the microstructure of the electrode has not changed substantially between the two rounds, and further iteration cannot improve the compaction effect. In this case, the current compaction density optimization command is used as the final command output. When the distance is not less than the convergence threshold, it indicates that the electrode state is still changing after the execution of the previous round of commands, and further iteration is expected to optimize it further. Therefore, a new round of commands is issued and executed until convergence. This closed-loop mechanism enables the method to have the ability to adaptively adjust in multiple rounds. The actual production feedback after each round of execution is transformed into new electrode cross-sectional data and re-enters the analysis-inversion-verification process, gradually eliminating model prediction bias and making the compaction density optimization command approximate the optimal parameter combination of the electrode system under the current equipment conditions.

[0061] The above describes a method for optimizing the compaction density of an LFP positive electrode sheet according to an embodiment of this application. The following describes a system for optimizing the compaction density of an LFP positive electrode sheet according to an embodiment of this application. Please refer to [link / reference]. Figure 3 One embodiment of an LFP positive electrode compaction density optimization system in this application includes: The sample construction unit is used to obtain cross-sectional images by cross-sectional sampling of LFP positive electrode sheets, and construct electrode cross-sectional particle topology samples based on the cross-sectional images; target particle size particles are selected from the electrode cross-sectional particle topology samples, and the area ratio, local aggregation index and interlayer distribution deviation of the target particle size particles in the cross-sectional observation field of view are calculated, and the proportion state vector is generated by splicing. The graph construction unit is used to construct particle nodes, pore nodes and connecting edges based on the particle topology sample of the electrode section, and generate a double adjacency graph of particles and pores. The function construction unit is used to construct the scenario constraint loss function based on the proportion state vector by weighted summation of the compaction density error term, the target particle size proportion window penalty term, the pore discontinuity penalty term, and the overpressure rebound penalty term; The graph propagation unit is used to perform layer depth weighted graph propagation on the particle and pore double adjacency graph based on the particle topology sample of the electrode section, and generate the layer depth compaction contribution matrix. The parameter inversion unit is used to input the layer depth compaction contribution matrix and the proportion state vector into the pre-trained inversion model, and output the rolling process parameters and mixing parameters based on the scenario constraint loss function; it performs multi-level rule verification on the rolling process parameters and mixing parameters, and generates compaction density optimization instructions when the verification passes.

[0062] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0063] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0064] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for optimizing the compaction density of LFP positive electrode sheets, characterized in that, The method includes: Cross-sectional images are obtained by cross-sectional sampling of the LFP positive electrode sheet, and a cross-sectional particle topology sample of the electrode sheet is constructed based on the cross-sectional image. Target particle size particles are selected from the cross-sectional particle topology sample of the electrode sheet, and the area ratio, local aggregation index and interlayer distribution deviation of the target particle size particles in the cross-sectional observation field of view are calculated. The particles are then spliced ​​to generate a ratio state vector. Based on the particle topology sample of the electrode section, particle nodes, pore nodes and connecting edges are constructed to generate a double adjacency graph of particles and pores. Based on the aforementioned proportion state vector, a scenario constraint loss function is constructed by weighted summation of the compaction density error term, the target particle size proportion window penalty term, the pore discontinuity penalty term, and the overpressure rebound penalty term. Based on the particle topology sample of the electrode section, layer depth weighted graph propagation is performed on the particle and pore double adjacency map to generate a layer depth compaction contribution matrix; The layer depth compaction contribution matrix and the proportion state vector are input into the pre-trained inversion model, and the rolling process parameters and mixing parameters are output based on the scenario constraint loss function; the rolling process parameters and the mixing parameters are subjected to multi-level rule verification, and when the verification passes, a compaction density optimization instruction is generated.

2. The method for optimizing the compaction density of LFP positive electrode sheet according to claim 1, characterized in that, Constructing polarimetric cross-sectional particle topology samples includes: A preset number of sampling positions are selected at equal intervals along the width of the LFP positive electrode sheet. After slicing the sampling positions in a direction perpendicular to the aluminum foil current collector, cross-sectional images are obtained to identify the contour region of each LFP active particle. For each contour region, the equivalent diameter and cross-sectional area of ​​the particles are calculated according to the principle of equal area circles. Morphological features and carbon coating layer response features are extracted, and the layer depth coordinates are defined along the electrode thickness direction with the aluminum foil current collector surface as the zero point. Width weights are assigned according to the width coordinates of each sampling location. The attribute records of all LFP active particles identified at each sampling location are merged into a unified particle set, and the width weights are marked to generate the particle topology sample of the electrode cross section.

3. The method for optimizing the compaction density of LFP positive electrode sheet according to claim 1, characterized in that, The proportion state vector is generated by concatenation, including: From the particle topology sample of the electrode cross section, extract the target particle size particles whose equivalent diameter is within the target particle size range. Sum the cross-sectional areas of all target particle size particles to obtain the total cross-sectional area of ​​the target particle size. Calculate the ratio of the total cross-sectional area of ​​the target particle size to the total area of ​​the cross-sectional observation field of view to obtain the area ratio. The cross-sectional observation field of view is divided into equally spaced grids, and the number of target particle size particles in each grid is counted to obtain a distribution series. The ratio of the variance to the mean of the distribution series is used as the local aggregation index. The target particle size particles are grouped into three depth segments: the current collector side, the middle layer, and the surface layer. The range or standard deviation of the three groups is used as the interlayer distribution deviation. The area proportion, the local aggregation index, and the interlayer distribution deviation are normalized and then concatenated to generate the proportion state vector.

4. The method for optimizing the compaction density of LFP positive electrode sheet according to claim 3, characterized in that, After calculating the local aggregation index, the following is also included: Calculate the center distance between each target particle size and its nearest neighbor of the same type, compare the mean of all center distances with the expected nearest neighbor distance, and use the ratio of the expected nearest neighbor distance to the mean as an auxiliary verification index; when the auxiliary verification index is less than a preset verification threshold, it is determined that there is a target particle size aggregation phenomenon, the preset verification threshold is greater than or equal to 1, and the weight coefficient of the target particle size proportion window penalty term is increased when constructing the scene constraint loss function.

5. The method for optimizing the compaction density of LFP positive electrode sheet according to claim 1, characterized in that, Generate a double adjacency map of particles and pores, including: For each particle in the topological sample of the electrode cross section, extract the convex hull profile, determine the adjacent particle pairs whose contact arc length exceeds the preset arc length threshold as effective contact, abstract each particle as a particle node, and establish a first connection edge between the particle nodes in effective contact. The cross-sectional image is segmented using multiple thresholds to distinguish the LFP active particle phase, the porous phase, and the conductive agent interstitial phase. The porous aggregates are abstracted into porous nodes through connected component analysis. A second connection edge is established between porous nodes whose channel width is greater than a preset connection threshold. Calculate the nearest distance between the outer contours of particle nodes and pore nodes, and establish a third connecting edge when the nearest distance is less than a preset proximity threshold; merge particle nodes and pore nodes into a unified node set, merge the three types of connecting edges into a unified edge set, and generate the particle and pore double adjacency graph.

6. The method for optimizing the compaction density of LFP positive electrode sheet according to claim 1, characterized in that, Construct the scenario constraint loss function, including: The regression model trained with historical rolling process data is used as a positive prediction model. The candidate process parameter group and the proportion state vector are used as inputs to the positive prediction model. The predicted compaction density value is output, and the difference between the predicted compaction density and the preset target compaction density is used as the compaction density error term. The deviation between the area ratio and the preset target particle size ratio window is used as the penalty term for the target particle size ratio window. When the area ratio is within the preset target particle size ratio window, the deviation is zero. The difference between the preset pore connectivity threshold and the percentage of the maximum connected component in the pore node subgraph of the double adjacent graph, and the value of the difference being zero when it is negative, is used as the pore disconnection penalty term. The morphological characteristics of the target particle size and the response characteristics of the carbon coating layer in the particle topology sample of the electrode section are combined with the extent to which the candidate roll pressure exceeds the yield pressure of the LFP material, and the rebound rate estimated by the rebound rate estimation function is used as the overpressure rebound penalty term. The four penalty terms are assigned weight coefficients and then summed in a weighted manner to construct the scenario constraint loss function.

7. The method for optimizing the compaction density of LFP positive electrode sheet according to claim 1, characterized in that, Generate the deep compaction contribution matrix, including: Based on the layer depth coordinates of each node in the particle topology sample of the electrode cross-section, the double adjacency graph is divided into a current collector side subgraph, a middle layer subgraph, and a surface layer subgraph. A layer depth weight allocation rule determined based on the layer depth stress distribution data during the LFP cathode rolling process is obtained, and propagation weights are assigned to the three subgraphs according to this rule. The propagation weights are used as global scaling factors to perform graph neural network propagation operations on the three subgraphs to update the feature representations of each node. The particle node features and pore node features in each layer depth subgraph are pooled, and the pooling results of the three layers are arranged in layer depth order and normalized to generate the layer depth compaction contribution matrix.

8. The method for optimizing the compaction density of LFP positive electrode sheet according to claim 1, characterized in that, Before inputting the layer depth compaction contribution matrix into the pre-trained inversion model, the training process of the inversion model is as follows: Historical rolling process data and corresponding electrode cross-section particle topology samples were collected as historical samples. Proportion state vector calculation, double adjacency graph construction and layer depth weighted graph propagation were performed on the historical samples to obtain the historical feature matrix. The historical feature matrix is ​​used as the training input, and the actual rolling process parameters and mixing parameters corresponding to the historical samples are used as training labels to construct a training set. A neural network with an encoder-decoder structure is used as the basic architecture of the inversion model. The encoder part introduces a conditional input corresponding to the scene constraint loss function, so that the inversion model outputs differentiated combinations of process parameters under different constraints. The inversion model is trained by minimizing the mean square error between the predicted parameters and the actual parameters.

9. The method for optimizing the compaction density of LFP positive electrode sheet according to claim 8, characterized in that, The output rolling process parameters and mixing parameters also include: The encoder compresses the layer depth compaction contribution matrix into a high-dimensional latent vector. An inversion condition vector is constructed using the area ratio, the target compaction density within the target compaction density range, and a preset pore connectivity threshold. This high-dimensional latent vector is then injected into the condition input terminal for conditional modulation to obtain a conditionally modulated latent vector. The decoder decodes the conditionally modulated latent vector and outputs initial candidate parameters. These parameters are then substituted into the scene constraint loss function to calculate the loss value and backpropagate. The gradient step size is adaptively adjusted according to the proportion of each penalty term to update the latent vector and re-decode it. Repeat this step until the loss value converges to below the preset loss threshold. The candidate parameters at the time of convergence are determined as the rolling process parameters and the mixing parameters. The rolling process parameters include at least the rolling line pressure and the roll gap, and the mixing parameters include at least the secondary mixing time and the target particle size replenishment ratio.

10. A compaction density optimization system for LFP positive electrode sheets, used to implement the LFP positive electrode sheet compaction density optimization method as described in any one of claims 1-9, characterized in that, The system includes: The sample construction unit is used to perform cross-sectional sampling on the LFP positive electrode to obtain a cross-sectional image, and construct a cross-sectional particle topology sample of the electrode based on the cross-sectional image; select target particle size particles from the cross-sectional particle topology sample of the electrode, calculate the area ratio, local aggregation index and interlayer distribution deviation of the target particle size particles in the cross-sectional observation field of view, and splice them to generate a ratio state vector; The graph construction unit is used to construct particle nodes, pore nodes and connecting edges based on the particle topology sample of the electrode cross section, and generate a double adjacency graph of particles and pores. The function construction unit is used to construct a scenario constraint loss function based on the proportion state vector by weighted summation of the compaction density error term, the target particle size proportion window penalty term, the pore discontinuity penalty term, and the overpressure rebound penalty term. The graph propagation unit is used to perform layer depth weighted graph propagation on the particle and pore double adjacency graph based on the particle topology sample of the electrode section, and generate a layer depth compaction contribution matrix. The parameter inversion unit is used to input the layer depth compaction contribution matrix and the proportion state vector into the pre-trained inversion model, and output the rolling process parameters and mixing parameters based on the scenario constraint loss function; the rolling process parameters and the mixing parameters are subjected to multi-level rule verification, and a compaction density optimization instruction is generated when the verification passes.

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