A method and system for multi-objective optimization of wet recycling of waste lithium-ion batteries based on spatio-temporal graph neural networks

Abstract

The application discloses a kind of based on space-time graph neural network's waste lithium ion battery wet recovery multi-objective optimization method and system, method includes: obtaining wet recovery operation data and constructing dynamic graph dataset;Space-time graph neural network model including graph convolution network module, graph attention mechanism module and double-layer gate cycle module is constructed;Multi-task loss function of fusion metal recovery rate, energy consumption and operating cost is constructed, and model is trained in combination with graph structure enhancement strategy;Real-time receive current operation data, with process operation parameter as optimization object, the model trained is used as candidate parameter performance evaluation model, multi-objective dynamic optimization is carried out in combination with non-dominated sorting genetic algorithm, and optimal process operation parameter is obtained.The application can improve metal recovery rate prediction accuracy, and reduce energy consumption and operating cost.

Description

Technical Field

[0001] The present invention belongs to the technical fields of industrial process control, data processing and resource recycling engineering, and particularly relates to a multi-objective optimization method and system for wet recycling of spent lithium-ion batteries based on spatiotemporal graph neural network. Background Art

[0002] At present, hydrometallurgy (wet recycling) is the most widely applied method for realizing large-scale LIB recycling. Compared with pyrometallurgy, it has higher metal recovery rate and lower energy consumption cost. The wet recycling process usually includes steps such as pretreatment, acid leaching, solvent extraction separation and purification. However, the full-process optimization of this process faces great technical complexity: on the one hand, wet recycling is a typical multi-node, multi-coupling industrial process, and process units (such as reactors and extractors) are tightly coupled through material flow and energy flow, and the change of a single unit or parameter (such as temperature and pH) will cause a global linkage response of the system; on the other hand, with the difference in the composition of the input spent battery raw materials (such as the ratio of NMC and LFP batteries, aging degree, and fluctuation of metal content), the operating conditions of the system present strong random dynamic changes and concept drift over time.

[0003] Traditional optimization methods are difficult to properly solve the above problems. Although the first-principle mechanism model has physical significance, it often oversimplifies complex chemical interactions and requires a large number of professional parameter calibrations, making it difficult to cope with complex and variable unsteady working conditions; although data-driven methods dominated by statistics and traditional machine learning (such as XGBoost, LightGBM, ANN) have certain effects, existing studies often focus on a single process stage in isolation, and cannot explicitly characterize the physicochemical topological structure and its temporal dynamic drift between process units in the whole process. More importantly, even if attempts are made to introduce conventional Graph Neural Networks (GNN) or Graph Convolutional Networks (GCN) to process spatial topologies, standard graph models often treat all nodes and connections as homogeneous structures. They cannot effectively distinguish the "heterogeneous multilateral relationships" such as material flow, physical connections, chemical reactions and control signals in the wet recycling process, and it is also difficult to adaptively handle the temporal dynamic fluctuations of industrial field parameters. Under the conflicting objectives of pursuing maximum metal recovery rate while minimizing energy consumption and operating cost, the existing static and homogeneous black-box methods are very likely to lead to serious performance degradation. Therefore, there is an urgent need for a multi-objective joint optimization strategy that integrates graph spatial topology awareness and strong temporal dynamic adaptability. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention proposes a multi-objective optimization method and system for wet recycling of spent lithium-ion batteries based on a spatiotemporal graph neural network. By constructing a dynamic polygonal graph topology structure oriented towards the entire wet recycling process, it explicitly represents the various types of physicochemical relationships between process units, materials, and global parameters. Through an improved spatiotemporal graph neural network model combining graph convolutional networks, multi-head graph attention mechanisms, and double-layer gated recurrent units, it extracts spatial topological features and temporal dynamic features. Furthermore, it incorporates a non-dominated sorting genetic algorithm to achieve multi-objective joint dynamic optimization of wet recycling process operating parameters, thereby improving the accuracy of metal recovery rate prediction and reducing energy consumption and operating costs.

[0005] To achieve the above objectives, this invention provides a multi-objective optimization method for wet recycling of spent lithium-ion batteries based on a spatiotemporal graph neural network, comprising: Obtain operational data of the wet recycling process of waste lithium-ion batteries, and construct a dynamic graph dataset based on the operational data; A spatiotemporal graph neural network model is constructed based on the dynamic graph dataset. The spatiotemporal graph neural network model includes a graph convolutional network module for distinguishing different edge types and extracting spatial topological features, a graph attention mechanism module for dynamically allocating node and edge relationship weights, and a two-layer gated recurrent module for capturing the temporal evolution features of process states. A multi-task loss function integrating metal recovery rate, energy consumption, and operating costs is constructed, and the spatiotemporal graph neural network model is trained and optimized under a graph structure enhancement strategy; The system receives real-time data on the operation of wet recycling, optimizes process operating parameters, uses a trained spatiotemporal graph neural network model as a performance evaluation model for candidate process operating parameters, predicts the average metal recovery rate, energy consumption, and operating cost corresponding to each candidate process operating parameter, and combines a non-dominated sorting genetic algorithm to perform multi-objective joint dynamic optimization of candidate process operating parameters to obtain the optimal process operating parameters.

[0006] Optionally, acquiring operational data of the wet recycling process of spent lithium-ion batteries, and constructing a dynamic graph dataset based on the operational data includes: Acquire continuous industrial operation data, including battery raw material composition content, system process parameters, equipment operating status, and recycling performance indicators; The continuous industrial operation data is cleaned to obtain preprocessed operation data; A directed graph is constructed based on the preprocessed operating data, wherein the set of nodes is divided into process unit nodes, material nodes, and global parameter nodes; Based on the directed graph, a set of connection edges between the nodes is established. The set of connection edges includes material flow edges, unit connection edges, reaction edges, parameter influence edges, and time-series edges that connect the same node across time steps. The directed graphs at multiple time points are constructed into a dynamic graph dataset according to the time series.

[0007] Optionally, constructing a spatiotemporal graph neural network model based on the dynamic graph dataset includes: Based on the different types of connection edges in the dynamic graph dataset, an improved graph convolutional network module is constructed to extract the spatial topological features of each node under different physicochemical relationships. A multi-head graph attention mechanism module is introduced after the improved graph convolutional network module to calculate the attention coefficients between nodes and their neighboring nodes, so as to dynamically allocate the association weights of node features and edge relationships. The node features output by the multi-head graph attention mechanism module are converted into graph-level feature vectors and input into a series of two-layer gated loop unit modules to capture the long- and short-term time-series evolution features of operating parameters and system states. The spatiotemporal graph neural network model is constructed based on the improved graph convolutional network module, multi-head graph attention mechanism module, and double-layer gated recurrent unit module.

[0008] Optionally, based on different types of connection edges in the dynamic graph dataset, an improved graph convolutional network module is constructed to extract the spatial topological features of each node under different physicochemical relationships, including: For each type of connection edge, a corresponding learnable weight mapping matrix is ​​introduced to map the features of neighbor nodes under that connection edge type to the edge type-specific feature space. For each type of connecting edge, an independent adjacency matrix with self-loops and a corresponding degree matrix are established to determine the neighborhood range and normalization coefficient of node features propagating along that connecting edge type. By introducing learnable edge type weight balance coefficients, the features of various neighbor nodes after transformation by the corresponding weight mapping matrix and normalization propagation by the adjacency matrix are weighted and summed to obtain the updated node space topological features.

[0009] Optionally, the attention coefficients between a node and its neighboring nodes are calculated to dynamically assign association weights to node features and edge relationships, including: Calculate the attention score between the center node and its neighboring nodes using a learnable weight matrix and attention vector; The attention scores are normalized using a nonlinear activation function and a softmax function to obtain attention coefficients. The neighbor node features are weighted and summed based on the obtained attention coefficients to obtain the output features of a single attention head; Multiple parallel attention heads are used to perform attention calculations separately, and the output features of the multiple attention heads are concatenated or averaged and fused.

[0010] Optionally, capturing long- and short-term time-series evolution characteristics of operating parameters and system states includes: The node feature matrix output by the multi-head graph attention mechanism module is subjected to graph-level pooling to generate a graph-level comprehensive feature vector for the current time step. The graph-level integrated feature vectors of consecutive time steps are combined into a graph-level feature vector sequence; The graph-level feature vector sequence is sequentially input into the first-level gated loop unit and the second-level gated loop unit in series. The timing dependency of the operation parameters and system state is dynamically tracked through the update gate and reset gate mechanism. The hidden state output by the second-layer gated recurrent unit at the last time step is used as the spatiotemporal feature vector representing the global spatiotemporal evolution state.

[0011] Optionally, the multi-task loss function is: ; in, For metal recovery rate, multiple task loss items; This is the predicted loss item for total energy consumption; Forecast loss items for total operating costs; and These are weighting coefficients used to balance the contribution of various indicators to loss and prevent overfitting.

[0012] Optionally, a multi-objective joint dynamic optimization can be performed using a non-dominated sorting genetic algorithm to output optimal process operation parameters, including: Set safe physical operating boundaries for each process operation parameter and material mass conservation conditions for the system as hard constraints; A candidate population is initialized within the safe physical operating boundary, and each candidate individual in the candidate population corresponds to a set of process operation parameters; Based on the process operation parameters corresponding to each candidate individual, construct the corresponding operating condition diagram data, and input it into the trained and optimized spatiotemporal graph neural network model to obtain the corresponding average metal recovery rate, energy consumption and operating cost prediction values. Based on the predicted average metal recovery rate, energy consumption, and operating costs, candidate individuals are ranked non-dominated and their crowding is calculated. Offspring individuals are generated through selection, crossover, and mutation operations; Infeasible solutions that do not meet the aforementioned safe physical operating boundary or material mass conservation conditions are eliminated or projected for repair. An elite retention strategy is used to iteratively update the population, and the Pareto optimal operating frontier and corresponding process operating parameter configuration are output after the termination condition is met.

[0013] The present invention also provides a multi-objective optimization system for wet recycling of waste lithium-ion batteries based on spatiotemporal graph neural networks, comprising: a data acquisition and mapping module, a spatiotemporal network construction module, a training and optimization module, and a multi-objective control module; The data acquisition and mapping module is used to acquire operational data of the wet recycling process of waste lithium-ion batteries and construct a dynamic graph dataset based on the operational data. The spatiotemporal network construction module is used to construct a spatiotemporal graph neural network model based on the dynamic graph dataset. The spatiotemporal graph neural network model includes a graph convolutional network module for distinguishing different edge types and extracting spatial topological features, a graph attention mechanism module for dynamically allocating node and edge relationship weights, and a two-layer gated loop module for capturing the temporal evolution features of process states. The training optimization module is used to construct a multi-task loss function that integrates metal recovery rate, energy consumption and operating cost, and to train and optimize the spatiotemporal graph neural network model under the graph structure enhancement strategy. The multi-objective control module is used to receive the current wet recycling operation data in real time, take the process operation parameters as the optimization object, use the trained spatiotemporal graph neural network model as the performance evaluation model of the candidate process operation parameters, predict the average metal recovery rate, energy consumption and operating cost corresponding to each candidate process operation parameter, and combine the non-dominated sorting genetic algorithm to perform multi-objective joint dynamic optimization of the candidate process operation parameters to obtain the optimal process operation parameters.

[0014] Compared with the prior art, the present invention has the following advantages and technical effects: This invention constructs a dynamic polygon graph topology dataset containing process unit nodes, material nodes, and global parameter nodes. This dataset explicitly represents various relationships in the wet recycling process of spent lithium-ion batteries, including material flow, unit connections, reaction relationships, parameter influences, and temporal evolution, thus improving the model's ability to express the spatial coupling relationships throughout the wet recycling process. By setting learnable weight mapping matrices and edge type weight balance coefficients for different types of connections in the graph convolutional network, the model can distinguish the contributions of different physicochemical relationships to node feature aggregation, improving the targeting of spatial feature extraction in the wet recycling process. Furthermore, by introducing a multi-head graph attention mechanism, the weights of key process units, material nodes, and their connections can be dynamically adjusted according to the current operating conditions, enhancing the model's ability to represent key stages such as leaching and extraction separation. By inputting graph-level feature vector sequences into a cascaded, two-layer gated recurrent unit module, the model can capture temporal dynamic changes caused by fluctuations in raw material composition, equipment status changes, and adjustments in process parameters, thus improving the predictive stability of the model under unsteady industrial operating environments. Constructing a multi-task loss function that integrates metal recovery rate, total energy consumption, and total operating cost, and training it using a graph structure enhancement strategy, improves the model's robustness to industrial noise and operating condition fluctuations. Simultaneously, using the trained and optimized spatiotemporal graph neural network model as a performance evaluation model for candidate process operation parameters, and combining it with a non-dominated sorting genetic algorithm for multi-objective joint dynamic optimization, enables the output of Pareto optimal process operation parameter configurations under the constraints of equipment safety operation boundaries and material mass conservation, thereby providing technical support for the online optimization control of the wet recycling process of waste lithium-ion batteries. Attached Figure Description

[0015] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a flowchart of a multi-objective optimization method for wet recycling of waste lithium-ion batteries based on a spatiotemporal graph neural network, according to an embodiment of the present invention. Detailed Implementation

[0016] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0017] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0018] This embodiment proposes a multi-objective optimization method for wet recycling of spent lithium-ion batteries based on a spatiotemporal graph neural network, such as... Figure 1 As shown, the specific steps include: Obtain operational data of the wet recycling process of waste lithium-ion batteries, and construct a dynamic graph dataset based on the operational data; A spatiotemporal graph neural network model is constructed based on the dynamic graph dataset. The spatiotemporal graph neural network model includes a graph convolutional network module for distinguishing different edge types and extracting spatial topological features, a graph attention mechanism module for dynamically allocating node and edge relationship weights, and a two-layer gated recurrent module for capturing the temporal evolution features of process states. A multi-task loss function integrating metal recovery rate, energy consumption, and operating costs is constructed, and the spatiotemporal graph neural network model is trained and optimized under a graph structure enhancement strategy; The system receives real-time data on the operation of wet recycling, optimizes process operating parameters, uses a trained spatiotemporal graph neural network model as a performance evaluation model for candidate process operating parameters, predicts the average metal recovery rate, energy consumption, and operating cost corresponding to each candidate process operating parameter, and combines a non-dominated sorting genetic algorithm to perform multi-objective joint dynamic optimization of candidate process operating parameters to obtain the optimal process operating parameters.

[0019] Furthermore, the operational data of the wet recycling process of waste lithium-ion batteries is obtained, and a dynamic graph dataset is constructed based on the operational data, including: Acquire continuous industrial operation data, including battery raw material composition content, system process parameters, equipment operating status, and recycling performance indicators; The continuous industrial operation data is cleaned to obtain preprocessed operation data; A directed graph is constructed based on the preprocessed operating data, wherein the set of nodes is divided into process unit nodes, material nodes, and global parameter nodes; Based on the directed graph, a set of connection edges between the nodes is established. The set of connection edges includes material flow edges, unit connection edges, reaction edges, parameter influence edges, and time-series edges that connect the same node across time steps. The directed graphs at multiple time points are constructed into a dynamic graph dataset according to the time series.

[0020] Specifically, S1, acquire multi-source continuous operation data of the wet recycling process of waste lithium-ion batteries, and after preprocessing the multi-source continuous operation data, construct a dynamic polygon graph topology dataset.

[0021] This step utilizes a self-developed multi-parameter data acquisition hardware system to continuously collect operational records from a fully industrialized hydrometallurgical production line of spent lithium batteries. The dataset contains 12,000 high-quality, real industrial operational records, spanning a six-month period, with a sampling interval of 15 minutes for each record. The dataset comprehensively covers mainstream nickel-cobalt-manganese (NMC) ternary lithium batteries and lithium iron phosphate (LFP) batteries from different manufacturers, with varying degrees of aging, state of health (SOH), and initial material ratios.

[0022] The multi-source continuous operation data includes battery raw material composition data, system process parameter data, equipment operating status data, and recovery performance index data. Specifically, the battery raw material composition data includes the initial content of at least one metal among lithium, nickel, cobalt, and manganese, and / or the battery system type; the system process parameter data includes at least one of temperature, pH, reaction time, acid concentration, liquid-to-solid ratio, and feed flow rate; the equipment operating status data includes the operating status of the reactor, extraction and separation unit, pumping unit, or temperature control unit; and the recovery performance index data includes the recovery rates of the four metals (lithium, nickel, cobalt, and manganese), total system energy consumption, and total operating cost.

[0023] The preprocessing and mapping process includes the following sub-steps: S11. Perform data cleaning on the numerical sensor time series data, remove isolated noise points and outliers caused by sensor malfunctions, and fill in missing values ​​by averaging or interpolation; then use the Z-score standardization method to process the data into standardized time series data. S12. Construct a directed graph structure of the topology graph based on the preprocessed runtime data. To explicitly represent heterogeneous associations among multiple entities, the set of nodes in the graph is... Divided into process unit node sets Material node set and global parameter node set Three categories, the total node set is represented as follows: ; Wherein, the process unit node This includes acid leaching reactors at various stages and a group of solvent extraction and separation towers; the material nodes This includes the input waste battery black powder raw material, acidic leachate, organic phase extractant, and the final purified output metal products (Li, Ni, Co, Mn); the global parameter node. This represents the global control setpoints or physical environment boundary parameters that affect multiple process units.

[0024] S13. Constructing a set of edges connecting heterogeneous physicochemical relationships. The set of edges is explicitly defined as five different edge types: material flow edges. (with weight) (Characterizing the actual flow direction and mass flow rate of solid and liquid materials) and unit connection edges (Connecting different process unit nodes), chemical reaction edge (Connecting different material nodes to characterize the dissolution and precipitation reaction mechanism), parameter influence edge (Connecting global parameter nodes and process unit nodes to represent control effects) and timing edges connecting their own nodes across time steps. .

[0025] Based on the definition of edge relationships above, establish the adjacency matrix of the system. (in (Total number of nodes), if node With nodes If any of the above types of connecting edges exist, then let the adjacency matrix elements... ,otherwise .

[0026] S14, Accompanying production operation time step The evolution extends the above graph structure into a sequence of dynamic heterogeneous graph topologies. Each of the image slices The system represents time The dynamic drift characteristics of the real-time process status, node attributes, and multiphysics edge weights.

[0027] S15. The 12,000 constructed dynamic graph topology records are divided into a training set (70%), a validation set (15%), and a test set (15%) according to a strict chronological order (not random shuffling). Using chronological order partitioning realistically simulates the non-steady-state evolution and concept drift characteristics of data during online deployment in industrial settings, ensuring the rigor of the evaluation model's generalization ability.

[0028] Furthermore, constructing a spatiotemporal graph neural network model based on the dynamic graph dataset includes: Based on the different types of connection edges in the dynamic graph dataset, an improved graph convolutional network module is constructed to extract the spatial topological features of each node under different physicochemical relationships. A multi-head graph attention mechanism module is introduced after the improved graph convolutional network module to calculate the attention coefficients between nodes and their neighboring nodes, so as to dynamically allocate the association weights of node features and edge relationships. The node features output by the multi-head graph attention mechanism module are converted into graph-level feature vectors and input into a series of two-layer gated loop unit modules to capture the long- and short-term time-series evolution features of operating parameters and system states. The spatiotemporal graph neural network model is constructed based on the improved graph convolutional network module, multi-head graph attention mechanism module, and double-layer gated recurrent unit module.

[0029] Furthermore, based on the different types of connection edges in the dynamic graph dataset, an improved graph convolutional network module is constructed to extract the spatial topological features of each node under different physicochemical relationships, including: For each type of connection edge, a corresponding learnable weight mapping matrix is ​​introduced to map the features of neighbor nodes under that connection edge type to the edge type-specific feature space. For each type of connecting edge, an independent adjacency matrix with self-loops and a corresponding degree matrix are established to determine the neighborhood range and normalization coefficient of node features propagating along that connecting edge type. By introducing learnable edge type weight balance coefficients, the features of various neighbor nodes after transformation by the corresponding weight mapping matrix and normalization propagation by the adjacency matrix are weighted and summed to obtain the updated node space topological features.

[0030] Furthermore, the attention coefficients between a node and its neighboring nodes are calculated to dynamically assign association weights to node features and edge relationships, including: Calculate the attention score between the center node and its neighboring nodes using a learnable weight matrix and attention vector; The attention scores are normalized using a nonlinear activation function and a softmax function to obtain attention coefficients. The neighbor node features are weighted and summed based on the obtained attention coefficients to obtain the output features of a single attention head; Multiple parallel attention heads are used to perform attention calculations separately, and the output features of the multiple attention heads are concatenated or averaged and fused.

[0031] Furthermore, capturing the long- and short-term time-series evolution characteristics of operating parameters and system states includes: The node feature matrix output by the multi-head graph attention mechanism module is subjected to graph-level pooling to generate a graph-level comprehensive feature vector for the current time step. The graph-level integrated feature vectors of consecutive time steps are combined into a graph-level feature vector sequence; The graph-level feature vector sequence is sequentially input into the first-level gated loop unit and the second-level gated loop unit in series. The timing dependency of the operation parameters and system state is dynamically tracked through the update gate and reset gate mechanism. The hidden state output by the second-layer gated recurrent unit at the last time step is used as the spatiotemporal feature vector representing the global spatiotemporal evolution state.

[0032] Specifically, S2, based on the preprocessed dataset, construct a spatiotemporal graph neural network model.

[0033] The spatiotemporal graph neural network model comprises an input layer, an improved graph convolutional network module, a multi-head graph attention mechanism module, a two-layer gated recurrent unit module, and a fully connected output layer. The input layer receives node feature matrices and edge relationship data from each graph slice in the dynamic graph sequence; the improved graph convolutional network module distinguishes different types of connections and extracts spatial topological features; the multi-head graph attention mechanism module dynamically allocates the weights of key nodes and edge relationships based on the current operating conditions; the two-layer gated recurrent unit module captures the temporal evolution characteristics of the process state over time; and the fully connected output layer outputs the predicted results for the recovery rates of lithium, nickel, cobalt, and manganese, total energy consumption, and total operating costs.

[0034] In the improved graph convolutional network module, edge-type independent adjacency matrices are established for material flow edges, cell connection edges, reaction edges, parameter-affected edges, and temporal-sequence edges, respectively, and learnable weight mapping matrices are introduced for different types of connection edges. In contrast, the standard graph convolutional operation does not distinguish the physical attributes of edges when updating node features; its layer-by-layer feature update formula is: ; in, For the first The node feature matrix of the layer, each node contains Dimensional features; To introduce the identity matrix The adjacency matrix after the self-loop is used to ensure that nodes retain the characteristic attributes of their previous layer during aggregation; for The corresponding degree matrix has diagonal elements that satisfy ; This is the learnable weight matrix for this layer; For activation functions; Used to perform symmetric normalization on the adjacency matrix.

[0035] To enable the model to distinguish between different relationships in wet recycling processes, such as material flow, unit connectivity, chemical reactions, parameter influences, and temporal evolution, this embodiment introduces an edge-type independent modeling mechanism based on standard graph convolution operations. Specifically, firstly, an independent adjacency matrix and degree matrix are established for each edge type to determine the neighborhood range and normalization coefficients for node feature propagation under that edge type. Secondly, a learnable weight mapping matrix is ​​set for each edge type to map the features of neighboring nodes associated with that edge type to the edge type's dedicated feature space. Finally, the feature propagation results of different edge types are weighted and fused using learnable edge-type balance coefficients to obtain the updated node space topological features. The improved layer-by-layer feature update formula is as follows: ; in, For a specific edge type ( The independent adjacency matrix after introducing self-loops is used to characterize the neighborhood propagation relationship between nodes under this edge type; Its corresponding independence matrix is ​​used to normalize the adjacency relationships under this edge type; Specifically for edge types An initialized learnable weight mapping matrix is ​​used to perform feature transformation on the features of neighboring nodes associated with this edge type; The adaptive learning balance coefficients for various types of connecting edges are used to weight and fuse the propagation results of different edge types after each edge type has completed neighborhood propagation and feature mapping, thereby dynamically adjusting the contribution ratio of different physical and chemical associations in spatial feature aggregation. A LeakyReLU nonlinear activation function with a negative slope of 0.01 was used.

[0036] Subsequently, a multi-head graph attention mechanism is introduced after the graph convolutional layer. This utilizes a learnable weight matrix. and attention vector compute nodes Its neighboring nodes Unnormalized attention scores between : ; Using the Softmax function at nodes directed neighborhood set The non-standardized attention scores are normalized internally to obtain accurate attention coefficients. The formula is as follows: ; Based on the calculated attention coefficient The features of each neighboring node are weighted, summed, and aggregated to generate the output features of the single head of this layer, as shown in the following formula: ; In this embodiment, multiple parallel attention heads can be used to perform the above calculations separately, and the output features of the multiple attention heads can be spliced ​​and fused or averaged and fused to obtain the final output features of the multi-head graph attention mechanism module. Through this module, the model can adaptively adjust the feature weights of the acid leaching reaction unit, the solvent extraction and separation unit, and their core material flow connections according to the current operating conditions.

[0037] To transform the spatial features of heterogeneous graphs into a structure suitable for long-range temporal tracking, the node feature matrix output by the multi-head graph attention mechanism module is first processed. Perform graph-level average pooling, using the following formula: ; The average pooling is calculated at the current time. The average value of all node features in the entire graph is used to eliminate the influence of spatial node density and generate a graph-level feature vector that represents the current real-time spatial state of the entire process. (In this embodiment, its feature dimensions are set) ).

[0038] The dynamically generated graph-level comprehensive feature vector sequence The data is sequentially input into the cascaded first and second layer gated recurrent unit (GRU) networks. Each layer contains an embedded update gate. and reset door A mechanism is proposed to address the long-short-term dependence and state evolution issues in large time-delay processes of hydrometallurgical processes. Its time-series update governing equations are as follows: ; ; ; ; in, Enter the current time step; This is the hidden state vector from the previous time step; To update the gate vector, the proportion of features from the previous state retained in the current state is controlled; To reset the gate vector, control the degree to which features from the previous state are forgotten; This represents the candidate hidden state at the current moment; This is the final updated hidden state vector at the current moment; and This is the learnable weight matrix corresponding to the gating structure; It is the bias vector; Use the Sigmoid activation function; This represents element-wise multiplication between matrices or vectors.

[0039] In the design of this timing module, the input dimension of the first-layer GRU is... Hidden layer feature dimension The second-layer GRU has an input dimension of 64 and a hidden layer feature dimension of 64. The concatenated GRU network will have the second layer at the last historical time step. The output hidden state vector This serves as a global, comprehensive spatiotemporal feature vector representing the entire graph's topological history sequence. Finally, The fully connected output decoding layer, which includes a neuron failure layer, is connected to map and predict multi-task metrics.

[0040] Furthermore, the multi-task loss function is: ; in, For metal recovery rate, multiple task loss items; This is the predicted loss item for total energy consumption; Forecast loss items for total operating costs; and These are weighting coefficients used to balance the contribution of various indicators to loss and prevent overfitting.

[0041] Specifically, S3, based on the preprocessed dataset and the constructed spatiotemporal graph neural network model, a multi-task loss function is constructed, and the model is trained and optimized under the graph structure enhancement strategy.

[0042] This step constructs a weighted multi-task joint loss function that integrates the prediction errors of metal recovery rate, total system energy consumption, and overall operating cost. The network is trained using gradient backpropagation, as shown in the following formula: ; in, For metal recovery rate, multiple task loss items; This is the predicted loss item for total energy consumption; Forecast loss items for total operating costs; and These are weighting coefficients used to balance the contribution of various indicators to loss and prevent overfitting.

[0043] In this embodiment, metal recovery rate loss is used as the basic term. The mean square error between the predicted value and the actual test value is used for calculation, and the formula is as follows: ; in, This represents the total number of samples in the current training batch. They represent four metallic entities: Li, Ni, Co, and Mn, respectively. For the first Metal in each sample The actual laboratory recovery rate; This represents the corresponding model prediction value.

[0044] The total energy loss item Operating cost loss items Similarly, the calculation is based on the mean square error between the predicted value and the actual industrial value, and the formula is as follows: ; ; in It is a sample Actual energy consumption It predicts energy consumption. It is the actual cost. It is a predicted cost.

[0045] To determine the optimal weighting coefficients and The initial weight search interval is determined based on the initial average error proportion of each loss term in the training set, and a two-stage search strategy combining coarse-grid search and fine-grid search with cross-validation is used to determine the weight combination. In this embodiment, the final weight combination can be further determined from the candidate weight combinations using the TOPSIS method.

[0046] The Adam optimizer is used to iteratively update the model parameters. During training, a graph structure noise reduction strategy is introduced, specifically including randomly discarding a predetermined proportion of graph edges and injecting Gaussian noise with a mean of 0 into the node features. In this embodiment, 5% to 10% of the graph edges are randomly discarded, and Gaussian noise with a mean of 0 and a standard deviation of 0.01 is injected into the node features. Simultaneously, an early stopping mechanism is used; training stops when the validation set loss no longer decreases within a predetermined number of rounds, thereby improving the model's generalization ability and robustness in real-world industrial environments.

[0047] Furthermore, by combining a non-dominated sorting genetic algorithm with multi-objective joint dynamic optimization, the optimal process operation parameters are output, including: Set safe physical operating boundaries for each process operation parameter and material mass conservation conditions for the system as hard constraints; A candidate population is initialized within the safe physical operating boundary, and each candidate individual in the candidate population corresponds to a set of process operation parameters; Based on the process operation parameters corresponding to each candidate individual, construct the corresponding operating condition diagram data, and input it into the trained and optimized spatiotemporal graph neural network model to obtain the corresponding average metal recovery rate, energy consumption and operating cost prediction values. Based on the predicted average metal recovery rate, energy consumption, and operating costs, candidate individuals are ranked non-dominated and their crowding is calculated. Offspring individuals are generated through selection, crossover, and mutation operations; Infeasible solutions that do not meet the aforementioned safe physical operating boundary or material mass conservation conditions are eliminated or projected for repair. An elite retention strategy is used to iteratively update the population, and the Pareto optimal operating frontier and corresponding process operating parameter configuration are output after the termination condition is met.

[0048] Specifically, S4, based on the trained and optimized spatiotemporal graph neural network model, receives the current wet recycling operation data in real time and constructs the current operating condition graph data. The trained and optimized spatiotemporal graph neural network model is used as a performance evaluation model for candidate process operation parameters. Multi-objective joint dynamic optimization is performed in combination with the non-dominated sorting genetic algorithm to output Pareto optimal process operation parameters.

[0049] The trained and optimized spatiotemporal graph neural network model is encapsulated as a performance evaluation model for candidate process operation parameters. Individual vectors of optimization decision variables are defined. for: ; in, Indicates the leaching temperature. Indicates the leaching pH. Indicates leaching time. Indicates acid concentration. Indicates the liquid-to-solid ratio. This indicates the extraction temperature.

[0050] A multi-objective optimization objective function is defined to maximize the average metal recovery rate. At the same time, minimize total energy consumption and total operating costs : ; ; ; The optimization constraints include the physical operating boundary for equipment safety and the system material mass conservation condition. The physical operating boundary for equipment safety is used to limit each decision variable to within the industrially feasible range; the material mass conservation condition is used to constrain the mass balance relationship between input materials, output metallic products, and waste streams.

[0051] The process of multi-objective joint dynamic optimization using non-dominated sorting genetic algorithms includes: Initialize the candidate population within the safe physical operating boundary of each process operation parameter, with each candidate individual corresponding to a set of process operation parameters; Based on the process operation parameters corresponding to each candidate individual, construct the corresponding current operating condition diagram data, and input it into the trained and optimized spatiotemporal graph neural network model to predict the average metal recovery rate, total energy consumption and total operating cost corresponding to the candidate individual; Based on the predicted average metal recovery rate, total energy consumption, and total operating cost, candidate individuals are ranked non-dominated and crowding distance is calculated. Offspring individuals are generated through selection operations, simulated binary crossover operations, and polynomial mutation operations. Infeasible solutions that do not meet the equipment safety operation boundary or material mass conservation conditions are eliminated or projected for repair. An elite-preservation strategy is adopted to merge the parent and offspring populations, and the population is updated iteratively in a loop. After reaching the maximum number of iterations or meeting the convergence condition, the Pareto optimal operating front is extracted, and the final process operating parameter configuration is selected from the Pareto optimal operating front based on production preferences.

[0052] In this embodiment, the population size of the non-dominated sorting genetic algorithm can be set to 100, the maximum number of iterations can be set to 50 generations, the crossover probability can be set to 0.9, the mutation probability can be set to 0.07, the distribution exponent for simulated binary crossover can be set to 20, and the distribution exponent for polynomial mutation can be set to 20. The above parameters are only one specific implementation method and can be adjusted according to the actual production line scale, data acquisition frequency, and control cycle without departing from the technical concept of this invention.

[0053] Through the above steps, this embodiment can predict the performance of candidate process operating parameters using a spatiotemporal graph neural network model under conditions of fluctuating raw material composition, changes in equipment status, and dynamic adjustment of process parameters. It can also output Pareto optimal process operating parameters that take into account metal recovery rate, total energy consumption, and total operating cost through a non-dominated sorting genetic algorithm.

[0054] This embodiment also provides a multi-objective optimization system for wet recycling of waste lithium-ion batteries based on spatiotemporal graph neural networks, including: a data acquisition and mapping module, a spatiotemporal network construction module, a training and optimization module, and a multi-objective control module; The data acquisition and mapping module is used to acquire operational data of the wet recycling process of waste lithium-ion batteries and construct a dynamic graph dataset based on the operational data. The spatiotemporal network construction module is used to construct a spatiotemporal graph neural network model based on the dynamic graph dataset. The spatiotemporal graph neural network model includes a graph convolutional network module for distinguishing different edge types and extracting spatial topological features, a graph attention mechanism module for dynamically allocating node and edge relationship weights, and a two-layer gated loop module for capturing the temporal evolution features of process states. The training optimization module is used to construct a multi-task loss function that integrates metal recovery rate, energy consumption and operating cost, and to train and optimize the spatiotemporal graph neural network model under the graph structure enhancement strategy. The multi-objective control module is used to receive the current wet recycling operation data in real time, take the process operation parameters as the optimization object, use the trained spatiotemporal graph neural network model as the performance evaluation model of the candidate process operation parameters, predict the average metal recovery rate, energy consumption and operating cost corresponding to each candidate process operation parameter, and combine the non-dominated sorting genetic algorithm to perform multi-objective joint dynamic optimization of the candidate process operation parameters to obtain the optimal process operation parameter configuration.

[0055] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A multi-objective optimization method for wet recycling of spent lithium-ion batteries based on spatiotemporal graph neural networks, characterized in that, include: Obtain operational data of the wet recycling process of waste lithium-ion batteries, and construct a dynamic graph dataset based on the operational data; A spatiotemporal graph neural network model is constructed based on the dynamic graph dataset. The spatiotemporal graph neural network model includes a graph convolutional network module for distinguishing different edge types and extracting spatial topological features, a graph attention mechanism module for dynamically allocating node and edge relationship weights, and a two-layer gated recurrent module for capturing the temporal evolution features of process states. A multi-task loss function integrating metal recovery rate, energy consumption, and operating costs is constructed, and the spatiotemporal graph neural network model is trained and optimized under a graph structure enhancement strategy; The system receives real-time data on the operation of wet recycling, optimizes process operating parameters, uses a trained spatiotemporal graph neural network model as a performance evaluation model for candidate process operating parameters, predicts the average metal recovery rate, energy consumption, and operating cost corresponding to each candidate process operating parameter, and combines a non-dominated sorting genetic algorithm to perform multi-objective joint dynamic optimization of candidate process operating parameters to obtain the optimal process operating parameters.

2. The multi-objective optimization method for wet recycling of spent lithium-ion batteries based on spatiotemporal graph neural networks according to claim 1, characterized in that, Obtain operational data of the wet recycling process for spent lithium-ion batteries, and construct a dynamic graph dataset based on the operational data, including: Acquire continuous industrial operation data, including battery raw material composition content, system process parameters, equipment operating status, and recycling performance indicators; The continuous industrial operation data is cleaned to obtain preprocessed operation data; A directed graph is constructed based on the preprocessed operating data, wherein the set of nodes is divided into process unit nodes, material nodes, and global parameter nodes; Based on the directed graph, a set of connection edges between nodes is established, which includes material flow edges, unit connection edges, reaction edges, parameter influence edges, and time-series edges that connect the same node across time steps. The directed graphs at multiple time points are constructed into a dynamic graph dataset according to the time series.

3. The multi-objective optimization method for wet recycling of waste lithium-ion batteries based on spatiotemporal graph neural networks according to claim 2, characterized in that, Constructing a spatiotemporal graph neural network model based on the dynamic graph dataset includes: Based on the different types of connection edges in the dynamic graph dataset, an improved graph convolutional network module is constructed to extract the spatial topological features of each node under different physicochemical relationships. A multi-head graph attention mechanism module is introduced after the improved graph convolutional network module to calculate the attention coefficients between nodes and their neighboring nodes, so as to dynamically allocate the association weights of node features and edge relationships. The node features output by the multi-head graph attention mechanism module are converted into graph-level feature vectors and input into a series of two-layer gated loop unit modules to capture the long- and short-term time-series evolution features of operating parameters and system states. The spatiotemporal graph neural network model is constructed based on the improved graph convolutional network module, multi-head graph attention mechanism module, and double-layer gated recurrent unit module.

4. The multi-objective optimization method for wet recycling of spent lithium-ion batteries based on spatiotemporal graph neural networks according to claim 3, characterized in that, Based on the different types of connection edges in the dynamic graph dataset, an improved graph convolutional network module is constructed to extract the spatial topological features of each node under different physicochemical relationships, including: For each type of connection edge, a corresponding learnable weight mapping matrix is ​​introduced to map the features of neighbor nodes under that connection edge type to the edge type-specific feature space. For each type of connecting edge, an independent adjacency matrix with self-loops and a corresponding degree matrix are established to determine the neighborhood range and normalization coefficient of node features propagating along that connecting edge type. By introducing learnable edge type weight balance coefficients, the features of various neighbor nodes after transformation by the corresponding weight mapping matrix and normalization propagation by the adjacency matrix are weighted and summed to obtain the updated node space topological features.

5. A multi-objective optimization method for wet recycling of spent lithium-ion batteries based on a spatiotemporal graph neural network according to claim 3, characterized in that, The attention coefficients between a node and its neighboring nodes are calculated to dynamically assign association weights based on node features and edge relationships, including: Calculate the attention score between the center node and its neighboring nodes using a learnable weight matrix and attention vector; The attention scores are normalized using a nonlinear activation function and a softmax function to obtain attention coefficients. The neighbor node features are weighted and summed based on the obtained attention coefficients to obtain the output features of a single attention head; Multiple parallel attention heads are used to perform attention calculations separately, and the output features of the multiple attention heads are concatenated or averaged and fused.

6. The multi-objective optimization method for wet recycling of waste lithium-ion batteries based on spatiotemporal graph neural networks according to claim 3, characterized in that, Capturing the long- and short-term time-series evolution characteristics of operating parameters and system states includes: The node feature matrix output by the multi-head graph attention mechanism module is subjected to graph-level pooling to generate a graph-level comprehensive feature vector for the current time step. The graph-level integrated feature vectors of consecutive time steps are combined into a graph-level feature vector sequence; The graph-level feature vector sequence is sequentially input into the first-level gated loop unit and the second-level gated loop unit in series. The timing dependency of the operation parameters and system state is dynamically tracked through the update gate and reset gate mechanism. The hidden state output by the second-layer gated recurrent unit at the last time step is used as the spatiotemporal feature vector representing the global spatiotemporal evolution state.

7. The multi-objective optimization method for wet recycling of waste lithium-ion batteries based on spatiotemporal graph neural networks according to claim 1, characterized in that, The multi-task loss function is: ； in, For metal recovery rate, multiple task loss items; This is the predicted loss item for total energy consumption; Forecast loss items for total operating costs; and These are weighting coefficients used to balance the contribution of various indicators to loss and prevent overfitting.

8. The multi-objective optimization method for wet recycling of waste lithium-ion batteries based on spatiotemporal graph neural networks according to claim 1, characterized in that, Multi-objective joint dynamic optimization is performed using a non-dominated sorting genetic algorithm, and the optimal process operation parameters are output as follows: Set safe physical operating boundaries for each process operation parameter and material mass conservation conditions for the system as hard constraints; A candidate population is initialized within the safe physical operating boundary, and each candidate individual in the candidate population corresponds to a set of process operation parameters; Based on the process operation parameters corresponding to each candidate individual, construct the corresponding operating condition diagram data, and input it into the trained and optimized spatiotemporal graph neural network model to obtain the corresponding average metal recovery rate, energy consumption and operating cost prediction values. Based on the predicted average metal recovery rate, energy consumption, and operating costs, candidate individuals are ranked non-dominated and their crowding is calculated. Offspring individuals are generated through selection, crossover, and mutation operations; Infeasible solutions that do not meet the aforementioned safe physical operating boundary or material mass conservation conditions are eliminated or projected for repair. An elite retention strategy is used to iteratively update the population, and the Pareto optimal operating frontier and corresponding process operating parameter configuration are output after the termination condition is met.

9. A multi-objective optimization system for wet recycling of spent lithium-ion batteries based on a spatiotemporal graph neural network, used to implement the method described in any one of claims 1-8, characterized in that, include: The system includes a data acquisition and mapping module, a spatiotemporal network construction module, a training and optimization module, and a multi-objective control module. The data acquisition and mapping module is used to acquire operational data of the wet recycling process of waste lithium-ion batteries and construct a dynamic graph dataset based on the operational data. The spatiotemporal network construction module is used to construct a spatiotemporal graph neural network model based on the dynamic graph dataset. The spatiotemporal graph neural network model includes a graph convolutional network module for distinguishing different edge types and extracting spatial topological features, a graph attention mechanism module for dynamically allocating node and edge relationship weights, and a two-layer gated loop module for capturing the temporal evolution features of process states. The training optimization module is used to construct a multi-task loss function that integrates metal recovery rate, energy consumption and operating cost, and to train and optimize the spatiotemporal graph neural network model under the graph structure enhancement strategy. The multi-objective control module is used to receive the current wet recycling operation data in real time, take the process operation parameters as the optimization object, use the trained spatiotemporal graph neural network model as the performance evaluation model of the candidate process operation parameters, predict the average metal recovery rate, energy consumption and operating cost corresponding to each candidate process operation parameter, and combine the non-dominated sorting genetic algorithm to perform multi-objective joint dynamic optimization of the candidate process operation parameters to obtain the optimal process operation parameters.

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